Rotating Detonation Combustor Mechanics

A Dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in the Department of Aerospace Engineering and Engineering Mechanics of the College of Engineering and Applied Science April 23, 2018

Vijay G Anand

B.E. Aeronautical Engineering, Anna University, 2013

Dissertation Committee: Dr. Ephraim Gutmark (Advisor) Dr. Shaaban Abdallah Dr. Mark Turner

Abstract

Recent years have witnessed a notable increase in endeavors resorted to investigating unsteady combustion/pressure processes that offer a prospective increase in stagnation pressure due to a more efficient combustion of fuel. One such pressure gain combustion (PGC) concept is a rotating detonation combustor (RDC). RDCs make use of a rotating detonation wave that travels circumferentially about a hollow or annular chamber at kilohertz frequencies, continually combusting the supplied reactants without the need for more than one initial ignition event. Due to its simplicity in design, which can be integrated into existing systems’ architecture, and the lack of moving mechanical components, RDCs are at the forefront of PGC research. The current dissertation deals with the basic mechanics of these combustors. Specifically, the diverse modes of detonative operation in annular and hollow combustor configurations are experimentally studied, and the variables dictating these modes are extracted. The question of what exactly constitutes a rotating detonation combustor is answered, by “converting” a conventional atmospheric deflagrative hollow combustor into an RDC. Further, based on this demonstration, the numerous kinships between RDC operation and decades of observations pertaining to high frequency combustion instabilities in rocket engines are presented and discussed. It is argued that most of the poorly understood phenomena of high frequency instabilities can be explained by detonation-based physics. Finally, evidence is presented that suggests rotating detonations to be type of near-limit detonation behavior. The findings of this study are proposed to be useful for the three different communities of RDC research, rocket engine instabilities and fundamental detonation physics.

Acknowledgements

First and foremost, I thank my mother and father for all that they have done for me. It is fair to say that nurture is as important as nature in an individual’s growth, and they have contributed to my current standing in quantitatively equal, but qualitatively different ways. The sacrifices rendered by my family are recognized, and will be remembered.

Second, I extend my warmest regards to my advisor, Dr. Ephraim Gutmark, for providing the perfect combination of guidance and directives, and for respecting me as a researcher. Having an in-phase relationship with one’s advisor is an element of probabilistic slimness, and I was fortunate enough to experience the same over my years in graduate school. I also thank all the members of my committee and every staff in my lab that I have interacted with through the years — they have supported this endeavor.

Thirdly, I cannot emphasize enough the ways I have changed over my stay here in Cincinnati. In that regard, I am thankful for my colleagues from the lab, who collectively made me feel like I had a long bridge to gap (mostly unintentionally). As the saying goes, if one is the smartest person in the room, one is in the wrong room; I routinely found myself in the right room, especially during my first few years in the lab. Adversity is a beautiful thing. In the same vein, a special shout out is in order for the detonation engines research team of which I am a part of. For reasons unknown, every single member that has entered and exited this group appear to possess an uncanny affinity for extreme political inappropriateness and heightened on-point humor — for this I truly am thankful for. I am especially grateful to Andrew St. George for building the foundations of our group, and for helping me acquire my data through all those weary, wintery, sub-zero nights. I could not have done what I have, in the time that I did, if not for him.

Last, but most definitely not the least, I am grateful to the United States of America. I know for a fact, anecdotally and otherwise, that hard work and intellect can only get one so far in life. The x-factor is the privilege of opportunity, and for that I owe this country one.

“A hundred years from now, people will look back on us and laugh. They'll say, 'You know what people used to believe? They believed in photons and electrons. Can you imagine anything so silly?' They'll have a good laugh, because by then there will be newer, better fantasies... And meanwhile, you feel the way the boat moves? That's the sea. That's real. You smell the salt in the air? You feel the sunlight on your skin? That's all real. Life is wonderful. It's a gift to be alive, to see the sun and breathe the air. And there isn't really anything else.”

― Michael Crichton, in The Lost World, 1995

Preface

The current PhD thesis deals with the specifics of rotating detonation combustor mechanics. In particular, various modes of operation of the device are analyzed, predominantly experimentally. The following articles have resulted from this work, and constitute it:

1. Anand, V., Gutmark E. An extensive review of rotating detonation combustors, with parallels to rocket engine instabilities. Progress in Energy in Combustion Science (Invited – To be submitted). 2. Anand, V., St. George, A., Driscoll, R., Gutmark, E.: Investigation of rotating detonation combustor operation with H2-Air mixtures. Int. J. Hydrogen Energy. 41, 1281–1292 (2016) 3. Anand, V., St. George, A., Driscoll, R., Gutmark, E.: Characterization of instabilities in a Rotating Detonation Combustor. Int. J. Hydrogen Energy. 40, 16649–16659 (2015). 4. Anand, V., St. George, A., Driscoll, R., Gutmark, E.: Analysis of air inlet and fuel plenum behavior in a rotating detonation combustor. Exp. Therm. Fluid Sci. 70, 408–416 (2016). 5. Anand, V., St. George, A., Driscoll, R., Gutmark, E.: Longitudinal pulsed detonation instability in a rotating detonation combustor. Exp. Therm. Fluid Sci. 77, 212–225 (2016). 6. Anand, V., St. George, A., Gutmark, E.: Amplitude modulated instability in reactants plenum of a rotating detonation combustor. Int. J. Hydrogen Energy. 42, 12629–12644 (2017). 7. Anand, V., St. George A., Farbos De Luzan, C., Gutmark, E.: Rotating detonation wave mechanics through ethylene-air mixtures in hollow combustors, and implications to high frequency combustion instabilities. Exp. Therm. Fluid Sci. 92, 314–325 (2018). 8. Anand, V., Gutmark E. Rotating Detonations vs. Spinning Detonations: Similarities and Differences. AIAA J. (Accepted – 2018). 9. Anand, V., Farbos De Luzan C, Babu L, St. George A, Driscoll R, Gutmark E. On Mean Pressure Shifts and Chugging Oscillations in Back-pressurized Rotating Detonation Combustors (Awaiting clearance for submission).

10. Anand, V., St. George A, Jodele J, Knight E, Gutmark E. The Origins of Wave Directionality, Chaotic Propagation and Onset Time after Ignition in a Rotating Detonation Combustor (Awaiting clearance for submission).

In addition to the above, the following publications were also authored during the duration of the program, but are not a part of the current thesis:

i. Anand, V., St. George A, Driscoll R, Randall S, Gutmark EJ. Statistical Treatment of Wave Instability in Rotating Detonation Combustors. 53rd AIAA Aerosp. Sci. Meet., Kissimmee, Florida, (2015). ii. Anand, V., St. George A, Gutmark E. Hollow Rotating Detonation Combustor. 54th AIAA Aerosp. Sci. Meet., San Diego, California, (2016). iii. Anand, V., Jodele J, Knight E, Gutmark E. Dependence of Pressure, Combustion and Frequency Characteristics on Valved Pulsejet Combustor Geometries. Flow, Turbulence and Combustion (Accepted - 2017). iv. Anand, V., Glaser, A., Gutmark E. Acoustic Characterization of Pulse Detonation Combustors. AIAA J. (Accepted - 2018). v. Anand, V., Gutmark E. Rotating Detonation Combustor Research at the University of Cincinnati. Flow, Turbulence and Combustion (Invited - Accepted - 2018). vi. Anand, V., Gutmark E. Types of low frequency instabilities in a rotating detonation combustor. Active Flow and Combustion Control. Book Chapter. (Invited – Submitted - 2018).

Over the last two years, three PhD and two Master’s students have graduated from the Detonation Engine Test Facility in the Gas Dynamics and Propulsion Laboratory at the University of Cincinnati. Since the facility used has remained unaltered during this time, its minutiae will not be detailed in the current thesis for the sake of brevity. The author directs the readers to consult the following theses for detailed information on the same:

a. St. George, A., Development and Testing of Pulsed and Rotating Detonation Combustors. PhD Thesis (2016).

vii

b. Driscoll, R., Investigation of Sustained Detonation Devices: the Pulse Detonation Engine- Crossover System and the Rotating Detonation Engine System (2016). c. Wilhite, JM., Investigation of Various Novel Air-Breathing Propulsion Systems (2016). d. Knight, E., Effects of corrugated outerwall on rotating detonation combustor behavior (2018).

In addition, to avoid the time-consuming process of reorienting the published/accepted journal articles into a traditional thesis structure, the current document resorts to adopting the format of a PhD by publication. In this regard, the above-mentioned articles (1-10) are arranged as 10 separate stand-alone chapters. Chapter 1 — the introduction — connects the succeeding nine chapters and presents them in the scope of the broader research community. When such a connection and reference is made to the authored articles / chapters, the syntax of is used to identify the relevant material, thereby linking it. The last section on Chapter 1 also contains a brief summary of the focus of the succeeding chapters to provide a global view. It is also emphasized here that the ANSYS simulations in Chapter 7 and the COMSOL simulations in Chapter 9 were performed by Charles Farbos de Luzan and Libin Babu, respectively, during their tenure at the University of Cincinnati.

viii

Table of Contents

Abstract ……………………………………………………………………………………………………………… ii Acknowledgements ……………………………………………………………………………………………. iv Preface ……………………………………………………………………………………………………………..... vi Table of Contents ……………………………………………………………………………………………….. ix Chapter 1 ……………………………………………………………………………………………………………. 1 An extensive review of rotating detonation combustors, with parallels to rocket engine instabilities (prelude) Chapter 2 ……………………………………………………………………………………………………………. 107

Investigation of rotating detonation combustor operation with H2-air mixtures Chapter 3 ……………………………………………………………………………………………………………. 139 Characterization of instabilities in a rotating detonation combustor Chapter 4 ……………………………………………………………………………………………………………. 165 Analysis of air inlet and fuel plenum behavior in a rotating detonation combustor Chapter 5 ……………………………………………………………………………………………………………. 185 Longitudinal pulsed detonation instability in a rotating detonation combustor Chapter 6 ……………………………………………………………………………………………………………. 227 Amplitude modulated instability in reactants plenum of a rotating detonation combustor Chapter 7 ……………………………………………………………………………………………………………. 258 The origins of wave directionality, chaotic propagation and onset time after ignition in a rotating detonation combustor Chapter 8 ……………………………………………………………………………………………………………. 285 On mean pressure shifts and chugging oscillations in back-pressurized rotating detonation combustors Chapter 9 ……………………………………………………………………………………………………………. 313 Rotating detonation wave mechanics through ethylene-air mixtures in hollow combustors, and implications to high frequency combustion instabilities Chapter 10 ………………………………………………………………………………………………………….. 341 Rotating detonations and spinning detonations: similarities and differences Chapter 11 ………………………………………………………………………………………………………….. 357 Conclusions and Future Outlook References ..………………………………………………………………………………………………………... 364

CHAPTER 1: AN EXTENSIVE REVIEW OF ROTATING DETONATION COMBUSTORS,

WITH PARALLELS TO ROCKET ENGINE INSTABILITIES (PRELUDE)

1. Introduction

The supersonic combustion phenomenon of detonation produces a pressure ratio increase of

13-55 in gases [1] across the wave due to the shock wave linked to the combustion front. While pulsed detonation combustors (PDCs) were the widely investigated type of pressure gain combustion (PGC) systems, the majority of recent research has migrated to rotating detonation combustors (RDCs). Please consult the comprehensive review of Roy et al. for a broad description of the various facets of gaseous detonation physics and PDCs [2]. The higher power density [3], the lack of a need to regulate periodic ignition and fuel/oxidizer injection, as opposed to a PDC, and the steadier exit flow profile [4] circumvents the notable issues besetting PDCs. This is due to the very nature of RDCs, which constitutes one or more rotating detonation waves (in an ideal operation) spinning about the circumference of a combustor (with or without channels) in the kilohertz regime, as long as the reactants are fed into the device after the initial ignition. An image of a transparent RDC in operation is presented in Figure 1a. Figure 1b gives the averaged rotating detonation wave structure obtained from OH radical chemiluminescence, when viewed from the combustor side.

Despite the considerable progress made till date on the different facets of RDCs, substantial research is still warranted to ascertain the physics, and apply RDCs as a real-world, power- generation device. Until the last few years, the probable efficiency increases afforded by RDCs, due to detonative burning [5], remained a figment of numerical or analytical solutions, with studies claiming: a notable increased in total impulse over pulsed detonation combustors [4], an increase of up to 9% in fuel efficiency [6], an increase of up to 15% in the total pressure in the combustor due

to detonation [7], an increase of 5% in thermal efficiency [8], an increase in thermal efficiency of

1.6% [9], and finally up to 14% increase in power plant efficiency over conventional J class turbines

[10]. Recently however, a handful of experimental investigations have supported the theoretical promulgations of increased efficiency of the detonation cycle. For instance, in their rocket engine configuration, while duly noting the issue of unoptimized combustors, the Frolov et al. have shown that RDCs do indeed have a higher efficiency — by 7-13% — than corresponding deflagrative combustors [11]. Wolanski has estimated a reduced SFC — by 5% — when RDCs were integrated into their unoptimized GTD-350 helicopter engine [12]. In the USA, the Air Force Research

Laboratory’s investigation into an open looped, turbine-integrated RDC resulted in an increased turbine factor — defined as the comparison of the total fuel energy input to the system to the energy extracted by the turbines — with RDCs, as opposed to deflagrative combustors [13].

Members of the same team [14], along with Paxson [15], has shown that there is indeed a stagnation pressure rise across an RDC. These advancements have tentatively proven the efficacy of

RDCs to provide the required step-change increase in gas-turbine efficiency.

In the following sections of this chapter, a panoptic review of RDCs is presented. Since there have been other reviews on the same in the recent past [3,16–19], for brevity, the emphasis here is placed more on issues that have not been dealt with thoroughly. Wolanski’s review contains broad discussions on various combustors that utilize detonative combustion in general, and RDC behavior in particular [3]. A broad review of numerical simulations is also provided. The review by Lu and

Braun contains in-depth discussions about analytical models in describing RDC performance [18].

The survey by Schwer and Kailasanath on the progress (and some short-comings) of simulations in modeling detonation dynamics for pressure gain combustion (PGC) is thorough, recent, self- sufficient and provides the necessary background on the state-of-the-art methods and procedures

[19]. Kailasanath has also authored two other reviews on RDCs, with the first providing a detailed history of RDC development as an engine [16], and the second one detailing the country-wise

research impetus placed on RDCs [17]. Hence, in the current review, significant thrust is directed towards experimental findings and concomitant theories on fundamental mechanics. Numerical simulations and analytical models are discussed whenever pertinent to the broader discussion of

RDC physics. Special stress is placed on drawing parallels to rocket engine combustion instabilities, when appropriate. The decades-wide issue of the latter produces a wide gamut of unsteady phenomena — low frequency instabilities (LFI) and high frequency instabilities (HFI) — that closely align in observations attained from RDC mechanics. As will be argued later with evidence,

the observed kinship between both appears to be driven by the similar processes.

(a) (b)

Figure 1 (a) Transparent annular RDC in operation showing the pre-detonator (igniter that

deposits a blast wave for detonation initiation), and (b) OH* chemiluminescence imaging

showing the rotating detonation wave structure [20]

1.1. The Origins Of Rotating Detonation Waves

To appreciate the origins of rotating detonation waves, it needs to be viewed through the lens of fundamental gaseous detonation wave physics — a field that has been studied intensively

since its inception in 1883, when two French engineers discovered the phenomenon of detonations in coal mines [21]. Detonation was widely regarded as a one-dimensional combustion wave even after almost half a century after its discovery as the Chapman-Jouguet (C-J) theory of modified

Rankine-Hugoniot equations with “zero reaction width thickness” was able to accurately predict the peak pressures and wave speeds of the phenomenon. This perception, however, was shattered in 1926 when Campbell and Woodhead [22] reported the entirely three-dimensional phenomenon of spinning detonations (SD), which move helically in a tube with stationary mixture [23]. Since then, and due to intense research over the next several decades, several discoveries were made, the most important of which is the true nature of detonations — the complex three-dimensional interaction between Mach wave, incident wave, transverse wave and the reaction zone that together form what is now called the ‘detonation cell’ [21]. Thus, spinning detonations were responsible for the new outlook on detonation waves, and naturally have been researched extensively, in spite of which there are still outstanding issues and questions to be answered. One such research team that investigated the complex phenomenon was Voitsekhovskii et al. [24]. Since a comprehensive analysis of spinning detonations required detonation tubes of considerable length, depending on the mixture used (even up to 10 m [24]), Voitsekhovskii’s proposed “fixing” the detonation wave in a stationary frame of reference, which could potentially alleviate the demanding facility requirements. He reasoned that a premixed mixture of the required reactants, when fed into an annular chamber at the required inlet velocity (so as to balance the spinning detonations’ axial velocity in a stationary premixed tube) the transverse waves composing the detonation wave could be fixed in the laboratory frame, thereby lending it to be studied more easily. However, since such a premixed injection was prone to intense flash back events, he resorted to experimentally testing the next best configuration — a non-premixed injection that is continually fed into an annular chamber; or, in other words, what we now know to be a rotating detonation combustor. Voitsekhovskii’s intention seems to not have been to create a pressure gain device, but rather to efficiently study

spinning detonations. Over the next several decades, RDCs have been recognized as a device with very high potential, but the origins of its inception and its strong links to spinning detonations have apparently been overlooked for the most part, as pointed out by Anand and Gutmark [25]

10>.

The fundamental difference between the two is that a rotating detonation is axially fixed at a given point in space whereas a spinning detonation moves helically in an enclosed structure, and therefore has an axial velocity component [22]. Spinning detonations have a leading shock front

(incident wave) that is coupled to the transverse wave [26]. The secondary difference is that it travels in premixed stationary reactants [21], whereas rotating detonations move through non- stationary reactants [3]. A comprehensive explanation of spinning detonations is provided in Lee’s monograph [21] and will not be dealt with here. An image acquired from axially-compensated photography [24] of four laps of spinning detonations is given in Figure 2a. Figure 2b shows four laps of rotating detonations, once again acquired from open-shutter photography [27].

Immediately, the commonality in the structures is evident. Highest heat release (deciphered by the brightness) occurs at the transverse detonation wave (TDW), at the bottom of which is attached a

Mach stem (in the case of spinning detonations) [21] or an oblique shock wave (in rotating detonations) [28]. A simplified schematic of spinning detonation and its different elements is presented in Figure 2a from the illustration of Anand and Gutmark . The axial direction of motion of the leading detonation front is marked, along with the locus of the triple point (helical grooves marked on the tube wall in gray) inscribed by the transverse wave (red tab).

Note that the axially moving shock structure only marginally coincides with the cross-sectional plane of the tube, whereas the other regions of the front (composed of the incident wave and Mach stem circumferentially on the wall, and a Mach leg extending radially inwards towards the tube axis) are warped downstream in conjunction with the TDW. It can be seen that the incident wave pre-compresses and causes some contact surface burning of the mixture upstream of the TDW. The

intersection of the three waves (triple point) is thought to produce the fine helical striations seen on soot foil records in detonation tubes during spinning detonations [21]. One of the most interesting and important characteristics of spinning detonations is that the ratio of the pitch of this helix traced by the transverse wave composing a spin and the diameter of the enclosure is, for the most part, independent of the mixture used [21]. That is, the pitch-to-diameter ratio (p/d) of spinning detonations is notionally constant across a rather extensive spectrum of conditions, and is usually about 3 [26]. A simple schematic of rotating detonations (composed of the TDW and the attached oblique shock wave) in an annular space, with channel width wch, in given in Figure 2b.

Here, the detonation wave is fixed in the laboratory frame at a given axial location, unlike spinning detonations, while the reactants are injected at a velocity denoted by vfill. Thus, a single complete lap of rotating detonation entails that there be a column of fresh mixture of height, h, before the start of the second lap, which is called the fill height in RDC literature [27]. Anand and Gutmark

10> claim that this fill height is to a rotating detonation what the pitch is to a spinning detonation.

That is, if one were to “untangle” the rotating detonation wave spatially, in the axial direction, by taking into account the velocity of injected reactants it would result in a helical construct, the pitch of which is dependent on vfill, and is equal in magnitude to the fill height, h. Hence, for rotating detonations, the term analogous to p/d would be h/d. It is imperative to note here that p/d is to be construed as the ratio of the pitch to hydraulic diameter (dH) and not the geometric diameter. This effect of hydraulic dimension on spinning detonations in geometries other than a circular cross- sectional tube was established by analyzing the process in rectangular cross-sectional tubes [29] and annular tubes [30]. For annular cross-sections (RDCs), the term analogous to the diameter length is equal to twice the annular width [30], and hence dH = 2wch. Using a comprehensive literature review of the two detonation phenomena, it was shown that while the pitch-to-hydraulic diameter ratio of spinning detonations is known to range from 2 to 6 across a wide range of conditions, the fill height-to-hydraulic diameter of rotating detonations also extends across a

similar range — between 1 and 5 across diverse facilities and conditions [25]. Due to this similarity between both, the authors deliberated on the possibility that rotating detonations might be type of near-limit detonation propagation behavior, like spinning detonations, which Lee [21] ascertains is

“the nature’s last resort for maintaining the detonation mode of combustion for most mixtures.”

Detonation direction Detonation front

Channel

width, wch

TDW Mach TDW

leg Tube

mixture

Stationary Stationary diameter, d diameter,

Rotation Fill height, h Rotation

Pitch, p Cross-section Injected mixture, v fill

(a) (b)

Figure 2 (a) Spinning detonation wave structure [24], and (b) rotating detonation wave

structure [27]. Schematics from Ref [25]

Anand and Gutmark also identified twelve properties peculiar to the two processes, and the tabulation comparing both has been reproduced in Table 1, with original references. There is a noteworthy similarity in the observed characteristics of the processes (properties: 2-6, 8 and 9), with regard to the higher modes of onset and sustenance, and the velocity deficits. This qualitative confluence of different traits furthers the notion that the underlying physics might be common to both rotating and spinning detonations. Of the listed traits, the last (perturbation of shock front by downstream combustion) is the most important. If a detonation wave travels at C-J speed, then by definition, the products expand at a sonic speed relative to the upstream shock front [21]. However, considerable velocity deficit is observed in TDWs in spinning detonations. Consensus regarding this is that spinning detonations

are not C-J detonations and the continual propagation of TDW is due to the strong coupling of the shock wave with the products downstream which is only possible if the products are subsonic with respect to the shock wave. Such a condition normally only occurs in an overdriven detonation wave, which is not steadily propagating and fails after a finite time [21], unlike a spinning detonation. Lee attributes this “paradox” [21] to strong boundary layer effects and two-dimensionality of TDW, which is not captured in the ideal C-J theory. In light of this finding — of rotating detonation wave’s quantitative and qualitative similarity to spinning detonations — it is essential to consider the possibility that rotating detonations might be a type of near limit propagation of detonation waves.

Note that, in gaseous detonations near limit is defined not only by chemical limits imposed by equivalence ratio, but also by physical limits that are dependent on the boundary conditions [21]. It needs to be punctuated here that some of these overlap between spinning detonation characteristics and rotating detonations (or “detonation-like waves”) have been recognized before by Voitsekhovskii and his colleagues back in 1968 [31]. They noted that the different properties between spinning detonations and the tangential high frequency instability (to be discussed in the next section) in rocket engines “show them to be in many respects similar”. The difference, Ar’kov et al. argued, is that in spinning detonations the reactants upstream of the TDW are pre-compressed by the main detonation front composed of a strong shock wave, whereas in the “spinning detonation-like” waves they observed in rocket engines, there is no such pre-compression.

However, they claim that the only requirement for the propagation of the transverse front in both cases — spinning detonations and high frequency tangential instability — is that it be fed continuously by chemical reactions downstream of it; or in their words: “the conditions created in proximity of nozzles of a LRE (liquid rocket engine) are the same as those behind the forward front of a spinning detonation”. Apparently, it is this publication by the team composed of Voitsekhovskii that deliberated, probably for the first time, the idea of an RDC as we now know it: “The most effective means [of combating HFI] would apparently be the use of transverse waves for [improving

the] burning of fuel. It could ensure a more complete combustion in chambers of reduced dimensions, since the shock waves produce further atomization of [fuel] droplets and reduce ignition arrests”. In the next section we will dwell on this mostly forgotten kinship between detonations and HFI.

Table 1 Properties of interest for rotating detonations and spinning detonations [25]

NO. Property Rotating detonations Spinning detonations

1 Regime It is observed at wide ranges of It is observed at near limits of motionless

detonable mixtures with a detonable mixtures in tubes with circular,

subsonic or supersonic annular, rectangular, triangular cross-

injection velocity relative to section, etc. [21,29,30]

the RD, in hollow, annular,

oblong and disk-shaped

combustors. [27,32–36]

2 Cross-current Pressure difference across the Pressure difference across the transverse

/ swirl transverse wave causes high wave causes high positive fluid swirl (in

positive fluid swirl (in the the direction of the TDW). The same

direction of the TDW). The pressure difference causes low negative

same pressure difference fluid swirl (in the opposite direction of the

causes low negative fluid swirl TDW), such that the angular momentum is

(in the opposite direction of conserved. [38]

the TDW), such that the

angular momentum is

conserved. [37]

3 Multiplicity More than one TDW ‘wave’ is More than one TDW ‘head’ is possible

possible [27]. [21].

4 Mixture Increase in reactivity spawns Increase in reactivity spawns more ‘heads’

reactivity more ‘waves’ [39]. [21,24,26].

5 Pressure Increase in pressure spawns Increase in pressure spawns more ‘heads’

dependence more ‘waves’ [40]. [21,26].

6 Unreacted Pockets of unreacted mixtures Pockets are formed near the inner wall

pockets are formed when there is an when there is an annulus [42].

annulus [41].

7 Co-rotating It observed at heightened flow It is not observed; though theorized to be

waves/heads rates and pressures possible [23,24].

[27,39,40,43].

8 Counter- It is observed when there are It is observed when there are multiple

rotating multiple ‘waves’ [44,45]. ‘heads’ [21].

waves/heads

9 TDW velocity It is lower than C-J speed [43]. It is lower than C-J speed [21]. The

The individual speed of the individual speed of the TDW decreases

TDW decreases when the when the number of ‘heads’ increases. At a

number of ‘waves’ increases. very high number of heads, each head is

At a very high number of almost an “acoustic wave”.

waves, each head is almost an

“acoustic wave” [46,47].

10 Symmetricity It has been noted that when Two heads are unsymmetrical when there

(property of there are two waves, the is no axial insert (when the tube is

multiplicity of distance between them is circular), i.e. one head is stronger than the

waves/heads) lesser than half the other. Two heads are symmetric when

circumferential distance of the there is an axial insert with diameter that

RDC [48]. Hence, the multi- is 20% - 50% the tube diameter [24].

wave modes are not

symmetric.

11 Pre- There is no leading shock A strong leading shock front pre-

compression wave, and hence no such pre- compresses the upstream fresh reactants

of mixtures compression aiding the TDW before it is consumed by the TDW [24].

[16].

12 Perturbation This is not yet addressed / There is widespread contention that

of shock front reported. spinning detonation is sustained due to

by acoustic perturbations from the

downstream downstream products interacting with the

combustion upstream detonation front [21]. The

frequency and pitch angle of spinning

detonations can be rather accurately

explained using acoustic theory, by

considering pressure antinodes to exist in

the product gases behind the detonation

fronts [24]. For high frequency spins away

from the operational limits, acoustic

theory breaks down in describing the

frequency. When the cell size is small

compared to the tube diameter / annulus

width, the sustenance seems not to be due

to the acoustic eigen-mode but due to

chemistry [21]. This “paradox” of the

downstream products interacting with the

upstream shockwave suggests that these

detonations do not behave like C-J

detonations, despite travelling steadily (in

laboratory frame).

1.2. The High Frequency Combustion Instability Perspective

Broadly, detonations can be stable or unstable [21]. Unstable detonations exhibit a highly time-dependent three-dimensional behavior and manifest as different peculiar phenomena, such as spinning detonations discussed above. While their actual onset and exact physics are actively studied, there is common consensus that unstable detonations have a decoupled shock wave- reaction zone structure that is brought about due to the quality of reactants (high activation energy), boundary conditions, or both [21]. However, based on the mechanism of a coupled propagation, detonations exist in one of three sub-types: strong detonation, C-J detonation and weak detonation [21,49]. A strong detonation has a subsonic flow of products behind the detonation front, relative to it. As such, a strong detonation (“piston supported”) cannot sustain indefinitely, since the detonation wave weakens due to the expansion waves interacting with the reaction zone. C-J detonations (“unsupported”), on the other hand, can be freely propagating

(steady state), and most mixtures subscribe to the solutions obtained from the simple Rankine-

Hugoniot relation with an additional energy release term. Here, the combusted products are sonic with respect to the detonation front, which means the detonation wave can be continually sustained, provided the upstream and boundary conditions are held constant. The third detonation type — weak detonation — is theoretically possible [49], but requires special conditions to exist. In

fact, despite both Zel’dovich and Neumann showing the theoretical possibility of steady-state weak detonations [21], notable apprehensiveness seemed to exist for some time among experimentalists regarding its possibility in the physical world. Weak detonations have a shock wave that is supersonic relative to the expanding products, and as a result have a comparatively (to C-J) higher propagation velocity and lower peak detonation pressure [21,49]. It is at this juncture that we seek to divert the attention to the work of Adams [50], who tried to experimentally show that weak detonation waves can exist in gaseous mixtures, by varying the boundary conditions of the detonation tube. His work was partly motivated by the results of Voitsekhovskii, who was the first to show the possibility of having sustained and stably propagating rotating detonation waves in an annulus [51]. He observed detonation waves moving at half the C-J velocities of the mixture that was used. While the final conclusion of Adam’s investigation into weak detonations were ultimately inconclusive, the questions raised by him regarding the peculiarities observed by Voitsekhovskii in his rotating detonation combustor are of heightened significance, both from a fundamental physical inquiry and from an engineering perspective.

Multiple researchers [31,52–55] studying rocket engines (both liquid propellant engines and solid motors) have observed “detonation-like” waves spinning around the rocket combustion chamber at thousands of Hertz. This high-frequency tangential instability in rocket engines has been a source of constant adversity to the development of rocket engine programs, mainly due to the lack of understanding of the fundamental behavior of the complex combination of combustion and fluid dynamics. This had traditionally lead to the highly demanding and economically detrimental process of trying to treat the rocket-specific symptoms of the high-frequency instability by adopting a trial-and-error process of altering the rocket geometry and mixing scheme, among other things, rather than addressing the nuclei of the issue [56]. For instance, the F-1 engines for the Saturn V program had to be subject to over 2000 full-scale test runs to detect and avoid the intrinsic (starts only after injection of reactants and subsequent ignition) instabilities, as it

appeared to be highly sensitive to the injection scheme and flow rates used [57]. Of note is Ariane 5 rocket, which experienced significant high-frequency tangential instability events in its Viking engines [58]. The high-frequency instabilities in rocket engines have been attributed to a variety of factors, some making more sense than others depending on the research facility [56]. A combustion-acoustic coupling in the form of an acoustic wave, conforming to the Rayleigh heat addition criterion [59–61], velocity fluctuations, entropy waves, detonation-like waves, liquid stream shattering and supercritical droplets explosion are some of the proposed theories [56]. It is to be emphasized that significant contention still exists among the researchers of rocket engine instabilities on the fundamental nature of the high-frequency tangential instability. Most studies still prescribe to the Rayleigh heat addition process through in-phase pressure and heat addition and explain the “steep-fronted, detonation-like” waves to be a kind of acoustic wave. However, some other studies [31,52,62] have rightly pointed out the debilitating shortcomings, both logical and observational, of this theory. Flandro et al., who are responsible for one of the most accurate analytical models on these high-frequency instabilities [62–65], go as far as to say that the theories that are purely based on the acoustic wave point of view have spent “much time and energy on attempts to correct deficiencies in the linear model by introduction of ad hoc fixes that are often based on guesswork, and misinterpretation and/or distortion of experimental evidence”. Flandro et al. note that linear models that only take into account acoustic effects to describe HFIs in rocket engines are incorrect owing to the glossing over of the fact that shock waves are widely observed in rocket engines during unstable operation [64]. Therefore, the physical mechanisms responsible for these instabilities have not yet been pinpointed, and as a result two main unanswered questions remain: (i) what is the mechanism causing these shock-type fronts? [66], and (ii) why is the injector region always prone to highest erosion and degradation if the mode of propagation is acoustic, which would imply equal strength of the instability, combustor length-wise? [67]. The primary reason behind not considering detonation physics to explain HFI in rocket engines seems to be

attributed to the rather large mismatch between the ideal CJ model-predicted wave speeds and peak pressures and the measured values, when such an effort was undertaken [55,68]. However, this mismatch can now be explained by recent findings in the field of RDCs, where the rotating detonation wave speed and peak pressure across all the facilities worldwide always exhibit varying levels of deficiencies from the expected ideal C-J values in an RDC [36,48,51,69–71]. In this regard, rotating detonations differ from weak detonations since they actually exhibit lower wave speeds from C-J, which is in contrast to the higher wave speeds that should be sustained if they were weak detonations. Lower peak pressures and wave speeds suggest that rotating detonations are a type of near-limit detonation phenomena, and probably not weak detonations as questioned by Adams.

The preceding section on the similarities between spinning detonations (near-limit phenomenon) and rotating detonations offer additional support to this claim.

On the other hand, the rationale behind attributing the Rayleigh heat addition criterion to explain HFI processes in rocket engines is because there are indeed, oftentimes, clearly linear processes that tend to operate at very similar frequencies [55,72–74]. This is seen in symmetric sinusoidal pressure oscillations at high frequencies [75–79]. The problem arises when the same process is also used to explain the patently non-linear, non-isentropic detonation-like processes that are also categorized under the umbrella of high frequency instabilities [67,80]. The origins of this confusion could perhaps be exemplified in the pressure and ionization traces from a hollow

RDC studied by Anand et al. [81] . Shown in Figure 3 are pressure and ionization traces obtained from the same azimuth of continuous hot-fire operating point. This setup has the ability to track the relative changes between pressure and ionization since both sensors are at the same azimuth. Note that data acquisition is simultaneous and hence the data — pressure (blue) and ionization (red) — are time-synced, and since they are at the same station, they give the pressure and ionization behavior of the detonation wave as it passes through that point in the circumference.

Upon ignition (t ≈ 0 s), it is seen from Figure 3a, that initially there is no pressure activity; just

ionization activity. At t ≈ 0.02 s, rotating pressure waves with considerable peak pressure magnitudes (and hence rotating detonations) appear. However, at t ≈ 0.05 s, the rotating detonation wave seemingly descends into highly unstable propagations that are characterized by “packets” of subsequent laps that have amplitude modulated (AM) sinusoidal component. This unstable behavior extends till t ≈ 0.28 s, after which there is, once again, sustained periodic rotating detonations without the packets of instability. Of interest is the fact that, for a given packet of instability, ionization (red) is recorded for only about roughly the first half of the sinusoidal packet, whereas the second half is composed of just pressure activity (Figure 3a). Figure 3b shows pressure and ionization data from an arbitrary duration from the same test point when there is stable rotating detonation wave propagation. It can be seen that the shock wave precedes the ionization

(combustion) peak, as is to be expected in a detonation wave. A further magnified image of this snippet (Figure 3c) shows this distinction — pressure peak preceding the ionization peak — better.

The black circles denote the peak pressure and ionization values, and are acquired by a time-of- flight algorithm that captures peak values, for a given lap. Figure 3d contains pressure and ionization data during two subsequent packets of unstable operation, from the same test case. As explained earlier, for a given amplitude modulated packet of subsequent rotating pressure waves, ionization activity exists for roughly the first half of the packets. Periods between the two packets do not exhibit any ionization, but do exhibit very weak rotating pressure waves that do not exceed

0.5 bar — this is indicative of an acoustic wave and not a detonation wave generally. A striking difference from the pressure-ionization coupling behavior seen during stable operation (Figure 3c) is evident in Figure 3e during unstable behavior. During unstable propagation, most laps in a given cycle have the peak pressure succeeding the ionization / combustion peak. While this result is seemingly contradictory at first glance, Anand et al. [81] postulate this to be due to the flame acceleration and transition to detonation phenomenon, most commonly observed in ducts with deflagration-to-detonation inducing obstacles [82]. In their comprehensive review of the said

phenomena, Ciccarelli and Dorofeev state that “flame propagation in an enclosure generates acoustic waves that, after reflections from walls and obstacles, can interact with the flame front and develop flame perturbations through a variety of instability mechanisms” and say that if such a flame propagation is fast enough, it “can result in severe flame distortion which can induce flame acceleration and, in extreme cases, cause transition to detonation” [82]. Anand et al. postulate that the concave surface of the RDC outer wall acts like a reflecting obstacle thereby sustaining the propagation process. It is a well-known property of detonations in curved channels to have pronounced collision and subsequently stronger ignitions at the outer concave wall [83,84].

The alternate coupling and de-coupling of the pressure and ionization front is also widely noted in detonation propagation in tubes, where they are called galloping and stuttering detonations [21].

Indeed, very similar steepening of wave profiles from an initial wave that appears to be acoustic in nature, to a final form that is highly discontinuous has also been observed in rocket engines (see

Figure 4a reproduced from [85]). The usually non-linear nature of HFIs is clearly visible in the oscillogram-acquired pressure traces in a rocket engine chamber (Figure 4b). The propensity of highest erosion to occur close to the injector headwall (and not distributed through the chamber, if one assumes an acoustic mode) is seen by the image of an F-1 engine after an HFI event (Figure 4c).

Clearly, from the above information it can be ascertained that there seem to be two scientific communities operating rather independently of each other. The next section is a review of the findings related to the structure and propagation characteristics of rotating detonation waves that apparently answers the speed and pressure deficits, and the inclination to produce the highest heat transfer near the injector elements.

(a) Unstable Stable (a) Unstable Stable (a) Unstable Stable (a) Unstable Stable (a) Unstable Stable

(b) Continual ionization activity (b) Continual ionization activity (b) Continual ionization activity (b) Continual ionization activity (b) Continual ionization activity

(c) ∆t ∆t (c) ∆t Shock wave ∆t leading ionization ∆t Shock wave ∆t (c) leadingfront ionization ∆t ∆t (c) Shockfront wave leading ionization ∆t Shock wave ∆t (c) leadingfront ionization Shockfront wave leading ionization front

(d) Initial ionization Only pressure (d) onset revolutions Initial ionization Only pressure (d) onset No ionization revolutions Initial ionization Only pressure (d) activity Initialonset ionization No ionization Onlyrevolutions pressure (d) onset activity revolutions Initial ionization No ionization Only pressure onset No activityionization revolutions activity No ionization activity

(e) Combustion wave Ionization onset leading pressure wave (e) Combustion wave Ionization onset leading pressure∆t (negative)wave (e) Combustion wave Ionization onset (e) No ionization activity leadingCombustion pressure∆ wavet (negative)wave Ionization onset leading pressure wave (e) No ionization activity Combustion∆ wavet (negative) Ionization onset leading pressure∆t (negative)wave No ionization activity No ionization activity ∆t (negative)

No ionization activity

Figure 3 Pressure and ionization traces at 0.4 kg/s and an equivalence ratio of 1.6: (a) complete traces, (b) stable propagation, (c) magnified traces during stable propagation, (d)

unstable propagation, and (e) magnified traces during unstable propagation [81]

(a) (b) (c)

Figure 4 (a) Drastic growth rate of nonlinear oscillations in a rocket motor [85], (b) shock- fronted pressure profiles during tangential HFI [86], and (c) localized erosion patterns in F-1

engines at the injector and headwall after an HFI event [86]

2. Rotating Detonation Structure And Dynamics

Before proceeding further it is essential to realize that a rotating detonation wave is composed of multiple structures, namely the transverse detonation wave, attached oblique shock, and slip line, among other fluid dynamic phenomena. This is akin to spinning detonations which also include multiple parts: transverse detonation wave, primary shock front, Mach leg, etc., as explained in the previous section. A schematic of an annular RDC with an aerospike nozzle is presented in Figure 5a.

The specifics of different nozzles and other RDC geometries like hollow and disk will be dealt with later in the review. For understanding the most important particulars of the rotating detonation wave structure, annular configuration offers the best possibility. The schematic shown in Figure 5a can be unwrapped in a two-dimensional plane as shown in Figure 5b. Due to the high injection velocity required to stabilize the rotating detonation wave (D) at a given location axially near the

injector, the wave is always tilted towards the headwall as seen in the figure (a rotating detonation can be formed, at least in theory, for injection velocities ranging between a non-zero value to the ideal C-J value [87]; beyond this it becomes a standing oblique detonation). The process is better visualized when in a detonation-fixed frame of reference schematized by Nordeen et al [88]. Shown in Figure 6a is a detonation wave with moving with a tangential velocity, Uwave, when supplied by an injector with flow velocity, V. In this scenario, the true wave speed is the one that results in the closure of the velocity triangle composed of Uwave and V. That is, the actual rotating detonation wave speed is higher than the experimentally measured (mostly from a time-of-flight algorithm or frequency estimates) speeds. Despite Nordeen et al. noting this issue, most experimental investigations on RDCs resort to assuming the tangential wave speed as the actual wave speed.

While such an assumption induces only a small error at low injection velocities, it causes considerable error at higher flow rates. For instance, if V is 500 m/s (most RDC injectors are considerably choked to reduce the coupling between the supplies and combustor) and Uwave is 1500 m/s, D is actually 1580 m/s — a 5% error in estimated velocity. As can be seen in the figure, in a detonation-fixed frame, the reactants enter the detonation at an angle, get consumed by the wave and exit as a burnt products, also at an angle. Refocusing our attention back on Figure 5b, it is seen that a triangular wedge shaped region is formed upstream of the wave, composed of fresh reactants for the wave to consume. This shape in caused due to the nature of expansion of the products downstream of a rotating detonation wave, which has both an axial and lateral component, due to the initial momentum supplied by the injected reactants upstream of it. The net result of this is that there is considerable pressure-difference induced swirl (pressure downstream of the detonation front is higher than that upstream of it) throughout the combustor, as denoted by the laboratory- frame product velocity, up. Owing to this multi-dimensional expansion of the burnt products, which occurs at the high pressure region behind the detonation wave, the associated backpressure imparted by this process on the injectors cause them to completely cease supplying flow

momentarily. The subsequent relaxing of the injector is linked to the gradient in pressure in the products region (shown by orange for more intense pressures, and yellow for the less intense region). This pressure gradient is what causes the wedge shaped refill region of the upstream fresh reactants. Note that the nature of the swirl produced by RDCs is a region of notable debate. There is a net swirl in the flow-field exiting the combustor, when it exits into atmospheric conditions

[19,37]. However, addition of a convergent-divergent nozzle which chokes the exit flow, or pressurizing the combustor by other means, results in producing strong reflected shock waves from the exit plane that moves in a direction opposite to the rotating detonation wave [37,89], actively working on negating the swirl caused by the latter. This process was seen by Nordeen et al. [37], by analyzing the direction and magnitude of the velocity of multiple streamlines in an RDC with three different exit conditions. Other effects of nozzle addition will be discussed in later sections. The refill process is quantified in RDC literature by the maximum height of the region, and is called fill height. The importance of fill height in dictating not just stable one-wave mode, but also higher number of rotating detonation waves was discovered by Bykovskii et al. [27]. If the fresh mixture upstream exceeds a critical fill height, then more than one detonation wave is spawned and exists in the annulus simultaneously. This process of rotating detonation wave multiplicity is reviewed later in the chapter.

(a) (b)

Figure 5 Illustration of (a) a rotating detonation combustor with an aerospike nozzle, and (b)

“unwrapped” schematic of the RDC flow-field [90]

In the section above, attention was directed to the mechanism responsible for large deviations of waves in rocket engines and RDCs from CJ conditions. To explain this, one must first understand the velocity deficit mechanisms observed in fundamental studies on detonation propagations in tubes. As first explained by Lee and his associates [21,91,92], velocity deficits (from the C-J speed) at near-limits are due to two fundamentally different mechanisms. Using argon- diluted and argon-undiluted mixtures in a porous-walled tube, they established that there are two types of near-limit detonation wave behavior: stable and unstable. In stable detonation wave propagation (argon diluted), despite there being a velocity deficit, the detonation wave travels with a rather steady velocity over time and distance. In this case, the velocity deficit is due to the area divergence effects imparted by boundary layer effects. In the shock wave-fixed reference frame, there is a negative boundary layer displacement where the density is lower than that in the free- stream products and the velocity higher. This causes a divergence in the streamtube area, which

induces two-dimensionality to the detonation wave structure. This “area divergence” effect was first noted by Fay, who used it to explain the observed velocity deficits planar detonations [93].

Since the streamlines diverge due to negative boundary layer thickness, the products expand with subsonic velocities through the virtual diverging nozzle, thereby establishing a strong coupling between the downstream products and the upstream shock wave. This idea was expanded further by Dabora et al. [94] to account for the velocity deficits in detonations propagating with a lateral relief (inert compressible mixture on one side and flammable reactants on the other for detonation to sustain). The second mechanism responsible for velocity deficits at near limits (argon undiluted) is due to inherently unstable cellular detonation caused by severely limiting geometric constraints.

In this case, detonation propagation is not steady, and consistent failing and re-ignition of detonation waves is observed, which brings along with it considerable variations in detonation cell width and length. This effect is produced when the detonation cell size becomes comparable to the size of the geometric cross-section, thereby heightening the effect of TDW interaction with boundary layer losses [21]. It is important to note that the above two velocity deficit types not only vary in their driving physics, but also in their characteristic dimensions and magnitude of deficits.

Velocity deficits caused by area divergence (of which lateral relief is a subset of) exhibit only low deficits from CJ, not falling below 20% of the ideal speed. Higher deficits of more than 20% are caused by the unstable detonation propagation [21]. Area divergence is dependent on the parameter of the finite reaction width based on the Zel’dovich – von Neumann – Döring (ZND) model. Lee explains that shock plane and the C-J plane are separated by the reaction zone width

[94], which can be approximated to be the cell length, Lc, for stable detonations (chemistry dependent) [21]. For unstable detonations exhibiting large deficits, cell length is no longer the defining factor, owing to the high instability of the propagation front which ignites and fails. Here, the characteristic dimension is the cell width, λ, i.e. it is geometry dependent.

Some evidence for lateral relief causing velocity deficits in RDCs is shown by Paxson in his numerical simulations [95]. Contours of temperature in an RDC flow-field shown in Figure 6b represent the “turbulence induced reaction zone enlargement” effect of lateral relief accompanying rotating detonations. This enlargement resulted in reduced chemical reaction rate, and thus lower speeds and temperature. Deficits of 15%-40% were reported in the numerical study of Paxson, which tends to mimic the observed deficit magnitudes seen experimentally [95]. Paxson also notes that this effect is peculiar to RDCs and is not seen in pulsed detonation combustors. Uneven mixing due to non-premixed reactants injection, heat transfer to the combustor wall and wall friction also contribute to the velocity and pressure deficits, as shown by the simulations of Paxson and Nordeen et al. [15,88,96–100]. An endeavor trying to simulate an analogue to this unwrapped RDC structure

(detonation wave moving in a linear channel with an unbounded edge), without reactants injected laterally to the RDC, measure a deficit of not more than 20% [101]. This adds further emphasis to the notion that the peculiarity of wave speed deficits in RDCs is linked to the presence of a moving flow-field upstream of the detonation wave. Since Paxson attributes this effect to his observed deficits, one has to question why there is still a 20% deficit occurring even when there is no lateral mixture injection. This could perhaps be answered by the simulations of Houim and Fievisohn, who found that detonations moving through a layer of combustible and inert mixtures tend to propagate stably dependent on critical conditions pertinent to the acoustic impedance and shock structures formed at the inert boundary interface [102]. Strong cellular instabilities, akin to the unstable deficit mechanism discussed above, were observed due to formation of Mach lens structure at the interaction points. They argue that if one were to assume completely burnt products after a rotating detonation wave, it is reasonable to assume that the wave sees an inert boundary on one side and combustible mixtures in the wedge-shaped profile on the other side close to the injector wall (see

Figure 5b). Thus, results from diverse simulations and experiments suggest that rotating detonations are amenable to both types of velocity deficits observed in basic detonation

propagation mechanics — stable, predicated on chemistry, and unstable, dictated by physical bounds. In other words, it is possible to explain the discrepancy of the characteristics of detonation- like waves (with C-J estimates) in combustors based on “non-ideal detonation” physics [21].

(a) (b)

Figure 6 (a) Velocity triangle in the detonation-fixed frame of reference [88], and (b) non- dimensional reactants mass fraction (top) and product temperature showing enlargement of

streamlines (bottom) [95]

The remaining two prominent structures that need to be addressed are the oblique shock wave attached to the TDW, and the slip line. The oblique shock is produced due to the differential density between the inert layer (which is the burnt products of the prior detonation lap in RDCs) and the supersonically moving TDW [28]. A slip line is seen in RDC flow-field originating at the intersection of the TDW and oblique shock, since they are discontinuities that separate regions of different velocities, which are at pressure equilibrium [103]. Due to pockets of unburnt reactants, there is also significant burning here, and is sometimes called contact surface burning to indicate the different densities and temperatures behind the TDW and oblique shock [104]. At this juncture, the exact nature of this discontinuity is still under scrutiny and hence researchers have resorted to also using slip lines or contact surface to explain this discontinuity [104,105]. Hishida et al. discovered significant vortex-roll ups in the in the wedge of fresh mixture upstream and speculated it to be produced due to the Kelvin-Helmholtz instability (velocity difference across the interface)

[106]. Li et al. studied this interface between the products and fresh reactants further and confirmed that the interface is in actuality a second contact surface in the RDC flow field, owing to the difference in density and temperature on the two sides of it [107]. Additionally, they also obtained canonical structures that suggest strong Rayleigh-Taylor instability (density difference across the interface) to be present here, in addition to the previous instability (Figure 7a).

Considerable baroclinic torque was also discovered in this interface implying the possibility of high shear strength which might cause instabilities downstream. The same team, in another publication authored by Liu et al. [108] furthered this investigation by analyzing the slip region formed downstream of the intersection of the detonation wave and oblique shock. Interestingly, while the effects of baroclinic torque along the slip line were found to be negligible, two strongly unstable modes of vorticity were observed, with each exhibiting a spin in a direction opposing each other

(Figure 7b). This was attributed to originate from the transition shock (the protruding notch marked by red arrow in Figure 5a between the TDW and oblique shock) that connects the detonation wave with the oblique shock. Numerical simulations have indeed observed this transition shock in rotating detonation waves before [109], but did not address it in much detail.

The protrusion into the flow-field upstream of the detonation wave was posited to be caused due to the higher velocity of this wave owing to it’s passage through hot gas (higher sound speed). Uemura et al., however, proposed that the transverse detonation wave is formed due to explosions occurring at this transition shock region when it passed over the unreacted gas pockets at the interface between fresh reactants and products [110]. This newly formed wave was shown to move towards the injector elements and bounces off the surface and causes a subsequent explosion event at the transition shock point. Though Houim and Fievisohn did not simulate rotating detonations, they suggest the presence of both Kelvin-Helmholtz and Richtmyer-Meshkov instability (caused by impulsive acceleration of fluids with different densities) in the contact surface/slip line in their inert gas-bounded detonation motion in linear channels [102]. Additionally, Davidenko et al. [111]

observe two groups of expansion waves originating from the top and bottom point of the TDW. This is marked in Figure 7c. These waves are used to explain flow turning in the vicinity of the detonation wave. In this regard, there appears to be a disagreement between the actual points of origins of these groups of expansion waves. Zhdan et al. [112] in their numerical simulations and

Bykovskii et al. [113] in their interpretation of high speed images propose two groups of expansion fans, but both originating from within the base of the RDC, i.e. near the headwall where the detonation wave interacts with the fresh reactants. As shown by the derivation of the rotating detonation wave structure by Fievisohn and Yu [105] based on a first principles-based, method of characteristics approach, Prandtl-Meyer expansion fans would originate from the top and bottom of the TDW, as seen by Davidenko et al. [111]. This is a modification from the observed structure in an unbounded detonation moving through an inert mixture on one side and stationary reactants on the other. Since at C-J plane, the Mach number is unity and after it, the products expand supersonically, Prandtl-Meyer expansion fans are to be expected right after the C-J plane at the interface due to flow turning [94,114], as shown by Dabora’s seminal work on this issue [94], where he used a shock-tube analogy to systematically derive the resulting angle of the interface burning

(δ), which in turn causes an oblique attached shock with angle, θ.

(a) (b) (c)

Figure 7 (a) Fluid dynamic instabilities at the interface between fresh mixture and burnt

products gases (wave moving from bottom to top) [107], (b) strong vortical structures of different spins at the slip line originating from the transition shock between the detonation

wave and oblique shock [108], and (c) expansion waves (broken white lines: 2,3,4)

originating at the top and bottom points of the detonation wave (1) [111]

The exact nature of the axial flow velocity at the RDC exit appears to be a point of contention. Since there have been no experimental studies specifically investigating the same, simulations have been used to predict flow conditions downstream. Zhdan et al. [112,115,116] and

Bykovskii et al. [27] infer that there is a “normal Mach line” midline of the RDC at which “transonic transition” occurs. This line was posited to wrap onto itself thereby creating a purely supersonic axial flow at the RDC exit. This, however, appears to be an artifact of the methods used, since both

Schwer and Kailasanath [117], and Dubrovksii et al. [118] show the drastic variations in the two- dimensional unwrapped assumption of an actual RDC flow-field, by comparing it to a three- dimensional, more realistic, model. When three-dimensional, significant recirculation zones were found near the inner wall of an annular RDC where the detonation fails periodically. This effect of detonation enhancement on the outer wall and failure near the inner wall is a well-known occurrence in detonation propagation in curved channels — the outer wall acts as a compression surface and strengthens the wave while the inner wall acts as a decompression surface and causes detonation cell enlargement (weakening) [83,84,119]. This was found to cause extensive regions of subsonic axial flow at the RDC exit, which would not be attainable in two-dimensional simulations.

An example of this three-dimensionality of an RDC flow field is given in Figure 8a, from the word of

Schwer and Kailasanath [120]. One should note that the important element here is the three- dimensionality induced curvature, since a three-dimensional simulation of a linear RDC analogue with continuous injection of mixture also showed a completely supersonic exhaust [117]. Hence, the assumption of an “unwrapped” RDC flow-field being the same as the original three-dimensional

one should be brought into question [121]. Under the conditions of the propagation along a curvature with a finite width, the normal (perpendicular) detonation velocity-curvature relationship, commonly known as the Dn-κ rule [119,122], seems to have a significant impact on

RDC behavior. The effect of adding an exhaust plenum to the simulations [117] to generate real- world effects was also found to cause a notable change by removing two-dimensional artifacts of reflected shocks from the exit end of RDC as seen in Figure 8b. The phenomena described above are non-trivial to investigate on their own. When occurring in conjunction with each other in a high- frequency, high-temperature detonative environment with swirling flows and strong-systems level coupling (discussed later), the process of analyzing RDC flow fields becomes a monumental task.

The fast progress in computational fluid dynamic algorithms [123] and rapid increase in computing power [124] might help decipher internal RDC dynamics in the coming years.

(a) (b)

Figure 8 (a) Difference in detonation strength and shape on the outer wall vs. inner wall

(notice the pocket of green low temperature region behind the weak wave on the inner

wall), and (b) differences in axial velocity profiles (m/s) dependent on 2D (top) vs. 3D

(bottom) simulations [120]

3. Geometries

3.1. Annular

In this section, efforts pertaining to the most tested configuration of an annular cylinder are discussed. As such, the driving geometric variables are the annulus width, the overall combustor diameter and the length of the RDC. Each will be discussed one by one. Zhou and Wang [125], numerically, tested the effect of all of these parameters to reveal the differing behaviors.

Maintaining a constant diameter of the inner wall, while increasing the channel width was found to produce a curvature on the detonation front as well as additional reflected shocks from the outer wall, as shown in Figure 9. For the largest channel width, the detonation front is very weak at the inner wall due to decompression caused by the convex surface, which results in the production of expansion waves. The outer wall produces a stronger detonation region near it since it compresses the wave. Note that the outer portion of the wave also travels at a faster linear tangential velocity than the inner portion (it is a product of a constant angular velocity and radius). These effects result in considerably smaller cell sizes near the outer wall and enlarged cells by the inner wall, as seen in the experimental and numerical soot foil records obtained by Pan et al. [84] in a premixed, non- moving reactants setup (Figure 10a). A schematic of a detonation wave in a stable propagating mode as it traverses a curved channel is illustrated in Figure 10b from the work of Nakayama et al.

[83]. In the RDC, increasing the diameter, while having a constant channel width, produces shock trains that get progressively stronger and extend further downstream of the detonation wave. This was attributed to the reflection of shock waves, not only from the outer wall, but also from the inner wall, a process implied to be caused due to the product gases not fully exiting the chambers with larger diameter. A similar effect was also observed when the diameter and width were fixed, but the length was varied. Longer RDC lengths tended to causes stronger shock trains through the annulus, with a corresponding increase in the strength of the Mach wave reflecting from the inner wall.

Interesting, here, the shock train got shorter, despite getting stronger, as opposed to the cases with

increased diameter. These effects were explained to be the effect of product gas expansion — lack of complete exit from the annulus causes significant secondary and tertiary shock structures. This amplifies the discussion made in the last section that three-dimensionality is integral to the RDC flow-field. Support for these reflected shock waves is present in the pressure traces of Kindracki et al. [51], whose experimentally acquired pressure traces show secondary peaks adjacent to the main detonation peak pressures at lower annulus widths. This double-peak behavior is also seen by

Zhang et al. [126] in their experimental investigation of different annulus widths. It should be noted that having reflected shock waves emanating from the annulus walls do not hinder RDC stability. In fact, the results of Kindracki et al. suggest the contrary. Larger diameter and larger annulus widths, overall, aid in having highly stable RDC operation defined by repeatable peak pressure and detonation lap speeds. This appears to be an effect of geometry-confined, near-limit cellular instability (discussed before) occurring in the detonation waves when the channel width is small, and is comparable to the detonation cell width, i.e. boundary layers losses occur at lower widths.

Additionally, increasing the diameter has the effect of producing higher plenum recovery after every passage of the wave, since the detonation wave now has to travel a longer circumferential distance, which would entail enough time for the injector elements to recovery to allow proper propellant flow. These effects are inferable from the data of Kindracki et al. [127] presented in

Figure 11. Results from Driscoll et al. also indicate higher stability at increased channel widths, and widespread unstable RDC operation at smaller widths [128]. However, as pointed out by Bykovskii et al. [27,129], it is important to bear in mind the effects of changing a channel width at a given flow rate. Higher width tends to lower the overall mass flux through the annulus, which in turn translates to lower fill height of the fresh mixture upstream of the wave. Under these low fill height conditions, once again the combustor is prone to unstable operation. A similar facet holds true for

RDC diameter as well, with lower fill heights being produced at larger diameter. Hence, it is apparent that there are multiple tradeoffs pertaining to the annulus width and diameter. This could

be attributed to the largest RDCs tested so far in laboratories not exceeding 20’’ in diameter

[48,54,71,130]. Attaining stable detonation wave propagation depends on all of the above- mentioned factors.

Figure 9 Radial pressure profiles of rotating detonation waves through three annulus widths

at constant inner diameter: (a) 4 mm, (b) 10 mm, and (c) 16 mm [125]

(a) (b)

Figure 10 (a) Experimentally (left) and numerically (right) acquired soot foil records of a

detonation wave through a curved channel [84], and (b) schematic of the evolution of the

detonation wave, expansion wave and the associated particle travel path [83]

(a) (b)

Figure 11 Pressure profiles from four geometrically diverse (changes in internal diameter, d, and annulus width, w) RDCs: (a) d = 95 mm, w = 5 mm, (b) d = 95 mm, w = 10 mm, (c) d = 100

mm, w = 5 mm, (d) d = 100 mm, w = 10 mm [127]

3.2. Hollow

The parameters dictating annular RDC physics also holds true for hollow RDCs. However, here, there are additional parameters owing to the removal of the inner wall. In such a scenario the

“unwrapped” RDC analogue does not hold owing to the very pronounced three-dimensionality of the wave [34,131]. In a hollow RDC, curvature of the rotating detonation front, radially, is unavoidable as seen in Figure 12a from Tang et al. [132]. The outermost part of the wave

propagates at about twice the speed of the lower tail end of the wave. As explained earlier, this is due to the compressibility provided by the concave wall. From the simulations of Tang et al. and

Songbai et al. [41,133], it can be seen that the there is a finite radial depth to the detonation wave structure, after which the “tail” terminates (Figure 12a and c). Currently, it is unclear if this is an effect of the injection schemes used in the simulations (fresh mixture is not injected at the center of the combustor), or if it’s the natural tendency of a detonation wave to always terminate at the center. This causes considerable burning by deflagration at the RDC axis (Figure 12a and b), where the burnt products are imparted considerable swirl before they exit the chamber. Moreover, it was noted that the fresh mixture is dispersed more evenly in the hollow RDC, as opposed to the annular one. Songbai et al. show this effect by comparing the fill height of the fresh mixture upstream of the detonation wave for both the cases, and showed that hollow RDC is prone to producing a more even fill height, radially. This was proposed to be a negative effect, as the strongest part of the detonation front is by the outerwall, which would mean that the annular RDC would produce a more efficient burning of the reactants since the fill height is highest near the wall. Owing to the two reasons discussed in the section above (inefficient non-detonative burning and product entrapment in the combustor), hollow RDCs might be prone to an inherent loss in efficiency. On the other hand, because of the removal of the channel width-dependent dimensional constraint, it would be possible to attain detonations in mixtures, which were otherwise non-detonable. Evidence for this is seen in ethylene-air powered annular RDCs of Wilhite et al. [134] and Andrus et al. [135]. Both non-premixed (former) and premixed (latter) injection only resulted in barely isobaric sound speeds of the rotating detonation wave, for a wide range of flow rates and equivalence ratios. The presence of continuous sharp, discontinuous pressure waveforms traveling at isobaric speeds suggests the propagation mode to be quasi-detonations, per Lee [21]. Since quasi-detonations can travel even at 30% of the C-J speed, they have velocity overlaps with fast deflagrations, which makes their mechanism hard to understand [21]. It should be noted that these detonations are

mostly seen in rough-walled tubes, suggesting geometric limitations or factors causing their occurrence. Hence, less reactive mixtures in annular RDC appear to be affected by the channel width. However, a study by Anand et al. utilizing the same RDC outer diameter (6’’) showed wave speeds upwards of 95% of the C-J speeds (assuming a global equivalence ratio) at select operating points in their hollow combustor in ethylene-air mixtures [81]. Peak pressures of this wave were considerably high and even exceeded 20 bar for certain laps. It seems likely that this is an effect of removing the boundary-based losses associated with detonation propagation in an annulus, similar to the same effect seen in planar detonations through tubes which become progressively weaker at smaller characteristic dimensions [21]. Perhaps, hollow RDCs are one of the solutions that could tackle the widely measured velocity deficits seen in annular RDCs

[36,48,51,69–71]. It is yet to be quantified if this increased strength of detonations is worth the tradeoff of having vast regions of deflagrative burning. One method to overcome this is to provide an air stream through the center of the device. Stoddard et al. have shown both numerically and experimentally that rotating detonations can be sustained in a “flow-through” hollow RDC, where injection is done transverse to the combustor, which in turn does not have a headwall [136–139]. A specially shaped lip at the upstream end of the RDC helps entrain significant air flow from the atmosphere into the combustor. Simulations and experiments show that, in such a scenario, there is very minimal burning at the RDC center, which could lower the inefficiencies of hollow RDC designs. It should be noted that rotating detonation through a hollow combustor was first demonstrated by Bykovskii et al. [33] in 1997 in a disk-shaped RDC.

(a) (b) (c)

Figure 12 (a) “Looking into” view of a hollow RDC with two detonation waves traveling

counterclockwise [132], (b) reactants fill region (blue) and central deflagrative burning

formed in a hollow RDC when there are two waves [41], and (c) rotating detonation wave

shape in a hollow RDC with de Laval nozzle at the exit [133]

At this juncture, it is essential to reconsider the discussions from Section 1.2 regarding high frequency instabilities in rocket engines. As argued earlier if one were to only observe the essence of the instabilities — very fast moving, shock-fronted, steep, rotating waves capable of producing high heat transfer close to the injectors, in hollow combustors — there should be very less objective difference between a hollow RDC and a rocket engine experiencing HFI. Figure 13a shows high- speed aft-end images from a hollow RDC studied by Anand et al. [32] that shows a detonation wave

(the foremost part clearly visible and marked with a red dot) propagating clockwise after the initial blast wave deposition from the pre-detonator (red arrow). There is a brief period of apparently non-luminescent activity (but considerable pressure activity at low magnitudes) that separates the ignition event from the onset of a stable rotating detonation wave, suggesting a complex DDT event

[32,140]. Also shown (Figure 13b) is the high speed images obtained from the exit of a rocket engine with tangential HFI (clockwise rotation), from the experiments of Clayton et al. [68]. One could see the qualitative congruence of the combustion activity of the two devices —characterized by a sectorally-distributed combustion wave stronger (more luminescent) at the wall, and less so at the center — with the rotating detonation wave temperature profile from the simulations of Tang et al. (see Figure 12a). Additionally, this “rotating detonation-like wave” captured by Clayton et al.

[68] in a series of experiments performed at the Jet Propulsion Laboratory (consult the references section of the cited paper) shows that “the peak amplitude of the disturbance varies with the location of the measurement” with “the greatest amplitudes occur near the injector end of the chamber wall and in the outer half- radius of the injector face (i.e., near the corner of the chamber)”.

They measured pressure ratios of 20:1 near the injector, which decays to 4:1 at the entrance of the nozzle. Heat transfer was measured to exceed rates obtained during normal steady combustion by an order of magnitude at the injector headwall section. Shown in Figure 14a are their pressure profiles obtained at various radial distances in their rocket engine headwall, clearly representing the propensity for highest pressure near the concave combustor wall, and considerably lower pressure towards the rocket engine’s central axis. Based on the compilation of the phase and peak pressure obtained by the different circumferentially and axially distributed probes, Clayton et al. presented an “artist’s conception of the rotating detonation-like wave front”. The original image along with the complete title used for it is, is given in Figure 14b. The striking similarity of the rendering of the wave’s shape to the pressure contour plot obtained by Songbai et al. [133] in a hollow RDC with a nozzle cannot be overlooked (see Figure 12c). Flandro et al. [64,67], using their novel analytical model using a superposition of twenty acoustic modes (to indirectly obtain nonlinearity), were able to match the pressure and shape of the nonlinear waves seen by Clayton et al. The tangential nonlinear wave modeled by them is shown in Figure 14c, as it moves in a clockwise direction. They also proposed this high speed spinning wave to be behind the production of “sloshing” in a rocket engine, which is an occurrence characterized by circumferentially or radially varying reactants flow rate due to “transverse oscillations” [64]. In RDCs, this is attributed to the reactants filling height after detonation wave passage. Also of importance is that Clayton et al. do not see significant pressure activity after the choked nozzle from their instrumentation setup.

This is also the case in RDCs with a CD nozzle at the exit (see the section on RDC boundary conditions). Different names have been used over the years in rocket engine literature to describe this occurrence, namely tangential instability, resonant combustion, acoustical disturbance, transverse instability, spinning instability, screaming instability, etc. [55,56,68,141]. However, the observations across these studies regarding shock-fronted waves, very high peak pressures and heat transfer rates have remained the same. Clayton et al. deliberate on this conundrum as follows:

“Regardless of whether the phenomenon is called a detonative or an acoustical disturbance, it is believed that the definition of the parameters controlling it requires understanding of the generating and sustaining mechanisms for steep-fronted combustion-supported pressure waves sweeping about the periphery of circular cross-section chambers”. In subsequent sections, discussions on RDC physics will be further supplemented by similarities seen in rocket engines.

(a) (b)

Figure 13 (a) Aft-end images of a hollow RDC with the primary detonation front (initial onset

counterclockwise, but stable operation clockwise) marked by red dots [32] , and (b)

tangential HFI in a rocket engine recorded from the chamber exit [68]

2 4 1 3

(a) (b) (c)

Figure 14 (a) Pressure profiles obtained from five sensors mounted to a rocket engine headwall showing shock-fronted waves that are not in-phase [68], (b) “Artist's conception of

rotating detonation-like wave front. (1) Shock wave rotating within sensitive reaction zone

near injector, strong coupling between wave environment, and energy release from

reactants. (2) Fresh reactants continuously replenished during wave rotation period. (3)

Frontal surface inclined to chamber longitudinal axis and oriented non-radially in planes of

chamber cross section. (4) Intersection of wave with chamber boundaries. (5) Possible helical path of burned gas immediately following the wave.” – Clayton et al. [68] (c) pressure

contour of a tangentially traveling wave [64]

4. Reactants

A variety of reactants have been tested so far across different facilities world-wide. This includes gaseous, liquid and solid particulates to promote rotating detonations. A brief summary of the different fuels used to power RDCs is arranged in Table 2, country wise.

Table 2 Reactants used successfully in RDCs by different countries

Country Reactants

China [126,142] H2-Air, H2-O2

Japan [143] C2H4-O2

Poland [3,144] H2, CH4, C2H6, C3H8 with O2,

H2, Kerosene-H2 with air

France [145,146] Kerosene-Air, Kerosene-O2, Kerosene-LOX,

Propane-O2, H2-O2, GH2-LOx

Russia [27,129,147] Propane-O2, Acetone-O2, Kerosene-O2, H2-Air,

Syngas-Air (1/1,1/2,1/3 CO-H2 by volume), Solid

Coal-Air mixtures, Anthracite-H2-Air

USA [10,81,148–150] H2- Air, H2-O2, CH4-O2, H2-C2H4-Air, C2H4-Air,

Liquid Hydrocarbons- O2

5. Ignition and onset

During the beginnings of what would become a decade of intense research on RDC, considerable focus was directed towards the problem of properly ignition RDC [18,71,151,152].

However, multiple recent efforts have shown that detonation initiation in an RDC is one of the simpler problems to overcome, since mixing is the dictating factor as discussed in the section above.

A very brief overview of detonation initiation is in order. Broadly speaking, detonations can be initiated in one of two ways: (i) direct detonation, and (ii) deflagration-to-detonation transition

(DDT) [21]. The first method produces a detonation wave in a combustible mixture almost instantaneously [refs], with the caveat that it requires ignition energy deposition that is usually about an order of magnitude higher than the DDT process, in a given mixture [21]. For a propulsive device, direct detonation cannot be depended upon due to the prohibitive requirements of energy to be carried onboard, and hence DDT is preferable for RDC ignition. DDT, however, is one of the most complex physicochemical processes observed widely in nature, in both confined and unconfined spaces. An excellent compilation of the apparently disparate events that are dependent on DDT is given by Oran [123], aptly titled: Understanding explosions – From catastrophic accidents to creation of the universe. DDT, in its essence, is a process dependent on small-scale fluid dynamic and chemical interaction. However, when the right conditions are met, it can rather dependably produce detonations that manifest as large-scale events, through a variety of mechanisms. While the right conditions are a subject of intense scrutiny [2,123], some of the processes responsible for

DDT are known currently, and range from hot spots through flame accelerations to turbulence generation [21,123]. For the purposes of the current review, DDT in mostly gaseous media within

confined spaces is of interest. In this regard, flame acceleration seems to be the primary mechanism responsible for DDT [82]. Since this process requires a certain run up length for the deflagration wave to transform into a detonation wave, different mixtures require different tube geometries to induce DDT [82]. To overcome this geometric limitation, methods like turbulence enhancing obstacles [153], shock wave deposition [154], etc. have been used in PDCs to continually produce detonations, reliably [2].

In RDCs, the widely adopted way to ignite the device is to use what is called a “pre- detonator”, which is essentially a miniature PDC that is oriented in a way (either directly into the combustor [155], or facing into it from the aft-end [44]) that would let it deposit a blast wave into an RDC. This is similar to the “pulse guns” used to bomb rocket engines to ascertain if the geometry and reactants can be triggered to produce HFI [56]. When the mixture inside the combustor is amenable to sustain detonations, this blast wave from the pre-detonator can easily and constantly induce DDT inside an RDC. Over the years, a variety of techniques other than pre-detonators have been used to initiate RDCs, each as efficient as the other (mixing is key; method of ignition is apparently trivial). A prior review from Lu and Braun [18] on RDCs has a comprehensive list of the different procedures used to initiate RDCs — we recommend reading their publication for information regarding the same. Irrespective of the strategy used RDC initiation has to follow the

DDT process. This was verified by a study from St. George et al. dedicated to quantifying the energy deposited by the pre-detonator blast wave into an RDC annulus [156]. They found that the estimated energies are significantly lower than that required to cause direct detonations — by an order for the hydrogen-air mixtures tested. After the instance of the blast wave injection (or the first instance of a high peak pressure event inside the previously cold-flow RDC), there is always a visible period of chaos. This duration, called the “onset time” [157], varies significantly depending on the reporting facility, even for the same fuel-oxidizer mixtures. An example of RDC ignition and onset process is seen in Figure 15a, b and c, which shows pressure and ionization traces from three

sectors in the combustor, along with the pressure dynamics in the air injector. As seen, detonation wave propagation barely completes a lap (cannot be tracked across the three sectors) from ignition

(time of about 0 s) until stable propagation begins at approximately 0.022 s. From this point onwards there is a set directionality and speed for the rotating detonation wave (red -> black -> blue traces till fuel supply lasts). A study by Peng et al. utilizing a 30 mJ spark found that, for a given operating point, the onset time lasts between 1 ms and 7 ms [158]. They followed up this study with another utilizing three different ignition sources with vastly different energy depositions and found that the onset time remained largely unaffected [159], which should be unlikely if the onset times are dependent only on the DDT process, since such a process lasts merely for a few milliseconds in tubes [160]. While there is still a large degree of variability in the onset time for the same case (±50%), the higher energy ignition source only yields a slightly lower average DDT time, differing by a few milliseconds. Bykovskii et al. [161] utilized multiple initiation strategies to achieve detonation of fuel-air mixtures in an RDC, including a low-power heat pulse, injection of a product jet, and transmission of a detonation. For the detonation transmission case, none of the experiments resulted in a direct transition of the initiating wave into a stable rotating detonation.

All cases exhibited a transitional process of 4-80 ms duration, which was associated with the recovery of uniform air injection for detonation transmission, or the development of tangential instability and subsequent DDT when using the other ignition sources. Another study by St. George et al. also strongly pointed towards the supply plenums as the primary reason for the onset times seen in RDCs [157]. They investigated four different operating points ten times each to attain statistical rigidity (since the onset process is highly chaotic). By changing the air flow rates, the equivalence ratios and the backpressure, it was revealed that despite some variability between tests, the average onset time between the different cases was clearly distinguishable based on the operating conditions. For an air flow rate of 0.5 kg/s, the onset time was in tens of milliseconds, whereas 0.4 kg/s (at two different equivalence ratios) always tends to produce onset times that

extend to hundreds of milliseconds. When the system is backpressurized, there is very low variability in onset times between the ten tests and stable detonation propagation always started within 6-7 ms. Fotia et al. have also gathered some evidence that suggests injector conditions dictate RDC ignition process [155]. It is, thus, apparent that there is a plenum conditions-related variable that dictates a significant duration of the onset times reported for RDCs.

Towards this end, Anand et al. assumed the pressure dynamics in the combustor and air inlet to be a type of feedback loop defined by a single input (combustor dynamics) and single output system (air injector dynamics) [162]. By using a systems-identification model capable of validating and predicting the output of the system (air inlet dynamics), it was found that the settling time of the air injector impulse response was behind the onset times observed in pressurized RDC operations. However, in an atmospheric RDC, the onset time seemed to be linked to intense reverberations occurring inside the fuel plenum due to shock wave leakage from the detonation wave. This caused the fuel plenum to come to rest a considerably longer time after the air plenum. Because of these reverberations, the fuel plenum acts as a notably higher order system and was not able to be modeled like the air inlet (third order). The experimental settling time of the air inlet after the initial blast wave deposition in cold-flow RDC (no fuel supplied, and hence no combustion) and the impulse response function obtained by the modeling approach is given in Figure 16a and b respectively. It can be seen that the settling times match decently within an order of magnitude; so does the underdamped nature of the air injector pressure oscillations after the disturbance from steady air flow conditions. The pulse guns used in rocket engines are known to trigger both tangential spinning and standing modes inside the chamber, irrespective of the angular orientation to the combustor [56]. A similar scenario was discovered by Miller et al., who determined that the rotating detonation wave propagation is not linked to the direction of orientation of the pre-detonator [152]. Similar to RDCs, there is also a settling time linked to this “initial shock wave’s perturbation of steady-state”, which can be easily

ascertained experimentally by using only cold-flow. This impulse response of a rocket engine combustor is observed in Figure 16c from Ref [56]. From this section, it should be clear that: (i) detonation initiation in an RDC is through a DDT process, and (ii) the onset times are predominantly caused due to the injector and plenum recovery from steady-state conditions of cold-flow. In subsequent sections, evidence is presented that shows injection and mixing are perhaps the most important feature that dictates RDC operation. Note that the method of ignition should not cause any drastic changes in the onset times, per Peng et al.’s findings. Since the peak pressure of detonations inside the combustor is roughly equal to the initial blast wave from the pre- detonator (see Figure 15b), this implies that regardless of the method used, one should expect a similar magnitude of disturbance when a detonation wave is formed inside an RDC. The authors’ own experience and anecdotal statements from other researchers support using spark plugs to ignite RDCs, as opposed to pre-detonators, since the former is highly reliable, durable and easily replaceable. The added complexity of pre-detonator ignition is warranted only when it is not possible to ignite the engine any other way; quartz walled RDCs need to be ignited by a pre- detonator shooting into the combustor from the exit since, quartz cannot be machined to have grooves [44].

Ignition Onset period Stable Propagation

(a)

Stable Ignition Onset period Propagation

(b)

Ignition Stable Onset period

(c)

Figure 15 (a) Ionization traces from three azimuthal sensors in an RDC indicating the onset

period and stable operation, (b) pressure traces from the same azimuths tracing the pressure dynamics in the combustor during onset and stable propagation, and (c) pressure

dynamics from the air inlet indicating the strong disturbance induced in it [162]

(a) (b)

(c)

Figure 16 (a) Normalized (by peak pressure value) pressure amplitude of the dynamics in an

RDC air inlet when disturbed by the blast wave from pre-detonator during cold-flow [162],

(b) impulse response of the air inlet after RDC ignition during hot-flow [162], and (c)

pressure traces depicting the difference between “triggering” of a rocket engine using a

pulse gun, without and with combustible mixtures — former subsided, whereas the latter

sustains, which indicates the intrinsic nature of HFIs [56]

6. Injection and Mixing

Injection and mixing are perhaps the most important parameters that constitute RDC operation.

In fact, as evident from the discussion in the above sections, the onset and sustenance of detonations in an RDC is almost assured if the reactivity and quality of the mixture is susceptible to

DDT; just like in planar detonation waves [21,82]. This, of course, is a highly non-trivial to accomplish owing to two reasons: (i) strong coupling of the injector elements with the detonation wave, and (ii) the unknowns of the mixture requirements needed to generate detonation waves in an annular or hollow RDC. Broadly, both non-premixed and premixed reactants injection can be used in RDCs. However, the latter is harder to obtain owing to the very high probability of flashback occurring because of the considerable shock leakage and combusted products backflow from the detonation wave into the injector. A study by St. George et al. [149] utilizing a partially premixed

RDC (ethylene and air was premixed, but hydrogen was supplied separately) showed that higher

equivalence ratios tended to produce severe flashback events that permanently stopped hot-fire operation. In order to avoid this, Andrus et al. [163–165] resorted to using specially-designed premixing and flame-arresting injectors in their ethylene-air powered RDC, which resulted in the comprehensive avoidance of flashbacks throughout the tested points. However, usage of hydrogen- air in the same premixed RDC resulted in violent flashback events that curtailed RDC operation to a few milliseconds. Another study by Li et al. [166] showed the possibility of attaining rotating detonations by premixing pre-vaporized liquid Jet A-1 with heated air. However, the premixed operation tended to behave poorly in comparison to the non-premixed operation, showing a continual weakening of the wave (in terms of peak pressures) as the test progressed. The results above indicate that premixing of an RDC might not necessarily be an advisable venture. This is due to the presence of a detonation wave that produces, locally, both upstream product flow and shock wave leakage into the supply plenums (see Figure 17a and b) which could subsequently ignite the reactants when premixed [135]. Bedick et al. investigated the extent of plenum penetration from

“one-shot” detonation events from a pre-detonator to find that very strong shock waves leak into the air plenum (slotted injection) due to the blast wave from the pre-detonator (comparable peak pressure to rotating detonation waves). This initial strong shock wave then proceeded to get reflected from the multiple corners of the encasing plenum as well as bounce off as reflected waves from its base. A similar effect was also observed in the fuel plenum, albeit at a much lower level, due to the damping / isolation provided by the small-holed injectors of the fuel plenum, as opposed to the slotted air injector [167]. Numerical investigations of RDC behavior and its dependence on injection usually utilize premixed schemes because of the simplicity in boundary conditions setup

[89,112,132,168,169]. However, there is a notable variation between idealized models with a slotted injection, in comparison to a non-ideal model with discrete injection elements and associated plenums [170]. Such simulations observe pronounced shock trains inside the supply plenums stemming from the incident wave leaked from the rotating detonation front [171,172].

Considerable overpressure-to-underpressure ratio fluctuation in the reactants plenum with an increase in the ratio of exit area to throat area of the injector micro-nozzles is observed [171,172].

Relative to the detonation wave, the reflected waves travel opposite to it, inside the plenum, as observed in Figure 17c [173]. These results indicate the importance of pressure ratios across the injectors in determining stable RDC operation [14,27,128,129,174]. Choked injectors are susceptible to disturbance only momentarily, at a given location in space, whereas unchoked injectors are prone to significant alteration of internal flow and pressure dynamics [43,174]. On the flip side, it should be noted that too high a pressure injection ratio would counteract the performance gain offered by detonative combustion, thereby making the overall process inefficient, as pointed out by Paxson [15]. Very high ratios cause a pressure loss across the system, whereas lower ratios produce an increase in entropy (total pressure loss) due to the backflow into the injectors and subsequent reorientation of the streamlines towards the RDC exit [15]. Besides this, the actual spacing and shape between the injectors is also of a high consequence. Generally, a dense injector spacing tends to promote uniform mixing, thereby avoiding random auto-ignitions that can spawn a new detonation wave in an altered direction (more on this under RDC modes below)

[44,172,175].

Uniformity of mixing needs to be enforced, not only in the circumferential direction, but also in the radial direction, as seen by the results of Liu et al. [169] who showed that the fresh mixture is predisposed to significant deflagrative burning (wasteful) along the radius, when the injection schemes were altered along this axis. Depending on the injector shape (cylindrical, convergent nozzle, divergent nozzle, pintel, cavity slot, diode slot, etc), there could also be trackable changes pertaining to the wave propagation [171,172]. Strong reflected shocks are produced as the detonation wave interacts with the individual injector elements [172,173]. Also of importance is the fact that slanting orientations of the injector appear to predicate the nature of the flow after the choked nozzles, i.e. overexpanded jets are not observed when the tilt of the cylindrical slots are 40o

to the RDC headwall, irrespective of the relative direction of the detonation wave [172].

Researchers have also proposed having angled wedges on the injector headwall and differential injection velocities to promote a stable and single directionality of the wave — to the detonation wave, a backward facing step would produce divergence and cause failure — but this needs to be tested experimentally [139,176]. Thrust vectoring has also been demonstrated, numerically [177] and experimentally [146], in RDCs by altering the local stagnation pressure of the injection plenums, sectorally. Despite all this progress, there is yet to be broad guidelines dedicated to RDC injector designing, as none of the parameters tested to date offer a significant reduction in plenum disturbance.

(a) (b)

(c)

Figure 17 (a) Schlieren imaging of a detonation wave passing through a transverse array of jets along with the interaction schematic [178], (b) Schlieren imaging of air and fuel plenum

dynamics when disturbed by a detonation event in a two-dimensional RDC analogue [179],

and (c) the shock wave dynamics inside the plenum due to detonation wave passage (RW

denotes reflected waves) [180]

The above discussion pertains purely to premixed RDCs. In actuality, almost all RDCs successfully tested so far are non-premixed. This produces more layers of complexity — the relative temporal and spatial recovery of the different plenums after interaction with the detonation wave

[128,155,162,181,182], and the required mixing between oxidizer and fuel [19,81,170,183]. An

“unwrapped” RDC experimental study by Fotia et al. visualized the fuel plenum dynamics and concluded that detonation wave passage inflicted a time delay of 200 μs before the plenum could recover to its nominal fuel supply state (this would be higher for air plenum due to the larger injection area) [184]. The pressure wave inside this plenum was found to travel at about 60% of the detonation wave’s speed in the combustor, which led the authors to postulate a possible “pressure beating” phenomenon in the air and fuel plenum due to the relative difference in the two waves’ speeds (the leaked shock wave from the second lap of the detonation wave will interact with the one from the first lap causing interference by superposition). These effects can cause strong secondary coupling effects as well (discussed in the sections below). Depending on the fluidic

damping provided by the injector sizes and the pressure ratio across it, different supply plenums exhibit varied responses to the forcing impulse function (detonation event) [162,185]. Driscoll et al.

[128], followed by Deng et al. [182], showed, using basic gas dynamic equations and experimentally measured pressure values, that this uneven plenum recovery can be approximated by a function called blockage ratio, which essentially is the percentage of the injection area of the fuel/oxidizer that is completely occluded and cannot supply gases through it due to detonation wave passage.

Driscoll et al. correlated the values of this function for air and fuel plenum separately and found that unstable operation (chaotic propagation; discussed later) of RDCs is prevalent when there is a mismatch between the two. This relative recovery produces a process called “stratification” where the mixture in the region of the detonation wave could either be highly lean or rich depending on which plenum starts proving gas supply again [44]. As a result, the local equivalence ratio tends to be drastically different from the global equivalence ratio. The same mismatch is possible even if the recovery times are equal. Driscoll et al. [186] identified the widely used slotted air-fuel injection holes mixing scheme to be a type of jets in a cross flow (JICF) issue. By varying diverse injection parameters, it was shown that strong recirculation zones and counter-rotating vortex pairs (CVPs) are prevalent in the RDC flow-field (Figure 18a), even during cold-flow conditions, making the assumption of minimal changes in local equivalence ratios invalid. Bluemner et al. [187] and Rankin et al. [188] have identified this large recirculating zone experimentally. Since most RDC testing so far has resorted to using choked flow for both fuel and oxidizer, the jets-based issue at hand is compounded, since supersonic JICF produces a wide array of fluid dynamic structures, such as strong bow shocks, shock barrels, separation bubbles that oscillate at a low frequency, etc. [189–

192]. Though it might be tempting to avoid these processes by using rocket engine-type injectors where both oxidizer and fuel are supplied through meticulously arranged holes [193], it should be noted that such a setup would cause tangible pressure losses across the air injectors, which as was discussed earlier counterproductive to increasing RDC efficiency. So far, Bykovskii et al. [194],

experimentally, and Gaillard et al. [117,195], numerically, appear to be the only research groups to analyze RDC operation with impinging injectors. The importance of using non-premixed simulations in describing RDC injectors is seen in Figure 18b from Fujii et al. [180]. They imitated a non-premixed injection scheme in a two-dimensional simulation to show that vast regions of deflagrative burning exist in the RDC. When the spacing between the injection holes is increased, for the non-premixed scheme, the rotating detonation wave structure deviates tremendously from the ideal, as seen in the figure. They quantified the effect of the detonation wave passing through vast regions of burned gas to cause a deficit of 16% from the ideal C-J value for the mixtures used.

However, from the discussions above, it is apparent that there are many other factors that contribute to this deficit in addition to improper burning. While a three-dimensional reactive flow simulation of an RDC with separate plenums is time- and computation-intensive, it is able to qualitatively and quantitatively predict the detonation wave shapes recorded experimentally [44], as shown by Cocks et al. [170], and is warranted for the problem at hand.

(a) (b)

Figure 18 (a) Local equivalence ratio variation and vorticity magnitudes in an axisymmetric

annulus depicting an RDC chamber (global equivalence ratio of 1.0) [186], and (b) the

variations in the RDC flow-field and detonation wave structure produced by altering the

number and type of injection [180]

Edwards [54] was the first to propose pre-burned mixtures to be behind the pressure and velocity deficits seen in rotating detonation waves, and specifically used this inefficient burning process to try to link tangential HFI in rocket engines to RDC physics, in his annular 20’’ combustor running on ethylene and enriched air. In this regard, it is crucial to ask a very important question: if rotating detonation waves can be produced in both a hollow and an annular combustor, what is the physical mechanism responsible for its production and continued sustenance? That is, under what conditions does an ordinary combustor become a rotating detonation combustor and vice versa,

and is it something that can be controlled? In fact, if rotating detonation waves can be produced in a hollow combustor that are of equal strength (in terms of pressure and velocity) to the waves produced in an annular combustor, it would be logical to resort to this design, considering the heightened heat transfer to the annular walls [132]. Since it is well known that a planar detonation in a tube with the same mixture concentration gets progressively weaker, and eventually fails when the tube diameter is reduced below a critical value of detonation cell size [21], logic dictates that we move away from the annular designs that have been the singular signature of rotating detonation combustors until now. Towards the resolution of this question, Anand et al. showed that mixing is the primary variable that dictates the functioning of a hollow combustor as an RDC

[81]. They demonstrated that a hollow combustor exhibiting transverse (radial) acoustic oscillations (high frequency) with peak pressures ranging below 2 bar, can be “converted” into an

RDC capable of sustaining strong rotating detonation waves with speeds of more than 95% of the C-

J velocity and peak pressures sometimes exceeding 20 bar, by merely integrating a 3 mm thick circular plate on the RDC headwall to divert the incoming flow towards the combustor’s outerwall

(every other parameter was held constant). The hollow RDC geometry with the flow-turning obstacle is depicted in Figure 19a, along with contours of variation in ethylene mass fraction with radius, from a notional two-dimensional simulation. It was concluded that having fresh reactants by the concave wall of the combustor and proper injection velocities (so as to not cause decoupling of the wave, or produce a lift-off) were required to produce and sustain rotating detonations.

Incidentally, in an unrelated work from 1960s rocket engine researchers appear to have asked a similar question [56,196,197], differing only in semantics: how does injection layout affect the performance of the engine, stability-wise? Multiple injector configurations were parametrically tested, with the resulting velocity profiles shown in Figure 19b. Their problem was characterized as one of “energy release per unit area”. Of the six profiles depicted in Figure 19b (predicated on the energy and velocity input into the three concentric regions of the combustor, A, B and C), profiles II

and V produced stable smooth deflagrative combustion. Profile IV showed radial HFI with peak pressures of 13 psi, which was attributed to all the energy deposited in circle B, where a pressure antinode could be sustained by Rayleigh criterion. Profiles I, III and VI were recorded to produce tangential HFI, having peak pressures of 7 psi, 11 psi and 40 psi, respectively, i.e. increasing amount of energy deposition near the combustor wall produced increasingly stronger tangential instabilities. Though the rocket scientists state that the formation of pressure antinodes (powered by Rayleigh oscillations) near the wall are responsible for “Profile VI (injection near the chamber wall) resulting in very strong tangential oscillations”, one must question this claim. Acoustic waves

(sound waves) are longitudinal waves that propagate adiabatically, by compression and rarefaction

[198]. Hence, for a wave to be acoustic, it has to be sinusoidal with equal magnitude of over- and underpressure [198]. These requirements cannot be met in an oscillation with a peak pressure of

40 psi, because of the high nonlinearity and impossibility of exhibiting a negative 40 psi oscillation

(pressure cannot go below vacuum). As per the thesis put forth in the prior sections, it seems more likely that shock waves are associated with Profile VI, and not sound waves. It should also be mentioned that the observations from Anand et al. in hollow RDCs [81]and Osborn et al. [196,197] in rocket engines match — radial oscillations are produced when the fuel concentration is at the combustor axis, and tangential oscillations (rotating detonations) are incurred when the concentration is close to the combustor wall. It is likely that the concave wall of combustors is a fundamental aspect of rotating detonation waves due to the compressibility they provide to strengthen and sustain detonation waves (explored in the above sections). This proposal may, however, not be an absolute requirement since Bykovskii et al. [199] were able to sustain rotating detonations through an annular layer of gaseous mixture injected radially outwards from a tubular structure, with no outer enclosing boundary. But, the short duration of testing (0.2 s) and the fact that only pairs (four or five) of counter-rotating detonation waves (which are inherently a

transitory phenomenon — explored later in this paper) were observed during this time, should bring additional scrutiny to the basic physics that allows such a phenomenon.

(a) (b)

Figure 19 (a) Side-view of an atmospheric RDC showing injection arrangement and obstacle

addition, along with the flow-turning effect of the obstacle, which alters ethylene mass fraction inside the combustor (Scheme-I has no obstacle, whereas Scheme II does) [81], and

(b) velocity profiles, indicating energy deposition variation (between the three concentric

circles, A, B and C), of six injection types in a premixed rocket engine [197]

7. Exit Conditions: Pressure and Nozzle Effects

The previous sections dealt with the rotating detonation combustor itself and the conditions upstream to it, i.e. the injection and plenum elements. Nevertheless, equally important are the boundary conditions downstream of an RDC. In this section, the issues bearing on the effect of different types of nozzles on RDCs is to be discussed along with a comprehensive survey of the effect of pressure (atmospheric vs. backpressurized vs. vacuum) on RDC dynamics. Broadly

speaking, based on the relative cross-section of the RDC exit plane with respect to the combustor cross-section, the nozzles can be either straight (just the annulus with no area change), divergent or convergent (or convergent-divergent). The straight nozzle RDC exit [43,200–202] is shown in

Figure 20a. Figure 20b shows two RDC schematics that produce an expanding, or diverging, nozzle

[203,204]. This configuration makes use of the inner wall of the RDC to effect this [51,144,204–

209], whereas the second sub-type uses the outer wall to give a higher exit area [203]. Note that both the walls can be used in tandem to provide the required divergence as well [203,210]. The last type is an RDC with a CD nozzle, the schematics of which are given in Figure 20c. Here, once again, two methods have been used to attain the required changes in area at the RDC exit. The first consists of using an aerospike integrated within a rocket engine-type CD nozzle that produces convergence at a finite distance away from the RDC centerbody [37,148,211,212]. The second method is to use the RDC centerbody itself to have a notch on it (or, have an aerospike with a bulging protrusion) to develop a CD section at the exit [14,43,48,150,211]. In general, for stand- alone RDC applications, shaped nozzle additions seem to be required to prevent strong recirculation zones at the exit of the engine [19,120]. Nozzle addition also causes considerable changes to the supersonic flow field after RDC exit, as observed in Figure 21 and Figure 22. These effects must be taken into consideration when designing an RDC for integration into existing engines.

Combustor annulus

Central axis

Inner wall

Outer wall

(a) (b) (c)

Figure 20 (a) Annular exit with straight nozzle, (b) divergent nozzle, and (c) convergent-

divergent nozzle

(a) (b)

Figure 21 RDC exhaust plume with (a) an annular exit without expansion nozzle producing an annular Mach disc and weak shock train, and (b) an aerospike nozzle producing a strong

shock train due to recompression shock emerging at the nozzle tip [213]

(a) (b)

Figure 22 RDC exhaust plume with (a) atmospheric exhaust, and (b) choked throat

producing strong shock diamonds [214]

Drastic variations in performance, defined in terms of specific impulse, are noted between the three boundary conditions. For the discussions herein, the baseline case will be that of the straight-nozzled RDC. The specific impulse of the divergent nozzle is lower in comparison to the baseline case, as established by both numerical and experimental studies [51,210,214]. The CD nozzled RDC, on the other hand, provides considerably higher specific impulse than the baseline, thereby making it the most efficient configuration of all the cases [14,133,210,214–217]. For instance, Kato et al. report a 10% increase when using a CD nozzle [216]. This is mostly attributed to the presence of a sonic choke at the CD nozzle throat which in turn causes a pressure increase upstream of the nozzle [14,218,219]. Note that Fotia et al., and Paxson and Naples have shown, mathematically, based on empirical evidence related to the mass flow parameter (MFP) that RDC does indeed provide a stagnation pressure increase [14,15], owing to the presence of one or more detonation waves. It has also been speculated that this increase in pressure upstream of the nozzle throat causes significant deflagrative burning of the unburnt / vitiated mixtures, thereby extracting the maximum possible efficiency from these devices [220]. It is emphasized here that the driving factor behind these performance increases is linked to the increase in pressure in the combustor, and not the mere nozzle geometry itself. This pressure increase could be arrived at either by using a choked nozzle at the exit [43], or by increasing the ambient exit pressure aft of the combustor using backpressurizing valves or operating in a high pressure ambient medium [174]. Indeed, direct

evidence for this is presented by Bykovskii et al. [174] who show that the most defining fact of backpressurized RDC operation — longitudinal pulsed detonation which will be discussed later — can be induced even in a significantly expanded nozzle RDC configuration provided the exit pressure is exalted enough. Roy et al. also observe LPD even though their RDC had a straight nozzle

[40]. Overall, the reported specific impulse in RDCs extend even up to 7000 s with hydrogen-air mixtures, with the caution that this would incur a tradeoff with the thrust produced — a 20% thrust increase would require a 25% decrease in specific impulse [220]. Irrespective, these results bode positively for the attainment of the prospective benefits of RDCs.

Continuing further on the effect of pressure on RDC behavior, other than just its import on the global performance, Bykovskii et al. found that it exerts significant control on the internal combustion and fluid mechanics [129,204]. The normal Mach line of existence after which the products expand supersonically, axially, moves considerably upstream, towards the RDC injector headwall, when the device is backpressurized [27,174]. It should be noted, however, that further proof of this Mach line is required to confirm its existence, as discussed in Section 2. When the counterpressure is high enough at the RDC exit, the shock waves from the exit are found to penetrate the fresh injection region in front of the detonation front, thereby causing significant stochastic occlusion of the feed orifices [174]. By utilizing several hundred images acquired from their Plexiglas-integrated visualizable RDC, Bykovskii et al. found that there is a sweet spot which defines RDC operation under such backpressurized (subsonic injection) conditions. This is based on the fill height of the fresh reactants, which when decreased below a threshold value due to the reflected shock waves from the exit causes the inception and sustenance of LPD in their RDC. Above this threshold value, the RDC is still able to sustain rotating detonations. When the fill height is reduced even further than that of the LPD regime, completely chaotic detonation is observed by

Bykovskii et al., which they attribute to a total breakdown of the injection process and destructive coupling between the reflected waves from the pressurized exit and the injector elements. Anand et

al. [43] and Codoni et al. [221] also claim a reduction in mixture fill height when the combustor is pressurized. The latter also observes highly unstable behavior in their RDC with a CD nozzle. Interestingly, Schwer and Kailasanath report that their three-dimensional simulation of an

RDC with backpressure encountered glaring issues stemming from very strong reflected waves from the nozzle throat [222]. In another study, they report seeing strong shock waves moving inwards towards the plenum when the RDC backpressure is increased [89], as does Paxson [181].

Moreover, Anand et al. [69] and Driscoll et al. [128] observe an RDC conduct similar to that elucidated by Bykovskii et al. However, as opposed to demarcating RDC behavior (LPD vs rotating detonation) based on visual imaging and estimated fill heights, Anand et al. attained an operating map based on pressure ratios across the air inlet and combustor across multiple flow rates and geometries, and found that LPD was only prone to occur between ratios of

1.2 and 1.6. Anything higher tended to produce rotating detonations and pressure ratios of injection lower than 1.2 tended to produce completely chaotic detonations existence. The latter phenomenon of chaotic detonation presence in RDCs will be dealt with later in this paper. It is important to note here that the fill height is proportional to the pressure ratios across the injector. Hence, the experimental findings from the above researchers concur — when the RDC is backpressurized, it produces LPD by virtue of not having enough fill height to sustain a proper rotating detonation.

Bykovskii et al. [174] thus arrive at the conclusion that RDC stability is inversely proportional to the backpressure. They also tested an extension of this idea by integrating their RDC exhaust to a vacuum tank with sub-ambient pressure conditions. This resulted in widespread improvement in the stability of the rotating detonation waves with the proposed Mach line now pushed further downstream, close to the exit of the nozzle [204]. A similar behavior is also observed at ambient exit conditions, but with expanding nozzles [204]. Therefore, existing data on RDC suggests a conundrum: increase the propulsive performance of the device at the cost of stability, or sacrifice stability and probably the required mode of operation at the price of higher efficiency. Note that the

decreased stability is inside the RDC chamber itself and not at the exit of the nozzle after the choked throat. Rankin et al. [223] and Nordeen et al. [37] remark that a CD nozzle addition causes the removal of flow unsteadiness after the choked throat. Nordeen et al. further found that the flow swirl induced by the very motion of the rotating detonation waves is curtailed by the CD nozzle, thereby producing an exit flow field without any significant azimuthal velocity component. This is in contrast to the other nozzles, where a significant swirling flow is persistent in the exit flow field

[37] — this is well suited for turbine integration. Since most practical RDC operation is bound to have a backpressure at its exit plane, either by having a choked nozzle or turbine blades [224], this issue is posited to assume paramount importance as the community moves towards engineering this process in practical applications and has accordingly been given increasing attention as seen by the specific impetus towards pressurized RDC operation [11,13–

15,40,43,48,51,128,131,133,144,148,150,174,210,214,216,217,220–222,224–230].

Unfortunately, besides the above-mentioned issues, there are still many other complex secondary issues related to backpressurized RDC operation. As explained earlier, Fotia et al. has shown that RDCs sustain stagnation pressure gain. This is in line with the claims of Zel’dovich

[231]. The net effect of this increase is to produce a sharp transient increase in the static pressure inside the combustor when its exit is choked by any appropriate means, which is the RDC system attaining another new steady-state condition from the initial conditions of cold-flow operation prior to ignition. Predictably, all facilities running their combustor at backpressurized conditions show these sharp low speed pressure shifts from their static gauge sensors [14,214,216,232,233].

Still, owing to the lack of understanding of the specifics of this process this transience is either ignored and not discussed or has been even attributed to improper sensors [229,230]. However, as noted by Anand et al. [43] , there is indeed a physical, transient average static pressure increase when a backpressurized RDC is ignited; lasting about 0.95 s for the conditions we tested. Fotia et al. [14], subsequently, also noted the same transience in their RDC testing as well,

but there it lasted between 0.75 s and 1.25 s, after which it plateaued to a steady-state pressure. In this aspect, the mean pressure shift in RDCs described above is similar to the “DC shift” seen in rocket engines [234–241]. The DC shift (derived from the electrical terminology of direct currents, owing to a net non-zero average in the obtained signal) is defined as an increase in the average static pressure of a rocket engine combustor that almost always accompanies the onset and sustenance of high frequency combustion instabilities [63]. Interestingly, this DC shift instability in rocket engine seemingly occurs only during the presence of HFI events inside the rocket engine combustion chamber, and its exact origins appear to be unknown to those specialists dealing with the same. This congruence between HFI and DC shift is best explained in the words of Flandro et al.

[66] who conclusively proved the causality of the latter as an effect of the former, and pronounced:

“…the same mechanism that drives the non-linear oscillations is also the source of the DC shift phenomenon. This is a new result that has been shown to agree very well with experimental data in the solid motor case.”

One should note that DC shifts usually result in catastrophic destruction of rocket engines, specifically solid rocket motors [80,239]. Figure 23a gives two pressure traces obtained from the same flow rates, but at two different geometries — without and with a CD choked nozzle at the exit

— from data published by Anand et al. [43] . The clear shift in mean pressure acquired by the high speed piezoresistive sensors is patently seen. Provided in Figure 23b is two other pressure traces from the data of Blomshield [239], which was in turn used by Flandro et al. to arrive at their highly accurate model to predict this instability [63,66]. Red traces represent a normal functioning solid rocket motor without any high frequency non-linear oscillations despite multiple pulsing (triggering to cause instabilities [56]). The blue trace is an operation characterized by the successful triggering and sustained presence of HFI. The phenomenon of DC shift is clearly visible in the latter case, and is nonexistent in the former case. Owing to the tremendous increase in the static pressure throughout the solid rocket motor, it underwent catastrophic failure at about 3 seconds.

This is a direct result of DC shift, and establishes its maliciousness in a rocket engine environment.

As rightly pointed out by Stechmann et al. the operating chamber pressures in RDCs at present barely coincide with the lower threshold (25 bar) of what would be expected in rocket engine combustion chambers [242]. Thus, one should expect DC shifts in RDCs to have as drastic an impact as it does on rocket engines, as we move forward, towards higher pressure variants required for conventional propulsion and power generation systems. As was argued earlier, the difference between RDC and a rocket engine in HFI operation appears to be a case of semantics dependent on the people researching it. The work of Zhang et al. best exemplifies this argument, where they call their hollow combustor with a de Laval nozzle a rotating detonation engine [131]. Another phenomenon of interest relevant to rockets and other traditional combustors is the chugging instability that is characterized by acoustic coupling between the injector plenums and the combustor [56,57,243–245]. It is considered a type of low frequency instability (LFI) since the occurrence frequency is below 500 Hz 32. Sometimes, this instability sets up “organ-pipe” oscillations throughout the entire reactants supply manifolds at distances significantly upstream of the combustor, as witnessed in F-1 engines [56]. While the exact cause of its onset is yet unknown, it appears that higher reactants feed pressures remove this instability due to increased fluidic impedance across the injectors that resist the feedback from the combustors [56]. Expectedly, akin to all the other kinships with rocket engines discussed so far, RDCs also happen to exhibit chugging instability. While this is observed even without backpressurization at select operating points

[218,246,247], addition of pressure at the RDC exit appears to pronounce the effects. This is characterized a base-pressure oscillation (frequency modulated signal on top of the carrier wave signal that is from the detonation wave propagation) inside the combustor, upstream of the choked nozzle throat. Figure 24a shows pressure traces from static piezoresistive pressure sensors acquired during pressurized RDC operation with a CD nozzle at the back end. Although DC shifting is clearly visible from the traces after ignition at about 0.1 s, one can also easily notice considerable

low frequency variations built on top of the detonation wave pressures. A magnified image provided in the same figure clearly shows the frequency modulated low frequency oscillation that is chugging in an RDC annulus. Not coincidentally, numerical simulations performed by Levin et al.

[248] of an RDC fed from an air plenum with linearly decreasing stagnation pressure showed combustor pressure traces very similar to the experimentally attained measurements. This is seen in Figure 24b which gives the ratio of cycle-averaged (cycle was defined as the period composing of one low frequency sinusoidal oscillation) static pressure to the constant stagnation pressure of the plenum in the y-axis and the time passed in x-axis. The authors do not explain the origins for this

“complex, periodic and oscillatory” behavior, but Anand et al. [218] in a separate effort showed that there is considerable mismatch between predicted static pressure increases in the pressurized combustor (using MFP and CJ detonation conditions) and the measured pressures at the end of DC shift only at higher mass flow rates. At lower flow rates, the developed model appeared to predict the plateaued pressure rather well, leading to the suggestion that higher flow rates produce highly inefficient combustion characterized by notable stagnation temperature losses. Thus, once again, there appears to be harmony in inferences across different facilities to describe some of the RDC mechanics. This drastic and continual change in temperature was postulated to produce acoustic oscillations defined as chugging.

(a) (b)

Figure 23 (a) Difference in pressure dynamics between a choked (blue) and atmospheric

(red) RDC for the same flow rate (0.5 kg/s) and equivalence ratio (1.1) [233], and (b) “DC

shift” occurring in a rocket engine chamber where there is a mean pressure rise

accompanying the onset of nonlinear HFI (blue), as opposed to a stable case (red) —

pulsations are done by a pulse gun to try to “trigger” instabilities [63]

(a) (b)

Figure 24 (a) Static pressure traces inside a choked RDC chamber showing a mean pressure rise from 0 s (~ ignition) to 1 s, along with strong chugging oscillations after 0.7 s [218], and

(b) numerically obtained averaged (by low frequency oscillation duration) pressure traces in

an RDC when stagnation temperature is made to decrease throughout the simulated

duration [248]

8. Modes of Operation at Off-design Conditions

8.1. Chaotic Propagation

RDC operation near the lean operating limits tends to produce non-repeatable, varying pressure profiles suggesting the lack of proper detonation propagation [127]. These traces resemble those obtained during the onset period shown in Figure 15. While the pressure suggests the presence of detonations inside the combustor, the lack of repeatability of pressure profiles and the vastly differing detonation speeds [249] suggest the disintegration of the detonation wave into a deflagration wave, and a subsequent re-ignition into a detonation wave again. Kindracki et al. proposed this mechanism of “small detonation wavelets propagating chaotically and eventually transitioning to deflagration” and attributed it to substandard mixing [127]. They also performed numerical simulations of the process, by altering the injection conditions to effect poor mixing. The resulting pressure trace, defined by stochasticity, and the unwrapped annulus showing multiple detonation waves propagating transiently is seen in Figure 25 [127]. The poor mixing causing this process is due to under-recovery of supply plenums owing to the reduced pressure ratio across the injectors which is ineffective in counteracting the instantaneous high backpressures produced by the detonation wave, and hence occurs at low flow rates [127,174,250]. An example of the effect of detonation waves on the injectors is seen in Figure 26a, b and c. Peak pressure values in the air inlet and the base of the fuel plenum are about 60% and 20% of the values seen inside the combustor

[246]. They are also excited at the same frequency of the rotating detonation wave, which is indicative of high frequency coupling between the plenum and the injector. An ideal RDC design should incorporate methods by which this pressure feedback into the injectors is as low as possible

[171]. However, this is easier said than done, as a similar plenum disturbance is caused in rocket engines also, when there is rough combustion in the chamber. Shown in Figure 26d are the pressure traces from the combustor, oxidizer injector and fuel manifold used in F-1 engines [57,86].

During HFI in the combustor the peak dynamic pressures were found to routinely increase

instantaneously to 5000 psi, causing a similar magnitude of oscillation in the reactants supply assembly. Owing to the vast variety of variables to be considered when designing injectors, this problem has been difficult to overcome [56,74].

Because of this inherent randomness in wave propagation, when the RDC operates in this mode, it renders usual wave speed calculations futile, since speed is predicated on the requirement that there is a continuous wave travelling between two sensing locations [249–253]. Alternatively, an additional step could be incorporated in the usually simple time-of-flight algorithm to filter out fallacious values by making sure that three consecutive speed magnitudes fall within 10% of each other, thereby constituting what is probably a full wave rotation [250]. This method has been used successfully by Deng et al. to characterize wave speeds accurately [182]. This type of RDC operation is widespread when the combustor is backpressurized (choking at the nozzled exit causes injection to become subsonic and hence once again uneven recovery causing substandard mixing).

Chemiluminescence imaging [44,254] of RDCs with subsonic reactants (atmospheric and backpressurized cases) injection record highly chaotic propagation of detonation waves with considerable deflagration activity. This implies a loss of RDC’s prospective efficiency due to non- detonative burning of fuel. Another offshoot of this mode is the directionality (clockwise to counterclockwise, and vice versa) of the rotating detonation wave, which is observed to stochastically change within the same hot-fire, across multiple facilities [18,152,157,159]. It is a major issue since owing to the drastic changes the wave’s direction produces in it’s interaction with downstream and upstream components, owing to the effect of the angular arrangement of the turbine vanes on the reflected shock wave from the detonation wave. Zhou et al obtain notably different pressure profiles and coupling with downstream turbine vanes depending on the direction of rotation of the detonation wave [255]. At higher flow rates, chaotic propagation and directionality changes are present only during the transient onset time and steady rotating detonation is formed after. Since an RDC is required to operate unsteady by its very conception, high importance needs to be placed

on injector design to avoid chaotic propagations. At present, there are no design guidelines to approach this problem in RDCs. It can also be concluded that during chaotic detonations, RDC operates as if it is in perpetual onset.

Figure 25 Pressure traces showing chaotic detonation propagation in an RDC (left), along

with the numerical visualization of the flow-field during the chaotic mode where multiple

detonation wavelets can be seen (right) [127]

(a) (b) (c)

(d)

Figure 26 Pressure traces showing the high-frequency coupling between the (a) RDC (b) air

injector and (c) fuel plenum [246]. (d) Pressure traces from an F-1 rocket engine demonstrating the coupling between the chamber, oxidizer fuel supply manifold during HFI

[57,86]

8.2. Multiplicity: Co-rotating and Counter-rotating Waves

At certain conditions RDCs house more than a single rotating detonation wave at a given instance inside the combustor annulus. This occurs in two ways: (i) co-rotating, and (ii) counter- rotating. In the first case, as the name implies, all the waves move in the same direction, in contrast to the counter-rotating waves discussed later in this section. The common finding among various studies is that increasing the mass flow rates seemingly increments the number of rotating detonations [27,40,43,48,256–258]. RDC operation with one wave [27,51,70,151,259], two

[10,27,43,256], three [10,27,39,40], four [48,150], five [150], six [24,150], seven [47], eight [150] and even nine waves [260] have been observed — see Figure 27. Considering the content provided in the prior sections of this paper, not surprisingly, rocket engines are also susceptible to one or

more waves rotating about the combustor circumference; it is called first, second-tangential spinning mode, and so on [56], as evident in Figure 28. Like RDCs, the direction of these waves is random and prefers either clockwise or counterclockwise direction to rotate [76]. In RDCs, smaller fuel orifice area [233] also supports multiple detonation waves inside the combustor. While the waves themselves might be relatively stable (repeatable wave speeds), the actual switching from a wave mode to another (and sometimes, back) rather abruptly during a same testing duration [250] suggests the presence of a strong instability associated with certain RDC operating regions.

Moreover, the peak pressures of the detonation in the chamber are much higher for one-wave mode, as opposed to the two-wave mode — it is roughly about twice that of the single detonation in one wave mode [257]. The symptoms of wave multiplicity extend to more than just the variations in peak pressures. When there is ascension to a higher-wave mode in an RDC, the individual velocity of each wave drops sharply, as seen by a telling plot from Bykovskii et al. [27], reproduced in Figure

29a. This multiplicity-linked velocity deficit from the idea CJ speeds has also been a recurring theme about rotating detonation waves [27,129]. In fact, when there is eight [150] or nine-waves mode

[260], it was noted that they could be “acoustic waves” instead of C-J detonations, owing to the very high wave speed deficit (about 50%). It is emphasized here that for detonation propagation along a curved boundary, as in the case of RD, the ‘true’ detonation velocity is given by the normal velocity component to the outer wall [83]. However, all experimental studies on RDCs to date resort to presenting and analyzing the detonation wave in terms of the tangential velocity, and not the normal velocity. This is due to the technological impediments in acquiring the angular inclination of

RDs on the combustor walls, experimentally [188]. While numerical simulations have shown that channel width has a significant impact on this orientation angle (with no inclination when the width is very small, to very high inclination at higher widths [125]), this is yet to be validated experimentally. However, since the normal velocity of RD would always be the product of the tangential velocity and the cosine of an acute angle, the former would always be smaller in

magnitude than the latter [132]. Hence, when resorting to describing RDs with normal velocities, it is expected to see higher velocity deficits from the C-J conditions, than when we only compare the tangential velocities.

At present, neither the mechanism behind multiplicity nor the deficit related to it is known.

Irrespective, these phenomena can be construed as a physical homeostasis peculiar to RDCs where the magnitude of pressure and speed of each detonation wave in the system varies depending on the number of detonation waves in the system at any given moment, which in turn depends on a critical fill height that each wave can consume [3]. This is the proposition by Zhdan and Syryamin

[116] who show this issue to be an eigenvalue problem and subsequently show that a stable solution is attained when the domain supporting the detonation has the shortest possible length; or in other words, the equilibrium state of RDCs is to have the highest possible number of waves at a given time. Bykovskii et al. [27] and later Anand et al [233] claim that there the ratio of this critical fill height (function of mass flux) to cell width, λ, determines the number of detonation waves in the combustor. Bykovskii et al. note from their extensive visualization studies that the minimum h/ λ required to sustain a rotating detonation wave is 12±5, after which it would bifurcate into unit-incrementally higher modes. Anand et al., using mass conversation conditions estimate an h/ λ of about 7 for bifurcation to occur. Though not explicitly stated, we can estimate the h/ λ values from the data of Frolov et al. [48] and Rankin et al [44] to be 8-11 and 2-5 respectively. Such a wide discrepancy does not lend itself towards easy engineering of RDCs.

Nevertheless, by altering the RDC geometry using three channel widths and the mixture reactivity by altering the amount of oxygen enrichment (at an almost constant equivalence ratio), St. George et al. also considered the third variable of channel width to ascertain its importance in determining multiplicity [39]. Increasing the oxygen percentage (of the enriched air oxidizer) at a given channel width caused a shift from one-wave to two-wave mode, and finally three-wave mode, for a given channel width. A similar multiplicity behavior was also observed when the channel width is

reduced for a given oxygen percentage and equivalence ratio. The tangential speed of the individual detonation waves decreases every time a new wave is spawned, as reported by other studies.

Assuming the cross-sectional area of the rotating detonation to be a rectangle (dimensioned by the

RDC channel width and the detonation wave height), they recognized that the three apparently independent factors — fill height, channel width and mixture reactivity— could be linked together by normalizing the detonation wave’s perimeter (P) by the cell size, λ, of the global mixture. A new detonation wave spawned when the ratio of the perimeter of the individual rotating detonation wave’s P/λ exceeds 7.4. To elaborate, one wave operation transcends to two wave operation when

P/λ (a function of mixture reactivity and channel width) exceeds 7.4, for the given conditions of geometry and flow rate. Another divergence from two waves to three waves occurred when the normalized perimeter of the newly formed waves increases above 7.4, as witnessed in Figure 29b.

Thus, it is apparent that detonation scaling that has been so successful in characterizing the diverse behaviors seen in conventional detonation wave propagation [21] is also useful in ascertaining rotating detonation wave dynamics.

Finally, it is worth pointing out that this issue is far from resolved, as knowledge of the exact physics determining multiplicity is lacking. Though there have been numerous numerical simulations that have reported producing multiple rotating detonation waves in their computational models, most have so far not been able to predict the velocity deficits that go in tandem with wave multiplicity. Hence, one should question the notion of excessive presence of unburnt pockets of cold reactants being responsible for this intriguing RDC behavior, which is what is contemplated by many numerical studies [106,127,173,175,261,262]. Songbai et al., however, do observe a relative decrease in wave velocity with more waves (dependent on the number of ignition points), but their absolute individual wave speeds are very close to the CJ speed, unlike the considerable deficits seen experimentally [263]. Furthermore, they observe up to eight simultaneous waves in hydrogen-air mixtures which has not been reported elsewhere. Hence, it is

apparent that an integral part of fundamental detonation physics is still missing in these models.

Consideration of the same would provide closure of to the issue at hand, and once again, aid in treating rocket engine combustion instabilities as well.

Figure 27 Co-rotating detonation waves’ multiplicity showing (from left to right, zigzag) one

[264], two [216], three [10], four [214], five [265], six [150], seven [47] and eight [266]

waves.

Figure 28 Illustration of first spinning tangential mode (1T) and second spinning tangential

mode (2T) of a transparent rocket engine chamber, when acquired from images acquired using a rolling strip camera (induces helical inclinations in the obtained records due to the

relative velocities between the camera strip and the waves) — broken lines indicate the

wave moving along the circumference of the sector away from the camera [56]

(a) (b)

Figure 29 (a) Dependence of detonation wave multiplicity (n) on mass flux and its effect on

the wave speed showing increased velocity deficits after each bifurcation [27], and (b) dependence of multiplicity on the non-dimensional parameters of fill height/cell width and

channel width/cell width showing bifurcations at the criticality of perimeter/cell width of

7.4 [39]

Counter-rotating waves are also observed widely in RDCs

[44,45,118,140,156,221,261,264,267–270]. Their driving physics can be reasoned to be quite different from co-rotating waves, because of the regime and nature of occurrence. First, counter- rotation seemingly occurs only at lower flow rates [44,264,270,271], which is in complete contrast to co-rotating waves which only occurs at higher flow rates. Second, most observations of counter- rotations in RDC indicate that is a very transient event, that might quickly evolve into a steadier mode within a finite passage of time [156,261,268,271]. Though Bluemner et al. [264] have posited that this is a steady-state process from their data it is possible that the very short run durations used in their study (150 ms) might have incurred this appearance. Further testing is required to

claim the same. Third, there is very strong evidence that counter-rotation is linked to the mixture quality inside the RDC. Rankin et al. observe that for the same flow rates at a constant air injection width and total fuel injection area, counter-rotation is only seen for the case with a smaller number of fuel holes [44]. OH* chemiluminescence of an RDC during counter-rotation mode is presented in

Figure 30a. This was attributed by Rankin et al. to improper mixing brought about by the longer distance between each individual hole. Zahn et al. see a similar behavior, where counter-rotation is a function of the spacing between fuel injection holes [271]. Additionally, they see two different types of counter-rotations: (i) stationary collision point, and (ii) moving collision point [271]. In the first case the collision point rotates about the annulus at a much lower frequency than the detonation wave, whereas in the second case, the point appears to be fixed at a given azimuthal sector. Collision point has been defined by different researchers as that localized region where the two (or sometimes more [261]) opposite moving waves pass each other [44,264]. During this interaction, constructive superposition appears to cause a two-fold rise in peak pressures at the collision points [271]. It should be realized that, experimentally in an RDC, it is rather difficult to have direct evidence of whether the waves after colliding merely pass over each other, or explode

(explosions causing another explosion) and retreat their respective paths. However, it could be inferred from the visualization data of Bluemner et al. (see Figure 30b) that there is no time lag in the waves’ speeds as they move about the annulus, suggesting no momentum loss — they are probably passing over each other.

(a) (b)

Figure 30 (a) Sidewise images of counter-rotating waves obtained from a transparent RDC

(OH* chemiluminescence) showing the waves passing over [44], and (b) radially-averaged

luminosity of two counter-rotating waves converted from aft-end high speed imaging,

showing one wave traveling faster than the other (note the slow movement of the collision

point as time progresses) [264]

Dubrovskii et al. have numerically studied this process and offer a compelling explanation that tends to explain most of the experimental observations [118]. They claim that the production of two waves of varying strength is an inevitable component of the RDC ignition process, especially in an annulus. Depending on the point of ignition and how far away it is from the most reactable pocket of mixture, the stronger wave is always the one that is formed closest to the fresh mixture.

They further explain that owing to the instantaneous backpressure produced by the detonation event after ignition, the injector location closest to the ignition point will tend to occlude, thereby causing what they call a “non-uniform spreading” due to reactants inhomogeneity. This is clearly seen in their images reproduced in Figure 31. Note that the very slight offset of the ignition point from the air inlet manifold causes the right moving detonation wave to be stronger in contrast to the left moving wave, when they both collide with each other at the diametrically opposite point

(not seen here). This is implied to be an effect of DDT, which requires sufficient mixture strength and distance to produce a strong detonation wave [21]. In such a scenario of unevenly intense detonation waves, Dubrovskii et al. further note that their simulations always resulted in the

“dominant” wave exerting its influence over the other wave, since the latter originates in the tail of the former, thereby only consuming inhomogeneous mixtures (uneven plenum recovery by the time the weak wave comes to the recovering injector elements) and hot products from the former wave. This can either result in a two-wave co-rotating mode as seen in their three-dimensional simulations, or produce a single rotating detonation wave as seen in experiments [261,264]. It also

explains the apparent difference in strength between the two counter-moving waves (see the increased speed of one wave in comparison to the other in Figure 30). It is of interest to note that two-dimensional simulations of counter-rotating waves cause both the waves to extinguish owing to the lack of fresh mixture upstream to them [171]. This might be an effect of an inherent multi- dimensionality of the process, or a result of assuming an ideal injection.

In light of this theory, it could be formulated that the final outcome of all fixed colliding point counter-rotations is to become moving colliding point counter-rotations that ends in either a one-wave or multi-wave mode depending on the previously discussed conditions of high flow rates and reactivity. One can also explain the propensity for this process to occur at larger fuel injection areas (but constant flow rates) by considering the fact that large areas, and thus lower pressure ratios across the injectors, are affected to a larger degree than injector designs with smaller areas

[43]. Since the former is disturbed more than the latter by the initial detonation event, it produced relatively pronounced inhomogeneity in the newly formed fill height region, which as Dubrovskii et al. showed is the asymmetry that is essential to the subsidence of counter-rotating detonation waves. Pointedly, co- and counter-rotating waves are a prevalent type of azimuthal instability in annular gas-turbine combustors [272–274]. However, there, it is composed of rotating acoustic waves with equal strength in pressure nodes and anti-nodes. It is for this reason that gas-turbine burners employ “symmetry breaking” — a process in which unevenness in mixture distributed is effected by altering the geometry or type of burners distributed over the combustor — to reduce azimuthal instabilities [273]. Wolf et al. also show that a standing azimuthal acoustic instability mode is always unstable since its natural state is to rotate, which depending on the experiments can be between seconds to hours [272,275].

Figure 31 Onset and propagation of two counter-rotating detonation waves after ignition at a point slightly offset from the airline indicated by the broken white lines (first frame) — right

propagating wave is dominant [118]

8.3. Longitudinal Pulsed Detonation

Though the preferred operating mode of RDC is to have the eponymous rotating detonation inside the chamber, it has been observed by a few prior studies

[27,40,45,48,128,174,214,226,227,250,261,276] that at certain geometries and mass flow rates, the

RDC transitions from housing continuous rotating detonations to producing axially-moving pulsed detonation inside the combustion chamber, like a PDC. This pulsation, which was first observed in an RDC and christened longitudinal pulsed detonation (LPD) by Bykovskii et al. [27,194,208,209], is an intriguing phenomenon because it occurs in the absence of any mechanical valves to actuate the reactant flow, which is tantamount to a PDC of the simplest design. Additionally, the frequency of the pulsation is noted to occur in the kilohertz regime, which betters the operating frequency of any known PDC by more than an order of magnitude. Frolov et al. [48] noted the existence of LPD for

H2-air mixtures in their larger RDC with a diameter of 406 mm. LPD was found to occur at 1 kHz at higher air injection gap width. While a specific case of LPD was discussed for an operating case with the higher injection area and a convergent nozzle (and hence presumptively a choked RDC exit

leading to subsonic air injection), it is unclear if they observed the phenomenon without a choked exit. Simultaneous azimuthal pulsations in the RDC are also noted by Wang et al. [45] during their

RDC operation with vitiated air. It could be speculated that heat addition may have caused a thermally choked exit in the RDC. While Frolov et al. used ion probes in their study and Wang et al. used pressure sensors in theirs, both concurred that the instigation for LPD started downstream, near the RDC exit. Anand et al. [69,250] and Driscoll et al. [128] observed LPD at lean operating conditions for H2-air mixtures with a CD nozzle, and thus, once again, subsonic air injection.

The proclivity to occur at subsonic air injection and lean equivalence ratios was explained by Bykovskii et al. to be due to the causality of having a backpressurized RDC which causes the fill height to drop below the critical value required to allow rotating detonation wave existence, as explained in the section on RDC exit boundary conditions [174]. In terms of equivalence ratio,

Bykovskii et al. discovered that the LPD mode demarcates the regions of deflagrative combustion and rotating detonative combustion at lean and rich limits of H2-air operation [276]. Anand et al.

observed a similar conduct in their pressurized RDC, where LPD was only prone to occur between pressure ratios of 1.4 and 1.85. Below and above this there was chaotic detonation existence and rotating detonations, respectively. They subsequently proposed shock wave amplification by coherent energy release (SWACER) as the mechanism by which the weak reflected shock waves from an RDC exit can cause instantaneous explosions near the injector headwall.

SWACER, named as such by Lee et al. [277] in analogy to LASER, requires a mixture with gradually varying reactivity that would be susceptible to cause direction detonations when an acoustic wave is incident on it [21]. A mutation of this effect is used in homogenous charge compression ignition

(HCCI) engines and shockless explosion combustion (SEC) cycles [278], and has even been suggested to be responsible for pulsejet operation [279]. In RDC, this was hypothesized to be the case, axially, during LPD by Anand et al. , who showed there is a complete occlusion of

injector elements circumferentially during LPD in an RDC. See the pressure traces from three azimuthal sensors in the air inlet in Figure 32a that shows this simultaneous hammering of the slotted air inlet. During such an event, it is reasonable to assume that there would be an axial stratification of reactivity after the relaxation of the injectors. Pressure traces (Figure 32b) from four axially distributed pressure sensors in the same RDC clearly shows the primary explosion

(blue peaks from Axial #1) which descends to a weak acoustic wave as it moves towards the CD nozzle throat is given. This weak acoustic wave after reflecting from the nozzle transforms into a weak shock wave (aqua blue trace from Axial #4) with a strength of about 1 bar and propagates upstream, finally causing another primary explosion in between Axial #1 and the headwall, thereby maintaining the high frequency cycle of LPD. The frequency of operation was also found to vary proportionally with the chamber pressure prior to ignition and the global equivalence ratio. At this juncture, it is imperative to point out that no numerical studies exist at present that have been able to demonstrate LPD, even though it is a major component of pressurized RDCs.

Similar to the notable kinships between tangential HFI in rocket engines and rotating detonations in an RDC, liquid rocket engines are known to be susceptible to longitudinal HFI, which is also characterized by axially travelling pressure pulses between the injection head and the nozzle throat at frequencies greater than 1 kHz; they are not yet comprehensively explained, despite the considerable research into the phenomenon during 1950-90s [56,74]. An example pressure trace during longitudinal LFI from a location near a rocket engine injector headwall is presented in

Figure 32c, where the uncanny resemblance to the LPD pressure profile (Figure 32b) is patently seen. Male et al. [55] visually captured the onset of “longitudinal shocks” moving within the thrust chamber at 1000 Hz when fuel transition was effected from furfuryl alchohol to JP-3. Hybrid modes of operation with both the longitudinal and other high-frequency instability — lateral oscillations

— at 6000 Hz were also recorded. The shock waves were found to occur with a maximum pressure ratio of 2.8, with the highest recorded pressure peak of about 44 bar. Highly uniform rocket

chamber erosion was observed near the injectors for operations with the longitudinal instability. A nonlinear analytical method to model this instability, based on its “shock wave characteristics” was developed by Lores et al. [280], while conceding the model’s shortcomings in predicting the triggering of the instability. Commendable work was done by Berman et al. [281,282] in subsequent articles in visually characterizing this longitudinal instability. They recorded the presence of this

“intermittent shock-type axial instability” around 1000 Hz upstream of the nozzle throat when the total reactants flow rate was lowered beyond a critical value, for a constant head pressure drop

(pressure ratio across injectors). Moreover, the instances of tests producing these instabilities were lowered progressively when the nozzle throat area is gradually increased. In RDC terminology, both these parameters would result in decreasing the effect fill height of fresh reactants — however, since this was observed in rocket engines no such inferences were made. Using a novel moving slit photography technique, their partially transparent rocket engine revealed a process consisting of an upstream moving shock wave with gradually increasing strength, which eventually impinges on the injector head (with an absolute velocity of 1005 m/s), and almost instantaneously initiates a highly luminous downstream propagating shock wave (absolute velocity of 1433 m/s). Berman and

Cheney also observed that the presence and strength of this longitudinal instability is a function of the angle of convergence of nozzle throat (amplifier and reflector), injector type, and chamber length, finally concluding that while the chamber pressure (predicated by flow rate and throat area) had a significant influence on this instability, the head pressure drop across the injectors was the driving factor. In synopsis, the above-mentioned sources on rocket engine combustion instability implicitly attribute the phenomenon in rocket thrust chambers to be caused due to periodic explosions. The confluence of similar observations made by disparate facilities over a period of several decades should not be assumed to be merely happenstance, and evidence suggests that LPD in an RDC is dictated by the same physics as longitudinal HFI in rocket engines. Gray-scale images

(during LPD) morphed from the voltage magnitudes of 9 axially arranged ion probes and 8

circumferentially distributed ion probes in an RDC operated by Frolov et al. [48] are given in Figure

33a. Since the x-axis is time, one can see the periodic excursion of combustion events (ionization activity gathered by the probes) from the injector headwall (bottom edge of the image) to the choked nozzle throat section (top edge). The instantaneity of the pulsed explosions can also be observed based on the relative time the combustion wave spends near the injectors. Since LPD is azimuthally simultaneous, the circumferential ion probes are excited at the same time, and hence appear as vertical bands when the x-axis is unwrapped in the temporal coordinate. In Figure 33b, high speed images captured during longitudinal HFI by Berman and Cheney [281] in their rocket engine using a continuous rolling strip camera (of the type Bykovskii et al. use for RDC visualization) is laid out. Again, the remarkable qualitative similarity between the processes in the supposedly different engines is hard to neglect. Thus, this pulsed detonation instability in an RDC is of paramount importance, because: 1) it could commence research into truly valve-less PDCs with an increase in frequency by at least an order, 2) it is imperative to understand this significant instability, if literal employment of RDCs is ever to be realized since most RDC operation would require it to be pressurized, and 3) understanding the kinship between the longitudinal instabilities in rotating detonation engines and rocket engines would greatly further the development of both propulsive devices.

D D U U U

(a) (b)

(c)

Figure 32 (a) Pressure profiles from three sectors of an RDC showing simultaneous

excitation [69], (b) profiles from four axially distributed sensors in a choked RDC showing the upstream (U) and downstream (D) propagation of pressure waves (Axial #1 is closest to

the headwall) [69], and (c) pressure traces near the injector headwall of a rocket engine

during longitudinal HFI [55]

(a)

(b)

Figure 33 (a) Gray-scale (converted) “images” from axially and circumferentially distributed

ion probes during LPD [48], and (b) high-speed images acquired from strip camera during longitudinal HFI showing the back and forth propagation of combustion waves between the

nozzle throat and injector elements [281]

8.4. Low Frequency Oscillations / Instabilities

LFI in an RDC seems to be almost ubiquitous, and is qualified by sinusoidal variations in the maximum pressure of multiple laps of rotating detonations. A brief survey of the pressure-time traces published by the different RDC facilities worldwide gives concrete evidence of the overarching existence of this instability [70,71,127,142,144,151,246,250,256,257,264,283,284].

Two very alike hypotheses were put forth initially to explain LFI in an RDC. Anand et al. [251] and

Liu et al. [142] proposed that the occlusion caused by the detonation wave as it passes by the injector elements causes the next lap of the wave to see a less-than-optimal fill height which was posited to cause the current lap to weaken in strength. This weakened lap of detonation wave would then produce a lesser-than-average occlusion on the injectors thereby causing the succeeding lap to pass through an optimal fill height thereby making the wave stronger again. This cycle of feedback between “fluidic hammering” of the injectors and detonation wave strength was used to explain LFI in RDCs. Yet, this proposed process does not explain why a “packet” of LFI is composed of more than three waves; in actuality there are anywhere between five and about five hundred rotating detonations per packet of LFI, depending on the flow rates and fuel injection hole sizing, as pointed out by Anand et al. [251]. Since both of the above facilities employed only one pressure sensor in the combustor, they subsequently have drawbacks in accurately capturing the spatial variance of LFI, and hence the inference presented could be corrupted. Follow up studies by

Anand et al. have identified three distinctly different types of LFIs in RDC [285].

While all three types are characterized by a sinusoidal amplitude modulation of the rotating

detonation wave’s peak pressure, their driving mechanisms appear to be divergent: (i) acoustic resonance-induced spatially homogenous oscillations in the air injector, (ii) detonation-induced disturbance causing spatially non-homogenous oscillations in the same injector, and (iii) combustion-induced spatially homogenous oscillations inside the combustor. The first two types of

LFI are linked to the supply plenum dynamics [218,246,247], and the last is inherently combustion- induced [81]. One could differentiate the first two types from the last one by recording the wave speed between subsequent laps of rotating detonations. Only the combustion-induced LFI manifests a sinusoidal variation in successive laps’ wave speeds in addition to the oscillation in the wave’s peak pressures [81]. No such congruence is observed in the first two. For the first case, a

“locked-in” [286], azimuthally simultaneous, low frequency mode was observed at 235 Hz in the air inlet, at all air and fuel flow rates tested, which was attributed to a Helmholtz resonation coupling between the air plenum and the combustor [218,246,247]. The locked-in oscillations in the air inlet manifests as a low frequency instability in the combustor, albeit at a broader frequency range [250].

Such a coupling is observed in gas-turbine combustors with a choked exit nozzle [287] and is also similar to the chugging instability widely reported in rocket engines (and discussed previously).

There as well, it is proclaimed to depend on supply line and plenum acoustics. Additionally, similar to chugging occurrence in most rocket engine occurrences [288], the RDC chugging instability exists usually only during the initial transient phase after ignition of the engine, suggesting it might be linked to the system reaching a new dynamic state after ignition [218,246,285]. An example pressure trace from the air inlet of an RDC during chugging (showing the base-pressure oscillation) and the associated locked-in chugging frequency 235 Hz) along with the detonation wave frequency

(3642 Hz) is given in Figure 34a and b. In Figure 35, a similar base-pressure oscillation and the locked in chugging mode during the presence of “first tangential acoustic mode” in NASA’s cryogenic methane-oxygen rocket engine (part of the broader Propulsion and Cryogenic Advanced

Development project) is given [289]. Hulka and Jones report LFI across most of the injector

patterns tested, with frequencies between 150-250 Hz. For select injector configurations, chugging magnitude was lowered by increasing the injection pressure ratio. Once again, it is worth noting that the asymmetric, shock-fronted pressure traces with peak overpressures exceeding 50 psi were attributed to acoustic modes in the chamber.

235 HZ 3642 HZ

(a) (b)

Figure 34 (a) Base-pressure chugging oscillation in an RDC air inlet superimposed on the

shock leakage from the detonation wave, and (b) frequency spectrum of the same point

showing the oscillation and detonation wave frequency [246]

(a) (b)

Figure 35 (a) Chugging oscillation leading to strong tangential HFI in a rocket engine

chamber, (b) the associated frequency spectrum showing both the oscillations [289]

The second type of LFI is distinguished by a slow-moving rotary event in the combustor and the air inlet and combustor [247]. Figure 36a shows pressure traces from three sensors distributed at three azimuthal locations 120o from each other in an RDC air inlet from the study of St. George et al. [290] that shows the sectorally varying, non-homogenous nature of this instability. Figure 36b shows the same type of instability in the facility of Bluemner et al. [264] during counter-rotating detonation waves propagation (described above in detail). Note that counter rotation produces a crisscross of the low frequency packets (see the relative position of the dark blue packets with respect to the aqua blue and yellow packets as the test progresses). It is evident that, once again, the individual wave’s high speed motion causes a low speed AM event, and should thus be taken to be independent of the mode (one-wave, multi-wave, counter-rotating, etc.). This type of LFI is also witnessed in rocket engines during it sustaining tangential HFI and is termed a “precessing tangential mode” [56]. Figure 36c shows this mode in a rocket engine as recorded by four pressure sensors distributed at different azimuths in the combustor, recording about 8 cycles/ period. In

RDC, this rotary sinusoidal oscillation in detonation peak pressure moves in a direction opposite to the direction of the rotating detonation wave, and was subsequently hypothesized to be caused due to a complex constructive and destructive interference of the shock waves leaked into the supply plenum [247]. This is based on experimental and numerical studies that show the detonation wave significantly altering the plenum dynamics owing to the locally high peak pressures

[171,179,184,291]. A trailing shock wave that is attached to the rotating detonation wave tends to travel into the reactants plenum, thereby significantly altering the dynamics [171,179,184]. Schwer and Kailasanath note the existence of a subsequent reflected wave (from the back of the plenum) that is spawned when this trailing shock wave reaches the base of the reactants plenum [171]. This reflected wave moves in a direction opposite to the detonation wave, in the latter’s frame of reference [171,173]. Fotia et al. note that the trailing shock wave moves at about 60% of the rotating detonation wave’s speed and proposed the possibility of “pressure beating” inside the

slotted air injector owing to the relative difference in the two speeds [184]. However, in their two- dimensional experimental unwrapped analogue of the RDC-plenum system, this pressure beating effect was not observed due to the study using only a single detonation wave (rotating detonations cannot be produced in a linear setup). The postulation of Anand et al. regarding the origins of this rotary LFI needs to be confirmed in future studies. Finally, the last LFI type is linked to the combustion wave dynamics. It was shown that such an LFI is marked by a complex interplay between the pressure wave and the combustion front that together make a revolving wave. During stable operation in a hollow RDC, the shock wave precedes the combustion front, whereas during

LFI-defined unstable operation in the same RDC, the combustion wave precedes the pressure wave implying the presence of the phenomenon of flame-acceleration in ducts causing a detonation wave, rather than a detonation event itself. This process is similar to the alternative coupling and decoupling of the shock wave and combustion front, which is observed widely in unstable detonation propagation at near-limits in tubes [21]. This LFI was discussed extensive in Section 1.2.

The field of instabilities analysis in RDCs is nascent in comparison to the decades of research on the same in rocket engines, where there are considerable unknowns even at present. Considering the crippling effects of LFI in rocket engines, supersonic inlets and hypersonic vehicles owing to their tendency to couple with the natural resonant frequency of the structure [68,189], it is imperative to acknowledge and treat LFI as we move forward with RDC research.

(a)

(b)

(c)

Figure 36 (a) Rotary amplitude modulated low frequency oscillations in the air inlet [290],

(b) similar rotary AM LFI in the combustor during counter-rotating waves showing the

crisscross between the different sectors [264], and (c) “precessing tangential mode” in a rocket engine tracked by four pressure sensors distributed azimuthally in the chamber [56]

9. Heat production and transfer

As can be noted from the preceding and succeeding sections, it is apparent that tremendous strides have been made with regard to understanding the internal physico-chemical mechanics of

RDCs within the last few years. While there are still many outstanding issues to be resolved, perhaps none is more pressing and adverse to overcome than the heat loading produced by RDCs.

By virtue of using detonation to combust fuel, extreme product temperatures are an inherent nature of RDCs, which in turn causes structural and sensor-related degradation. The wall surface exposed to the gases shows about a rises to 1000 K (from atmospheric conditions) in 3.5 s after ignition in the study of Randall et al. [292], whereas it increases to about 500 K in the experiments by Bykovskii et al. [293], and to 1600 K in 2.5 s in Kindracki’s experiments [224]. Falempin et al. note a climb to approximately 1300 K in 0.6 s when their RDC is run on kerosene –oxygen and to

1000 K in 0.35 s when run on hydrogen-oxygen, and subsequently propose composite RDC walls to overcome this drastic heat transfer [294]. Ishihara et al. record a temperature growth to up to 1000

K after 6.3 s since ignition at higher flow rates in their carbon-carbon composite-bodied RDC running on ethylene-oxygen [295]. Despite using composites, the last study reported significant thermal erosion of their wall. This is the primary reason that a vast majority of experimental tests from across multiple facilities worldwide curtail their hot-fire durations to within a second

[293,294,296]. So far, the longest publicly reported continuous RDC operation under detonative regime is 30 s by Stoddard et al. [137], by making use of their 3D-printed and water-cooled, flow- through RDC which does not require headwall cooling, on account of the lack of the very structure.

The second longest run was demonstrated by Ishihara et al. [216] and Roy et al. [40], who achieved a run time of 6-10 s. This is closely followed by Aerojet Rocketdyne who tested their RDC for about

7 s [297]. Other long duration tests are usually about 3 s, as seen in the publications of Randall et al.

[292] and Kindracki [224]. The obvious result of such relatively short testing durations is that the sub-field of heat transfer characteristics of RDC is rudimentary, owing to the lack of a steady-state heat transfer analysis. Despite this, multiple studies have lent significant insights using a wide array of techniques, both numerical and experimental.

Since the primary source of heat in RDCs is the rotating detonation wave (and LPD, depending on the mode), the temperature produced therein is of foremost importance. Because the detonation wave propagates in the kilohertz regime, traditional temperature sensing using thermocouples

cannot capture the time-resolved temperature values of the waves. This necessitates usage of state- of-the-art techniques for accurate high-frequency measurement. Goldstein et al. used two-color tunable diode laser (TDL) absorption sensors in a high-bandwidth, scanned-wavelength-modulated spectroscopy setup to attain temperature and H2O information at the throat section of a nozzled

RDC [298]. The two sensors used in the tunable diode laser absorption spectroscopy (TDLAS) technique had different characteristics, with the first one utilizing two near infra-red TDLs modulated at 225 kHz and 2858 kHz, whereas the second sensor used two mid-infrared TDLs that were modulated at 90 kHz and 1132 kHz. By integrating the two sensors in an orthogonal, co- planar arrangement at their throat, it was shown that the temperature and H2O oscillation frequency obtained by this method coincided precisely with the detonation wave frequency, thereby giving credence to the notion of time-resolved temperature diagnostics. Both sensors recorded a temperature oscillation about 1500 K per lap at the nozzle throat. Increasing the global equivalence ratio tended to increase the recorded average temperature; however no such trend was observed for H2O mole fraction. McGahan et al. also applied the TDLAS technique in two different RDC geometries (same combustor diameter, but different nozzle throat diameters) to attain not only temperature and water vapor concentration like the previous study, but also velocity at the measuring location [299]. Note that unlike the last study which measured at the nozzle throat, this one contained sensors instrumented in a duct a finite distance away from the throat. Across diverse flow rates, the average temperature of the exhaust tended to stay around

1500 K, like the prior study. They also reported mean velocities of around 400 m/s at the exhaust duct, while conceding that this value could take into account acoustic modes that might incur inside the duct / RDC. Rein et al. also used a tunable laser system (at 100 kHz) to record gas temperatures, but this time inside the actual RDC annulus (and by extension, the detonation region), and not at the exhaust [300]. This was achieved by using multiple photodiodes to decipher the difference between the transmitted light through sapphire windows on the RDC outer-body and the subsequent

reflected light from a mirror-polished RDC inner-body. A given cycle of rotating detonation varied from 1000 K (deflagration) to 1500 K (detonation) at 0.61 kg/s at stoichiometric hydrogen-air conditions, 25.4 mm away from the RDC headwall. Interestingly, this value changed considerably at different air flow rates, even when the equivalence ratio was maintained constant, with the lowest flow rate of 0.15 kg/s exhibiting very minimal temperature oscillations about 500 K, suggesting chaotic detonations (discussed before). A follow-up study from Rein et al. extended their prior setup to four axial sensing locations / beams (simultaneously) thereby arriving at a rigorous characterization of rotating detonation wave temperature in both space and time, at different flow rates and equivalence ratios [301]. A remarkable finding from this study was that both the average and peak-to-bottom temperatures, cycle-to-cycle, was lowest and comparable for axial locations right near the headwall and right at the exhaust. It was higher at the mid-axis regions of the RDC

(see Figure 37a — beam 1 is closest to the headwall and beam 4 is farthest).

(a) (b)

Figure 37 (a) Gas temperatures acquired from four axial locations in an RDC (beam 1 is

closest to the headwall and beam 4 is farthest) [301], and (b) Temperature distribution of gases acquired from simulations showing lower temperatures right near the headwall, due to

convective cooling [302]

Incidentally, a similar (but not same) finding was also reported by Bykovskii et al. [293] in their acetylene-air and hydrogen-air powered RDCs using six axially distributed Chromel–Alumel thermocouples ensconced in steel casings. Though testing was performed only for about 0.5 s, and therefore not thermally steady-state, highest average temperatures were measured at the mid- plane, where the detonation front attaches to the oblique shock wave, followed by locations near the injector headwall (detonation front itself), and finally axial locations near the exhaust (product gases). Kindracki performed a similar experiment of axially distributed type-k thermocouple array to reveal that, contrarily, his RDC has highest average temperature closest to the headwall [224].

However, it is to be remarked that the used thermocouples had a specified range of 1600 K, and hence the higher values recorded by the different sensors by the end of the test needs to be cautiously interpreted. Bykovskii et al. explained the tendency to have lower temperature at the detonation wave location to be due to regenerative cooling provided by the high-velocity fresh mixture that is injected during every passage of the wave. Incidentally, regenerative cooling due to pronounced convection at the fill zone is used also by Roy et al. to explain the same observation seen in their 1-D analytical and 2-D numerical models [302]. Since their model was validated to an appreciable degree with the experimental results of Randall et al. who characterized the temperature rise time using type-k thermocouples at different depths along the combustor outerwall [292], one needs to properly consider this effect in future studies on rotating detonation wave’s heat production.

Overall, numerical simulations tend to accurately predict the detonation wave temperature and structure well, as seen in Figure 37b where detonation temperatures are alike to that obtained by the multi-beam technique. Rankin et al. used mid-infrared imaging using a high speed camera integrated with a bandpass filter that allowed for visualizing the radiation intensity of water vapor at a sampling rate of 1.2 kHz [303]. Even though this is below the detonation propagation frequency in their RDC, they were able to attain instantaneous images from select frames to affirm, both

qualitatively and quantitatively, the detonation wave shape and size acquired from the simulations performed by Cocks et al. [170]. The detonation wave temperature from the simulations of Cocks et al. matches well with the experimentally obtained temperatures from the multi-beam method of

Rein et al. These results bode well for the predictive capability and efficacy of numerical simulations in understanding RDC dynamics. By using convective boundary conditions Roy et al. estimate that a long duration RDC operation (10 minutes) would inevitably result in thermal fatigue of the metallic walls owing to the asymptotic trend of the wall temperature towards the product gas temperature inside the RDC, and suggest that a hollow RDC is preferable to avoid the requirement of cooling by convection two walls of the combustor [302]. Fundamental calorimetry estimation based on the flow rate of water and the associated change in water temperature was used to arrive at accurate values of convective coefficients by Stevens et al. in their RDC geometries [304]. They tested two outer-bodies, which differ in their thickness and the number and geometry of water cooling passages, at different flow rates and backpressurization (atmospheric vs. with nozzle) to reveal that the convection coefficient ranges from 300 to 900 W/m2-K. It was found to be proportional to the detonation wave frequency and the extent of back-pressurization (which would cause extensive pre-burning throughout the combustor due to a choked exit downstream), and appears to marginally increase with increased mass flux and heat addition (equivalence ratio).

These values are noted to be in line with those attained by Ishihara et al. (627 W/m2-K to 1114

W/m2-K, depending on the axial location in the combustor) and Meyer et al. (200 to 1000 W/m2-K)

[305].

The latter result from Meyer et al. is a part of a broader endeavor from AFRL, which has pioneered heat flux characterization of RDCs using specially made resistance temperature detector

(RTD) sensors. A trial-and-error process was carried out to overcome the considerable challenges using the same in their initial studies on account of sensor destruction [296,306]. Increase in mass flow rate and equivalence ratio always tended to raise the heat flux to the walls. Using time-synced

high speed chemiluminescence imaging from the aft-end and an array consisting of axially arranged four two-sided RTD sensors, Theuerkauf et al. found that the unsteady heat flux of an RDC has a distinctly different profile during the onset time, not exceeding 4 MW/m2 until a duration of 100 ms

(onset time in their RDC) [269]. After onset and during steady operation, however, individual detonation laps tended to produce at least 4 MW/m2 cycle-to-cycle, with the tendency to even exceed 9 MW/m2 routinely. They also note intriguing instances of negative heat fluxes after detonation wave passage, which was theorized to be due to the high-velocity reactants fill region recovering after detonation passage. This would be in accordance with the regenerative cooling process proposed by Bykovskii et al. and later by Roy et al. This study was furthered by using a heat flux surface sensor consisting of a twelve element array that was able to accurately capture the detonation wave structure based on part-dependent heat production [307]. A quasi-two dimensional, single species, reactive Euler equations-based numerical simulation performed by

Paxson, to attain heat flux data for similar flow rates and combustor size showed congruence with the experimentally attained heat flux shape, but over-predicted the actual values by 40%. This is seen in Figure 38. A follow-up study by Meyer et al. utilizing the same twelve element array gauge in addition to TDLAS sampling of the gas in the annulus and derived, for the first time, high frequency heat transfer coefficients [305]. Significant lap-to-lap variations in heat flux was reported for the largest annulus width of 22.9 mm, which was attributed to the possibility of the detonation wave exhibiting considerable radius-wise motion in addition to the circumferential propagation

[308]. However, the relationship between heat flux and channel width exhibited a complex, nonlinear trend. Moving from a 7.6 mm annulus width to 16.3 mm width produced a decrease in flux by

73%-82%, whereas moving from 16.3 mm to 22.9 mm caused a heat flux increase of 12%. The exact reason behind this is unknown currently, but was alluded to be a function of the strength and size of the recirculation zone associated with their injection scheme [302]. Further experimentation is required to validate this. One also needs to consider the findings of Schwer and Kailasanath, who

found that the mixedness of the fill region, the injector size and shape and even the supply plenum pressures controlled the minutiae of heat release from different regions of the combustor [309].

Additionally, both Bykovskii et al. and Stevens et al. report higher heat flux during higher modes of operation, such as two waves or more. It is unclear if this is an effect of the implicit efficiency of multi-wave modes in burning the reactants, or the higher heat loading produced by having an increase in the operating frequency of the device. Addition of an aerospike nozzle (probably a choked exit which can cause LPD, as discussed above) appears to cause a notable change in the location of the highest heat flux — it increased at lower axial locations, but decreased at regions close to the nozzle [308]. However, it is unclear if this constituted a fundamental mode change to

LPD. These are open questions that are yet to be answered.

Similar to the above sections where an effort was made to link the findings from RDC to those from rocket engine combustion instabilities, we offer a very peripheral discussion of the same here. Time and again, during HFI in rockets, the highest erosion levels are either reported at the injector headwall and the combustor wall close to it or at the nozzle throat section, depending on if the HFI is tangential (spinning) or longitudinal, respectively. Both these erosion mechanisms have proven to be catastrophic to rocket engines causing instances where the injector headwall causes a significant degradation producing highly uneven reactants injection leading to an explosion, or producing enough heat loading and structural degradation at the nozzle throat to cause the nozzle to completely separate from the main combustion chamber. Though it has been reported that the highest heat flux is not at the injectors in an RDC, we should also consider the observations of Cho et al. who saw detonations through ethylene-air mixtures lifted-off from the injector wall to a higher distance than that through hydrogen-air [310]. This “stand-off” behavior was postulated to be due to the lower reactivity of ethylene which induces a finite distance to react. Considering that

Nordeen et al. also notice this stand-off behavior in their simulations when there is higher “un- mixedness” upstream of the detonation wave [100], one needs to consider the possibility that the

injection style used predominantly in RDCs (slotted oxidizer-holes for fuel) or even the mixture itself could be the driving factor that causes lower heat flux at the injector headwall. Moving forward, one should expect these pitfalls in long duration RDC operation as well, which makes an in-depth analysis of heat production in an RDC even more important. Besides these systems-level impact of heat flux, numerical study by Wang et al. report a fundamental change in the rotating detonation wave structure (radially) when the wall temperature is maintained at or above 800 K — an oblique detonation is formed adjacent to both the inner and outer walls of the annulus due to heightened kinetic rate of reaction at the boundary regions near the wall [311]. Increase in the rotating detonation wave speed is also observed when the RDC wall heating is significant. It is the contention of the authors that heat transfer characteristics of an RDC is the foremost impediment in its path to realize highly efficiency power generation and propulsion systems.

Figure 38 Heat flux profile of the RDC flow-field obtained from twelve-array heat flux gauge

(top) and heat flux profile from numerical simulation (bottom) [307]

10. Emissions

10.1. Pollutants

Owing to a variety of issues ranging from very short experimental run times due to prohibitions from pronounced heat transfer from the detonation wave to the lack of a well- established experimental methodology to characterize the spatially and temporally varying wave, studies pertaining to gaseous pollutants emissions from RDCs are sparse. At present, open literature contains only two studies — one numerical and the other experimental — that deals with

RDC emissions characteristics. Numerically, Schwer and Kailasanath [312] used the Jachimowski

H2/O2 kinetic mechanism [313] which was later incorporated with NOx chemistry as a 12 species,

27 steps reaction by Yungster [314] to tackle pulsed detonative combustion to attain two- dimensional RDC emissions profile with representative hydrogen-air mixtures. The greatest production of NOx occurred right after the detonation front, where the temperature is highest (see

Figure 39a). Three independent parameters were studied; namely, feed pressure in the plenums, equivalence ratio and RDC length and radius. While the NOx emissions index varied from 1 to 26, it strongly depended on some of the varied parameters. Feed pressure and RDC length were found to cause a negligible change in NOx production, whereas equivalence ratio impacted a considerable variation with a lower equivalence ratio of 0.6 producing a NOx flux of 20 ppm in contrast to stoichiometric conditions that produces about 500 ppm — emissions indices reduce by about 16 times. This is to be expected since NOx emission is a function of temperature, which in turn is dependent on the hydrogen-air equivalence ratios [315]. NOx emissions were also found to vary proportionally with the RDC radius owing to the increase in residence times at higher temperatures

(bigger volume for the mixture to traverse). By extension, having multiple waves in the device also produced lower emissions because of the decrease in residence times. Nonetheless, this needs to be confirmed by experimental affirmations of the same.

Experimentally, a flow-through hollow water-cooled RDC powered by hydrogen and enriched air was run for 30 s to allow for proper plateaued measurement of NOx emissions at a single operating point (Figure 39b), which was tested multiple times to ensure statistical rigor

[137]. Four different locations at the aft-end of the combustor were sampled to gather the emissions profile across the RDC cross-section. Highest NOx was produced consistently by the combustor wall, whereas there was almost no NOx being recorded at the central axis of the device.

This is attributed to the inherent design of such flow-through RDCs which have a core flow that is cold and for the vast majority, non-reacting [138,139]. Average NOx measurement by this method stayed at approximately 35 ppm (by volume) across the multiple test cases investigated, forecasting promising RDC NOx emissions characteristics in future configurations and fuels. It is also noted here that though the numerical simulation was two-dimensional and assumed an ideal injector, the estimated values of NOx are within an agreeable range (in terms of ppm) of the experimental measurements. Moving forward, it is essential to attain hydrocarbon-related emissions such as unburned hydrocarbons (UHC), carbon monoxide (CO) and carbon dioxide (CO2). This, however, needs to be preceded by stable hydrocarbon fueled RDC operation, which has proven to be a non- trivial task.

(a) (b)

Figure 39 (a) Unwrapped image of RDC flow-field showing regions of NO production (1011 mol/cm3/s) [312], and (b) NOx ppm (by volume) and O2% profile from a flow-through hollow

RDC obtained from the exit, at the chamber wall (ignition at 5 s) [137]

100

10.2. Noise

Similar to the field of gaseous emissions characterization of RDCs, the arena of acoustic emissions produced by RDCs is also nascent. To date, the authors have not come across an acoustic analysis of this device that is performed in an anechoic chamber. However, some studies have dealt with nominal measurements of the sound produced by RDCs [306,316–318]. Using a microphone placed 1 m away, perpendicularly, from the RDC central axis, Bykovskii et al. determined that the magnitude of sound produced by their RDC is inversely proportional to the number of rotating detonation waves in the chamber, with the three-wave mode producing about 100 dB, and the two- wave and one-wave mode producing 120 dB and 150 dB respectively [317]. By comparing their acoustic pressure trace with the luminosity time trace acquired from high speed imaging, they were also able to determine that the acoustic sensing was able to capture the different dynamics (based on frequency) of the RDC, such as the number of waves in the annulus and the onset period after ignition. Additionally, by using radial partitions in the combustor, the noise produced in the same combustor during deflagration was also measured at the same flow rates to ensure a proper comparison, which resulted in the surprising finding that, in their study, the rotating detonation mode did not exceed the sound produced by traditional deflagrative burning. The highest frequency of the acoustic spectrum was also comparable across both the burning modes, with the caveat that the source of such frequency during deflagrative burning remained unidentified. A concomitant study in the same paper also researched the vibration dynamics of RDCs during operation in detonation vs. deflagration mode, and concluded that vibration sensors are also efficient in ascertaining the operating frequency (detonation speed and mode) of RDCs. However, as opposed to the noise production, lower number of waves tended to produce lesser vibration of the combustor. The cause behind this is unknown. All the tested operating points were also noted to exhibit a distinct start-up period (for both detonation and deflagration), vibration-wise, after ignition, which had a frequency of about 8 Hz and amplitude of 430 dB. This is attributed to an

101

“intrinsic oscillation” of the products-gathering tank at the end of the RDC which is posited to produce this oscillation in the accumulated mixture owing to the disturbance (ignition) of the initially non-combusting system from its steady, stable state. It is worth noting here, in the same vein, that the shape of the amplitude measured by the vibration sensor during the onset period is very similar to the impulse response function of an RDC that was acquired by a systems- identification approach mentioned previously (ignition and onset section). Figure 40a shows this decaying wave after ignition. Figure 40b is a representation of the vibration amplitude during rotating detonation propagation (trace 1) compared with the luminosity profiles from imaging

(trace 2). Fig.xxc is a snippet of a trace that shows DDT occurrence inside the RDC, and it can be seen that there is negligible difference in vibration amplitudes between the two modes.

This method — of using far-field acoustic signatures to determine the operating mode — was also used by Theuerkauf et al. to remotely monitor the dynamics of their RDC which was water cooled to run for prolonged durations, which is inhospitable to flush-mounted sensors that are prone to destruction [306]. Thus, acoustic sensing is useful from the perspective of monitoring RDC behavior without hindering the internal fluid mechanics and sensor disintegration during prolonged runs. Pandiya et al. furthered acoustic analysis of RDCs by using two microphones perpendicular to the RDC axis to attain azimuthal recordings of noise [316]. Using these microphones in conjunction with exit-plane PCB piezoelectric pressure sensors revealed, once again, that microphones are indeed highly sensitive to not just obtaining frequency changes inside the RDC, but also to the mode changes responsible for it. For instance, both the pressure sensors and the microphones are exited in-phase during the azimuthally simultaneous LPD operation and out-of-phase excitation during rotating detonations. Amplitudes of up to 134 dB were observed, depending on the mode and equivalence ratio of the hydrogen-air mixture that was tested — this value is in line with the findings of Bykovskii et al. It is important to note here that both Bykovskii et al. and Pandiya et al. contend that LPD mode of operation produces higher noise than RD mode.

102

This was hypothesized by Bykovskii et al. to be due to the very nature of the axially travelling pressure pulses which would presumably produce higher exhaust velocities as opposed to the products from the slanted RD, thereby emitting higher noise owing to the eighth-power dependency that noise has on flow velocities [319]. Irrespective, since experimental details about the RDC exhaust flow-field is still lacking, we need more evidence to corroborate these claims.

Currently, it can be contended that there is considerable congruence between different groups on

RDC acoustic signature in non-anechoic test facilities. Moving forward, detailed experiments are required to assess the sound generation mechanisms in RDCs.

Figure 40 (a) Vibration after RDC ignition, (b) vibrations during two-wave mode (1) and luminosity profiles of detonation waves during the same period (2), and (c) vibration of the

RDC during DDT. Plots are from Ref [317].

11. Chapter-wise descriptions

The current chapter dealt with a comprehensive review of rotating detonation combustors, and its kinships with rocket engine combustion instabilities. When relevant, the findings of the current thesis as it pertains to the overall scope of the community were referenced. In the present sub- section, the specific details of each individual chapter that follow are mentioned. Note that Chapter

2-8 deal with an RDC utilizing hydrogen-air mixtures, whereas Chapter 9 pertains to RDC operation

103

with ethylene-air mixtures. Chapter 10 is predominantly a literature review. The descriptions are as follows:

Chapter 2: Investigation of rotating detonation combustor operation with H2-air mixtures

The effects of three different geometric variations on RDC operation are tested. They are fuel injection scheme, air injection slot width (choked vs. subsonic air flow) and the presence/absence of a CD nozzle (pressurization) at the RDC exit. The variation in operation is quantified based on operating regimes, wave speed behavior and the frequency of operation (mode).

Chapter 3: Characterization of instabilities in a rotating detonation combustor

The modular RDC configurations tested in the prior chapter is analyzed to reveal four diverse off- design modes/ instabilities. The conditions of occurrence of these instabilities, and their qualitative and quantitative descriptors are dealt with here.

Chapter 4: Analysis of air inlet and fuel plenum behavior in a rotating detonation combustor

In this chapter, the nature of high frequency coupling between the rotating detonation combustor and the two supply plenums (air and fuel) are studied by making use of a total of nine high-speed pressure sensors, three each in the combustor, air inlet and fuel plenum, respectively.

Chapter 5: Longitudinal pulsed detonation instability in a rotating detonation combustor

The specific phenomenon of longitudinal pulsed detonation in backpressurized rotating detonation combustors is studied in this chapter by making use of two geometric variations: air inlet slot width and nozzle exit area. This allows altering pressure ratio across injection and pre-ignition combustor pressure independently of each other to ascertain the driving mechanisms. By making use of axially and azimuthally distributed pressure sensors, a mechanism is proposed to explain the peculiar off- design mode.

104

Chapter 6: Amplitude modulated instability in reactants plenum of a rotating detonation combustor

Two types of low frequency oscillation are discovered in the air inlet, which are linked to the low frequency instability inside the combustor. Subsequently, case studies are performed to understand the origins of the amplitude modulated oscillation, and a mechanism is proposed to describe the nature of this coupling between the air plenum and the combustor.

Chapter 7: The origins of wave directionality, chaotic propagation and onset time after ignition in a rotating detonation combustor

Both atmospheric and backpressurized RDCs are studied to analyze the origins of the distinct and finite onset times seen in RDCs after ignition. A black-box systems identification approach is used to determine the settling time of the air plenum. Pressure dynamics of the fuel plenum are analyzed in the frequency spectrum to ascertain the impact of fuel supply on the onset times, as well.

Chapter 8: On mean pressure shifts and chugging oscillations in back-pressurized rotating detonation combustors

This chapter is dedicated to the analysis of the transient increase in static pressure of a pressurized

RDC after ignition. Additionally, the difference in combustor behavior and its coupling to the plenums by virtue of being pressurized is studied. The driving factor behind the transient nature of frequency modulated oscillations in the air inlet is studied for both atmospheric and pressurized cases. The effect of this oscillation on the operating mode of the RDC is also analyzed.

Chapter 9: Rotating detonation wave mechanics through ethylene-air mixtures in hollow combustors, and implications to high frequency combustion instabilities

The question of what constitutes a rotating detonation combustor is studied in this chapter. More specifically, the factors responsible for a hollow combustor to sustain stable rotating detonation

105

waves inside it are investigated using ethylene-air mixtures by making using of different flow rates, equivalence ratios and two geometric variations.

Chapter 10: Rotating detonations and spinning detonations: similarities and differences

From the results obtained from the prior chapters, and the findings from literature on rotating detonations and spinning detonations, a theory is proposed to connect the two seemingly unrelated detonation phenomena.

106

CHAPTER 2: INVESTIGATION OF ROTATING DETONATION COMBUSTOR OPERATION

WITH H2-AIR MIXTURES

Chapter Abstract

The operating range and wave speed performance of a Rotating Detonation Combustor (RDC) is characterized for hydrogen-air mixtures for three fuel injection schemes and two air injection schemes. The fuel injection scheme is altered by changing the total number of injection orifices and the individual orifice area, while maintaining the same fuel mass flux across the three schemes. The operability, performance and combustion-induced pressure rise due to the addition of a back- pressurizing convergent nozzle is also characterized. While the operating range is largely unaffected by changes in the length-to-diameter ratio of the fuel injector orifices, higher length-to-diameter ratios correspond to a lower number of transitional RDC operation where there is a sudden abatement of the continuously propagating detonation wave, once established inside the combustor.

Increased air injection area diminishes the operability, while producing high stochasticity in the performance of the RDC. The length-to-diameter ratio of the fuel orifices has a significant impact on the number of detonation waves that can exist in the chamber. For the highest length-to-diameter ratio of the fuel orifices, and at the highest air flow rates, the RDC supports multiple detonation waves inside the chamber. Without the convergent nozzle attachment, 80% of Chapman-Jouguet (C-

J) detonation speed is achieved for all three fuel injection schemes. C-J detonation wave speed is achieved in the annulus when the RDC is back-pressurized using the nozzle. The ratio of reactant fill-height to the detonation cell-width tapers at the lean and rich operating conditions, while peaking at an equivalence ratio of around 1.2. The detonation-induced static pressure rise produced in the RDC is found to be dependent on the air flow rate and the equivalence ratio of the reactants.

107

Nomenclature

CEA NASA Chemical Equilibrium and Analysis Program

ṁ Total Mass Flow Rate (kg/s)

ṁH2 Mass flow rate of air (g/s)

ṁair Mass flow rate of air (kg/s)

FP Fuel Injection Plate

gFuel Fuel Mass Flux (kg/s*m2)

L/D Length to diameter ratio of the Fuel Injection Orifices f Frequency (kHz) d Mean diameter of the RDC annulus (mm) h Reactants Fill Height (mm)

PAnnulus(t) Combustor Annulus Pressure Time History (bar)

PPlenum(t) Air Plenum Pressure Time History (bar) t Time (sec)

Ws Combustion Wave Speed (km/s)

λ Detonation Cell Size (mm)

Φ Equivalence Ratio

PR Combustion induced pressure ratio

108

PF Static pressure at end of test run (bar)

PI Static pressure before detonation initiation (bar)

PL Static pressure loss across the system (bar)

1. Introduction

Detonation is a combustion wave driven by an exothermic reaction that is sustained by a shock wave. One dimensional detonation theory proposed by Chapman, Jouguet, and Mikhelson assumes detonation to be a shock wave followed by a zero-thickness reaction zone where the chemically reacting mixtures attain sonic velocity in the reference frame of the shock wave. Zel’dovich, Von-

Neumann, and Doering are responsible for the modern detonation theory which explains detonation as a combination of a shock wave, an induction zone, and a reaction zone. There is a marked rise in temperature, pressure and density in the reactants due to the passage of the shock wave, followed by a region of near constant gas properties called the induction zone, where there is chemical decomposition and radical formation. This region is followed by the reaction zone, which is characterized by rapid reaction rates causing a surge in temperature, and decrease in pressure and density due to the expansion of products. Detonation raises the fluid pressure across its front as opposed to the loss of pressure across a deflagrating flame front. This feature of detonation has prompted research to supersede deflagration in combustors because of the hypothetical high work availability. Heiser and Pratt [320] estimate a cycle efficiency of 30% for an engine using detonation cycle in contrast to the 0% efficiency for the Brayton cycle engine, considering no pre-compression.

Pulse Detonation Combustors (PDC) have been thoroughly studied in the past as a promising

Pressure Gain Combustion (PGC) System. Use of PDC in lieu of traditional constant pressure combustors has diminished because of complex construction, periodic reactant refill, and highly unsteady exhaust of the PDCs. Rotating Detonation Combustors (RDC) are postulated to negate the

109

disadvantages of the PDC, owing to the quasi-steady exhaust flow produced by a detonation wave spinning around the combustor annulus at frequencies on the order of thousands of Hertz. Fuel and oxidizer are typically injected at the head-wall of the RDC, and ignited by the chosen initiation method. Once detonation is achieved inside the annulus, the detonation wave travels circumferentially in the chamber continually feeding on the fresh reactants, and simultaneously expanding the combusted products through the RDC exit.

The effect of fuel injectors on the performance of the RDC has been numerically studied by many research groups [106,171]. Numerical studies performed by Schwer and Kailasanath [172], and Hishida et al. [106] have studied the relation between fuel plenum stagnation pressure and combustor pressure during rotating detonation propagation on the injection of fresh H2-Air premixed reactants into the combustor. The reactant influx into the chamber is dependent on the stagnation pressure of the mixture plenum, and combustor pressure. If the latter is smaller than the former, the injectors are either choked or un-choked while still allowing reactant flow into the combustor. If the combustor pressure is greater, the reactant influx into the chamber completely ceases leading to the failure of detonation propagation [171,321].

The detonation wave is accompanied by a trailing edge wave at its base, which enters the reactant plenum at every instance the detonation passes an injector. Schwer et al. observes a considerable overpressure-to-underpressure ratio fluctuation in the reactant plenum with an increase in the ratio of exit area to throat area of the injector micro-nozzles [171]. An “unwrapped”

RDC experimental study by Fotia et al. visualized the fuel plenum dynamics and concluded that detonation wave passage inflicted a time delay of 200 μs before the plenum could recover to its nominal fuel supply state [184]. The un-choking and subsequent disruption of the fuel plenum was attributed to a bulk fluid motion due to the motion of the detonation wave across the test section.

Studies on fuel injectors are limited to numerical studies and the two-dimensional experimental

110

investigation, and may overlook some of the three-dimensional effects and other physical processes within the RDC environment that occur for limit-cycle operation.

Gas-turbine integration of an RDC necessitates studying the effect of back-pressurizing the combustor to simulate actual in-engine operation, since addition of a turbine increases the backpressure experienced by the combustor. In a numerical study, back pressure was found to have a strong impact on existence of secondary and tertiary shocks, occurring at the mid-axial and near- exit portion, respectively, of the RDC [89]. Schwer and Kailasanath correlated higher back pressures to gases getting compressed again through the secondary and tertiary shock structures thereby having a performance drop and subsonic exit velocity [89,168]. A three-dimensional numerical study by Schwer also hinted at detonation wave failure due to wave feedback from a converging

RDC exit geometry designed to provide compression within the channel [222]. Experimental efforts at back-pressurization of an RDC were performed by Tellefsen et al. [229] by attaching a convergent nozzle to the RDC exhaust, and DeBarmore et al. [230] by integrating nozzle guide vanes to an RDC.

Tellefsen operated an RDC between total mass flow rates (ṁ) of 0.23 kg/s and 0.45 kg/s and observed comparatively leaner operation when compared to the ambient exit condition case. The successful operation of the RDC at lower equivalence ratios (Φ) renders logical sense as elevated pressures reduce the detonation cell size, which is directly related to lower detonation initiation energy requirements. The RDC of both Tellefsen and DeBarmore exhibited similar chamber pressure behavior after the onset of detonation, which was characterized by a sharp initial spike followed by convergence to a plateaued pressure which remained approximately stable until the end of the test. The settling time of the measured chamber pressure was attributed to the low response time of the respective pressure transducers used in the testing.

The H2-Air operating map is defined as the range of total mass flow rate (ṁ) and equivalence ratio (Φ) over which the RDC under consideration houses the successful detonation wave or a rotating quasi-detonation wave (choked flame) [21,276]. Bykovskii et al. refers to the rotating

111

thermally choked flame as an acoustic wave, and its emergence was attributed to improper mixing

[27]. Shank et al. mapped the operating map of a 150 mm RDC with associated detonation wave speed (Ws) across all operating points. A maximum WS of ≈ 1500 m/s was attained [151]. Russo et al achieved Ws ≈ 1500 m/s in a 76 mm diameter RDC with H2-Air [252]. The study by Suchocki et al. investigated the operating range of the 76 mm RDC with H2 and enriched air, clocking a maximum

WS of ≈ 1600 m/s [256]. Kindracki et al. studied WS performance of H2-Air mixtures for a 150 mm diameter and 95 mm diameter RDC geometries and achieved ≈ 1500 m/s maximum wave speed

[127]. Bykovskii et al. also demonstrated successful H2-Air operation with highest recorded WS of ≈

1450 m/s by varying the annulus depth [276]. Frolov et al. [322] attained notably higher speeds of up to 1800 m/s in their relatively larger RDC (outer diameter of 406 mm), while also testing RDC operation with different exit blockage ratios. However, the effect of backpressure on the RDC operation was not discussed extensively, whereas Tellefsen et al. expanded the successful operating region from the configuration of Suchocki et al. by adding a converging nozzle to the RDC exhaust and noted a maximum WS ≈ 1250 m/s. Bykovskii et al., Suchocki et al. and Frolov et al. have observed the presence of multiple waves inside the chamber at higher ṁ. Bykovskii et al. linked the existence of multiple detonation fronts to the mixing effectiveness of a given setup [27].

The present study experimentally investigates the operating map of an RDC with three different fuel injection plates (FP). The FP having the better performance is selected to study the effects of convergent nozzle addition and increased air injection area. Increased air area is essentially a study of the effects of un-choked air injection on the RDC operability. The RDC in use is the Shank et al. model [151], but with the original fuel plate replaced with three derivative proprietary designs, which are designed to offer enhanced fuel-air mixing. In contrast to the success-or-failure method of prior studies [151,252,256] in the construction of an operating map, this study introduces a third label to an RDC operation: “Pop-Out” or transition points, where there is a detonation wave existing in the chamber initially, but ceases to exist abruptly before the test ends. The study also aims to

112

characterize the different modes of operation of the RDC, in terms of the predominant presence of either one or more rotating detonation waves in the chamber, for changes in ṁ, Φ, fuel plate, backpressure and increased air injection area (decreased air mass flux). Absolute pressure rise, which is different from the desired net pressure gain, is characterized within the combustor for test cases run with the back-pressurizing nozzle.

2. Experimental Methodology

The current research has been performed at the University of Cincinnati Detonation Engine Test

Facility situated in the Gas Dynamics and Propulsion Laboratory. The RDC consists of an outer body and a center body, where the space between constitutes the combustor annulus. The RDC and the associated setup are shown in Figure 41. Fuel is injected through the multi-holed, modular fuel plate and rests on an oxidizer spacer ring (Figure 42). The instrumentation schematic is show in

Figure 43. Dimensions of the RDC parts are given in Table 3. The three FPs: A, B and C are of equal thickness and total injection area. The FPs are designed to offer the same fuel mass flux (gfuel), but differ by the number of injection orifices, ascending from A to C (i.e., all three fuel plate have the same total injection area). The length-to-diameter ratio (L/D) of the fuel orifices for the three FPs is given in Table 3. It is to be noted that the length of the orifices across all three FPs remain the same, by virtue of all three FPs having the same thickness. The convergent nozzle sits on the exit face of the center body thereby causing a constriction in the detonation annulus exit. The oxidizer spacer plate thickness determines the injection gap for the radially-inward moving air. The RDC outer body has a total of 12 instrumentation ports, distributed over four axial rows of three stations, each separated by 120o as shown in Figure 43. The instrumentation schematic is given in Table 4. Detailed description of the test facility and associated devices and instrumentation are dealt with in detail by

St. George et al. [323].

113

Figure 41 University of Cincinnati RDC

Figure 42 RDC internal schematic

114

Figure 43 RDC instrumentation schematic

Table 3 RDC hardware dimensions

Part Geometry Measured Dimension

FP A L/D 12.8

FP B L/D 14.6

FP C L/D 17.0

Oxidizer Spacer I Air injection area 490 mm2

Oxidizer Spacer II Air injection area 1400 mm2

Combustor Channel Width of channel 7.6 mm

Inner Diameter 139 mm

Outer Diameter 154 mm

Annulus area 3500 mm2

Converging Nozzle Exit area 760 mm2

Table 4 Instrumentation location information

Sensor Station Number Row Number

115

PCB transducers 1,2,3 2

Kulite transducer 3 4

Ionization Probes 1,2,3 3

Three PCB pressure transducers (Model 113B24) are installed to pick up the wave passage instances. These sensors are flush-mounted in station 1, 2 and 3 of the 2nd row of the instrumentation ports in the RDC. Two water-cooled Kulite (WCT-312-35BarA) pressure transducers are used during testing, with one in the air plenum (Pplenum(t)) to detect time-accurate absolute pressure inside the plenum and one in the 3rd Station of the 4th row of instrumentation ports. The second water-cooled Kulite transducer (Pannulus(t)) is attached to a 150 mm perpendicular standoff tube. This is done to protect the Kulite from the extreme temperature inside the RDC. The 150 mm standoff is attached to a 2 m long flexible plastic tubing of 8 mm inner diameter to implement an Infinite Tube Pressure (ITP) setup. Three ionization probes are installed in 3rd row of the instrumentation ports to measure voltage drop signals that correlate with ion formation associated with detonation. This facilitates the accurate capture of the time period during which there is ion-producing combustion in the chamber, hereafter referred to as “burn time” (tb).

All of the test cases in the present study are operated for a period of one second after which the fuel valves close. It should be noted that there is remnant fuel flow for a brief period after the valves are closed. Test cases having tb of 1 second or more are deemed successful and those with 0.1 s < tb < 1 s are termed “pop-out”. Pop-out refers to transitional cases where the initially established rotating combustion front ceases to exist. Pop-out phenomena are validated by the Pannulus time-series and visual cues from the live CCTV footage of the test run. Data acquisition is enabled by both low speed channels (sampling rate, fs=1 kHz), which are used to obtain pressure and temperature data of fuel and air supplies, and high speed channels (fs=1 MHz), which are used for capturing time-accurate pressure and ionization. Initiation is achieved in the injected reactants by using a pre-detonator

116

that propagates a detonation tangentially into the annulus. The spark-ignited pre-detonator uses an ethylene-oxygen mixture supplied by a pair of Bosch automotive valves at an injection pressure of

7.5 bar.

The first objective of the study is to acquire the RDC operating maps for FPs A, B, and C to determine the relative merit of the fuel injection designs. The best FP is selected based on the operability, and is used in the nozzle and air injection area studies. The next objective is to characterize the successful detonation mode in the chamber through the frequency content of the waves, followed by characterization of Ws performance at the successful operating cases. An analysis between the calculated fill height (h) and the detonation cell size (λ) (obtained from literature) is performed. The study ends with characterization of pressure rise in the chamber under back-pressurization. . Four air flow rates (0.2 kg/s, 0.3 kg/s, 0.4 kg/s and 0.5 kg/s) are used in this study. Maximum Φ is approximately 1.2 for 0.5 kg/s, 1.3 for 0.4 kg/s, 1.8 for 0.3 kg/s and 2.0 for 0.2 kg/s. Higher Φ is not examined owing to a combination of facility limitation (maximum ṁ H2 =

16 g/s) and the logical inference that practical applications of a gas-turbine combustor necessitates an RDC to function at lean to stoichiometric ratios. The testing commenced at the highest equivalence ratio and gradually moved to leaner mixtures until successive failure points are observed, thereby defining the lean limit of the RDC operation under the different configurations.

During the course of the first five hot fire tests, the PCB sensors underwent catastrophic failure, probably due to a combination of extreme temperatures and high-frequency, high-amplitude pressure pulses. Every test case henceforth depended on Pannulus on the standoff-ITP for frequency and wave speed information. Fig. 4 gives the comparison between the Fast Fourier Transform (FFT) obtained from the Kulite, and the PCB before it disintegrated. It can be seen that the Kulite in the

ITP records the same dominant frequency as the flush-mounted PCB, thereby proving the validity of the calculated wave speeds.

117

Figure 44 Comparison of frequency spectrum of flush-mounted and ITP-mounted sensors at

ṁ= 0.2 kg/s and Φ= 1.0

A peak-finding algorithm is used to estimate Ws. Conditional averages of lap velocities for each test run are obtained for both single-wave, and multi-wave detonation modes. A Fast Fourier

Transform is simultaneously performed on the Pannulus time history to extract the detonation wave frequency. Erroneous frequencies from the FFT are disregarded if they fail to fall within 10% of the frequency obtained from the WS data. Frequency from Ws is obtained from the following equation.

f = Ws / πd (1)

Here, ‘d’ is the mean diameter of the RDC chamber annulus. In addition to frequency and wave speed, the reactants’ fill height into the combustor is normalized by the detonation cell width to arrive at a non-dimensional parameter that is useful for understanding the scaling necessities.

2.1. Uncertainty

The uncertainty in pressure and temperature sensors (used in reactants delivery) is ±0.069 bar and ±1 K, respectively. This uncertainty is used in linearized systematic error analysis to estimate an error of 2.1% in the air mass flow rate and 2.8% in fuel mass flow rate, which in turn

118

results in a maximum error of 3.4% in equivalence ratio, for the lowest flow rates. The frequency resolution is 1%, since the testing duration is 1 s and the sampling rate is 1 MHz. The difference between the acquired wave speed from the peak-tracking algorithm and the fundamental frequency is found to be negligible. The cell size estimates have been prone to an uncertainty of anywhere between 3% and 55% error [324], and are to be treated qualitatively.

3. Results and discussion

3.1. Operating map

The RDC is classified to be functioning under three fundamental operating conditions: (1) successful continuous propagation of a rotating detonation wave or quasi-detonation inside the chamber, (2) complete failure to attain any azimuthally moving flame front, and (3) transitional

“pop-out” events that are distinguished by the presence of a rotating flame front for a finite time in the chamber before extinguishing or changing to a burner-type axial flame. The pressure time-trace of a pop-out event is shown in Figure 45. It can be seen than the rotating detonation ceases to exist at t= 0.4 s. Regimes of successful operation between the three FPs are similar with subtle differences. Inspection of the tb and Pannulus time history reveal that despite this general presevation of successful test points, there is a noticeable trend in the number of pop-out events. Incidence of pop-out cases is highest for FP A, with 3 pop-out events (Figure 46), followed by fuel plate B with 1 pop-out events (Figure 47), while no pop-out is observed for FP C (Figure 48). Pop-out events occur for lean conditions for FP A and FP B, and are interspersed between successful and failure cases. It is concluded that while the number of pop-out events are always higher for FP A, and none exist for

FP C, the exact operating point where pop-out occurs is stochastic for a given geometry.

Schwer and Kailasanath noted that smaller injector holes act against the occlusion effects produced due to detonation wave propagation, due to enhanced viscosity inside the orifices [321].

From this point from the literature, and the fact that pop-out events did not occur for FP C, it is

119

postulated that the L/D of fuel orifice determines the occurrence of pop-outs. Fluidic hammering by the wave on the fuel injectors may completely cut-off the fuel flow into the combustor when the plenum pressure is low (i.e., at the lean limits of operation) leading to a spontaneous abatement of the wave at the lean limit, causing "pop-out events", which are intrinsically unstable. While the modes of operation of the RDC will be dealt with in detail in the next section, it is imperative to mention here that the prevalence of multi-detonation wave operation is highest for FP C. Suchocki

[256] established that multi-wave activity in an RDC produces higher thrust than a one-wave mode, for the same operating condition. Noting that pop-out events did not occur for FP C, and tests run with FP C exhibit greater instances of multiple detonation wave activity, FP C is selected as the baseline plate for the remainder of the study.

For the next part of the study, a converging nozzle is mounted onto the center-body to restrict the RDC exit area and generate high back-pressure. Addition of the nozzle created an initial combustor pressure of ≈1.0 bar for 0.2 kg/s, ≈1.9 bar for 0.3 kg/s, ≈2.6 bar for 0.4 kg/s and ≈3.3 bar for 0.5 kg/s. Elevated pressures correspond to smaller detonation cell size and lower initiation energy [21], corresponding to lower fill height and initiation requirements. Despite this relationship, it is interesting to note that while the H2-enriched air testing of Tellefsen et al. changed the success regime, the nozzle had no effect when H2- standard air was used [229]. The present study, however, records an expanded lean operating range at high air flow rates of 0.4 kg/s and 0.5 kg/s as could be seen in Figure 49.

The third parameter of the current study is the effect of the air injection gap on the oberability and the performance of an RDC. The initial air gap of 490 mm2 is increased to 1400 mm2 by changing to a thinner oxidizer spacer. Increased air injection area un-chokes the air gap. Air injection is deemed to be un-choked if (Pplenum(t)) / (Pannulus(t)) < 1.9 which is the case for tests run with the large air injection area. For instance, at an air flow rate of 0.5 kg/s, the upstream air supply pressure and the chamber pressure are almost the same, remaining at ≈2.2 bar prior to detonation.

120

The resulting operation map is given in Figure 50. Successful cases are rare compared to failures.

There are a multitude of pop-out cases which occupy a considerable part of the rich and lean regions of the map. For the first time in the course of this study, a distinct rich limit of operation for the RDC is observed. The strong reduction in operability highlights the importance of air injection as an RDC design parameter. There is also a distinct change in lean boundary of operation, for flow rates of 0.3 kg/s, 0.4 kg/s and 0.5 kg/s where the previously failed test points for FP C, and FP C with nozzle, are replaced by pop-out events and rarely successful operation. Note that with the large air injection area, certain test cases exhibit multiple transtitions between detonation and deflagration (not shown here), and thus multiple pop-outs. This futhers the argument that pop-outs are intrinsically unstable, and are indeed caused by the heightened effect of detonation wave on increased injection area. As a general trend, for all the setups, an equivalence ratio of Φ≈ 0.5 is found to be the lean limit for successful operation, which is in agreement with the theory that detonation propagation is improbable below an equivalence ratio of 0.5 due to insufficient heat release behind the shock wave [21,325].

Figure 45 Combustor annulus pressure time-trace for ṁair = 0.3 kg/s, Φ= 0.703, FP A,

showing pop-out

Table 5 Experimental results legend

121

Figure 46 Operating map (Φ vs. ṁ) for Fuel Plate A

Figure 47 Operating map (Φ vs. ṁ) for Fuel Plate B

122

Figure 48 Operating map (Φ vs. ṁ) for Fuel Plate C

Figure 49 Operating map (Φ vs. ṁ) for Fuel Plate C with nozzle integration

Figure 50 Operating map (Φ vs. ṁ) for Fuel Plate C with increased air injection area

123

3.2. Modes of operation of the RDC (Co-rotating waves)

The mode of operation of the RDC is defined to be “one-wave” if there is a single detonation wave inside the annulus, or “two-wave” if there are two detonation waves rotating simultaneously in the chamber. An FFT performed on the Pannulus time history yields an accurate measure of the operational frequency “f”. H2-Air C-J speeds translate to f ≈ 4.5 kHz. Hence, frequency, f ≥ 4.5 kHz, implies the existence of two or more waves in the RDC. While FP A exhibits one wave mode for all the successful operating cases (Figure 51), FPs B and C tend towards two detonation wave mode at the highest air flow rate of ṁ = 0.5 kg/s. From Figure 52, it is seen that, for FP B, there are two operating points around Φ ≈ 1.2, for 0.5 kg/s that exhibit two wave activity. Two detonation waves are spinning at ≈ 7.5 kHz. For tests run with FP C, all the cases at 0.5 kg/s exhibit two-wave mode

(Figure 53), as seen by the existence of three cases with frequency around 7 kHz. Bykovskii et al. observed different modes of operation for constant mass flux, for changes in air injection area and channel width [27,276], indicating the importance of geometry. As explained earlier, the fuel mass flux (gfuel) through the injection orifices in all the FPs remains relatively constant because the combined area of the orifices for each FP is the same. Hence, for a fixed air injection geometry, fill height h is deemed to be similar for all FPs by design. Since gfuel is the same for a given operating point, and the only difference between the three FPs is L/D, it is hypothesized that the fill height recovery is faster when L/D is higher, which could be due to the faster recovery of the fuel plenum after the passage of a detonation wave. While the fuel orifice-L/D postulation may relate multi- detonation modes and plenum recovery time, it leads to the natural question of what causes the furcation of one wave into multiple waves at discrete time periods, considering the fact that the current study along with several other studies [252,256] have noticed mode shifts at the different time periods through the test. Wang and Shao [326] have numerically determined that increase in velocity of injected fuel causes the detonation wave to slant towards the fuel plate to avoid being blown out of the annulus. The above two factors may explain the formation of multiple detonation

124

waves in an RDC. At the high flow rate of 0.5 kg/s, the detonation wave is more slanted towards the fuel plate than at the lower flow rates. This could cause the recovered reactant fill height to exceed the detonation height, thereby entering the oblique shock that is adjoined to the wave. This may cause autoignition of the fresh mixture, thereby leading to the formation of the second wave. From

Figure 54, it can be seen that nozzle operation is limited to predominantly one wave mode (since f ≤

4.5 kHz) which can be attributed to reduced fill height due to increased back pressure. RDC operation with increased air gap is in the one wave mode as seen from Figure 55.

Figure 51 Operational modes (Φ vs. f) for Fuel Plate A

Figure 52 Operational modes (Φ vs. f) for Fuel Plate B

125

Figure 53 Operational modes (Φ vs. f) for Fuel Plate C

Figure 54 Operational modes (Φ vs. f) for Fuel Plate C with nozzle integration

126

Figure 55 Operational modes (Φ vs. f) for Fuel Plate C with increased air injection area

3.3. Wave speed performance

The performance of the RDC is evaluated in terms of the detonation wave speed. For FP A, FP B and FP C, at flow rates of ṁ = 0.4 kg/s and ṁ = 0.5 kg/s, the WS is at least 80% of the ideal C-J detonation wave speed (Figure 56, Figure 57, Figure 58). The C-J speed trend line and the isobaric sound speed at different Φ are calculated using data from NASA CEA (Chemical Equilibrium and

Analysis), assuming reactant pressure and temperature of 1.0 bar and 300 K, respectively. Certain test cases at these high ṁ conditions also reached 90% C-J detonation wave speed of H2-Air. At flow rates of ṁ = 0.2 kg/s and ṁ = 0.3 kg/s, the speed ranged from 70% to 80% of the C-J detonation WS.

Aberrant behavior in performance is seen for ṁ= 0.3 kg/s where there is a sudden escalation of Ws at Φ ≈1.1 for all the three fuel plates. The Ws plot for the large air injection area is given in Figure 60.

Even for the working points, the large air gap setting gives poor Ws performance, staying around

60% C-J speed for all cases. This suggests that un-choked air injection gap is affected greatly by the initiated detonation wave. The back pressure induced by the wave on the large air injection area is postulated to be significant enough to erratically alter the oxidizer supply thereby leading to an overall poor operability and WS performance. The Ws performance changes considerably for the nozzle configuration (Figure 59). Ideal C-J speed is achieved at air flow rates of 0.3-0.5 kg/s in H2-

127

Air mixtures when the RDC is back-pressurized. For the cases with nozzle, a pressure of 2.5 bar and temperature of 300 K are used to obtain the C-J detonation conditions.

Figure 56 Detonation wave speed variation (Φ vs. WS) for Fuel Plate A

Figure 57 Detonation wave speed variation (Φ vs. WS) for Fuel Plate B

128

Figure 58 Detonation wave speed variation (Φ vs. Ws) for Fuel Plate C

Figure 59 Detonation wave speed variation (Φ vs. WS) for Fuel Plate C with nozzle

integration

129

Figure 60 Detonation wave speed variation (Φ VS. WS) for Fuel Plate C with increased air

injection area

Schwer and Kailasanath attempted to numerically model the effect of reduced radial depths at the RDC chamber exit, but were not able to simulate stable detonation due to “feedback waves” from the exit section which caused detonation wave failure [171]. Tellefsen et al. peripherally discuss the distinction between startup and steady RDC operation with nozzle, from visual cues

[229,327]. The above two points suggest that RDC operation with a convergent nozzle involves a distinct “start-up” behavior followed by steady-state operation. Many cases for FP C with nozzle exhibit significant initial scatter in Ws followed by a period of stabilization of the Ws to a lower value.

It is seen from Figure 61 that there is considerable change in the Ws for the initial ≈ 2000 wave laps, but eventually stabilizes to ≈ 2000 m/s. While the Ws decreases gradually, the pressure inside the chamber exhibits considerable increase from initiation to the end of the test when it attains a steady value (Figure 62).

130

Figure 61 Lap count vs. WS for Fuel Plate C with nozzle integration, ṁAir = 0.4 kg/s, Φ = 0.847

Figure 62 Pressure trace for Fuel Plate C, ṁAir = 0.5 kg/s, Φ = 1.1

3.4. Detonation cell size and fill height comparison

The cell size of the H2-air mixture at 1 bar is obtained from the empirical findings of Ciccarelli et al. [324], and the fill height, h, is non-dimensionalized by λ, assuming a combustor pressure of 1 bar.

This method of attaining a ratio of h/λ was championed by Bykovskii et al. [27], for prospective geometric scaling of RDCs. Cell size reaches a minimum near stoichiometric conditions and rises sharply for lean and rich Φ. This explains the drop in h/λ at lean and rich conditions in Figure 63,

Figure 64, Figure 65 and Figure 66. For one-wave mode, maximum observed h/λ is 6.5 using FP A.

131

Two-wave mode is observed at h/λ ≈ 3.5 for FP B and FP C. The cases with increased air injection area lack sufficient successful cases to infer a meaningful trend (Figure 67). The data available from

Ng [328] is interpolated to attain H2-Air detonation cell size at higher pressures of 2.5 bar [329]. It is to be noted that h/λ value for different air flow rates with nozzle coincide with each other (Figure

66). This implies that h/λ is highly dependent on the equivalence ratio and does not depend on the air flow rate when the RDC exit is choked through the convergent nozzle. Assuming atmospheric exit conditions, it is established that the exit flow is choked for 0.3 kg/s, 0.4 kg/s and 0.5 kg/s. It is theorized that for RDC operation with a choked exit, there is a distinct relationship between fill height, cell size and initial pressure. The initial pressure in the RDC annulus increases due to back- pressurization, which in turn lowers the fill height of the fresh reactants. But due to the higher pressure, the detonation cell size reduces, hence maintaining a relatively constant h/λ value at different flow rates with the same Φ. It is to be noted that the current h/λ estimates are in slight contrast to the values obtained by Bykovskii et al [27]. They obtained h/λ ranging between 7 and 17

(12 ± 5). It is possible that the assumption of a constant cell size in an RDC underestimates h/λ, since Hishida et al. [106] determined computationally that the detonation cell size is notably reduced near the injection region due to the triple shock structures colliding with the RDC headwall.

Figure 63 Number of detonation cells (Φ vs. h/λ) for Fuel Plate A

132

Two- wave mode

Figure 64 Number of detonation cells (Φ vs. h/λ) for Fuel Plate B

Two- wave mode

Figure 65 Number of detonation cells (Φ vs. h/λ) for Fuel Plate C

133

Figure 66 Number of detonation cells (Φ vs. h/λ) for Fuel Plate C with nozzle integration

Figure 67 Number of detonation cells (Φ vs. h/λ) for Fuel Plate C with increased air injection

area

3.5. Pressure rise in the chamber

Pressure rise is different from the net pressure gain in a system. Pressure rise is defined as the difference between static pressure in the combustor at the end of a test (PF) and the static pressure in the combustor before detonation initiation (PI). Net pressure gain is defined as the positive difference between the static pressure at the end of the test (PF) and the upstream air plenum supply pressure (Pplenum(t)). While the current study did not produce net pressure gain,

134

considerable pressure rise is achived in the RDC. The combustion induced pressure ratio (PR) and pressure loss (PL) are calculated as follows:

PR = PF / PI (2)

PL = Pplenum(t) – PF (3)

The test cases that are run without the back-pressurizing nozzle achieved a pressure rise of not more than 0.35 bar. However, addition of a nozzle increases PR significantly (as discussed before).

The pressure within the RDC with nozzle plateaus and stabilizes at the end of the test. PF is calculated as the average of the pressure traces for t = 0.05 s before the fuel shut-off. The time period of 0.05 s is chosen as most tests stabilize at t = 0.95 s. The increment in the chamber pressure around t =1 s denotes the start of fuel injection into the combustor. PR versus fuel flow rate follows a similar trendline to the operational frequency (Figure 68). This implies that PR is dependent on Φ. PR also increases by a significant factor at higher air flow rates. The pressure loss,

PL, across the system does not exhibit any clear dependence on equivalence ratio (Figure 69). While un-choked air injection highly degrades the operability and WS performance of the RDC, a highly choked injection causes significant pressure losses. The current study does not estimate the total pressure rise during the RDC operation, which is a more prudent indicator of the effectiveness of detonative combustion. Estimation of stagnation pressure in an RDC is noted to be a complicated endeavour. Welsh et al. had attempted to quantify the stagnation pressure in an RDC flowfield [330].

However, because of the presence of considerable swirl in the chamber [37], the measured values may not be accurate. This is because, the wave orientation changes at different operating conditions

[326]. Hence, an overall stagnation pressure measurement by an obstructing pressure probe necessitates definitive knowledge of the RDC flowfield. Additionally, the presence of strong bow shocks may further alter the measured stagnation pressure. Accurate measurement of velocity,

135

temperature and mixture composition is needed to accurately characterize stagnation pressure in the RDC. In the current study, it can be commented that convergent nozzle addition causes the dynamic pressure to drop, due to a choked exit, while the static pressure increases significantly.

Figure 68 Combustion induced pressure ratio PR vs. Φ for Fuel Plate C with nozzle

integration

Figure 69 Static pressure loss across the system PL vs. Φ for Fuel Plate C with nozzle

integration

136

4. Conclusions

This study analyzes the performance of an RDC with three fuel injection schemes. Three fuel plates with equal injection area but different fuel orifice length-to-diameter ratios are studied to generate a comprehensive comparison of operating range, modes of operation, and detonation wave speed performance. All three fuel plates have similar operability except at the lean limit. The fuel plate with the highest L/D exhibits lean operation devoid of transitional or “pop-out” events. This suggests that smaller fuel orifice sizes reduce the effect of the detonation waves on fuel plenum dynamics. Further testing is conducted on this fuel plate to understand the effects of back-pressure, and decreased air mass flux through an increased air injection area which enables a nominally un- choked injection. Back pressurizing the RDC has a favorable impact on operability and extends the lean-limit operating boundary for higher flow rate cases. Increase in air injection area increases the number of pop-out events, leading to a stochastic and poor performance overall. Stable operation, without pop-out events, is contingent upon both the L/D of the fuel injection orifices and the method of air injection. The L/D of the fuel orifices and the mass flow rate determines the mode of operation of an RDC, as multiple detonation waves are preferred in the RDC for higher L/D at the highest air mass flow rate. It is hypothesized that higher L/D promotes faster recovery of the reactant fill height which may encourage multi-detonation operation. The attained detonation wave speeds are at least 80% of ideal C-J wave speed for higher flow rates of 0.4 kg/s and 0.5 kg/s, and

70% of C-J speed for 0.2 kg/s and 0.3 kg/s. Addition of a back-pressurizing nozzle enables the detonation wave to propagate in ideal C-J wave speed, thereby demonstrating the positive effect of increased initial pressure in an RDC environment. The increased air injection scheme performs poorly, exhibiting large deficits in wave speed compared to ideal C-J condition.

The fill height-detonation cell size ratio exhibits similar trend for all three fuel plates and peaks at an equivalence ratio of ≈1.2. For nozzle added cases, due to the exit flow being choked at the convergent nozzle section, there is a strong interdependence between the reactant fill height and

137

the initial chamber pressure, leading to the ratio of fill height and detonation cell size being similar for all the air flow rates for a given equivalence ratio. The convergent nozzle addition causes the static pressure in the chamber to increase by a factor of up to 2.5. The combustion induced static pressure-rise is highly dependent on the equivalence ratio and air flow rate. Significant pressure loss, of up to 1.3 bar, is recorded from the air plenum to the combustor annulus at plateaued detonation pressure. It is recommended to use air injection schemes with much lower pressure loss from the air plenum to the combustor annulus. This creates a design tradeoff between pressure loss through air injection and the desired operability and performance, as an un-choked air injection performed poorly overall.

138

CHAPTER 3: CHARACTERIZATION OF INSTABILITIES IN A ROTATING DETONATION

COMBUSTOR

Chapter Abstract

Rotating Detonation Combustor (RDC) operation is investigated under different air and fuel flow rates, and varied geometries to reveal four fundamentally different instabilities. Select test points are chosen to study these instabilities using qualitative and quantitative tools. First, for RDC operation at lean limits, or with subsonic air injection, or with large fuel injection orifices, the detonation wave inside the combustor undergoes aperiodic chaotic propagation around the combustor annulus characterized by incoherent pressure-time traces. The high incoherence in recorded pressure, along with the considerable variation in subsequent pressure peaks suggests numerous failure and re-initiation of the detonation wave. Second, almost all operating points at the variety of conditions tested exhibit some degree of low frequency sinusoidal oscillations characterized by periodic waxing and waning of subsequent detonation peak pressures. It occurs between 200 Hz and 500 Hz for the operating maps studied. Third, the phenomenon of mode switching in the RDC is also defined as instability since the sudden change in the number of detonation waves existing in the combustor is temporally unpredictable, and often unpredictable for a given geometry. It is found that RDC operation is more stable when there are multiple detonation waves inside the chamber. With a back-pressurizing convergent nozzle, at certain operating points, the RDC exhibits axisymmetric pulsed operation like the Pulsed Detonation

Combustor (PDC). There is significant evidence to suggest that these longitudinal pulsed detonations (LPD) are manifested due to shock-reflection from the RDC exit followed by a subsequent shock-initiation of the fresh reactants. The frequency of this instability is around 3.8 kHz for the test case investigated.

139

Nomenclature f - frequency (Hz) t - time (s)

Ws - wave speed (m/s)

Φ - equivalence ratio

ṁ - air flow rate (kg/s)

1. Introduction

The use of detonation as the primary combustion mechanism in combustors and stand- alone engines is theoretically promulgated to enable higher combustion efficiency and work output when compared to traditional Brayton-cycle combustors [320]. Detonation is a supersonic combustion phenomenon characterized by the coupling of a shock wave with the reaction front behind it. The property of a detonation wave to produce pressure rise across the combustion front is the main motivation behind the research on combustors utilizing detonation instead of deflagration. Detonation combustors are further broadly classified into Pulsed Detonation

Combustors (PDC) and Rotating Detonation Combustors (RDC). The operating frequency of the

PDCs can extend up to 100 Hz [2], and is often limited by the cyclic ignition and valving requirements, since reactants filling, ignition and the subsequent purging are to be repeated every cycle. This produces very high mechanical complexity, which when added to the large dimensions of a PDC tube (due to the length required to enable DDT) [82] does not bode well for effortless integration with a gas-turbine engine. An RDC on the other hand, is characterized by its relatively smaller size with a much higher power density and the quasi-steady exit flow which is in contrast

140

with the highly pulsating pressure profile attained at the PDC exit [4]. The RDC also necessitates continuous fuel and oxidizer injection that are combusted by an azimuthally propagating rotating detonation wave with the operating frequency at least an order of magnitude higher than that of the PDC. These attributes of the RDC have re-oriented research efforts from PDC to RDC. Over the last half-century, considerable research has been performed on various facets of the RDC. Different combustor designs have been tested [27]. Several numerical studies [104,168,219] have studied the effects of the detonation wave on the injector orifices and determined that the detonation wave forces the injection to be locally un-choked. Different RDC operating modes, like single wave and dual wave propagation, have also been discussed both experimentally [5,8,17-19] and numerically

[20-22]. However, the issue of various combustion instabilities in an RDC has not yet taken center stage.

At certain conditions the pressure-time trace breaks down into complete incoherence [127], and may indicate sporadic failure and subsequent re-ignition of the detonation wave inside the combustor annulus. Periodic “bursting”, where the detonation is initiated and extinguished alternatively, probably by a low speed deflagration flame or flame-holding inside the combustor, has also been recorded by prior studies [149]. Besides this, the other modes of off-design operation detailed in Chapter 1 can be considered to be unstable operations. While the above-mentioned instabilities are unique in their manifestation and behavior from each other, they have been amalgamated under the broad canopy of “instabilities”, hitherto. Thus, the primary aim of the current study is to qualitatively and quantitatively segregate all the different types of instabilities in an RDC. Results from RDC hot-fire tests using hydrogen-air mixtures are used to characterize the instabilities seen in an RDC to date. Commentary is provided along with each instability type to relate to studies that have previously observed them.

141

2. Experimental methodology

The current paper utilizes data collected from RDC testing using H2-air mixtures for varied flow rates, equivalence ratios, geometry and back-pressures. The RDC facility (Figure 70) is part of the

Gas Dynamics and Propulsion Laboratory at the University of Cincinnati (UC). The highly modular

RDC (based on [151]) can be easily re-arranged to have different fuel injection schemes, nominally choked/ completely subsonic air injection, and back-pressure by utilizing a convergent nozzle [43].

A schematic of the RDC geometry is given in Figure 71. Increasing the thickness of the oxidizer spacer increases the pressure ratio across the air injection, and vice versa. The fuel plate can be similarly changed to attain different fuel injection schemes, while the combustor annulus width can be altered by varying the diameter of the center body. Fuel is injected axially into the combustor annulus through the fuel plate having an annular arrangement of orifices, and the air is injected radially inward as shown in Figure 72. The dimensions of the RDC are given in Table 6. Detonation is initiated in the combustor annulus through DDT attained by introducing an overdriven detonation wave from the pre-detonator, which is an ethylene-oxygen tributary [156]. Both high- speed (1 MHz sampling rate) and low-speed (1 kHz sampling rate) data acquisition is used for the study. Since the current paper involves data collected from different test campaigns at chronologically varied periods, different instrumentation schemes were utilized for the acquired high-speed data. The two different schemes are: 1) one piezoresistive Kulite pressure sensor in station 3, row 4 (see Figure 73 for the instrumentation schematic), and 2) three piezoelectric PCB sensors in the three stations in row 1 of the RDC. It is to be noted that piezoresistive sensors measure the static pressure while piezoelectric sensors measure only the dynamic fluctuating component of pressure. The low-speed data acquisition is composed solely of two Capillary Tube

Averaged Pressure (CTAP) sensors with one CTAP sensor in the air plenum and one in the combustor. An injection pressure ratio of > 1.89 (obtained from the ratio of specific heat capacities for air), produces a nominally (since the air inlet is locally unchoked due to the detonation wave

142

passage [104,168,219]) choked air injection while <1.89 causes subsonic injection of air into the combustor.

Figure 70 UC RDC Facility

Figure 71 Schematic of the RDC geometry

143

Figure 72 Schematic of the RDC injection method

Table 6 RDC geometry dimensions

Part Geometry Dimension

Measured

Fuel injection orifice Length/diameter 17.0

Oxidizer Spacer Air injection area 490 mm2

Combustor Channel Width of channel 7.6 mm

Inner Diameter 139 mm

Outer Diameter 154 mm

Annulus area 3500 mm2

Converging Nozzle Exit area 760 mm2

144

PCB Sensor Kulite Sensor

Figure 73 RDC instrumentation schematic

Nominal operating maps are provided using data from Chapter 2, and the regime of occurrence of instabilities is distinguished from the stable regime using colored demarcation.

Pressure-time traces and detonation wave speed (Ws) plots of the propagating detonation wave are used to qualitatively discuss the different instabilities. The Ws is acquired using a novel time-of- flight peak-tracking algorithm. A flowchart depicting the algorithm is shown in Figure 74. It is to be noted that the first four steps have been used by other researchers to attain the pressure value corresponding to the detonation propagation [256,327]. However, as will be discussed in later sections of the paper, instabilities in the RDC tend to have a prominent effect on the Ws plot, and thus the average value of detonation Ws attained by the first four steps could be skewed. In order to predict the actual detonation Ws it is thus necessary to use an algorithm that can differentiate between an actual lap of the detonation wave and random pressure peaks caused by strong instabilities in the combustor. This is enabled by collecting the estimated speed of three subsequent detonation peaks and checking if they fall within 10% of each other. This grouping of three continuous detonation pressure peaks together filters the actual physical detonation wave lap from the non-physical artifact produced due to the previously used algorithm, thereby arriving at a better estimate of the average speed of the detonation wave for a given test point. An example of the peak-tracking performed by the algorithm is shown for a stable RDC operating case in Figure

145

75, with the threshold pressure value shown as a blue line. Pressure traces produced by the unstable detonation wave propagation are inherently non-stationary, i.e. they evolve over time.

Hence, in addition to frequency analysis using Fast-Fourier Transform (FFT), study of frequency in time domain is employed to study the non-stationary signal.

Figure 74 Flowchart showing Ws algorithm

146

Figure 75 Stable pressure time trace with the detonation peaks showing in red

3. Results and Discussion -Types of RDC instability

3.1. Chaotic instability

Detonation wave propagation at certain conditions, like the lean operating boundary

(shown by orange area in Figure 76) produces extremely incoherent, chaotic pressure-time traces inside the annulus. Figure 77 shows the pressure-time trace for the RDC operation with choked air injection, near the lean limit, for 0.3 kg/s. While the pressure suggests the presence of a detonation wave inside the combustor, the lack of repeatability of pressure profiles and the vastly differing subsequent detonation Ws (Figure 78) suggest the disintegration of the detonation wave into a deflagration wave, and a subsequent DDT mechanism into a detonation wave again. Kindracki et al.

[127] have proposed a similar mechanism of “small detonation wavelets propagating chaotically and eventually transitioning to deflagration” and attributed it to substandard mixing. The difference in pressure trace between the unstable case (Figure 77) and the stable case (Figure 75), and its associated implication in determining the Ws can be readily observed. For instance, if the minimum pressure threshold is set to 1.3 bar, the two detonation peaks shown by the red and blue arrow will be fallaciously considered to be an actual detonation lap, while it is apparent that there is period of considerable chaos in between the two peaks. This renders a wave speed calculation which is greater than Chapman-Jouguet wave speed. The previously explained algorithm helps to filter out these fallacious Ws (denoted by orange bracket in Figure 78) due to the presence of strong

147

chaotic instability, and estimates the actual detonation Ws to be ≈ 1.2 km/s, on an average. If the incorrect values had been amalgamated with the actual detonation Ws, the resulting Ws approximation for a given test point becomes highly skewed depending on the intensity of the instability.

Because of the high aperiodicity, the FFT does not reveal a clear fundamental frequency

(Figure 79). The spectrogram also reveals highly time-varying fluctuations in frequency (Figure

80). It is to be noted that this instability is also observed for RDC operation with subsonic air injection and large fuel injection orifices. Figure 81 shows the pressure-time trace for an RDC test case with subsonic air injection. Additionally, when the fuel plate is changed to mimic the injection scheme (lesser number of orifices with a much larger area) used by Shank et al. [151], the pressure trace is found to exhibit the trademark chaos. Thus this instability is occurrent for: 1) lean equivalence ratios, 2) low air injection pressure ratios, and 3) large fuel injection orifices. Schwer and Kailasanath [171] have established that the pressure feedback from the detonation wave affects larger reactant injection orifices more. Lower air flow rates (and hence lower injection pressure ratios) are more susceptible to experiencing higher pressure feedback from the detonation wave [246], a logical extension of which is that subsonic air injection predicates improper reactants mixing. Moreover, the fuel and air plenums have different injection pressure ratios. As a result, the plenum recovery time after detonation propagation may be different for the fuel and air injection [128,181]. This could promote stratified mixing of fuel and air, “particularly during lean operation” [181], after the respective plenum’s recovery which may once again cause improper mixing, thereby leading to periodic failure and re-initiation of the detonation wave. Since this instability only occurs for the above-mentioned three RDC operating conditions, it is concluded that this instability may be the result of improper mixing engendered by differential fuel and air plenum recovery after subsequent detonation wave passage. Thus, it could be theorized that having

148

a higher number of injection orifices while maintaining the total injection area constant can reduce the prominence of chaotic instability.

Figure 76 Nominal operating map showing regime of chaotic instability

Figure 77 Pressure-time trace, ṁ = 0.3 kg/s, Φ = 0.786

149

Figure 78 Ws plot, ṁ = 0.3 kg/s, Φ = 0.786

Figure 79 FFT plot, ṁ = 0.3 kg/s, Φ = 0.786

Figure 80 Spectrogram plot, ṁ = 0.3 kg/s, Φ = 0.786

150

Figure 81 Pressure-time trace, ṁ = 0.3 kg/s, Φ = 0.986, Subsonic air injection

3.2. Waxing and waning (low frequency oscillation) instability

Low frequency oscillations occur for most of the operating points tested (Figure 82). These oscillations are identified by periodic waxing and waning in strength of the continuously propagating detonation wave as measured by the peak pressure (Figure 83). This type of detonation instability has been discussed previously in [142,251,331]. Each period of the sinusoidal base oscillation can be considered as a “detonation wave packet,” containing numerous consecutive cycles (with a median lap number of around 10) of rotating detonation [251]. The detonation wave packet sometimes concludes with a breakdown of the wave structure and a period of incoherent pressure evolution (Figure 83) similar to the previously discussed chaotic instability.

The frequency of the waxing and waning did not have any distinct trend with equivalence ratio, air flow rate or fuel orifice area [251]. Refs [251,331] hypothesized that the waxing and waning may be due to a period of increasing occlusion, followed by a period of subsequent unblocking of fuel injectors, both of which is locked in a cyclic loop with the detonation wave. However, recent study by the authors discovered a low frequency oscillation of similar magnitude in the RDC air inlet which centered around 235 Hz, irrespective of the air flow rate or the equivalence ratio [246]. It was postulated that the sinusoidal oscillation in the air inlet is due to Helmholtz resonance in the air plenum, instigated by the rotating detonation wave [246]. This Helmholtz resonance may cause notable fluctuation in the air supply to the RDC, which in turn could be the reason behind the

151

waxing and waning instability in the combustor due to the periodic change in detonation wave strength. Note that this instability is predominantly observed only for nominally choked air injection.

This instability type can also be identified using the Ws plot (Figure 84). Because of periodic incoherence of smaller pressure (which are lower than the previously discussed threshold value in the algorithm) between subsequent detonation packets, this instability manifests itself as a secondary, non-physical, lower velocity band in the Ws plot (red arrow). It can, once again, be seen that the algorithm is efficient in segregating actual detonation Ws from the artifacts produced by instabilities. In Figure 85, the FFT reveals heightened activity at f ≈ 3.2 kHz and ≈ 6.2 kHz. The sinusoidal oscillations are discernible in the FFT plot at f ≈ fundamental frequency - 500 Hz (orange arrow) because of the smaller magnitude of fluctuation when compared to the detonation pressure magnitudes. This instability is, once again, difficult to locate in the spectrogram (Figure 86) because of the low amplitude associated with it. The pressure time-traces obtained from PCB sensors in the air inlet and the combustor for an arbitrary test case from [246] is shown in Figure 87 and Figure

88. The magnitude of the low frequency oscillation is considerably higher in the air inlet in comparison to the combustor, which lends support to the contention that this instability may be caused by resonance in the air inlet. Interestingly, Yusi et al. [142] and Wang et al. [331] observed the same instability in their RDC that used axial oxidizer injection which leads to the conclusion that this instability is injection style-independent.

152

Figure 82 Nominal operating map showing regime of waxing and waning instability

Figure 83 Pressure-time trace, ṁ = 0.3 kg/s, equivalence ratio, Φ = 1.84

153

Figure 84 Ws plot, ṁ = 0.3 kg/s, equivalence ratio, Φ = 1.84

Figure 85 FFT plot, ṁ = 0.3 kg/s, equivalence ratio, Φ = 1.84

Figure 86 Spectrogram plot, ṁ = 0.3 kg/s, equivalence ratio, Φ = 1.84

Figure 87 Pressure-time trace, Air Inlet, ṁ = 0.4 kg/s, equivalence ratio, Φ = 0.997

154

Figure 88 Pressure-time trace, Combustor, ṁ = 0.4 kg/s, equivalence ratio, Φ = 0.997

3.3 Mode switching

An instantaneous change from one operating mode to another (defined by the number of detonation waves in the chamber) has been recorded before by many prior studies, although the reason behind such a transient shift is still unknown [27,43,256,257,322]. However, it has been possible for researchers to predict the general regime of multiple detonation waves occurrence.

Traditionally, higher mixture mass flux tends to support multiple detonation waves simultaneously inside the combustor, whereas lower air flow rates tend to support only one detonation wave

[27,256,332]. Additionally, smaller fuel orifice area [43] and smaller channel width (and hence higher mass flux) also supports multiple detonation waves inside the combustor. While the modes

(one, two or multiple detonation waves) themselves may be highly stable, the actual switching from one mode to another (and back) rather abruptly at the same test points suggests the presence of a strong instability associated with certain RDC operating regions. For instance, in the current study, there is always an instantaneous mode shift from one to two waves only at 0.5 kg/s (Figure 89). It is postulated in [43,276] that there is a critical fill height (dependent on mass flux) which determines the number of detonation waves in the combustor. A pressure-time trace of an operating point with this transient instability of mode switching is shown in Figure 90, along with the magnified trace in

155

Figure 91. It can be seen that the RDC operates with one wave initially, and instantaneously transitions to two detonation wave operation at t ~ 0.67 second.

Additionally, it can also be established from the figure that the pressure of the detonation in the chamber is much higher for one wave mode, as opposed to the two wave mode. In fact, when there are two waves in the chamber, the pressure of the two individual waves are almost half that of the single detonation in one wave mode. A similar finding is discussed in [257]. This can be construed as a physical homeostasis peculiar to RDCs where the magnitude of pressure of each detonation wave in the system varies depending on the number of detonation waves in the system at any given moment. The associated Ws plot (Figure 92) also detects the sudden shift from one to two waves. For the first 3000 laps the RDC houses one detonation wave (black circle) which suddenly disintegrates into two waves and executes another 2000 laps, on aggregate. Since the algorithm inherently subtracts the time indices of subsequent detonation wave peaks, two wave

(blue circle) mode renders a calculated Ws of around 3.2 km/s. This is to be interpreted as two waves propagating at 1.6 km/s each. The red circles are the miscellaneous peak pressures which are not considered a detonation lap by the anterior algorithm. The algorithm with the previously explained “grouping” of subsequent speed values indicates that there are brief periods of two wave activity interspersed with the initial predominantly one wave activity, as inferred by the presence of multiple blue circles (denoted by black arrow) within the first 3000 laps. The pressure-time series and the Ws plot qualitatively suggest the presence of the chaotic instability during one wave operation. However, once transitioned to two waves, the RDC seems to exhibit highly repeatable

Ws. The FFT plot shown in Figure 93 indicates two dominant frequencies: a very distributed one wave activity (f ~ 3.8 kHz), and highly regular two wave activity (f ~ 7 kHz). These frequencies are related to the modes based on the current RDC annulus dimensions. It takes ~ 285 microseconds for a single detonation wave to circumscribe the annulus once. Multiple wave mode also exhibits very high stability in comparison to the lower wave modes as seen in the spectrogram (Figure 94).

156

Suchoki et al. [256] also arrived at the same finding. After the onset of two detonation waves, there is almost no activity in other frequency ranges, suggesting multiple detonation waves may be the preferred RDC operation owing to reduced disruption of the air and fuel supply because of lower pressure of the individual waves.

Figure 89 Nominal operating map showing regime of mode-switching instability

Figure 90 Pressure-time trace, ṁ = 0.5 kg/s, equivalence ratio, Φ = 0.981

157

Figure 91 Pressure-time trace-enlarged, ṁ = 0.5 kg/s, equivalence ratio, Φ = 0.981

Figure 92 Ws plot, ṁ = 0.5 kg/s, equivalence ratio, Φ = 0.981

Figure 93 FFT plot, ṁ = 0.5 kg/s, equivalence ratio, Φ = 0.981

158

Figure 94 Spectrogram plot, ṁ = 0.5 kg/s, equivalence ratio, Φ = 0.981

3.4 Longitudinal Pulsed Detonation instability

This instability is characterized by azimuthally simultaneous, pulsed, high-amplitude pressure fluctuations (of same magnitude as the rotating detonation wave) of high frequency (f ~

3.8 kHz, in this study) in the RDC chamber. Hence, it is imperative to have azimuthally distributed sensors to distinguish this instability from the traditional rotating detonation. Longitudinal Pulsed

Detonation (LPD) is an intriguing instability in an RDC. Bykovskii et al. [27,174,276] have made remarks of certain operating points where the pressure oscillations inside the RDC are axial, rather than azimuthal. Both Bykovskii et al. and Frolov et al. [322] have noticed the occurrence of LPD for

RDC operation with an increased air injection area, and hence presumptively subsonic injection.

LPD may occur in conjunction with the mode switching instability where there is an abrupt shift from the normal rotating detonation wave propagation to the longitudinal pulsed mode. LPD also occurs with the waxing and waning instability, at certain conditions, where the pulsed detonations seem to exhibit a periodic, low-frequency, basal oscillation. Figure 95 shows the nominal operating map from the current study and Chapter 5, with the LPD regime shown in blue.

This regime only occurred for tests with a converging nozzle at the RDC exit. The pressure-time trace of the three circumferential PCB sensors is shown in Figure 96. The magnified trace (Figure

97) shows the peculiar simultaneous azimuthal pulsing more clearly. Both the FFT plot (Figure 98)

159

and the spectrogram (Figure 99) showcase the very high steadiness of LPD after onset by the continuous fixed pulsation at f ≈ 3.8 kHz. Axial distribution of pressure sensors shed more light on the mechanism behind this instability. Four PCB sensors are instrumented from near the headwall to the RDC exit in rows #1-4 of station 1. Pressure time-traces from an arbitrary test point exhibiting the two cycles of the pulsed detonations is shown in Figure 100. Two facets can be readily observed: 1) there is a definitive strong pressure wave moving from the headwall of the

RDC (as suggested by the very high pressure peak at t ≈0.20565 s) to the RDC exit (seen by the gradual decrease in the strength of the initial pressure wave from the headwall to the exit), and 2)

The presumably reflected shock waves from the exit move with lesser than 50% speed (for the first cycle the reflected wave starts at t ≈ 0.20574 s and ends at t ≈ 0.20585 s) of the forward travelling wave (starts at t ≈ 0.20565 s and ends at t ≈ 0.2057 s). This behavior of the faster travelling forward wave (with greater than 80% Chapman-Jouguet ideal velocity for H2-Air mixtures, which is significantly greater than the speed of Mach waves) and the slower moving reflected wave (about

30% of the C-J value) strongly suggests a mechanism that starts with a strong detonation event which is followed by the axially moving detonation wave being reflected from the converging nozzle at the RDC exit. After reflection, the detonation seems to have decoupled into a shock wave and a combustion front, thereby leading to a large C-J deficit in the recorded wave speed. But, this decoupled shock wave is of sufficient strength to shock-initiate the fresh reactants that it meets at the RDC headwall, causing a detonation once again. Hence, the LPD instability is sustained continuously without an external ignition source. Thus, the reason behind the apparent similarity in the frequency of operation between the normal rotating detonation (refer Section 3.2) and the pulsed detonation can be explained by the notable difference in the propagation speeds of the faster forward moving wave and the slower reflected wave from the RDC exit, both of which constitute a single cycle of LPD. LPD frequency is dependent on the RDC axial length. Although LPD is an instability by definition of what an RDC is, once established, this mode seems to be highly regular.

160

In a sense, the Rotating Detonation Combustor operation with the longitudinal pulsed detonation instability can be envisaged to be the fastest (in terms of operating frequency) and the only truly valve-less Pulsed Detonation Combustor ever conceived or designed. It remains to be researched, however, if the frequency, magnitude and regime of occurrence of LPD are propitious or pernicious to the imagined applications of RDCs, specifically the integration of RDC with turbine, which is a back-pressurizing device by function.

Figure 95 Nominal operating map with back-pressurization showing regime of LPD

instability

Figure 96 Pressure-time trace-enlarged, ṁ = 0.4 kg/s, equivalence ratio, Φ = 0.78

161

Figure 97 Pressure-time trace-enlarged, ṁ = 0.4 kg/s, equivalence ratio, Φ = 0.78

Figure 98 FFT plot, ṁ = 0.4 kg/s, equivalence ratio, Φ = 0.78

Figure 99 DWT plot, ṁ = 0.4 kg/s, equivalence ratio,

Φ = 0.78

162

Axial #1 Axial #2 Axial #3 Axial #4

Figure 100 Axial pressure profile during pulsed detonation in the RDC, ṁa = 0.3 kg/s and Φ =

1.03

4. Conclusions

Rotating Detonation Combustor operation is tested for hydrogen-air mixtures at a variety of conditions, including equivalence ratio, air flow rate, back-pressurization, different air and fuel injection schemes, and four fundamentally dissimilar instabilities are identified and the probable mechanisms discussed. While the different instabilities seem to be functionally independent of each other, it is observed that they can occur in tandem at certain operating conditions. Chaotic instability is the first instability type identified. It is characterized by a highly fluctuating and random pressure-time trace signature and occurs at three conditions, namely: 1) lean operating boundary of the RDC for a given configuration, 2) lower air injection pressure ratio, and 3) larger fuel injection orifices. From the conditions of occurrence, Ws analysis and comments from literature, this instability is suggested to be a sole function of sub-par mixing of the reactants, brought about by the unequal fuel and air plenum recovery after the disturbance imparted by the detonation wave in the combustor. It could be construed that control of this instability necessitates the design of the reactants plenums such that the respective stagnation pressure in the plenums enable similar recovery times for both the fuel and the air, thereby producing proper mixing. The second instability is distinguished by a periodic, low-frequency, waxing and waning of subsequent peak detonation wave pressures and is found to occur for most of the geometries, at a variety of the

163

flow rates tested. Further studies are required to precisely diagnose the cause of this instability.

However, with the current knowledge, it is likely that this instability in the combustor is caused due to a low frequency oscillation in the air inlet, which in turn may be generated by Helmholtz resonance instigated in the air inlet by the rotating detonation wave.

Sudden, transient mode switching in the RDC is distinguished as the third instability. The exact mechanism behind the instantaneous permutation of the number of detonation waves in the combustor annulus is still unclear. But this study reinforces a previous finding that higher number of detonation waves augurs for better overall stability in the RDC. Visualization, by means of high speed video recording of the RDC aft-end, and a transparent combustor outer-wall is necessary to lend support to previous hypotheses from the literature that higher reactants fill height produces multiple detonation wave activity. Finally, the oft-overlooked, intriguing mechanism of pulsed detonations in the continuous detonation RDC is discussed, and classified as instability. Subsonic air injection is postulated as the primary mechanism behind the inception of LPD, whereas backpressure is speculated to be a secondary, driving mechanism. The magnitude and frequency of the pulsed detonations are very similar to the rotating detonation under the particular backpressurized conditions, leading to the conclusion that an RDC operating with the pulsed detonation instability is the fastest PDC ever observed. Significant research is required to arrive at rigid theories on the mechanism of this instability.

164

CHAPTER 4: ANALYSIS OF AIR INLET AND FUEL PLENUM BEHAVIOR IN A ROTATING

DETONATION COMBUSTOR

Chapter Abstract

The behavior of the oxidizer inlet and the fuel injection plenums during the operation of a Rotating

Detonation Combustor (RDC) is studied using pressure sensors in the air injection gap, the fuel plenum, and in the combustor. Significant pressure feedback from the rotating detonation wave is observed in the air injection gap. Pressure feedback into the fuel plenum is relatively weaker. The average normalized cross-correlation between the pressure-time series in the air injection gap and within the combustor is greater than 0.3. The air injection gap has a considerable base sinusoidal oscillation in the same frequency range as a previously discovered waxing-and-waning instability in the combustor. The fundamental frequency in the air injection gap is the same as the RDC operation frequency for almost all test cases, indicating the high efficacy of the sensors in the air inlet to attain the operating frequency. Frequency analysis reveals notable spatial variation in the fuel plenum dynamics. The low frequency oscillation in the air injection gap is found to be constant at 235 (+/-

2.5) Hz for all the air flow rates and equivalence ratios tested.

Nomenclature f frequency (Hz)

Φ equivalence ratio t Time

R Normalized cross-correlation x arbitrary first pressure-time series (bar)

165

y arbitrary second pressure-time series (bar) n sample number

N maximum number of samples in a time series

PC averaged combustor pressure during operation

PA averaged air plenum pressure during operation (bar)

PF averaged fuel plenum pressure during operation (bar)

PRA air injection pressure ratio during operation

PRF fuel injection pressure ratio during operation ff fundamental frequency (Hz)

σ standard deviation

1. Introduction

Detonation is a supersonic combustion wave distinguished by the coupling between a shock wave with the exothermic reaction zone behind it. This is in contrast to a deflagration wave which only travels at subsonic speeds. Across a detonation wave there is always a pressure rise due to the presence of the shock wave, while a deflagration wave always produces a slight pressure loss across it. This property of a detonation to produce an increase in pressure renders it useful in detonation combustors due to the theoretical increase in thermal efficiency that can be achieved

[320]. Detonation combustors are mainly classified into Pulsed Detonation Combustors (PDC) and

Rotating Detonation Combustors (RDC). RDCs are relatively more compact in size, and mechanically simpler than a PDC. Additionally, unlike PDCs, RDCs do not require valving to inject the fuel and the oxidizer. The reactant supply is continuous, and is combusted by an azimuthally travelling detonation wave inside the combustor. By virtue of the high frequency rotating detonation and the relatively lower pressure amplitude, the exit flow of an RDC is quasi-steady and

166

hence more amenable to turbine-integration, as opposed to the PDC which produces large fluctuations in pressure at the exit [4].

The above-mentioned advantages of an RDC over a PDC have been responsible for the increased scientific interest in an RDC in recent years. However, comparatively, the RDC is less developed than the PDC technologically, and there are significant facets of RDC operation that are yet to be investigated. Of considerable interest is the effect of the rotating detonation waves on the air and the fuel plenum. Numerical simulations by Schwer and Kailasanath [171] determined the presence of pressure feedback into the mixture plenum by the detonation wave, but mass feedback was not observed. Mixture plenum dynamics was found to be minimally affected by the height of the plenum. Fotia et al. [184] used shadowgraph in a two-dimensional RDC analogue to observe the effect of a detonation wave on the fuel plenum. Significant pressure feedback was observed from the detonation wave into the fuel plenum which was sufficient to temporarily disturb the fuel plenum dynamics by 200 microseconds. In addition to the original pressure wave manifested due to the detonation wave propagation, secondary pressure waves were also found to occur in the opposite direction in the two-dimensional setup. It was postulated that in an actual RDC, these secondary reflected pressure waves may cause significant interactions with the next detonation lap.

Naples et al. [291] estimated the fuel injection velocity in an RDC by utilizing hot film anemometers and observed a noticeable decrease in velocity as the detonation wave passed through, indicating periodic local un-choking of the fuel supply by the detonation. While these studies confirm the pressure feedback exerted by the detonation on the fuel injection plenum, the three-dimensional spatial variation in fuel plenum dynamics has not been investigated. Rankin et al. [333] used pressure sensors in the air plenum to determine that higher air injection pressure ratios caused lower periodic pressure fluctuations in the plenum by the detonation wave. However, since the effect of the detonation wave would be lesser in the air plenum when compared to the actual air

167

injection gap, a better understanding of the detonation pressure feedback can be attained by instrumenting the actual air inlet.

In this study, the pressure feedback by the detonation wave on the air injection gap, instead of the air plenum, is studied using three azimuthally-distributed piezoelectric sensors in the air inlet.

Directly flush-mounted pressure sensors are prone to permanent failure due to the very high- temperature RDC environment [43], and hence recent research has concentrated on using Infinite

Tube Pressure (ITP) [43,334] setups to evaluate the RDC operation. Hence, the sensors in the air inlet are also investigated for their efficacy in determining the RDC operating frequency. Three pressure sensors are also integrated into the fuel plenum to analyze the spatial variation in fuel plenum dynamics. In addition to the sensors in the air injection gap and the fuel plenum, the combustor annulus is also instrumented with three flush-mounted pressure sensors to evaluate the correlation between the sensors in different locations.

2. Experimental methodology

The current study utilizes data collected from hydrogen-air RDC tests performed at the Gas

Dynamics and Propulsion Laboratory (GDPL) at the University of Cincinnati. The facility is shown in

Figure 101. The modular RDC has radially inward air-injection and axial fuel injection (Figure 102).

Ignition is achieved with a pre-detonator tube filled with ethylene and oxygen [156], which exhausts tangentially into the annulus. Detonation develops briefly after the ignition event through a Deflagration-to-Detonation transition (DDT) mechanism. The air injection width and the fuel injection scheme are varied with interchangeable combustor components. A detailed description of the different fuel injection schemes are dealt with in Chapter 2. For this study, the fuel plate with the highest number of orifices is used. The combustor and air plenum are instrumented with a

Capillary Tube Averaged Pressure (CTAP) sensor setup [323,335] to estimate the injection pressure drop from the air and fuel plenum to the RDC combustion annulus. A total of 9 PCB pressure

168

sensors are instrumented in the RDC with a data acquisition rate of 1 MHz. The facility (Figure 101) is described in detail by St. George et al. [323].

Figure 101 RDC facility at University of Cincinnati

The general location of the piezoelectric sensor in the air injection gap (blue) and the fuel plenum (violet) is shown in Figure 102. A schematic of the RDC instrumentation ports is given in

Figure 103. The combustor has 3 PCB (red) sensors (1, 2 and 3), separated by 120o and flush- mounted in the three stations in the first row of instrumentation port. To analyze the pressure feedback into the air inlet, 3 PCB sensors (4, 5 and 6) are instrumented in the air injection gap, ≈

2.54 cm from the combustor. To study fuel plenum dynamics, 3 more PCB sensors (7, 8 and 9) are integrated at the base of the plenum (Figure 103). The individual air inlet and fuel plenum PCB sensors are displaced by approximately 21o from the corresponding flush-mounted combustor PCB sensor (Figure 103). Finally, a CTAP pressure sensor (orange circle) is placed in station 3, row 4

(Figure 103) to get absolute pressure variations.

169

Figure 102 RDC schematic with the injection scheme

Figure 103 RDC instrumentation schematic

The air flow rates and equivalence ratios tested are given in Table 7. In the remainder of the paper, individual tests will be denoted by the test number. For instance, test number II-B denotes an air flow rate of 0.3 kg/s and an equivalence ratio of Φ = 1.03. All testing is limited to t ≈ 0.3 second (hence a frequency resolution of 2.5 Hz) to avoid damage to the flush-mounted sensors due to prolonged exposure to the high temperature, high pressure environment. In addition to the qualitative study of the pressure-time traces, Fast-Fourier Transformation (FFT) is used to study

170

the frequency of pressure feedback into the air inlet and fuel plenum. Cross-correlation is also used to estimate the similarity of the pressure-time series obtained from sensors in different locations.

Table 7 Test Matrix

Series Air flow rate, kg/s Equivalence ratios, Φ

A B C

I 0.2 0.874 1.0 1.21

II 0.3 0.871 1.03 1.22

III 0.4 0.917 0.997 1.2

3. Results and Discussion

3.1. Pressure feedback into the air inlet and fuel plenum

A study of the pressure feedback into the air injection gap and the fuel plenum can be done by juxtaposing the pressure-time trace with the associated flush-mounted combustor sensors. Figure

104 shows the pressure-time traces in the flush mounted PCB sensor, air gap sensor, and the fuel plenum sensor respectively, for an arbitrary time interval for tests I-B and III-B. Figure 104a and

Figure 104b shows the similarity between pressure magnitude (for test I-B) seen in the flush mount due to the detonation wave and the magnitude of pressure feedback experienced by the air injection gap area due to the detonation wave in the combustor. It is to be noted that the reason behind the apparent higher pressure in the air inlet when compared to the combustor at certain time instances is due to the inherent property of the piezoelectric sensors to only record dynamics pressures while neglecting the steady component. The air inlet exhibits sinusoidal low-frequency pressure oscillations of significant magnitude (up to 0.5 bar fluctuation in Figure 104b). For the same test point, the fuel plenum sensors record relatively lower pressure fluctuations, not

171

exceeding 0.2 bar. This highlights the heightened impact of the detonation wave on the air inlet in comparison to the fuel plenum. Test III-B exhibits similar trends in pressure-time traces for the fuel plenum (Figure 104f). While the pressure oscillations exceed to 0.4 bar now, they are consistently below the pressure fluctuations in the air inlet which extend up to 1 bar (Figure 104e) for the 0.4 kg/s case. Figure 104e shows the pressure-time trace at the air inlet and once again there are significant sinusoidal oscillations with frequency close to the prior condition, at f ≈ 230 Hz.

Two features can be inferred about RDC operation from the above discussion. One, the air inlet experiences much higher pressure feedback when compared to the fuel plenum. Two, there is a strong low-frequency oscillation in the air inlet, even when the combustor has almost no oscillation at the same time.

(a) (d)

(b) (e)

172

Figure 104 Pressure-time traces of sensors 3 and 6 for I-B (left) and III-B (right)

3.2. Correlation of pressure-time traces

The prior section is instrumental in deciphering easily observable trends in the pressure-time series. However, to get at the general pattern of air inlet and fuel plenum behavior at different air flow rates and equivalence ratios the method of cross-correlating the individual sensors with the respective flush-mounted combustor sensors is done using the following equation:

푁−1 ∑푛=0 푥[푛] 푦[푛] R푥,푦 = 푁−1 2 푁−1 2 (1) √(∑푛=0 푥 [푛] ∑푛=0 푦 [푛])

Here, 푥[푛]and 푦[푛] are the pressure-time series from the combustor sensors and the air inlet/ fuel plenum sensors respectively, each having n discrete samples, amounting to a maximum number of N. Figure 105a shows a plot of the cross-correlation between sensors 3 and 6, for test III-

C. It is a known fact that cross-correlation peaks when the two signals under consideration are identical to each other which is the case when one directly influences the other. Hence, from Figure

105b, since the correlation coefficient is maximum at time, t ≈ 119 μs, it implies an almost instantaneously pressure feedback from the detonation wave into the air inlet.

173

(a) (b)

Figure 105 Cross-correlation plot of sensors 3 and 6 for test III-C (a) and magnified plot

(b)

A typical pressure trace from the CTAP sensor in the air and fuel plenum, and the combustor before and during RDC operation is shown in Figure 106. The air supply (green line) is continuous, but the fuel supply (blue line) starts only at time t ≈ -1.7 s. Ignition from the pre-detonator is initiated at t = 0 s, and the increase in pressure in the combustor during operation can be seen (red line). The combustor pressure during operation (PC) is defined as the average pressure in the RDC for 0.3 s after initiation. The air plenum pressure during operation (PA) and the fuel plenum pressure during operation (PF) are defined similarly. The air injection pressure ratio and the fuel injection pressure ratio can thus be acquired from CTAP sensors using PC, PA and PF.

PRA = PA / PC (2)

PRF = PF / PC (3)

The combustor pressure during operation reaches a maximum of 1.2 bar (+/- 0.028) for test

III-A, but is relatively low for all the other tests (Figure 107). Uncertainty is calculated from 1σ value of the pressure-time series. The pressure rise due to detonation in the combustor is higher at the higher flow rate of 0.4 kg/s and decreases to around 1.05 bar (+/- 0.027) and 1.02 bar (+/-

0.02) for the lower flow rates of 0.3 kg/s and 0.2 kg/s, respectively, as seen in Figure 107. There is

174

also a slight increase in pressure with an increase in equivalence ratio with the exception of test III-

A. The above two observations infer that the combustor pressure during operation (Pc) has a strong dependence on air flow rate and a lower dependence on equivalence ratio.

Air plenum Fuel Combustorplenum

P F

P C

Fuel supply Air supply

Figure 106 Correlation coefficient for air inlet - sensors 3 and 6 (left) III-C

1.25

1.2

1.15

1.1

1.05 Pc Pc (bar) 1

0.95 0.8 0.9 1 1.1 1.2 1.3

Combustorpressureduringoperation, Equivalence ratio, Φ

0.2 kg/s 0.3 kg/s 0.4 kg/s

Figure 107 Combustor pressure during operation vs. equivalence ratio

175

The air injection pressure ratio, PRA (Figure 108) remains relatively unaltered with equivalence ratio for test points other than test III-A. The fuel injection pressure ratio, PRF, has a stronger dependence on equivalence ratio and increases notably for higher equivalence ratios.

Error in injection pressure ratios is calculated by linear sensitivity analysis of the obtained PC, PA

and PF, for 1σ, and is found to be negligible.

3.5 3.5

3 3 2.5 2.5 2 2 1.5

1.5 1

0.8 0.9 1 1.1 1.2 1.3 0.8 0.9 1 1.1 1.2 1.3 Air injection Air pressure ratio Equivalence ratio, Φ injection Fuel pressure ratio Equivalence ratio, Φ

0.2 kg/s 0.3 kg/s 0.4 kg/s 0.2 kg/s 0.3 kg/s 0.4 kg/s

Figure 108 Air injection pressure ratio (left), and fuel injection pressure ratio (right)

When the combustor flush-mounted sensors 2 and 3 are cross-correlated among themselves, they show poor correlation despite being in the same generic location of the RDC annulus. The correlations are, on an average, 0.24 for all 9 tests, which is very low. This indicates a considerable spatial variation in the strength of detonation wave, the exact reasons to which are currently unknown. The correlation coefficients for the sensor pairs 1 and 4, 2 and 5, and 3 and 6 (combustor sensor with the air inlet sensor) have similar trends. Hence, for brevity, only the sensor pair of 3 and 6 is going to be discussed, since it consistently has a higher correlation. Overall, the cross- correlation coefficient for the pair of 3 and 6 does not exceed 0.55 which may be a result of the high-amplitude low frequency oscillation in the air inlet skewing the correlation. It is to be noted that this value is still considerably higher than the correlation among different sensors in the combustor itself. At higher flow rates, the pressure ratio across the air injection gap increases.

176

Hence, it makes sense for correlation between the air inlet and the combustor to reduce with increase in air flow rate since a higher air plenum pressure would act against the pressure feedback from the detonation wave (Figure 109).

Like the air inlet analysis, fuel plenum analysis only deals with the sensor pair of 3 and 9

(combustor sensor with the fuel plenum sensor). The correlation coefficient is higher at increased

PRF for flow rates of 0.2 kg/s and 0.3 kg/s (Figure 110) which could be attributed to the higher plenum pressure acting against the pressure feedback from the detonation wave. However, for 0.4 kg/s the correlation increases with increased PRF which may be suggestive of the detonation wave being strong enough to counteract the higher fuel plenum pressure.

0.6

0.5 0.4 0.3 0.2

0.1 Correlation coefficient Correlation 0 1.5 2 2.5 3 3.5 Air injection pressure ratio

0.2 0.3 0.4

Figure 109 Correlation coefficient for air inlet - sensors 3 and 6

0.35

0.3 0.25 0.2 0.15 0.1

0.05 Correlation coefficient Correlation 0 1.5 2 2.5 3 3.5 Fuel injection pressure ratio

0.2 0.3 0.4

177

Figure 110 Correlation coefficient for fuel plenum - 3 and 9

3.3. Frequency analysis

3.3.1. Comparative study

Frequency analysis of the pressure-time traces has the potential to reveal interesting characteristics of the different sensors that cannot be observed from pressure-time traces and correlations. The fundamental frequencies obtained from the FFT analysis are assembled for the combustor, air inlet and fuel plenum sensors (Table 8). If the fundamental frequency, ff, in the air inlet or the fuel plenum is different from the operating frequency in the combustor by 10% or more, the cell is colored yellow in contrast to the green-colored cells of the table which indicate a lesser than 10% difference from the ff obtained from the combustor. It can be seen that the ff is the same as the operating frequency for most of the air inlet and fuel plenum sensors. Only test III-A has a different fundamental frequency in the air inlet and fuel plenum in comparison to the combustor.

However, it is to be noted that, for certain tests, one or two of the fuel plenum sensors out of the three had a different ff from the operating frequency of the RDC. This suggests a spatial variation in fuel plenum dynamics. But, all the air inlet sensors always registered the same ff irrespective of the operating point. Since the ff in the air inlet sensors and the combustor matches exactly for the eight of the nine tests conducted, the strong efficacy of the air inlet sensors in determining the operating frequency of the RDC at all regions except at the lean operating boundary is established.

Table 8 Fundamental frequencies in the combustor, air inlet and the fuel plenum

Test Combustor ff Air inlet ff Fuel plenum ff

(Hz) (Hz) (Hz)

I-A 2942 2942 2942

178

I-B 3042 3042 3042

I-C 3100 3080 3100

II- A 2935 2935 2935

II- B 3045 3045 3045

II- C 3143 3055 3122

III- A 1705 235 2705

III- B 3643 3645 3642

III- C 3755 3755 3760

3.3.2. Fuel plenum

The frequency response of the RDC fuel plenum has been studied previously by Naples et al.

[291]. But, that study only used one sensor in the plenum which precludes spatial analysis of the plenum. Since the current study uses three piezoelectric sensors in the fuel plenum, an FFT analysis could further the study on fuel plenum by observing the spatial response in the plenum to the rotating detonation wave in the combustor. Figure 111 shows the FFT plot for the fuel plenum sensors 8 and 9 for tests I-B (Figure 111a, b), II-B (Figure 111c, d) and III-B (Figure 111e, f). The plots show a notable difference in the ff experienced by each sensor, which is an indicant of considerable spatial variation in the fuel plenum dynamics. This may be due to the detonation wave varying in strength as it propagates through the annulus (as inferred previously by the poor

179

correlation between two combustor sensors for all tests), or a complex pressure wave interaction due to reflection within the fuel plenum, or a combination of both. A similar hypothesis was arrived at by Fotia et al. due to the fuel jet being deflected in a direction opposite to the detonation wave propagation direction, in their 2D setup [184]. It is unclear at present if the spatial variation in plenum dynamics causes a detonation wave of varying strength in the combustor, or vice versa.

(a) (b)

(e) (f)

Figure 111 FFT plots for fuel plenum sensors 8 (left) and 9 (right) for test I-B, II-B and III-B

180

3.3.3 Air inlet oscillations

Pressure-time traces from the prior section led to the discovery of low-frequency oscillations of considerable amplitude in the air inlet. It is thus desirable to try to analyze the oscillation in the air inlet and compare it to the previously discovered oscillation in the combustor.

This led to an investigation of the oscillation for all the tests. Figure 112a, b and c show the FFT plot for three stoichiometric test cases, i.e. tests I-B, II-B and III-B. While the ff (also the operation frequency as discussed in the previous section) is easily observable from the three plots at f ≈ 3 kHz, f ≈ 3 kHz and f ≈ 3.8 kHz respectively, there is also considerable activity in all three test cases at f ≤ 0.5 kHz. The secondary dominant frequency is identified to be f ≈ 235 Hz (shown by red circle) and is the same for all the three tests which have different air flow rates. When all the tests are analyzed for the oscillation frequency, it is found that the frequency of oscillation in the air inlet always centered on f ≈ 235 Hz for all the 9 tests. This is an interesting discovery since it implies that irrespective of the air flow rate or the equivalence ratio of the operating point, the inlet of the RDC in use for the current study always oscillates at f ≈ 235 Hz. The f ≈ 235 Hz oscillation (black arrow) does not extend throughout the test, but rather is sporadically occurring with time as shown by the spectrogram of tests I-B, II-B and III-B, in Figure 111d, e and f respectively. To confirm that the oscillation is caused by the detonation wave and not due to an inherent oscillation in the air supply, the RDC was operated under cold-flow conditions without ignition of the reactants, which revealed the lack of any activity in the 235 Hz region. Since the cold flow RDC testing did not produce any oscillation at the same frequency, it can be understood that the oscillation in the air gap is linked to detonation wave propagation in the annulus. The Helmholtz frequency for the air plenum under study is estimated to be ≈ 355 Hz for all flow rates since the speed of sound is relatively unaltered due to an almost constant supply temperature. But, the complex geometry of the plenum would skew the resonance frequency obtained from the basic Helmholtz equation considerably [336]. For instance, a ≈ 15% error is incurred between the calculated and the experimentally obtained

181

frequency when the basic Helmholtz equation is used to calculate the resonance frequency for a cylindrical prism with a long neck [336]. Hence, to get an accurate resonance frequency value, geometry-specific equations need to be developed, even for simple geometries. Despite these unknown variables, since the approximately estimated resonance frequency is different from the oscillation frequency in the inlet by only 33%, it is a strong indication of the air plenum’s functioning as a Helmholtz resonator due to the excitation produced by the high-frequency detonation wave in the combustor.

(a) (d)

(b) (e)

182

Figure 112 FFT plot (left) showing the fundamental low-frequency oscillation for I-B, II-B, III-

B, and spectrogram (right) of the respective test points

4. Conclusion

Rotating Detonation Combustor operation is analyzed at three air flow rates and three equivalence ratios for each of the air flow rate to study the pressure feedback from the rotating detonation wave onto the air inlet and fuel plenum. A total of nine dynamic piezoelectric sensors are used for the analysis, three each in the combustor, the air inlet and the fuel plenum. Pressure- time traces are studied for the air inlet and the fuel plenum and compared with the flush-mounted combustor sensors. For the most part, the pressure fluctuation in the air inlet is between 45% and

70% of the pressure fluctuation due to detonation passage in the combustor annulus. Pressure fluctuations in the fuel plenum are significantly lower than that experienced by the air inlet, and is usually around 20% of the pressure fluctuation in the combustor. Additionally, low-frequency pressure oscillations of high amplitude are discovered in the air plenum. These oscillations are similar, and occur around the same time scale as the waxing and waning detonation instability observed in the same RDC in a prior study [251].

Cross-correlation between sensors in the combustor reveals very poor conformity of signal shape for all the tests run, thereby indication significant changes in detonation wave strength as it propagates azimuthally around the annulus. Cross-correlation reaches a maximum of 0.55 between air inlet sensors and the corresponding flush-mounted combustor sensors. The cross-correlation coefficient does not exceed 0.35 for the fuel plenum sensors, indicating that the pressure feedback into the air inlet is higher in comparison to the fuel plenum. As a general trend, correlation decreases with increasing injection pressure ratios. Thus, higher injection pressure is required to reduce pressure feedback from the detonation wave, especially for the air inlet.

It is found that the fundamental frequency recorded by all the air inlet sensors is exactly the same as the operating frequency of the RDC, found by the flush-mounted combustor sensors. Only

183

at the very lean limits of operation do the air inlet sensors fail to pick up RDC operating frequency.

This finding is of significant importance as it establishes that air inlet sensors are an extremely viable substitute to flush-mounted sensors in the actual combustor. Traditionally, pressure sensors used in the actual combustor have been prone to mechanical disintegration due to the high- pressure and high-temperature environment of the RDC. Hence, some studies have used an Infinite

Tube Pressure (ITP) setup to analyze the RDC operating mode to avoid sensor damage. However, implementing pressure sensors in the air inlet can be an easier method to ascertain RDC operating modes without risking the destruction of the sensor.

The three sensors in the fuel plenum have different fundamental frequencies for many of the test cases indicating strong spatial non-uniformity in the fuel plenum dynamics. The spatial non- uniformity may be a result of a change in the detonation wave strength as it propagates through the annulus, or may be due to complex interaction of the pressure wave from the detonation with already existing, reflected pressure waves from the walls of the plenum.

Finally, the low frequency oscillation in the air gap is investigated for all the tests, and it’s found that the fundamental oscillation frequency in the air inlet is always ≈ 235 Hz. There is strong evidence to suggest that this is a manifestation of Helmholtz resonance in the air inlet. Further experimentation is required to clearly investigate the linkage, if any, between this low frequency oscillation in the air inlet and the waxing-and-waning detonation instability in the combustor.

184

CHAPTER 5: LONGITUDINAL PULSED DETONATION INSTABILITY IN A ROTATING

DETONATION COMBUSTOR

Chapter Abstract

The peculiar phenomenon of longitudinal pulsed detonation (LPD) in a rotating detonation combustor (RDC) is studied using hydrogen-air mixtures, by utilizing: i) two air injection schemes having different inlet areas, and ii) a convergent nozzle assembly with different spacers that affixes to the RDC exit. By varying the air injection pressure ratio and the backpressure, the regime of occurrence and the mechanism of this pulsed detonation instability are investigated. Immense evidence to suggest that LPD is caused by a peculiar detonation initiation mechanism enabled by a reflected shock wave from the RDC exit is discovered through an ensemble axial pressure profile analysis. Distance-time plots show that a single cycle of the pulsed detonation has two components: a fast-moving axial forward decaying detonation wave (with 75% of the ideal detonation speed) and a slower reflected detached shock wave (with 30% of the ideal speed). When the weak reflected wave comes in contact with the fresh reactants at the RDC headwall, another strong axial detonation is produced, thereby continuing the cycle without external ignition. LPD is also found to have three diverse facets, namely, inception, sustenance and operating frequency. For similar backpressures, the two air injection schemes have completely different operating regimes, leading to the inference that while backpressure is necessary for the onset of the pulsed detonation instability, by virtue of enabling reflected shock waves from the exit, lower air injection pressure ratio dictates the sustenance of the instability. A narrow band of injection pressure ratios, between

1.4 and 1.85, under back-pressurized RDC operation has high proclivity to produce sustained periodic longitudinal pulsed detonations in the combustor. Above this range, stable rotating detonation is preferred, and below this range, the operation is distinguished by the mixed presence

185

of both rotating and pulsed detonations for a given test point, finally breaking down into chaotic instability for lower pressure ratios. The frequency of the pulsed detonation operation is found to depend on the initial combustor pressure and equivalence ratio, with higher frequency observed with an increase in backpressure and equivalence ratio.

Nomenclature f - frequency (Hz)

Φ - equivalence ratio

ṁa - air flow rate (kg/s) t - time (s)

PR - average pressure ratio across air inlet before ignition

PC - time-averaged combustor pressure before ignition (bar)

PA - time-averaged air plenum pressure before ignition (bar) x - axial distance from RDC headwall (cm)

1. Introduction

Combustion is broadly classified into two types: deflagration and detonation. When the combustion wave travels with subsonic velocity in the reactant mixture it is a deflagration. In detonation, the combustion wave is coupled to a shock wave and travels faster than the sound speed in the mixture. Detonation, due to its inherent linkage to a shock wave, produces pressure

186

ratios of 13-55 [1] across the detonation wave. This property of enabling a pressure gain by a detonation wave could be profitably used in a detonation combustor [320]. Pulsed detonation combustor (PDC) and rotating detonation combustor (RDC) are the two prominent detonation devices. PDC is characterized by relatively larger size, periodic reactants injection and purge using valves, and highly pulsating (of up to 100 Hz) exhaust pressures [2]. It is prohibitive to increase the frequency of operation, f, beyond 100 Hz due to the mechanical limitations imposed on valves assembly. RDCs on the other hand are smaller than a PDC of comparable mass flow and have continuous reactants fill into the combustor. Depending on the mass flow rate and the geometry

[27,43], the RDC can have one or more detonation waves propagating continuously inside the chamber. Though the preferred operating mode of RDC is to have the eponymous rotating detonation inside the chamber, it has been observed by a few prior studies

[27,45,128,149,174,250,276,322] that at certain geometries and mass flow rates, the RDC transitions from housing a continuous rotating detonation to producing axial pulsed detonation inside the combustion chamber, like the PDC. This pulsation, which was first observed in an RDC and named as longitudinal pulsed detonation (LPD) by Bykovskii et al. [174], is an intriguing phenomenon because it occurs in the absence of any mechanical valves to actuate the reactant flow, which is tantamount to a PDC of the simplest design. Additionally, the frequency of the pulsation is noted to be in thousands of Hertz [45,174,250,322], which, once again, betters the operating frequency of any known PDC by more than an order of magnitude.

However, the cause behind the onset and sustenance of LPD has not yet been deliberated in detail in literature. Bykovskii et al. [174,276] established that LPD onsets in an RDC operating with

H2-air when the chamber width is dropped below a threshold value which in turn may influence the detonation cell-width of a given mixture. LPD also occurs for RDC operation with relatively lower chamber pressure and substandard mixing with subsonic air injection [174]. In terms of equivalence ratio, Φ, Bykovskii et al. discovered that the LPD mode demarcates the regions of

187

deflagrative combustion and detonative combustion at lean and rich limits of H2-air operation, for their RDC setup [276]. They measured the frequency of pulsations to be around 1.6 kHz. Frolov et al. [322] noted the existence of LPD for H2-air mixtures in their larger RDC with a diameter of 406 mm. LPD was found to occur at f ≈ 1 kHz at higher air injection gap width. While a specific case of

LPD was discussed for an operating case with the higher injection area and a convergent nozzle

(and hence presumptively a choked RDC exit leading to subsonic air injection), it is unclear if they observed the phenomenon without a choked exit. Simultaneous azimuthal pulsations in the RDC are also noted by Wang et al. [45] during their RDC operation with vitiated air. It could be speculated that heat addition may have caused a choked exit in the RDC. While Frolov et al. used ion probes in their study and Wang et al. used pressure sensors in theirs, both concurred that the instigation for

LPD started downstream, near the RDC exit. Additionally, the presence of the LPD mode is also observed in ethylene-hydrogen-air mixtures in an RDC with convergent nozzle by St. George et al.

[149], indicating that the instability is reactant mixtures independent. Driscoll et al. [128] have observed LPD at lean operating conditions for H2-air mixtures with a convergent nozzle, and thus, once again, subsonic air injection. Finally, a preliminary discussion on LPD as one of the prominent instabilities in a back-pressurized RDC is discussed by Anand et al. [250], where for a given restricted exit area of an RDC, LPD was found to occur only below a critical Φ. Hence, from literature, it is clear that LPD has high propensity to occur for subsonic air injection, and for operation near the lean boundary.

Furthermore, liquid rocket engines are known to be susceptible to “high-frequency instabilities”, the fundamental mechanics of which are yet to be clearly understood. Interestingly,

“longitudinal instability”, which is characterized by axially travelling pressure pulses between the injection head and the nozzle throat at f ≥ 1000 Hz are a prominent subset of the high-frequency instabilities in rocket engines, and are not comprehensively explained, despite the considerable research into the phenomenon during 1950-80s [74]. Male et al. [55] visually captured the onset of

188

“longitudinal shocks” moving within the thrust chamber at f ≈ 1000 Hz when fuel transition was effected from furfuryl alchohol to JP-3. Hybrid modes of operation with both the longitudinal and other high-frequency instability- lateral oscillations at f ≈ 6000 Hz- were also recorded. The shock waves were found to occur with a maximum pressure ratio of 2.8, with the highest recorded pressure peak of ≈ 44 bar. Highly uniform rocket chamber erosion was observed near the injectors for operations with the longitudinal instability. A nonlinear analytical method to model this instability, based on its “shock wave characteristics” was developed by Lores et al. [280], while conceding the model’s shortcomings in predicting the triggering of the instability. Commendable work was done by Berman et al. [281,282] in subsequent articles in visually characterizing this longitudinal instability. Berman et al. [281] recorded the presence of “intermittent shock-type axial instability” around 1000 Hz upstream of the nozzle throat when the total reactants flow rate was lowered beyond a critical value, for a constant head pressure drop (pressure ratio across injectors).

Moreover, the instances of tests producing these instabilities were lowered progressively when the nozzle throat area is gradually increased. Using a novel moving slit photography technique, their partially transparent rocket engine revealed a process consisting of an upstream moving shock wave with gradually increasing strength, which eventually impinges on the injector head (with an absolute velocity of 1005 m/s), and almost instantaneously initiates a highly luminous downstream propagating shock wave (absolute velocity of 1433 m/s). Berman et al. also observed that the presence and strength of this longitudinal instability is a function of the angle of convergence of nozzle throat (amplifier and reflector), injector type, and chamber length, finally concluding that while the chamber pressure (predicated by flow rate and throat area) had a significant influence on this instability, the head pressure drop across the injectors was the driving factor. In synopsis, the above-mentioned sources on rocket engine combustion instability implicitly attribute the phenomenon in rocket thrust chambers to be caused due to periodic explosions.

189

Thus, this pulsed detonation instability in an RDC is of paramount importance, because: 1) it could commence research into truly valve-less PDCs with an increase in frequency by at least an order, 2) it is imperative to understand this significant instability, if practical employment of RDCs is ever to be realized, and 3) understanding the kinship between the longitudinal instabilities in rotating detonation engines and rocket engines would greatly further the development of both propulsive devices. Since this phenomenon has been observed sporadically through the literature, and since there has not been any substantial theory describing the mechanism yet, the current paper aims to address LPD through a systematic parametric investigation of RDC operation at lean equivalence ratios of H2-air mixtures, utilizing two air injection areas and varied levels of backpressures.

2. Experimental Methodology

The current research is performed at the Detonation Engines Test Facility in the Gas Dynamics and Propulsion Laboratory at the University of Cincinnati for RDC operation with H2-air mixtures for two air flow rates, ṁa, of 0.2 kg/s and 0.3 kg/s. The air and fuel flow rates are controlled by a closed-loop system of nitrogen-driven pilot regulators and a set of Flowmaxx sonic nozzles.

Norgren VP50 proportional control valves (pilot) are linked to Norgren pilot-operated regulators to isolate electrical components from the primary fuel supply. GE Unik 5000 sensors are linked to the choked-flow nozzle assemblies to monitor air and fuel flow rates. Fuel flow is administered to the rig through a pneumatically-actuated Bi-Torq isolation valve located just upstream of the fuel plenum, which allows fuel flow rates to stabilize within 0.5 s of fuel introduction. The uncertainty in the pressure and temperature sensors (used in the reactants delivery) is ± 0.069 bar and ± 1 K, respectively. The linearized systematic error analysis of this uncertainty results in an estimate of

2.1% error in the air mass flow rate and 2.8% in fuel mass flow rate, which in turn results in a maximum error of 3.4% (seen for the lowest flow rates) in equivalence ratio. For a detailed

190

description of the facility, the readers are directed to [323]. Two air injection schemes are used in this study by utilizing two oxidizer spacers (Figure 113) of different widths. Air injection scheme – I has an injection area of 490 mm2, whereas air injection scheme – II has an increased injection area of 1400 mm2. A back-pressurizing convergent nozzle is integrated with the RDC exit by means of concentric spacers (Figure 113). For a given air flow rate, irrespective of the injection scheme, the nozzle throat area dictates the backpressure on the combustor, since the flow is choked at the converging throat. Three spacers are used for each air injection scheme to enable similar backpressures for the air flow rates tested (Table 9). Therefore, using six different spacer widths, the nozzle throat area is controlled to be approximately 407, 685 and 962 mm2 respectively, for both the air injection schemes. Thus, this study delineates the effects of air injection pressure ratio and combustor pressure on LPD, by altering the air injection area and the nozzle throat area.

Henceforth, the nomenclature of [air injection area/nozzle throat area] mm2 will be used throughout the paper to refer to a specific scheme of air injection and nozzle throat. For instance, from Table 9, it is apparent that scheme 490/407 mm2 produces the highest backpressure, for a given flow rate, while scheme 1400/962 mm2 produces the lowest backpressure in the RDC.

The instrumentation schematic, shown in Figure 114, is indicative of the two different instrumentation schemes adopted during this study. In addition to the three stations in the combustor that are distributed azimuthally with 120o between them, with each individual station having four axially distributed ports for sensor affixation, there are three more ports in the air inlet through which sensors can be attached to analyze pressure fluctuations in the air inlet. A previous study by the authors have established that air inlet sensors are a viable approach to predict the RDC operating mode when it sustains rotating detonation [246]. PCB piezoelectric dynamic sensors are used to analyze the high frequency pressure fluctuations in both the combustor and the air inlet.

PCB sensors that are used in both the instrumentation schemes are marked by a black dot/bar, while sensors that are used only in the first scheme are marked with blue and those that are used

191

only in the second scheme are shown in green. To summarize the instrumentation, the first scheme utilizes three PCB sensors in the air inlet and the combustor to investigate the pressure fluctuations caused by the LPD instability, and to test the efficacy of the sensors in the air inlet in capturing the

LPD in the combustor. The second instrumentation uses two sensors in the air inlet to predict the axisymmetric pulsed detonation and four axial sensors in station 3 to analyze the axial pressure fluctuations in the combustor when the RDC exhibits the LPD instability. Both the instrumentation schemes use an ionization probe [323] to approximately estimate the strength of the ionization produced by the detonation waves, and are integrated in station 2, row 2 (not shown in Figure

114). In addition to the data from PCB sensors and the ion probe acquired at 1 MHz sampling rate, three static capillary tube averaged pressure (CTAP) sensors, with one each in the combustor, air plenum and fuel plenum, are used with sampling rate of 1 kHz. This aids in estimating the time averaged air and fuel injection pressures before ignition and during operation. Every test is run for t ≈ 0.35 s to avoid damage to the PCB sensors from the very high temperature environment of the

RDCs.

Figure 113 Schematic of the RDC geometry showing a) a cutout section without nozzle and b)

side view with nozzle assembly

192

Table 9 RDC configurations used

Air flow, kg/s Air Injection – I Air Injection – II

490 mm2 1400 mm2

Exit area Exit area

mm2 mm2

→ Spacer width → → Spacer width →

increases increases

0.2/ 0.3 407 685 962 407 685 962

→ Backpressure → → Backpressure →

decreases decreases

Figure 114 Instrumentation schematic utilized in the study

193

3. Results and Discussion

3.1 Pulsed Detonation Instability (or LPD)

The characteristics of the pulsed detonation instability in the RDC have to be discussed before progressing to the particulars of the analysis. Under backpressurized operation, the static pressure in the combustor is prone to an approximately 1 s transient state distinguished by continuous increase in pressure (which cannot be sensed by piezoelectric transducers) in both the combustor and the reactants supply manifolds (due to a choked RDC exit caused by the back-pressurizing nozzle), up to a limiting steady-state value [43]. A similar transient operation is observed for the current study (Figure 115). As a result, the dynamic PCB sensors cannot record this steady, low- frequency change in the base-static pressure in the combustor. The pressure peaks that are obtained from the PCB sensors are thus, the actual value of the detonation peak pressure and are not adulterated by the transient behavior of the back-pressurized RDC. Injection of the hydrogen fuel causes an instantaneous spike in combustor pressure (PC) at t ≈ -0.75 s. A corresponding increase is seen in the fuel plenum pressure, PF, can be observed at the same time. After ignition at t

≈ 0 s, there is a gradual increase of the static pressure in the combustor, which plateaus after fuel shutoff, at time t ≈ 0.35 s. Since the current research involves RDC operation before the attainment of steady-state base pressure, injection pressure ratios are calculated for air plenum and combustor pressure before ignition (shown in Figure 115) to provide a relatable platform for comparison with future studies. The pressure ratio (PR) is defined as follows,

PR = PA / PC (1)

This methodology of using only the air plenum pressure to estimate PR in RDC is used in

[89,246,333].

194

Figure 115 Pressure-time trace of air plenum, fuel plenum and combustor

3.1.1. Pressure profile analysis

Every pressure-time series henceforth is from the PCB sensors and depict the nominal dynamic pressure fluctuations recorded by the sensors. Figure 116 shows the pressure-time trace acquired from the three azimuthally distributed PCB dynamic sensors for: a) conventional rotating detonation (RD) propagation, and b) longitudinal pulsed detonation (LPD) propagation, for two arbitrarily chosen test points having similar air flow rate and equivalence ratio. During LPD, all three sensors are excited simultaneously, thereby showcasing the characteristic axisymmetric pulsation of LPD. The pressure peaks during RD is similar in magnitude to the peaks obtained during LPD, indicating that the pulsations are indeed detonation events, as opposed to compression waves. Note that peak detonation pressures in an RDC environment do not obey the ideal C-J detonation pressure observed in tubes. This well-known effect is prevalent in almost all experimentally obtained RDC pressure time-traces. Paxson [337] has numerically demonstrated that detonative combustion in an RDC occurs with the reactants being considerably unconfined, which in turn causes the notable deviation from the ideal predicted wave speeds due to energy and momentum loss in the axial direction. This loss mechanism was attributed to the observed deficit in the detonation peak pressure and velocity from the C-J theory. Additionally, Edwards [54] obtained

195

experimental evidence that the universally observed deficit in detonation peak pressures and wave speed in an RDC is also a strong function of the amount of products remaining in the combustor from the previous cycle. Deflagrative burning or the heightened temperature of the incoming reactants upstream of the rotating detonation wave cause notable deficiency in the observed detonation pressure and velocity. The ion probe traces given in Figure 117 provide evidence of detonative events during the axisymmetric pulsations, as the strength of ionization (as witnessed by the drop in voltage magnitude) is similar for both the rotating (Figure 117a) and pulsed detonation (Figure 117b). Ion probes produce a negative voltage reading when the sensing head is exposed to high temperature, ionized gases, like the region behind a detonation wave. Ion probes have been widely used in detonation environments to predict detonation wave passage, and comprehensive description of its working is given in [323]. Note that annular detonation propagation is a rather stochastic event, and as such one cannot expect the combusting front to produce repeatable ionization signal shape for subsequent laps. The pressure fluctuations in the air inlet during RD and LPD are shown in Figure 118, from which it is inferred that both modes exert matching pressure feedback on the air inlet owing to the back-pressurizing nature of detonative combustion. Additionally, the pressure-time trace in the air inlet during LPD complies with the finding in [55] that established the high efficacy of the air inlet sensors in detecting detonation propagation in the combustor. While rotating detonation causes temporary localized occlusion of the injector orifices [89,171,246,291], longitudinal pulsed detonation causes temporary occlusion of the entire air injection slot area. Evidence for the same can be seen in Figure 118b of section

3.1.1. During LPD, all three of the circumferential sensors record simultaneous pressure feedback of

1 bar, whereas during RD, the pressure feedback is localized with a phase difference indicative of the location of the rotating detonation wave inside the combustor. This implies that after every pulsed detonation event there is an overall momentary stoppage of air supply, followed by the expulsion of the unvented air leading to the presence of a slug of fresh mixture near the injectors, so

196

that mass continuity is conserved. Even though the fuel injectors are not instrumented with PCB sensors, it is a reasonable assumption that a similar temporary occlusion of all the fuel injector orifices takes place after detonation.

The axial pressure profile during RD and LPD is given in Figure 119, with the sensor numbering conforming to the row number they are instrumented in. Considering the axial pressure profile during RD, shown in Figure 119a, it is observed that, interestingly, a system of weak reflected shock waves exist, albeit of lower magnitude than that seen during LPD (Figure 119b). Note that Axial #1 and Axial #2 probably record the pressure signature of the detonation front and the attached oblique shock of the rotating wave [89]. Moreover, it is imperative to note that the pressure rise caused by the reflected shock wave is highly dampened by the time it reaches sensors #3 and #2

(between t ≈ 0.2056 s and t ≈ 0.20565 s). The presence of reflected shock waves during RDC operation with increased combustor pressure has been discussed before, numerically, by Schwer and Kailasanath [89,222]. Moving on to the axial trace during LPD, as shown in Figure 119b, the axial propagation of strong shock waves due to LPD is clearly visible. Axial sensor #1 is closest to the detonation event as witnessed by the 2 bar pressure rise at t ≈ 0.20565 s. This is followed by subsequent decrements in pressure magnitudes recorded by Axial #2, #3 and finally #4 at t ≈

0.2057 s indicating the dissemination of the initial detonation into a decaying forward travelling detonation wave (towards the RDC exit). At time t ≈ 0.20577 s, the Axial #4 sensor records a heightened pressure pulse which seems to be transmitted to Axial sensors #3 and #2, in that order, having subsequently diminutive pressure peaks, which could be construed as the reflected backward travelling shock wave from the RDC exit. Finally, at t ≈ 0.20583 s, there is another notable pressure peak in Axial #1, finally resulting in the detonative pressure peak of 2 bar at t ≈ 0.20588 s.

This type of pressure profile distinguished by an initial sharp pressure spike, followed by gradual decrease in strength towards the exit, and a similar propagation from the RDC exit back to the RDC headwall, finally resulting in another sharp pressure rise is encountered in every LPD operation. It

197

is thus theorized that, during LPD, there is a detonation event between the air inlet and the first instrumentation row (which is approximately 1.905 cm from the headwall) which causes a forward travelling shock wave that continually decays till the RDC exit. The detonation decay can be explained by the results of Kuznetsova et al. [338]. They investigated the effect of sharp and smooth mixture gradient on the detonation transfer properties from a driver tube of stoichiometric H2-air mixture to a driven tube of lower H2 content. Sharp mixture gradient between the two tubes caused the detonation to decay into a leading shock wave with 30%-40% C-J velocity that was completely detached from the chemically reacting zone. Smooth mixture gradients, however, produced detonation decay distinguished by a notably faster wave with continuously increasing distance between the leading shock and the reaction front. Thus, the detonation decay of the forward wave can be attributed to the gradual variation in mixture concentration, axially, probably brought forth by the temporary occlusion of fuel and air injectors after each detonation event, at regions away from the injectors, such that the shock wave starts to detach from the chemically reacting front. The forward moving leading shock wave is reflected at the convergent nozzle and moves upstream.

Detonation initiation is possible through shock reflection/ focusing from a concave corner (the converging nozzle at the RDC exit), as explained by Ciccarelli et al. [82], and Bartenev and Gelfand

[339]. Hence, the decaying detonation front of the forward moving wave most probably undergoes shock-focusing at the convergent nozzle, which leads to detonation initiation in the upstream direction. This reflected shock wave propagates from the exit to the first instrumentation row and ignites the unburnt fresh accumulated reactants, thereby leading to the cyclic pulsation causing the

LPD instability. Detailed discussion of the above-described procedure along with enhanced supporting arguments will be dealt with, in subsequent sections, through a holistic parametric analysis of all the LPD incurring operating points.

198

Thus, from the fact that both the LPD and RD operations have reflected from the RDC exit that propagate upstream, with the waves being much stronger for the former than the latter, and the fact that the two test points discussed only differ from each other by Φ ≈ 0.1, it is theorized that there exists an inherent stochasticity that dictates the onset of LPD for RDC operation with a converging nozzle. But, strong evidence is discovered to suggest that the onset of LPD does not necessarily guarantee its sustenance as shown by Figure 120, which has pressure-time traces from two sensors in the air inlet, with one exhibiting LPD and the other exhibiting RD at different time periods during the same test, which is run with the second air injection having larger area. Thus, it is evident that just the mere temporary occurrence of LPD (as witnessed in Figure 120a and b) does not ensure its sustained, continual operation till the fuel shut-off. Moreover, the sustained LPD operation is always preceded by a period of chaotic, aperiodic pressure time-traces, which presumably depicts highly unstable rotating detonation waves in the RDC that are prone to subside into deflagration waves. An example of one such LPD onset is given in Figure 121, where the initiating blast wave from the pre-detonator [156], the transient chaotic rotating detonation propagation period, and finally, the sustained LPD onset are tagged in their order of occurrence.

Once the LPD is onset, in such a case, it is sustained continually as long as fuel supply is constantly maintained, for a given test case.

(a)

199

(b)

Figure 116 Circumferential pressure-time trace in combustor for (a) rotating detonation

at ṁa = 0.3 kg/s and Φ = 0.908, and (b) pulsed detonation at ṁa = 0.3 kg/s and Φ = 0.9,

with scheme 490/685 mm2

(a)

(b)

200

Figure 117 Ionization trace in combustor for (a) rotating detonation at ṁa = 0.3 kg/s and

Φ = 0.908, and (b) pulsed detonation at ṁa = 0.3 kg/s and Φ = 0.9, with scheme 490/685

mm2

(a)

(b)

Figure 118 Circumferential pressure-time trace in air inlet for (a) rotating detonation at

ṁa = 0.3 kg/s and Φ = 0.908, and (b) pulsed detonation at ṁa = 0.3 kg/s and Φ = 0.9, with

scheme 490/685 mm2

201

Axial #1 Axial #2 Axial #3 Axial #4

(a)

Axial #1 Axial #2 Axial #3 Axial #4

(b)

Figure 119 Axial pressure-time trace in combustor for (a) rotating detonation at ṁa = 0.3 kg/s and Φ = 0.93, and (b) pulsed detonation at ṁa = 0.3 kg/s and Φ = 1.03, with scheme

490/407 mm2

(a)

202

(b)

Figure 120 Circumferential pressure-time trace in air inlet with (a) pulsed, and (b)

rotating detonation for the same test point of ṁa = 0.3 kg/s and Φ = 1.02, with scheme

1400/407 mm2

Figure 121 Circumferential pressure-time trace in combustor showing the transient

aperiodic detonation propagation before sustained pulsed detonation onset for ṁa = 0.3

kg/s and Φ = 0.9, with scheme 490/685 mm2

3.1.2. Axial ensemble pressure profile investigation

Ensemble averaging the pressure trace from the four axial sensors (Axial #1, #2, #3 and #4) gives a general idea of the axial pressure propagation characteristics during RD and LPD in a backpressurized RDC. In the current study, 0.35 s of operation translates to roughly 1300 detonation laps for a given operating point. This ensures high statistical accuracy in the ensemble

203

averaged peak pressures. Standard deviations of the pressure peaks are extracted from the pressure-time traces of the four sensors. Maximum deviation is around 0.4 bar, and occurs for Axial

#1, at the lowest air flow rate of 0.2 kg/s. Figure 122a and b show the ensemble averaged axial pressure profile for two arbitrary test cases exhibiting rotating and pulsed detonation respectively.

Note that P1, P2, P3 and P4 are the averaged pressure peaks from the headwall to the nozzle, of the forward decaying detonation wave or the rotating detonation wave profile depending on whether the operating point exhibits LPD or RD. P5, P6, P7 and P8 are the pressure peaks obtained from the nozzle to the headwall, obtained during reflected wave propagation upstream due to LPD or RD. As discussed in the above section, reflected shock waves (tagged by dark blue, red, green arrow) of decaying strength exist even for the rotating detonation case (RD), and is observed in the ensemble axial pressure profile of an arbitrary operating point presented in Figure 122a. But these waves are of lower magnitude than the reflected waves during LPD (Figure 122b). Evidence of a detonation event disintegrating into a decaying forward moving shock wave is reinforced in the ensemble plot of LPD. Pressures P1, P2, P3 and P4 exhibit the forward wave motion for LPD, whereas for RD, it depicts the RD wave axial profile. Pressure peaks P5, P6 and P7 show the pressures of the reflected wave, which gathers more strength (P8), finally igniting the fresh reactants resulting in detonation

(P1). The whole process is completely self-sustained and devoid of any need of external ignition which assigns considerable importance to this phenomenon with regard to PDCs. While the general structure shown in Figure 122b is exemplary of most LPD test cases, occasionally, random periodic pressure peaks (black arrow) are observed in some test cases, lending credence to the belief that some test points are amenable to secondary “bursting” events near the RDC exit. This warrants a separate study, and these anomalous cases will, henceforth, be neglected. Comparison of ensemble averaged individual pressure peaks of RD and LPD gives further insight into the differences between the two operating modes in an RDC. First, an analysis of Figure 122a and b indicates that pressures P1, P2, P3 and P4 are of similar strength for both rotating and pulsed detonation, albeit

204

due to different reasons. Peaks P1, P2, P3 and P4 during RD show gradual decrease in magnitude due to the detonation wave-oblique shock structure characteristic of RD [89].

The difference between the two is apparent when the reflected pressure peaks – P5, P6, P7 and P8 - are considered. It can be seen that, for LPD, P5, P6 and P7 are relatively higher in comparison to RD, and also sharper, qualitatively, which leads to the inference that the reflected waves during RD vary in strength and propagation time, in opposition to the highly periodic reflected waves during LPD. This could also be observed by contrasting Figure 119a with b. More importantly, the averaged pressure peak of the reflected wave, P8, at instrumentation row 1 has a considerably higher pressure magnitude during LPD (Figure 122b), in contrast to the almost nonexistent pressure peak, P8, in the case of RD (Figure 122a). By the time the reflected wave during RD reaches Axial #1 (black arrow), its magnitude is ≈ 0.1 bar, in contrast to the higher ≈ 0.45 bar seen during LPD. Similar behavior is observed for all the other test cases. This indicates three factors- (1) RD is highly susceptible to produce reflected waves from the RDC exit with a convergent nozzle- Schwer et al. [222]have noticed similar reflected waves from an RDC exit with convergent nozzle, during RD, in their numerical study. However, the reflected waves from the exit during RD are susceptible to random variations in the magnitude and shape of the pressure profile,

(2) the pressure profile of the reflected wave during LPD is higher in magnitude than an RD, for similar RDC operating conditions, especially near the headwall of the RDC (P8 at Axial #1), and (3) the lower peak pressure magnitude of the reflected wave during LPD at Axial #2 and #3 (P6 and P7, respectively) suggests that the detonation initiated by shock-focusing at the converging nozzle has disintegrated in a detached shock wave. Further evidence for the above arguments is provided in subsequent sections. The notable increase in peak pressure of the reflected wave during LPD at row

#1 (P8), in comparison to the two prior rows of instrumentation through which it propagates suggests that the reflected wave comes into contact with fresh unburnt reactants. This reasoning is consistent with the finding established in section 3.1.1 that simultaneous expulsion of unvented air

205

occurs after every pulsed detonation event, which in turn entails the reflected wave from the exit to interact with the fresh slug of reactants near row #1. Further progression of the reflected wave towards the headwall enables a detonation event, which forms the next cycle of the LPD, thereby continuing the sustained process. The peak pressures of the forward and reflected wave, along with their respective time indices are extracted for all the operating points that exhibit LPD with air injection 490 mm2. These values are used in section 3.4 and 3.5 to analyze the various time- averaged facets of LPD. An in-depth analysis of reflected shock waves during RD is beyond the scope of this study, and hence, the remainder of the paper only deals with the self-sustained pulsed detonation (LPD).

P 1

P 2

P 5 P P 8 P 4 P 3 6 P 7

(a)

206

P 1

P 2

P P 3 8 P P 5 P 4 6 P 7

(b)

Figure 122 Ensemble pressure-time trace for (a) rotating detonation at ṁa = 0.3

kg/s and Φ = 1.14, and (b) pulsed detonation at ṁa = 0.3 kg/s and Φ = 0.82, with

scheme 490/685 mm2

Legend: Pressure peaks of rotating detonation/ forward wave- P1, P2, P3, P4, and

reflected wave- P5, P6, P7, P8 obtained from sensors Axial #1, #2, #3, #4,

respectively

3.2. Regime of occurrence

Using six nozzle spacers of different widths at the exit and two oxidizer spacer plates, 12 different air injection pressure ratio trend lines (6 for each air injection scheme) and 6 backpressures (and hence 6 different PC) are investigated through the use of the two ṁa of 0.2 kg/s and 0.3 kg/s. As explained above, by this altering of the oxidizer spacer width and the nozzle spacer width, the effect of initial combustor pressure (function of backpressure, which is in turn a function of the spacer width) and the air injection pressure ratio on LPD is delineated, because, for a given

ṁa and Φ, same combustor pressures, PC, are obtained irrespective of the air injection (490 mm2 or

1400 mm2). Thus, this section primarily deals with two parameters- PR and PC, each of which is to

207

be investigated for both the air injection schemes, in terms of the regime of occurrence of LPD, as shown in Figure 123 and Figure 124, respectively. It is, once again, emphasized that the ratio of air plenum to combustor pressure during operation is always below 1.89 (the nominal critical limit for air to promote choked flow). Data is presented as a function of cold pressure ratio (PR) to avoid confusion stemming from the transient RDC pressure response with a nozzle. The legend for the figures is given in Table 10. Note that 0.2 kg/s and 0.3 kg/s are denoted by circular and triangular markers, respectively. Solid, colored markers with black outline denotes LPD, whereas non-colored white markers with colored outline represent RD. Black colored markers with colored outline are used to denote the hybrid RD+LPD activity, while yellow colored markers with colored outlines represent test cases that only exhibit chaotic instability. Observing Figure 123a, it could be seen that there is a relative increase in the number of occurrence of LPD, in comparison to RD, when the

PR is decreased from PR ≈ 2.3 to PR ≈ 1.5, for air injection – 490 mm2. For instance, with air injection

- 490 mm2 (Figure 120a), at PR ≈ 2.3, for ṁa = 0.3 kg/s with spacer 962 mm2 (green triangle), RD predominates the regime of operation, whereas for PR ≈ 1.5, for ṁa = 0.2 kg/s with spacer 407 mm2

(pink circle), no cases of RD is observed. Thus, for air injection – 490 mm2, it could be inferred that the propensity for the occurrence of LPD in an RDC increases with decreasing PR, as witnessed by the reducing instances of RD activity.

The reflected waves from the exit may cause localized explosion that produce an axial detonation event, instead of rotating detonation, which can then attain sustained LPD. Wu et al.

[175] have discussed the prominent effect of random localized explosions in manifesting multiple rotating detonation waves in an RDC, in their numerical study. This kind of “explosion in an explosion” has been observed to produce detonation wave formation, by Lee [21]. A similar event may be responsible for the onset of pulsed detonations in an RDC, due to the axially moving, reflected waves from the exit. Moving on to Figure 123b (air injection – 1400 mm2), a combined mixture of rotating and pulsed detonation (RD+LPD), which is exemplified by Figure 120, is

208

observed for 1.13 ≤ PR ≤ 1.19. Further reduction in PR tends to completely hinder the occurrence of

LPD instability, but promotes chaotic instability [250] characterized by irregular, aperiodic propagation of rotating detonation waves. Hence, from Figure 123a, it is clear that there is a narrow band of PR (1.4 ≤ PR ≤ 1.85) that promotes the predominant occurrence and onset of sustained pulsed detonation in an RDC. Above this PR band, normal rotating detonation is preferred predominantly (PR ≥ 1.85), and below this PR band, RDC operation is prone to the combined process of both rotating and pulsed detonation wave propagation (1.12 ≤ PR ≤ 1.2, as seen in Figure 123b), for a given test point, finally leading to chaotic unstable detonation propagation for lower pressure ratios (PR ≤ 1.12). When the same operating regime is plotted as a function of PC (Figure 124), there is a distinct lack of any trend in the RDC operating mode. Comparison of Figure 124a (air injection –

490 mm2) and Figure 124b (air injection – 1400 mm2) reveals an interesting discovery that PR plots do not highlight. For a given ṁa, with a particular geometry, even though the six PC trend lines for air injection – 490 mm2 closely match with the trend lines for air injection –1400 mm2, the RDC operation is completely different across the two air injection schemes. Regimes of RD, LPD, LPD+RD and chaotic instability occur haphazardly when plotted with PC as the independent variable. For instance, with air injection 490 mm2 a combustor pressure of 1.3 ≤ PC ≤ 1.5 produces multiple RD events for 0.3 kg/s air flow, but only enables LPD for 0.2 kg/s. However, the same combustor pressure range, for air injection - 1400 mm2, leads to the formation of the hybrid RD+LPD activity for a given test case with 0.3 kg/s, while producing chaotic instability for 0.2 kg/s. This apparent lack of consistency in RDC mode with changes in PC leads to the conclusion that while LPD onset may be backpressure dependent (since it does not occur when there is no backpressure on the combustor due to the choked exit), its sustenance is linked to the air injection pressure ratio.

209

Table 10 Legend for operation regime figures

It is theorized that the sustenance of longitudinal pulsed detonations in an RDC is a function of the PR. Note that LPD is only observed in the current facility when the RDC exit is choked (and hence subsonic air injection) due to the presence of the converging nozzle. As pointed out in the introduction, other facilities seem to exhibit a similar affinity for LPD occurrence when air injection is subsonic. Higher PR may have enough air plenum pressure to counteract the strength of the reflected waves from the choked RDC exit, thereby only housing rotating detonation, and negating pulsed detonation. Lower PR may render momentary stoppage of air flow by the reflected wave from the exit due to increased susceptibility of the air inlet, thereby causing a fresh slug of mixture to be suddenly exposed to the reflected shock waves. Thus, the reflected wave probably ignites the fresh mixture of reactants that are rapidly injected into the chamber, after the momentary occlusion of the air inlet by the detonation wave of the previous cycle of LPD. While momentary occlusion of air inlet by the rotating detonation wave has been reported by multiple studies, a subsonic injection combined with a reflected shock wave from a choked RDC exit with a convergent nozzle produces the desired reactants plenum recovery time after successive air inlet occlusion to enable sustained longitudinal pulsed detonation. Lowering the PR further causes a regime of LPD+RD due to the injection ratio not being high enough to cause sustained LPD, nor being low enough to cause sporadic rotating detonation wave propagation (chaotic instability) [250]. Combining the ideas presented in section 3.1.1, 3.1.2 and 3.2, it could be theorized that, for a given PR that is amenable to produce LPD, there is an inherent randomness that could predicate the occurrence of RD, instead of

210

LPD. This stochasticity most probably stems from the transient chaotic period after initiation that is discussed in section 3.1.1. The sustained LPD activity is dependent on the pressure ratio of the air injection, but the onset of LPD is dependent on the backpressure experience by the combustor and the inherent stochasticity of the strength of the reflected waves during the transient period of operation after initiation. The single instances of RD, in an otherwise LPD-dominated region in

Figure 123a between 1.5 ≤ PR ≤ 1.85 strengthens this argument.

2.4

R 2.2

1.8

1.6

Injection pressure ratio, P ratio, pressure Injection 1.4

1.2 0.5 0.7 0.9 1.1 1.3 Equivalence ratio, Φ

(a)

1.2

1.18

R 1.16

1.14

1.12

1.1

1.08 Injection pressure ratio, P ratio, pressure Injection 1.06

1.04 0.5 0.7 0.9 1.1 1.3 Equivalence ratio, Φ

(b)

211

Figure 123 Regime of occurrence vs. PR (a) air injection – 490 mm2, and (b) air injection –

1400 mm2.

1.9

1.8

(bar)

C 1.7 1.6 1.5 1.4 1.3 1.2 Combusotr pressure, P pressure, Combusotr 1.1 1 0.5 0.7 0.9 1.1 1.3 Equivalence ratio, Φ

(a)

1.9

1.8

(bar)

C 1.7 1.6 1.5 1.4 1.3 1.2 Combusotr pressure, P pressure, Combusotr 1.1 1 0.5 0.7 0.9 1.1 1.3 Equivalence ratio, Φ

(b)

Figure 124 Regime of occurrence vs. PC (a) air injection – 490 mm2, and (b) air injection –

1400 mm2.

212

3.3. Frequency analysis

Fast Fourier transform (FFT) is used to attain the fundamental frequency, f, of the LPD instability, and is plotted as a function of ṁa, exit area and Φ in Figure 125. The operating frequency of RDC during rotating detonation has been discussed in literature [27,43,45,128,322] and will not be addressed here. Of considerable significance is the dependence of LPD frequency on combustor pressure before ignition. Since the above section established that air injection - 1400 mm2 does not produce sustained LPD throughout a given operating point, frequency analysis is limited to just air injection - 490 mm2, and is shown in Figure 125 as a function of PC and Φ. A concrete trend of increase in f with an increase in PC, with the highest frequency exhibited by 0.3 kg/s test cases with spacer 407 mm2, and the lowest frequency recorded for 0.2 kg/s with spacer 962 mm2, is observed.

Comparing Figure 125 with Figure 123a in the above section 3.1, the dissimilarity between the frequency and the regime of LPD occurrence as a function of PR is easily evident. More specifically, if operating frequency of LPD is a function of PR, any change in PR must manifest itself as a corresponding increase/decrease in f. However, there seems to be incongruity of the trends represented in Figure 125 and Figure 123a, which implies that although PR dictates the sustained operation with LPD, it does not influence the frequency of operation. In contrast, there is significant similarity in the trends exhibited by Figure 125 and Figure 123a. To illustrate, the highest PC is obtained for 0.3 kg/s with spacer 407 mm2, and gradually decreases to a minimum for 0.2 kg/s with spacer 962 mm2. Analysis of Figure 125 depicts the same pattern, with the highest frequency of operation at 0.3 kg/s with spacer 407 mm2 and the lowest LPD operating frequency at 0.2 kg/s with spacer 962 mm2. Note that the other test conditions/ geometry in between the two extremes of observed frequency conform to the conditions that produce the corresponding intermediate pressure. It is thus apparent that the LPD operating frequency, f, (which is dependent on the speed of the forward and reflected waves) is highly dependent on, and is a function of PC, but not PR. While

PR dictates the sustenance of LPD, PC controls not only the onset, but also the frequency of pulsation

213

of the LPD. The operating frequency, f, also tends to increase with Φ, for a given air flow rate, ṁa, as seen in Figure 125. While the dependence of f on Φ can be at least partially explained by the heightened increase in PC caused due to H2 addition (refer Figure 115), which in turn increases the detonation wave propagation speed [339], it is shown later in the paper that the speed of the reflected wave from the RDC exit is a function of Φ.

4200

4000

3800

3600

3400

Operation Frequency, f (Hz) f Frequency, Operation 3200

3000 0.5 0.7 0.9 1.1 1.3 Equivalence ratio, Φ

0.2 kg/s - IA 0.2 kg/s - IB 0.2 kg/s - IC 0.3 kg/s - IA 0.3 kg/s - IB 0.3 kg/s - IC

Figure 125 Frequency of pulsed operation for 0.2 kg/s and 0.3 kg/s vs. Equivalence ratio

3.4. Propagation pressure analysis

Since each test run contains about 1300 laps, ensemble averaging all the laps provides statistically rigid values that could help decipher the behavior of the forward and reflected waves for the operating points tested. For the sake of brevity, only two schemes utilizing ṁa = 0.2 kg/s is discussed to show the general trend. a (scheme 490/407 mm2) shows the pressure peaks acquired from the forward propagating shock wave which conveys that the pressure peak at Axial #1 (P1) is approximately twice the magnitude seen by Axial #2 (P2). Axial #3 and #4 (P3 and P4) record considerably lower pressure peaks during forward propagation. Since the detonative nature of this instability is established in section 3.1.1, the gradual decrease in the magnitude of the pressure

214

peaks acquired from ensemble averaging indicates detonation decay, a phenomenon discussed in detail by Kuznetsov et al. [338]. Figure 127a (scheme 490/962 mm2) depicts a similar trend- the magnitude of the pressure peaks decrease continually from Axial #1 (P1) to Axial #4 (P4). The reflected wave, however, does not conform to notable trends (Figure 126b and Figure 127b).

Generally, Axial #4 (P5) tends to have the highest peak pressures suggesting a shock-focused detonation initiation in the upstream direction. Axial #1 (P8) peak pressures are comparable to those of Axial #4, and have higher magnitudes than Axial #2 (P6) and Axial #3 (P7) for most operating points, suggesting that the reflected wave gains strength near row #1 (1.905 cm from the

RDC headwall). Thus, while there is a lack of a specific trend in the pressure peak magnitudes of the reflected wave across different operating points, indicating some variation during the upstream travel of the reflected wave, there is a definite trend of decreasing magnitude of the pressure peaks of the forward moving wave after detonation, indicating that, during LPD, every cycle contains an axisymmetric pulsed detonation near the RDC headwall, gradually decaying into a detached shock wave which then gets reflected by the convergent nozzle and travels upstream. It is stressed that a very similar mechanism was deciphered by Berman et al. [281] in the thrust chamber of their liquid rocket engine by analyzing the intensity of luminous radiation emitted during the forward and reflected wave motion during longitudinal high-frequency instability in their rocket. Additionally, detonation events were conjectured to take place near the rocket engine injector heads because of the presence of very high periodic luminosity at that region which followed the arrival of the reflected shock wave near the injectors. It is thus apparent through this study on RDCs and the findings obtained from transparent rocket engines [55,281,282] operating with high-frequency instabilities that the ‘longitudinal instability’ experienced by both the propulsive devices is caused most probably due to the same physical process- a high chamber pressure due to a choked exit at the nozzle throat which causes reflected waves moving upstream that eventually detonates a fresh slug of unburnt reactants to cause a detonation that decays into an axially moving shock wave,

215

thereby continuing the cycle. An x-t (space-time) analysis of the propagating wave would lend tangible evidence towards the effect of fuel quantity on the pulsed detonation phenomenon, and is discussed next.

1.6 1.4

1.2 1 0.8 0.6

Pressure (bar) Pressure 0.4 0.2 0 0.5 0.7 0.9 1.1 1.3 Equivalence ratio, Φ

Axial # 1 Axial # 2 Axial # 3 Axial # 4

(a)

0.35 0.3 0.25 0.2 0.15

Pressure (bar) Pressure 0.1 0.05 0 0.5 0.7 0.9 1.1 1.3 Equivalence ratio, Φ

Axial # 1 Axial # 2 Axial # 3 Axial # 4

(b)

Figure 126 Peak pressure analysis for (a) forward wave, and (b) reflected wave during

pulsed detonation for ṁa = 0.2 kg/s with scheme 490/407 mm2

216

1.6 1.4

1.2 1 0.8 0.6

Pressure (bar) Pressure 0.4 0.2 0 0.5 0.7 0.9 1.1 1.3 Equivalence ratio, Φ

Axial # 1 Axial # 2 Axial # 3 Axial # 4

(a)

0.35 0.3

0.25

0.2 0.15 0.1

0.05 Pressure (bar) Pressure 0 -0.05 0.5 0.7 0.9 1.1 1.3 -0.1 Equivalence ratio, Φ

Axial # 1 Axial # 2 Axial # 3 Axial # 4

(b)

Figure 127 Peak pressure analysis for (a) forward wave, and (b) reflected wave during

pulsed detonation for ṁa = 0.2 kg/s with scheme 490/962 mm2

3.5. Distance-Time analysis

Time indices are extracted from the pressure peaks discussed in the prior section, which are in turn acquired from ensemble averaging each lap of LPD, for a given test point. The forward and reflected shock waves are plotted in x-t coordinates as shown in Figure 128, Figure 129, and Figure

130. All the equivalence ratios for a given geometry scheme and ṁa are plotted together, with the Φ

217

shown to the right. Recall that the nozzle throat area is controlled by varying the width of the nozzle spacer, and as a result the shock wave needs to travel x ≈ 1.5 mm more for 490/685 mm2 and about 3 mm more for 490/962 mm2. Taking this small spatial variation into consideration, in order to estimate the arrival time of the shock wave at the exit (since there are no sensors at the actual exit), the time indices of P4 and P5 (refer Figure 122b) are averaged and plotted as the shock arrival time at the exit, thus forming the right-most point in the x-t diagrams. On an average for all the geometries, Φ and ṁa tested, the forward wave takes t ≈ 88 μs to reach the nozzle, and the reflected wave requires t ≈ 126 μs to reach Axial #1 indicating the lower strength of the reflected wave, as opposed to the shock wave formed by the initial detonation. The speed of the forward wave, on an average is about 1380 m/s (75% of Chapman-Jouguet speed for H2-Air mixtures at Φ =

1, at 1 bar), and that of the reflected wave is around 570 m/s (31 % of C-J speed). This finding is in implicit agreement with the results of Kuznetsov et al. [338,340], where detonation decay phenomenon was studied in mixtures with a sharp concentration gradient. Kuznetsov et al. observed 30%-40% C-J speed for the leading shock, which detached from the chemically reacting zone after detonation, due to a sharp concentration non-uniformity. Since the reflected wave travels at 31% C-J speed, it witnesses regions of sharp concentration gradients which would be the case if there is complete temporary occlusion of the injectors. Hence, the reflected wave propagation during LPD mechanism can be explained by attributing it to detonation decay and re-initiation in concentrations with a sharp gradient, whereas the forward wave’s detonation decay at 70-80% C-J speed is attributed to propagation in a mixture with smooth concentration gradient.

The reflected wave with 30% C-J speed is suddenly exposed to a fresh slug of reactants exhaled from the injectors after the temporary occlusion caused by the detonation event from the previous cycle (discussed in section 3.1.1 using air inlet sensors). Of paramount requirement is the need to explain detonation initiation by the weak reflected wave within the highly curtailed distance of lesser than 1.905 cm, which is too short a length to produce deflagration-to-detonation

218

transition (DDT) in H2-air mixtures. This process can then only be logically explained by the shock wave amplification by coherent energy release (SWACER) mechanism proposed by Lee [21,277], which, at present, seems to be the only probable process to explain direct detonation initiation by shock pulses too weak to produce shock-initiation of detonation. In essence, SWACER theorizes that a “weak shock pulse” can cause direct detonation initiation if the unburnt mixture it is moving through is pre-compressed and contains an induction-time gradient. When this pre-compressed mixture with an induction-gradient (requires dissociated species) is exposed to a weak shock, fast synchronous energy release occurs that produce a subsequent detonation, directly. Multiple experimental proofs of SWACER as a valid “shockless direct detonation initiation” theory are detailed by Bartenev and Gelfand [339]. Hence, it is hypothesized that the combination of the pre- compressed fresh slug of unburnt mixture (due to pressure feedback into injector from the detonation wave), the dissociated products of detonation from the prior cycle of LPD, and finally, the weak reflected wave from the converging nozzle effect direct detonation within 1.905 cm of the

RDC headwall. Therefore, the next cycle of LPD is actuated. It is beyond the scope of the current paper to provide direct evidence of SWACER. It is offered merely as a postulation and will be dealt with in a future work. Of additional interest is the amount of dispersion in time observed for different equivalence ratios for a given air flow rate and configuration. For instance, with scheme –

490/407 mm2, ṁa = 0.2 kg/s air flow has a forward travelling wave of similar speeds for different equivalence ratios (as indicated by the angle of the x-t slope). However, there is considerable observable difference in the speed of the reflected shock waves as seen in Figure 128, Figure 129, and Figure 130. Lower equivalence ratios tend to produce reflected waves of lower speed. The same trend exists for all the tests, which leads to the inference that the reflected wave speed is a strong function of Φ. This can be explained by the combination of two effects: 1) increasing amounts of hydrogen with increased Φ (lower density of the reactants) enables the reflected wave to travel faster at higher Φ, in comparison to lower Φ, and 2) the detonation initiated by shock-

219

focusing at the nozzle propagates faster in H2-air mixtures when Φ is increased. Hence, the frequency of LPD is intrinsically dependent on the reactant mixture in general, and the equivalence ratio in particular.

300 s) μ 250 0.62 200 0.75 150 0.87 100 0.92

50 1.05

Instance of transit, t t ( transit, of Instance 0 1.15 0 5 10 15 1.24 Axial location, x (cm)

(a)

300 s) μ 250 0.71 200 0.71 150 0.82 100 1.03 50 1.03 Instance of transit, t t ( transit, of Instance 0 0 5 10 15 1.14 Axial location, x (cm)

(b)

Figure 128 x-t plot of the forward and reflected waves for (a) 0.2 kg/s, and (b) 0.3 kg/s with

scheme 490/407 mm2

220

300 s) μ 250 0.63 200 0.72 150 0.84 100 0.95 50 0.96 Instance of transit, t t ( transit, of Instance 0 0 5 10 15 1.25 Axial location, x (cm)

(a)

300 s) μ 250 200 150 0.619 100 0.82

50 0.94

Instance of transit, t t ( transit, of Instance 0 0 5 10 15 Axial location, x (cm)

(b)

Figure 129 x-t plot of the forward and reflected waves for (a) 0.2 kg/s, and (b) 0.3 kg/s with

scheme 490/685 mm2

300 s) μ 250 200 150 0.76 100 0.826

50 1.04

Instance of transit, t t ( transit, of Instance 0 0 5 10 15 Axial location, x (cm)

(a)

221

300 s) μ 250 200 150 0.9

100 1.03

50 1.03

Instance of transit, t t ( transit, of Instance 0 0 5 10 15 Axial location, x (cm)

(b)

Figure 130 x-t plot of the forward and reflected waves for (a) 0.2 kg/s, and (b) 0.3 kg/s with

scheme 490/962 mm2

3.6. Proposed mechanism

From the above sections, it is clear that there are three facets to LPD instability, namely: inception, sustenance and frequency of operation, as schematized in Figure 131. From section 3.1, inception of LPD is theorized to be dependent on the backpressure (PC) before ignition, since for similar air injection pressure ratios tested in the same facility without a convergent nozzle [246] there was complete absence of LPD. This claim is supported by the finding by Schwer and

Kailasanath [89] where stronger tertiary shock waves near the RDC exit are observed with increasing backpressures. Thus PC is pertinent to induce reflected shock waves from the RDC exit, which is the primary requirement for LPD. While PC seems to cause the inception of LPD, its self- sustained existence is dependent on the air injection pressure ratio, PR. Regime of LPD operation is approximately demarcated by a band of PR (1.4 ≤ PR ≤ 1.85), with LPD being the preferred mode between the regime of normal rotating detonation (PR ≥ 1.85) and the mixed regime of both LPD and RD (1.12 ≤ PR ≤ 1.2). While brief instances of LPD are existent for 1.12 ≤ PR ≤ 1.2, it cannot

222

sustain continually, and decreasing the PR further (PR ≤ 1.12) completely removes LPD but produces chaotic instability which is distinguished by aperiodic rotating detonation. Note that chaotic instability is caused due to improper mixing of air and fuel caused by the varied time it takes for the air and fuel plenum to recover from the pressure feedback after subsequent detonation events

[250]. Hence, when the RDC operation is within the above-mentioned cordial PR, a complex combination of multiple processes occurs in close succession to sustain LPD. The individual facets of the processes discussed in section 3.1-3.5 are summarized in the flow chart presented in Figure

132.

The frequency of LPD is dependent on both PC and Φ. For H2-air mixtures in an RDC, increasing the ignition pressure (PC) prior to detonation causes faster detonation waves [21,43]. Increasing the

Φ also causes the operating frequency to increase by virtue of faster reflected wave propagation in the lower density brought about by the increased H2 content. The forward travelling decaying detonation wave is at around 75% C-J ideal speed, whereas the reflected wave is at approximately

31%, suggesting a similar mechanism as that discussed in [338]. This leading shock front from reflection is strong enough to initiate detonation again when it comes into contact with the slug of fresh reactants (expunged after the momentary occlusion of the air inlet due to the previous LPD cycle) between the RDC headwall and Axial #1 leading to another detonation with sharp increase in pressure (P1). Thus, the cyclic process of LPD in an RDC is continued indefinitely for a given PR without an external ignition source, or a mechanical valving assembly for fuel and air.

223

Inception Backpressure

Sustenance Air injection pressure LONGITUDINAL PULSED ratio DETONATION

Backpressure

Frequency

Equivalence ratio

Figure 131 Flowchart of LPD causality

Figure 132 Proposed mechanism during sustained LPD

4. Conclusions

A parametric study of the pulsed detonation phenomenon in rotating detonation combustors is conducted. By varying the backpressure, air injection pressure ratio, air flow rate and equivalence ratios of H2-air mixtures, the longitudinal pulsed detonation (LPD) instability is investigated in detail and the dependent variables are extracted. Three facets to LPD instability are discovered: inception, sustenance and frequency of pulsing. The inception of LPD instability is linked to the

224

backpressure experienced by the RDC, since this phenomenon does not exist when there is no throat at the RDC exit. The sustenance of this mechanism, however, is found to be dependent on the air injection pressure ratio. LPD occurs when the pressure ratio across the air injection is between

1.4 and 1.85. Above an injection ratio of 1.85, conventional rotating detonation manifests inside the combustor. Between pressure ratios of 1.12 and 1.2, rotating and pulsed detonation alternate each other for a given operating point, indicating the inherent stochasticity in the process at these pressure ratios. Below a pressure ratio of 1.12, chaotic detonation propagation characterized by widespread random failures and re-ignition of the detonation wave is observed. The frequency of the pulsed detonations is wholly dependent on the backpressure and equivalence ratio, and the increase of either causes an increase of the operating frequency. LPD is thus caused by the combined denouement of the above-mentioned factors and operates between 3100 Hz < f < 4200

Hz for the facility tested. The strength of the reflected wave from the choked RDC exit is found to not be of sufficient amplitude to cause direct detonation initiation. Additionally, the critical length required to produce deflagration-to-detonation transition in hydrogen-air mixtures is also not met in the RDC. Hence, we propose a mechanism that is predicated on detonation initiation through shock amplification by coherent energy release (SWACER) mechanism to explain the subsequent detonation ignition events by the weak reflected shock pulse. The fact that there is notable momentary stoppage of the air flow after each pulsed detonation event augments this hypothesis of the reflected wave coming into contact with a fresh slug of reactants that is heated by the products of the previous cycle.

The implications of the instability are multifold and significant. First, it is necessary to control the occurrence and operation of this instability if practical integration of RDCs with a downstream turbine (backpressurizing device) is ever to be realized. Thus, comprehensive future research, especially numerical and visual experimentation, is warranted to ascertain the facility-specific occurrence of LPD. Second, LPD seems to be the only means, at present, to attain a truly valve-less

225

pulsed detonation combustor which can operate in the kilohertz regime (an order of a magnitude higher than current capabilities), the likelihood of which was unfeasible thus far. Finally, the very high similarity between LPD in RDCs and ‘longitudinal high-frequency combustion instability’ in rocket engines cannot be understated. The multiple overlaps in the findings of the current article and those acquired from rocket engine research predicates an identical mechanism to be behind the cause of occurrence and sustenance of the longitudinal instability in both the devices. Hence,

LPD holds extreme implications for the future of RDCs, PDCs and rocket engines, and it is the contention of the authors that this phenomenon commands considerable investment of the future research of the said fields.

226

CHAPTER 6: AMPLITUDE MODULATED INSTABILITY IN REACTANTS PLENUM OF A

ROTATING DETONATION COMBUSTOR

Chapter Abstract

The pronounced interest in rotating detonation combustors (RDC) in recent years has witnessed the investigation of multiple facets of the combustor, like reactants, injection schemes and combustor geometry. The issue of instabilities in RDCs is a nascent field, and requires both the identification, and the subsequent explanation of different instability mechanisms. In particular, we are concerned with the low frequency instability exhibited by the detonation wave. This is attributed to two different types of low frequency instabilities— amplitude and frequency modulated— that are discovered in the air plenum of an RDC, and subsequently discussed. The occurrence of these instabilities is observed to depend on the fuel injection scheme used and the air flow rates through the combustor. The amplitude modulated instability in the air inlet is spatially varying, and rotates in a direction opposite to the direction of the detonation wave. At higher air flow rates, and thus higher pressure ratios across the air injection, this instability disappears. A preliminary hypothesis is proposed to explain this amplitude modulation.

Nomenclature

ṁa - mass flow rate of air (kg/s)

Φ - equivalence ratio t - time (s) lfo/ dfo - length of the fuel injector holes/ the diameter of the holes wcb - width of the combustor channel (mm) wap - width of the air inlet slot (mm)

227

dcb - radius of the combustor (mm) lcb - axial length of the combustor (mm) wfo - width of fuel injection slot with equivalent area (mm)

Ws - average wave speed (km/s)

PR - ratio of time-averaged static pressure in air plenum and combustor during hot-fire

∆t - detonation wave arrival time difference between two sectors (s)

∆T - low frequency oscillation arrival time difference between two sectors (s)

1. Introduction

Deflagration, the more commonly observed and studied combustion mechanism, is characterized by subsonic combustion waves that always have a miniscule pressure drop across them. Detonation, contrastingly, is distinguished by sonic to greater-than-sonic wave speeds, and is structured with a shock wave-chemical reaction zone coupling, with each entity sustaining the other through a feedback loop [21]. This usually produces a pressure gain of 13-55 in gaseous mixtures [1], a characteristic that has been seen as highly desirable in recent years due to a prospective increase in fuel efficiency since more work can be attained for a given supplied energy, in comparison to deflagration. Hence, detonation combustors are being studied with increasing frequency and effort, to orient the future of propulsion and power towards the detonation mechanism. Rotating detonation combustors (RDCs), unlike pulsed detonation combustors (PDCs), are not valved, and courtesy of the rotating detonation spinning azimuthally in the kiloHertz regime, the exhaust flow field is quasi-steady. Hence, recent research efforts worldwide have almost exclusively concentrated on RDCs. Research into RDCs has intensified only in recent times, despite the combustor itself having been conceived and built in the 1960s [341]. Multiple factors like the reactants type, combustor geometry, thrust, oxidizer and fuel flow rates, and the rotating detonation wave speed at these conditions have been studied. The next obvious step is to identify

228

and understand the various instabilities in RDCs. The field of combustion instabilities in RDCs is extremely nascent in comparison to the monumental work done in addressing the instabilities in gas-turbine combustors and rocket engines. Few studies exist at present that have addressed RDC instabilities to any appreciable degree [48,142,250,251,342]. The authors have addressed the four prominently occurring instabilities in an RDC of which low frequency instabilities (LFI) are a part of, and subsequently speculated on their mechanism in [250]. We use this abbreviation (of LFI) to be in continuation with the terminology used in gas-turbine combustors and rocket engines.

Traditionally, instabilities having a frequency range of 1-500 Hz are termed LFI, while those between 500-1000 Hz are termed intermediate frequency instabilities (IFI, “buzzing” in rocket engines), and those greater than 1000 Hz are named high frequency instabilities (HFI) [56]. Though the frequency of the instabilities is more often than not a function of the geometry of the combustor, historically speaking, it has been beneficial to group the instabilities this way since the underlying mechanism is generally relatable for a given frequency range. For instance, resonant acoustic interaction with the supply feeds in both the gas-turbine combustors and rocket engines manifest themselves in the LFI range [56,343].

LFI in an RDC seems to be almost ubiquitous. A brief analysis of the pressure-time traces published by the different RDC facilities worldwide gives concrete evidence of the overarching existence of this instability [70,71,127,142,144,151,246,250,256,257,283,284]. However, most studies have not made an effort to address either the existence, or the mechanism behind LFI.

Considering the crippling effects of LFI in rocket engines, supersonic inlets and hypersonic vehicles owing to their tendency to couple with the natural resonant frequency of the structure [68,189], it is imperative to acknowledge and treat LFI as we move forward with RDC research. Experimental and numerical studies have shown that the detonation wave tends to significantly alter the plenum dynamics owing to the high peak pressures [171,179,184,291]. A ‘trailing shock wave’ that is attached to the rotating detonation wave tends to travel into the reactants plenum, thereby

229

significantly altering the dynamics [171,179,184]. Schwer and Kailasanath [171] note the existence of a subsequent reflected wave (from the back of the plenum) that is spawned when this trailing shock wave reaches the base of the reactants plenum. However, in their two-dimensional numerical analogue of RDC-plenum system with orifice-type injectors, this reflected shock wave appears to have no effect on the detonation wave dynamics. Two different hypotheses were put forth in the past to explain LFI (previously characterized by periodic “waxing and waning” of detonation peak pressure strength) in an RDC. The authors [251] and Liu et al. [142] proposed that the LFI in the combustor could be due to periodic strengthening and weakening of the detonation wave, thereby periodically altering the reactants flow, and thus establishing feedback. However, both studies employed only one pressure sensor in the combustor and, as such, have drawbacks in accurately capturing the instability dynamics, thus corrupting the explanation. Additionally, the conjecture was not supplemented with any evidence. A sequel of the previously described study by the authors employed extensive pressure sensing in the combustor, air and fuel plenum. The sensors were distributed 120o from each other to obtain a comprehensive spatial view of the instability. A

“locked-in” [286], azimuthally simultaneous, low frequency mode was observed at 235 Hz in the air inlet, at all air and fuel flow rates tested, which was then attributed to a probable Helmholtz resonation-type coupling between the air plenum and the combustor [246]. The locked-in oscillations in the air inlet manifest as a low frequency instability in the combustor, albeit at a broader frequency range [250]. Such a coupling has indeed been observed in gas-turbine combustors with a choked exit nozzle [287]. This study, however, deals with a notably different LFI in an RDC that is not locked-in across different flow rates, and is characterized by amplitude modulated oscillations in the air plenum. And, similar to the locked-in LFI (frequency modulated oscillations in the air inlet), the LFI treated in the current paper induces instabilities in the combustor as well. In subsequent sections, we present the experimental methodology and the

230

concomitant results to support the claim that there are two distinct LFIs in RDCs. Then, we exclusively consider the amplitude modulated LFI, and discuss its characteristics.

2. Experimental Methodology

Hydrogen-air mixtures are used to operate the RDC at air flow rates (ṁa) of 0.2, 0.3 and 0.4 kg/s at different equivalence ratios (Φ). The supply temperature for the air is about 288 K. Rotating detonation wave onset and propagation in an RDC is not direct because it involves a complex combination of plenum coupling and deflagration-to-detonation transition (DDT) mechanism [161].

This produces a finite ‘transient / onset time’ which precedes steady-state RDC operation. In our previous study, we had established that this transient, onset time in RDCs is highly dependent on the flow rates and the presence of a choked exit [157]. For 0.4 kg/s (without nozzle — as is the case here), the transient onset time was observed to be not more than 207 ms [157]. Bykovskii et al.

[161] note onset times of 4-80 ms using varied ignition methods. Peng et al. [284] observed transient operation for roughly 7 ms after ignition. Hence, it is contended that the total testing time duration of 0.35 s used in this study is significantly longer than the detonation onset time, and hence can be concluded to be representative of steady-state RDC behavior. Note that the tested RDC attains thermal equilibrium far later (more than 3 s) after it attain operational steady-state [344].

The air and fuel flow rates are controlled by a closed-loop system of nitrogen-driven pilot regulators and a set of Flowmaxx sonic nozzles. The equivalence ratios discussed henceforth are global values estimated from the stagnation pressure and temperature upstream of the choked sonic nozzle. Three-dimensional numerical cold-flow simulations of the current type of mixing scheme (slot-orifice) have shown notable variations in the local equivalence ratio (varies from 0 — air — to about 2.5) depending on the flow rates and geometry [186]. Despite the local equivalence ratio fluctuation, the overall macroscopic dynamics of RDC seems to follow clear trends, as evidenced by operating maps and detonation wave speeds [27,40,43,128]. Hence, for the purposes

231

of the present study on RDC plenum coupling, we assume these local variations in reactivity inside the RDC annulus to have a negligible effect on LFI. Norgren VP50 proportional control valves (pilot) are linked to Norgren pilot-operated regulators to isolate electrical components from the primary fuel supply. GE Unik 5000 sensors are linked to the choked-flow nozzle assemblies to monitor air and fuel flow rates. Fuel flow is administered to the rig through a pneumatically-actuated Bi-Torq isolation ball valve located just upstream of the fuel plenum, which allows fuel flow rates to stabilize within 2 s of fuel introduction. Testing is done for a time period of about 0.35 s. The time- averaged stagnation pressure in the air plenum for these flow rates are about 2.4 bar, 3.3 bar and

3.8 bar respectively, during hot-fire operation. The static pressure evolution inside the air plenum, fuel plenum and combustor before and after ignition is shown in Figure 133. Our prior experience with RDCs has shown that high speed flush-mounted pressure sensors tend to permanently break if exposed to the RDC environment for more than a second [43]. This is usually circumvented by using stand-off tubes that attain the accurate frequency information, but this induces inaccuracies in pressure data [149]. Hence, longer operation times are avoided here since our goal in this study is to accurately capture the RDC dynamics. There is no zero / offset error in the sensors because this is removed through software before the hot-fire run. Thus, the systematic error in flow measurements is only from the scaling error of the instruments. The relative errors in the static pressure sensor and thermocouple are known from the associated instrument specifications. This is used to attain the uncertainty in the pressure and thermocouple sensors used in the reactants delivery, and is found to be ±0.069 bar and ±1 K (at the maximum output), respectively. This causes a ‘propagation of uncertainty’ from the sensors to the air and fuel flow rates, which in turn induces some error in the estimated equivalence ratios. The linearized error analysis of these uncertainties result in an estimate of 2.1% error in the air mass flow rate and 2.8% in fuel mass flow rate, which in turn results in a maximum error of 3.4% (seen for the lowest flow rates) in equivalence ratio.

The error in the discussed fundamental frequency is about 2.86 Hz (frequency resolution =

232

sampling rate / number of obtained samples). The standard deviation in the lap-to-lap detonation wave speed (Ws) acquired through a time of flight algorithm is not more than 5% of the average speed, for a given test point.

P Air plenum A

Fuel plenum

Fuel valve opening

Combustor PC

Ignition and hot-fire

Figure 133 Static pressure variation before and after RDC ignition, obtained from capillary

tube average pressure sensors

A front and side-view schematic of the RDC and the associated instrumentation is shown in

Figure 134a. Air and fuel are supplied from two separate plenums (blue and green, respectively) to attain non-premixed mixing. Air is injected radially inwards through a circumferential slot and fuel is injected axially through a circumferentially distributed array of fuel orifices. This slot-orifice mixing scheme is visualized in Figure 134b. The reactants mix through this orthogonal slot-orifice injection scheme and are ignited by a pre-detonator (grey tube). The pre-detonator tube is fed with opposing jets of ethylene and oxygen that are supplied at the headend through Parker solenoid valves. The stagnation pressure upstream of the valves is about 8 bar for both the reactants. Note that this stagnation pressure dictates the global equivalence ratio of the mixture inside the pre- detonator. However, our prior analysis of the initiation characteristics of the pre-detonator suggests that the energy input by this method of RDC ignition is about an order of magnitude

233

smaller than the energy requirement to attain direct detonation initiation inside the RDC [156].

RDC ignition is thus possible across a wide range of pre-detonator equivalence ratios [156]. The only requirement is to have a detonation wave deposit into the RDC channel from the pre- detonator. This initial detonation wave is theorized to cause a complex deflagration-to-detonation transition (DDT) mechanism [156] that finally results in the deposition of a detonation wave into the RDC channel (red area). A spark plug that is located in between the two solenoid valves is actuated to ignite the pre-detonator mixture, which eventually evolves into a detonation wave inside the pre-detonator. The presence of a detonation wave inside the pre-detonator tube is verified using two ionization probes (not shown here) that accurately capture the speed of the supersonic wave. For a detailed description of the pre-detonator system, we direct the attention of the readers to our previous work [156].

The air injection slot area is maintained constant throughout the testing, whereas two different fuel injection schemes having the same total injection area are used. The fuel scheme is altered by using the required “fuel plates”. These are essentially stainless steel plates with the required fuel orifices pattern. The first fuel injection scheme (which we will call FP-I) has one row of circumferentially distributed orifices (diameter of orifice, dfo ≈ 1mm) whereas the second scheme

(FP-II) has three rows of orifices (dfo ≈ 0.75 mm). Thus, the total number of holes is higher for FP-II, but the area of the individual holes are smaller than that of FP-I. The length-to-diameter ratio

(lfo/dfo) of FP-I is 12.8 for each individual orifice, whereas the lfo/dfo of FP-II is about 17. A generic schematic of the two schemes is given in Figure 134c. Both the schemes have orifices right at the outer wall of the RDC, i.e. by the opening of the air inlet. However, due to the three-rowed arrangement of FP-II, the fuel orifices extend to about 60% of the channel width, wcb. For FP-I, the orifices extends only to about 25% of the channel width. Other dimensions of interest of the RDC are given in Table 1. A detailed overview of the RDC geometry and the facility is presented in our previous publications [43,323].

234

(a)

Annulus Slot

Orifice Fuel plate

(b)

235

(c)

Figure 134 (a) RDC - front view, sectional cut and magnified RDC annulus (clockwise), (b)

magnified view of the injection scheme, and (c) generic front view schematic of the fuel

orifices layout in the two fuel schemes (Note: the pattern is repeated circumferentially)

The RDC under study has multiple instrumentation ports. There are three stations (I, II and III in Figure 134a) that are sectorial and are distributed 120o from each other, with each station having four axially distributed rows of instrumentation. The remainder of the paper will resort to this nomenclature of color-coding (blue -station I, black – station II, red – station III) to represent the three sectors/ stations in which the pressure sensors are placed. Note that a given station comprises of an axial array of four rows of instrumentation ports in the combustor and one port in the air inlet that is offset from the combustor ports by 20o. The small angular offset between the air inlet sensor and the combustor sensor is necessary to have pressure sensors in both the locations, which otherwise would not be possible since the finite lengths of the two pressure sensors would spatially block each other. This lets us monitor the RDC dynamics spatially by dividing the combustor into three sectors. Roman numerals are used to identify a given station and the usual numeration is used to identify a given axial port location. For instance, I-1 signifies an instrumentation port in the first row of the first station. A total of nine PCB piezoelectric pressure sensors are used— three in the air inlet (blue circles/ tabs in Figure 134a), three in the combustor

(red circles/ tabs in row 1 of all three stations in Figure 134a) and three in the base of the fuel plenum (green circles/ tabs in Figure 134a). The fuel plenum sensors are on the same angular plane as the combustor sensors, but their radial location (measured from the RDC axis) is offset inwards from the RDC annulus by about 6 cm. It is to be noted that data from the fuel plenum sensors are not discussed in the current paper. There are no piezoelectric sensors in rows 2, 3 and 4 of any of the stations. The data from the PCB piezoelectric pressure sensors are acquired at 1 MHz. In addition to the high-speed pressure sensors, three low-speed capillary tube averaged pressure

236

sensors (CTAP) are used at a 1 kHz acquisition rate. The CTAP arrangement consists of a long plastic tubing (about 120 cm) with an inner diameter of approximately 3 mm, at the end of which a low speed static gauge pressure sensor is attached. While the common notion is that CTAP sensors give a time-averaged value of static pressure, and have been extensively used in RDCs, recent discussions have questioned this assumption [334,345]. Irrespective, we resort to this sensor setup to attain the nominal static pressure values while protecting the sensors from the hostile RDC environment. One CTAP sensor is placed in the air plenum, fuel plenum and the combustor, each

(not shown in the figure), to ascertain the average nominal pressures in the air and fuel plenum, and the combustor, respectively. The three sensors in the combustor (row 1 – stations I, II and III) are located 1.9 cm away from the RDC headwall. The air inlet sensors are at a location that is 2.54 cm from the combustor outer wall. The three air inlet sensors (blue circles/ tabs in Figure 134a) obtain the plenum dynamics during rotating detonation in the combustor. Both numerical and experimental studies have shown that the rotating detonation wave causes considerable pressure feedback into the air inlet and a concomitant momentary localized occlusion due to its peak detonation pressure being higher than the plenum feed pressures [28,104,171,246,291]. Schlieren imaging of a two-dimensional analogue of the slot-orifice RDC mixing scheme by Bedick et al. [179] revealed considerable shock wave leakage from the detonation wave (using a timed pre-detonator to simulate rotating detonations) into both the air and fuel plenum. However, they note that rather strong shock waves are inducted into the air inlet owing to its higher injection area which in turn heightens the exposure to the detonation wave. In contrast, only relatively weak “pressure waves” leaked into the fuel plenum owing to the probable viscous damping caused by the small orifice size.

Fotia et al. also note “pressure waves” that propagate into the fuel plenum due to detonation wave propagation in their two-dimensional RDC analogue [184]. Hence, the common consensus seems to be that the slotted air inlet is prone to shock wave leakage from the detonation wave during each of its lap, whereas the multi-holed fuel injection is only prone to a weak pressure wave, which is

237

presumably just an acoustic wave. We have shown that this localized feedback into the slotted air inlet, through shock wave leakage, can be used to effectively capture (using piezoelectric sensors) not just the air plenum dynamics but also the detonation wave speed [246].

Table 11 RDC geometry

Part Geometry measured Dimension

Fuel scheme-I (FP-I) length/ diameter (lfo/dfo) 12.8

Fuel scheme –II (FP-II) length/ diameter (lfo/dfo) 17

Air injection slot width (wap) 1.02 mm

total slot area 490 mm2

Combustor channel width (wcb) 7.5 mm

inner diameter 139 mm

outer diameter (dcb) 154 mm

annulus area 760 mm2

length (lcb) 125 mm

3. Results and Discussion

3.1. Two types of low frequency instabilities (LFI)

Rotating detonation combustor operation in the current facility exhibits low frequency instabilities at most operating conditions, as described in [250,251]. We had statistically analyzed

LFI (in terms of the number of detonation laps occurring per “packet” of waxing and waning) using only a single pressure sensor in the RDC annulus for two air flow rates spanning a range of equivalence ratios for three different fuel injection schemes, and found there was an absence of a clear trend [251]. This motivated another study which used pressure sensors in the air inlet and the combustor [246]. A singular mechanism of LFI was conjectured to produce the low frequency

238

oscillations (150-500 Hz) seen in the combustor and the air plenum. However, upon a closer inspection, we observe two distinct physical mechanisms in the air inlet that seemingly produce unstable detonation propagation inside the combustor at the low frequency regime. Depending on the fuel injection scheme used and the air flow rates, the oscillation in the air inlet is either amplitude modulation (AM), or frequency modulated (FM), or both occurring in tandem. FM LFI is only observed when FP-II (lfo/dfo = 17) is used. AM LFI is observed only at the air flow rate of 0.4 kg/s and does not appear at 0.2 kg/s and 0.3 kg/s. To distinguish the two LFIs, it is imperative to study the pressure traces in both the combustor and the air inlet for the geometric case that sustains both (FP-II). Figure 135a is an arbitrary pressure trace from the combustor that shows highly unstable detonation wave propagation that varies sinusoidally in strength as the detonation wave moves circumferentially through the three instrumented sectors of the RDC, implying a continual variation in the rotating detonation wave strength. Figure 135b gives a pressure time series when there only FM oscillation in the air inlet. The carrier signal is the leaked shock wave from the detonation propagation through the three sectors. This carrier pressure signal, however, can be seen to have a sustained base pressure modulation (thereby, being frequency modulated) that is azimuthally simultaneous. That is, all three sectors are prone to sinusoidal increases and decreases in the base pressure. We will call this ‘spatial uniformity’ in the air inlet. This case can be contrasted with Figure 135c, which shows pressure traces depicting very high spatial non- uniformity, despite also exhibiting FM oscillations (once again at 235 Hz). Here, ‘spatial non- uniformity’ is defined as the phenomenon where for a given arbitrary temporal window, a particular sector of the RDC exhibits notably higher peak pressures (of subsequent detonation laps) than the other sectors. The alternating sectoral strength is depicted in Figure 135c, which shows stronger subsequent waves in station I (blue), followed by station III (red), and finally station II

(black). This is an amplitude modulation (AM) of the carrier shock wave pressure signal. In our previous work [246], the base pressure oscillation was discovered to be locked-in at 235 Hz in the

239

air inlet (the locked-in FM instability is an additive modulation, and thus, both the low and the high frequency signals can be easily observed in the FFT plot in Figure 135d and the spectrogram in

Figure 135e).

In Table 12, the fuel injection schemes used, the air flow rates and equivalence ratios tested for each of the scheme, and the corresponding presence/absence of the two LFI types— (1) sectoral spatial non-uniformity of peak detonation feedback pressures in the air inlet (AM), and (2) locked- in base pressure oscillation in the air inlet at 235 Hz (FM)— is indicated through a binary “yes/ no”

(Y/N). This dual classification is arrived at qualitatively by visually studying the complete pressure trace for a given operating point. Points which exhibit spatial uniformity are marked “no”, whereas those operating points that do not exhibit any uniformity are marked “yes”. As seen in Figure 135b and Figure 135c, this qualitative analysis is a rather efficient process of delineation since AM LFI exhibits markedly different, visually distinct pressure traces characterized by notable variation in peak pressure strength among the three RDC sectors. We are left with two important details from this tabulation. First, the locked-in base pressure FM oscillation is non-existent when the fuel injection scheme is FP-I irrespective of the air flow rate or equivalence ratio. Second, the spatial non-uniformity instability exists for both FP-I and FP-II for 0.2 kg/s and 0.3 kg/s, but vanishes for

0.4 kg/s (higher pressure ratio of 3.2 across the air plenum and the combustor, as obtained from

CTAP sensors). Thus, it is apparent that the presence of FM LFI in the air inlet is a function of the fuel injection scheme used, in some way, and the AM LFI is dependent on the pressure ratio across the air injection.

240

(a)

(b)

(c)

235 Hz

(d) (e)

241

Figure 135 (a) Pressure series from the combustor, (b) pressure series from the air inlet (0.4

kg/s) showing FM LFI, (c) pressure series from the air inlet (0.2 kg/s) showing FM and AM

LFI, (d) FFT plot marked with FM LFI, and (e) spectrogram plot showing pronounced activity

at about 235 Hz

Table 12 Test / injection scheme conditions and associated instabilities

Air FP I FP II

ṁa PR Φ AM FM Φ AM FM

kg/ Spatial non- Lock- Spatial non- Lock-in at

s uniformity in uniformity 235 Hz

0.2 2 1.0, 1.2 Y Y N N 0.87,1.0, Y Y Y Y Y Y

1.21

0.3 2.7 1.0, 1.2 Y Y N N 0.87,1.0, Y Y Y Y Y Y

5 1.22

0.4 3.2 1.0, 1.2 N N N N 0.92,1.0, N N N Y Y Y

1.2

The remainder of the analyses is on the test cases utilizing FP-I, so that only AM LFI is taken into account. FM LFI and its propensity to occur only for FP- II is to be dealt with in a separate paper. Figure 136a, b and c give the magnified pressure-time traces (it can be seen that the base pressure does not oscillate) from the three air inlet pressure sensors for an operating point at ṁa=

0.2 kg/s and Φ = 1.0. Note that the three images are continuous in time, i.e. Figure 136a ends at t =

0.302 s and Figure 136b starts at t = 0.302 s, and so on for Figure 136c. The facet to observe here is the direction of rotation of the detonation wave. The rotating detonation wave (as observed by the shock wave leaked into air inlet) moves in the counter-clockwise direction (black→red→blue /

242

station II →station III →station I) in the represented pressure traces. The spatially varying AM oscillation, however, exhibits the reverse order (blue→red→black / station II→station III→station

I). To clarify, the sinusoidal amplitude modulated variation is exhibiting a clockwise rotating motion. This kind of behavior— the spatially varying sinusoidal AM instability in the air inlet moving in the opposite direction to the rotating detonation wave— is witnessed whenever there is

AM LFI. It is thus apparent that AM LFI is characterized by the spatially varying detonation strength is not caused due to a stationary phenomenon in the air inlet or the combustor, but rather, a low- speed rotatory event in the air inlet. Since it is, in essence, a low frequency modulation of the amplitude of the high frequency carrier signal, it does not appear as a distinct frequency peak in

FFT plots in the frequency ranges of interest (100-500 Hz). Instead, AM LFI appears as a frequency peak offset from the carrier signal peak frequency (red arrow in Figure 136d). Such an offset frequency band is not observable in the spectrogram (red arrow in Figure 136e) indicating the lack of a distinct preferred frequency for AM LFI, unlike FM LFI.

(a)

243

(b)

(c)

(d) (e)

Figure 136 AM LFI pressure series from air inlet with FP – I at ṁa = 0.2 kg/s, Φ = 1.0 between

(a) t = 0.295 s and t = 0.302 s, (b) t = 0.302 s to t = 0.31 s, (c) t = 0.31 s to t = 0.317 s, and (d)

FFT plot and (e) Spectrogram plot

244

3.2. Analysis of AM instability

This section deals with the particular characteristics of AM LFI with respect to its association with the RDC air flow rate, detonation wave speed and directionality. Three operating points are chosen that best show the intricacies of AM LFI and perform case-studies on it. A peak-tracking algorithm was developed to capture the peak pressure (explained in detail in [250]) of the feedback from the rotating detonation wave on the air inlet from all the three air inlet sensors. This algorithm is further developed to have the capability to predict the detonation wave directionality

(clockwise/ counterclockwise) by analyzing the time difference of the peak detonation pressures through three sectors (∆t) from the three pressure signals simultaneously, for subsequent laps.

Thus, any switch in the detonation wave direction, which happens frequently in the RDC environment [151,152,156], is instantaneously captured. Note that such a direction shift capture necessitates that there be at least three circumferentially distributed sensors. Clockwise detonation wave rotation is associated with a positive detonation speed value, whereas counterclockwise rotation is represented with the negative of the detonation speed magnitude. Since the AM LFI is approximately sinusoidal among the different sectors (refer Figure 136), it is possible to extract the envelope of the amplitude modulation in the three sectors by using the peak pressure obtained from the individual detonation wave passage. Now, this envelope of AM LFI in the three sectors is used to obtain the peak pressure of the envelope. Thus, in a manner similar to the computation of the detonation wave speed, the speed of the rotary AM LFI is estimated by getting the time index of the highest point of the sinusoids. The circumferential distance at the position of the air inlet sensors (which is 154 + 25 = 179 mm away from the central RDC axis) is then divided by these temporal differences of subsequent amplitude modulations (∆T) to arrive at a value of AM rotary velocity (product of circumferential distance between each sensor in air inlet and time difference between each of the sensors) in the air inlet at the position of the pressure sensors. This algorithm is visualized in Figure 137. It is emphasized that the absence of AM LFI (for 0.4 kg/s) does not

245

produce this envelope of peak pressures, thereby enabling the algorithm to ascertain when there is no AM in the air inlet.

AM LFI rotating speed tracking Detonation wave speed tracking ∆T ∆T

Extracting ∆t ∆t envelope of AM

III II I III II I

Figure 137 Visualization of peak-tracking algorithm that computes detonation wave speed

and AM LFI rotating speed through obtaining peak pressures and time indices

In the current test matrix, the detonation wave flips direction often for all test cases run at 0.2 kg/s and 0.3 kg/s with the exception for the first case to be discussed below. Tests were repeated at this condition (ṁa = 0.2 kg/s, Φ = 1) multiple times, and we reached the conclusion that the rotating detonation wave is prone to random switching at this operating condition as well. This incurs an associated stochasticity in the direction of AM LFI. Thus, this AM instability is not rigidly repeatable for a given operating condition, as in the rotary speed of the AM LFI varies across different hot-fires since it is intrinsically linked to the detonation wave speed, which in turn is extremely random. But, the analysis of the pressure data from all the test points confirm that the AM LFI always propagates in a direction that is opposite to the detonation wave direction. In this sense, the first test case discussed below is a rather serendipitous event in that the detonation wave switched direction only three times throughout the whole test. The AM LFI seems to be “destroyed” every time the detonation wave changes direction since the detonation wave onset and propagation is fast and instantaneous, but the mechanism behind the amplitude modulation is apparently not. Therefore, unlike the detonation wave speed direction, the AM LFI direction is not acquired since it exists for too short a duration to clearly define for a complete test. But, it is possible to qualify AM LFI

246

direction at localized time intervals in the figures below. A magnified pressure-time trace of the three air inlet sensors, the complete pressure trace for the whole test duration of approximately

0.35 s, the normalized envelope of AM LFI, the AM LFI rotary speed, and the detonation wave speed with the associated directionality are given as subsections a,b,c,d, and e, respectively, in Figure 138,

Figure 139 and Figure 140. The envelope of AM LFI is normalized with respect to the maximum value from the complete pressure signal, which happens to be around 3 bar for all the cases presented. This maximum value is from the initial detonation wave from the pre-detonator which is used to ignite the RDC.

Figure 138 deals with ṁa= 0.2 kg/s and Φ = 1.0. From Figure 138a it can be seen that the rotating detonation wave is spinning counterclockwise and AM LFI (the sinusoidal overarching component) is clockwise. Figure 138b shows the highly dynamic nature of this instability. Initially, there is incoherence and there is no marked sinusoidal spatially varying oscillation. However, from t = 0.14 s, one could observe easily delineated sinusoidal variation existing until the end of the RDC hot-fire run. Additionally, it could also be seen that the sinusoidal variation gradually “thins” with time, occurring faster as time progresses. This kind of dynamic variation in the frequency of occurrence of a phenomenon is usually termed “bootstrapping”, a non-linear phenomenon that has been seen to occur in rocket engines [346], albeit for different reasons. The normalized pressure of the low frequency spatially instability is shown in Figure 138c for all three sensors. The spatial variation and the faster occurrence of the instability throughout the test can be easily noticed. In fact, the plot of the AM LFI velocity vs. time (Figure 138d) shows that initially the induced velocity is around 40 m/s, and continuously increases from t ≈ 0.135 s to t ≈ 0.275 s, after which time it plateaus to a speed of 100 m/s. The gradual increase in AM LFI velocity until a terminal condition can be better understood by analyzing the detonation wave speed and directionality plot shown in

Figure 138e. The rotating detonation wave establishes in the clockwise direction initially and rotates in this direction until t ≈ 0.135 s. However, at t ≈ 0.135 s there is a sudden stochastic flip in

247

the direction to counterclockwise rotation, and from t ≈ 0.135 s till t ≈ 0.34 s, the rotating detonation wave exhibits stable directionality in the counterclockwise direction. It is thus apparent that the steady increase in AM LFI to a terminal value from t ≈ 0.135 s is closely linked to the rotating detonation direction, i.e. as long as the detonation wave maintains its direction of rotation, the AM LFI in the air plenum maintains its direction. The amplitude modulation in the air inlet seems to exhibit a considerable transient operation followed by an apparent steady-state period where the rotary velocity of AM LFI is plateaued. This terminal rotary speed is approximately 100 m/s, for the present test condition. As will be shown below, this plateau in the rotary speed is not observed when the detonation wave flips direction frequently.

Figure 139 (ṁa= 0.3 kg/s and Φ = 1.0) is in contrast to Figure 138. The magnified pressure series in Figure 139a shows that while the spatial non-uniformity due to AM is still considerable, the oscillation time scale rapidly evolves as the instability rotates in the air plenum. A better view of the inherent stochasticity in the AM LFI magnitude and time scale can be observed in Figure 139b, which presents the complete pressure-time trace for the test point. The normalized oscillation magnitude of AM LFI (Figure 139c) also indicates the stochasticity for this test case of 0.3 kg/s.

Since the equivalence ratio is the same as the prior case, one could contend that the variation seen here is produced due to physical, fluid dynamic effects as opposed to chemical. To elucidate, the results from our three-dimensional simulation of cold-flow mixing characteristics of the current

RDC geometry showed that the variation in local equivalence ratio is negligible across different air flow rates, provided the global equivalence ratio across the air flow rates is held constant [186].

Hence, there is no reason to assume that the detonation wave strength is going to vary at 0.3 kg/s, at Φ = 1.0. The variation in AM LFI for 0.3 kg/s, must then, be an effect produced due to the increased pressure ratio across the air inlet (refer Table 12). Figure 139c shows two other facets: a) the oscillation magnitude is considerably lower than the 0.2 kg/s case, and b) the direction of AM

LFI is stochastic. The amplitude modulated sinusoids exhibit both blue→red→black pattern

248

(clockwise) or the black→red→blue direction (counterclockwise), thereby indicating a lack of preferred direction. Analysis of AM LFI velocity shown in Figure 139d also shows the effects of this stochasticity in magnitude. This is attributed to be a direct consequence of the rotating detonation wave directionality (which produces AM LFI in the air inlet, thereby creating a feedback loop). The current case has multiple random switches in the direction of detonation as seen in Figure 139e.

Throughout the test length, the detonation wave exhibits high propensity to randomly switch between clockwise and counterclockwise direction. As elucidated before, this arbitrary behavior of the detonation wave directionality is a well-observed phenomenon in RDCs. At present, the only proposed theory to explain this is from the numerical simulation of Yao et al. [175] who found that improper mixing (which could be the result of AM in the reactants plenum) of the reactants facilitate the formation of random “hot spots” in the combustor, which cause explosion and subsequent generation of a detonation wave in the opposite direction. Note that detonation initiation through this kind of “explosion within an explosion” is an established phenomenon to explain detonation formation under certain conditions, as explained by Lee [21].

Advancing to Figure 140, which is representative of ṁa= 0.4 kg/s and Φ = 1.0, the general behavior of AM LFI is seen to further evolve with additional characteristics not seen in the last two cases. There is an abrupt cessation of the instability at t ≈ 0.108 s (Figure 140a). This sudden termination of AM LFI can be better observed in Figure 140b. From the moment of initiation until a time of t ≈ 0.108 s, there is considerable amplitude modulation. But, after this time, there is no more

AM LFI in the air inlet and the remainder of the test duration is characterized by the rotating detonation wave exhibiting the desirable behavior of repeatable peak-to-peak pressure magnitudes with a complete absence of spatial non-uniformity among the different sectors. The phenomenon is also seen in the normalized AM LFI envelope plot (Figure 140c) which once again depicts the absence of AM LFI after an arbitrary time for this ṁa = 0.4 kg/s test. Additionally, the overall envelope of the pressure feedback magnitude into the air inlet is notably lower than the 0.3 kg/s

249

case, which in turn is lower than the case with an air flow rate of 0.2 kg/s. The AM LFI velocity is about 200 m/s on average initially (Figure 140d). As noted in a prior section, the tested RDC did not acquire thermal equilibrium even after 3 s. Hence, this behavior is most probably due to the increase in pressure ratio across the air injection (Table 12) with increasing air flow rates.

Assuming a rotating detonation wave of equal strength that is anchored to the RDC injection headwall for the three air flow rates (which is not the case — the distance between the detonation wave and the injection plane increases with increasing air flow rate [310]), the higher air flow rate, and hence the higher pressure ratio, PR, across the injection, will naturally tend to inhibit the strength of the leaked shock into the air inlet [246]. For the lowest air flow rate of 0.2 kg/s, owing to its lowest PR among the three cases, the shock wave leakage into the plenum would be the highest. Since Cho et al. [310] have established that there is increasing ‘stand-off’ of the detonation wave from the injection plane as the air flow rate is increased, the penetrative effect of the trailing shock wave into the air plenum must be lower at 0.4 kg/s in comparison to 0.2 kg/s. Finally, at t ≈

0.108 s, the rotating detonation wave attains an extremely steady periodicity and directionality that extends till the end of the test. This onset time of steady rotation can be observed to be directly coincident with the abrupt absence of AM. It is imperative to note that the stable onset of the detonation wave entails with it a notable increase in the detonation propagation speed as seen in

Figure 140e.

250

Figure 138 Variables of interest acquired from air inlet sensors at ṁa = 0.2 kg/s, Φ = 1

251

Stochastic AM directionality AM

Unstable directionality

Figure 139 Variables of interest acquired from air inlet sensors at ṁa = 0.3 kg/s, Φ = 1

252

Abrupt stability onset

No AM

No AM AM

Stable directionality

Figure 140 Variables of interest acquired from air inlet sensors at ṁa = 0.4 kg/s, Φ = 1

253

3.3. Proposed mechanism

From the above sections, we have enough information to hypothesize a mechanism behind the amplitude modulated instability in an RDC. AM LFI, as shown above, occurs as a rotary event in the air plenum. This rotation, with sinusoidal variation in peak pressures leaked into the air inlet, occurs in a direction opposite to the direction of the rotating detonation at all the points tested.

Additionally, the manifestation of AM LFI seems to be inherently linked to the pressure ratios across the air inlet, since at 0.4 kg/s (highest pressure ratio in the current study), the AM LFI subsides. Let us consider the former observation— of a reverse rotary AM event— first. Fotia et al.

[184], in their two-dimensional experimental RDC study, have noted that the trailing shock wave

(attached to the bottom of the detonation wave, as established by Schwer and Kailasanath [171]) moves at about 60% of the detonation wave speed. Owing to this relative velocity between the detonation wave in the combustor and the trailing shock wave in the reactants plenum, they postulated a “pressure beating” event when the next detonation wave lap interacts with the trailing shock wave in the plenum from the prior lap. However, their study was a ‘one’ detonation wave event, and hence the “pressure beating”, or more accurately, constructive / destructive interference was not observed. On the other hand, Schwer and Kailasanth [171], in their numerical simulation, have noted that this trailing shock wave (incident wave) travels to the base of the reactants plenum and gets reflected as another relatively strong wave. They tested two different reactant plenum depths (to vary the strength of the reflected wave) and concluded that this reflected wave did not impact the reactants conditions upstream of the next lap of the detonation wave. In Figure 141, we have presented a schematic of the detonation wave, the trailing shock wave that is the incident wave on the base of the air plenum and the concomitant reflected wave. This model of the wave system is adapted from the two-dimensional simulations of Schwer and Kailasanath [171]. Note that the whole system of waves moves with the detonation wave in the laboratory frame of reference. However, in a detonation-fixed reference frame both the incident wave and reflected

254

wave have a relative velocity (broken arrows) that moves away from the detonation wave. The reflected shock wave moves in the opposite direction when the incident shock wave interacts with a concave surface. Additionally, multiple reflected waves are produced at discrete times and locations along the concave surface, depending on curvature and other effects [347]. Evidence for this in an RDC can be seen in the Schlieren images of an air plenum (with curved base) exposed to a detonation wave, obtained by Bedick et al. [179].

Hence, one should expect a similar phenomenon of production of multiple reflected waves moving in the opposite direction of the trailing shock wave when it is incident on the concave curved surface of the base of the air plenum of the RDC. This is represented as a highly simplified multiple reflected waves in the schematic shown in Figure 141. Thus, the trailing shock wave of the next lap of detonation wave should interact with the multiple reflected waves that are moving towards it, thereby causing constructive / destructive interference that moves in a direction opposite to the direction of the detonation wave. This effect could be understood by noting the air inlet sensors in the three sectors of the RDC (color-coded as before). The trailing shock wave from the first lap of the detonation wave is recorded by the blue sensor. However, the constructive interference between the reflected wave from the base of the plenum and the trailing shock wave of the second lap should be captured as an amplitude modulation occurring in the opposite direction

(hence captured by the red sensor), as is the case here. It is possible that this effect was not observed in the simulations [171] because it used an orifice injection system (instead of slots, which have considerably higher area and hence lower viscous damping) and a straight plenum base

(since it was a two-dimensional study). We hypothesize here that AM LFI in the air inlet is probably due to this interaction of incident and reflected waves. This is an extension of the acoustic interference hypothesis that Fotia et al. [184] that is expanded to include the effects of the reflected wave as well, in an actual RDC. Naturally, one should expect this complex system of waves to develop much slower in comparison to the detonation wave. This could explain the lower speed of

255

the rotation and the stochasticity in AM LFI when the detonation wave randomly switches direction. The absence of this effect for the flow rate of 0.4 kg/s could be due to the increased impedance produced by the higher pressure ratio, which might hinder the production of a strong trailing shock wave into the air plenum. Cho et al. [310] found that the ‘stand-off distance’ increases almost linearly with increasing air flow rates. This fact that the detonation wave significantly “lift- offs” from the RDC injection plane at higher flow rates might also produce weaker shock waves that might not significantly penetrate the air plenum. Visualization of the reactants plenum is required to further test the proposed hypothesis.

Lap 1 Lap 2

Combustor - Plenum boundary

Curved Plenum outer-wall boundary

Figure 141 Schematic of the incident and reflected wave in the reactant plenum produced

due to the detonation wave in the combustor. Adapted from Schwer and Kailasanath [171]

4. Conclusions

Low frequency instabilities observed in rotating detonation combustors are linked to two distinctly different types of instabilities in the air plenum of RDCs. The first is recognized by frequency modulation in the air inlet, whereas the second is distinguished by amplitude modulation on top of the carrier signal that is the detonation wave. The occurrence of these instabilities seems to depend on the fuel injection scheme used and the air flow rates through the RDC. These instabilities occur either in tandem or exclusively depending on the operating conditions. The

256

amplitude modulation instability was considered specifically for further analysis. Amplitude modulation occurs as a rotary event that is tracked through the different sectors of the RDC. This type of phase-lagged low frequency rotating instability has been observed in rocket engines, as well

(Figure 9.7.1i in [56]). There, it is called a “precessing tangential mode” and is noted to have anywhere between five to hundred tangential wave laps per low frequency cycle. Here, it moves in a direction opposite to the direction of the detonation wave. Higher air flow rates, and thus higher pressure ratio across the air inlet, tend to remove this amplitude modulation. A hypothesis is proposed that attributes this instability to a probable constructive / destructive interference that could occur between the trailing shock wave from the detonation wave to the reverse moving system of incident wave and reflected wave (from the base of the plenum) from the previous lap of the detonation wave. Further experimentation is required to accurately capture and analyze this phenomenon. Regardless, the preliminary findings suggest that the nature of RDC-reactants plenum coupling is a complex process that requires considerable attention.

257

CHAPTER 7: THE ORIGINS OF WAVE DIRECTIONALITY, CHAOTIC PROPAGATION AND

ONSET TIME AFTER IGNITION IN A ROTATING DETONATION COMBUSTOR

Chapter Abstract

The phenomena of onset time after ignition, chaotic detonation propagation and stochastic wave directionality is dealt with in the current paper. By altering the air and fuel flow rates, plenum supply pressures and the backpressure on an RDC, the effect of the disturbance of the cold-flow system at rest by the onset of a detonation event ignition is studied. The RDC-plenum coupling is modelled as a black-box system to reveal that the onset time for the studied backpressurized operation is dictated by the settling time of the air plenum, whereas such a congruence does not exist for atmospheric RDCs. For the latter, the onset time is found to depend on the fuel plenum, where detonation propagation produces incrementally stronger reflections and reverberations at lower plenum pressures. This issue of plenum disturbance from the initially stable condition is also used to explain the process of chaotic, haphazard detonation propagation at lower flow rates and the associated stochasticity in the wave direction after ignition.

Nomenclature:

ṁa - mass flow rate of air (kg/s)

Φ - equivalence ratio t - time (s)

PA - air plenum pressure before ignition (bar)

PF - fuel plenum pressure before ignition (bar)

258

1. Introduction

Detonation waves are mostly distinguished by sonic to greater-than-sonic wave speeds, and are structured with a shock wave-chemical reaction zone coupling, with each entity sustaining the other through a feedback loop [21]. This usually produces a pressure gain of 13-55 in gases [1] — a highly desirable characteristic due to a prospective increase in fuel efficiency since more work can obtained, in comparison to deflagrations [320]. Hence, detonation combustors are studied with increasing frequency and effort. The most promising of such devices is the rotating detonation combustor (RDC). It is characterized by an annulus (usually) that is fed reactants continuously and one or more detonation waves propagation circumferentially in the kilo-Hertz regime. Multiple factors like the reactants type, combustor geometry, thrust, oxidizer and fuel flow rates, and the detonation wave speed at these conditions have been studied in recent years [18,148]. However, significant challenges still remain. One such issue is the directionality of the rotating detonation wave, which is observed to stochastically change across most operating conditions, across multiple facilities [18,152,157,159]. At seemingly random times, the wave reverses direction (clockwise to counter-clockwise, and vice versa) without any apparent changes in operating conditions. The source of this random wave directionality is not yet known, but is important to understand owing to the drastic changes the wave’s direction produces in it’s interaction with downstream and upstream components. For instance, notably different pressure profiles and coupling with downstream turbine vanes is observed depending on the direction of rotation of the detonation wave [255]. This is due to the effect of the angular arrangement of the turbine vanes on the reflected shock wave from the detonation wave. On the upstream end, we have observed an intrinsic (starts after ignition of the device) low frequency, amplitude modulated rotating instability inside the slotted air injection that also depends on the directionality of the rotating detonation wave — for the tested conditions, this instability moves in a direction that is always opposite to the direction of the detonation wave, resulting in a similar low frequency oscillation inside the

259

combustor [247]. Hence, it is imperative to decipher the physical mechanisms that cause this change.

On the other hand, RDC operation near the lean operating limits tends to produce non- repeatable, varying pressure profiles suggesting the lack of proper detonation propagation [127].

This type of haphazard, “chaotic propagation” is hypothesized to be due to under-recovery of supply plenums owing to the reduced pressure ratio across the injectors, that mostly occurs at lower flow rates [127,174,250]. Since the primary factor causing this type of propagation correlates well with lower injection ratios, this type of RDC operation is widespread when the combustor is backpressurized (choking at the nozzled exit causes injection to become subsonic). Both pressure profile and frequency analysis [69], and chemiluminescence imaging [254] of backpressurized

RDCs record highly chaotic propagation of detonation waves. In fact, one could argue that there is no “propagation” at all during this chaotic behavior, since there are only “events” of detonations.

Though we observed this behavior when the pressure ratio across the air injectors was lesser than

1.12 (when backpressurized), the exact cause of this behavior is not yet known, since it also occurs when the injection elements are properly choked.

Finally, the onset time to attain stable detonation propagation is also an extremely important factor that needs to be understood prior to practical implementation of these combustors. We have shown that detonation initiation in an RDC is through the deflagration-to-detonation transition

(DDT) mechanism, and not direct detonation initiation since the energy deposited by the pre- detonator in the tested conditions was lower than the required energy for direct initiation by an order of magnitude [156]. However, DDT alone cannot account for the start-up times in RDCs, since such a process lasts merely for a few milliseconds [160]. A study by Peng et al. utilizing a 30 mJ spark found that, for a given operating point, the onset time lasts between 1 ms and 7 ms [158].

They followed up this study with another utilizing three different ignition sources with vastly

260

different energy depositions and found that the onset time remained largely unaffected, which should be unlikely if the onset times are dependent only on the DDT process [159]. While there is still a large degree of variability in the DDT time for the same case (±50%), the higher energy ignition source only yields a slightly lower average DDT time, differing by a few milliseconds.

Bykovskii et al. [161] utilized multiple initiation strategies to achieve detonation of fuel-air mixtures in an RDC, including a low-power heat pulse, injection of a product jet, and transmission of a detonation. For the detonation transmission case, none of the experiments resulted in a direct transition of the initiating wave into a stable rotating detonation. All cases exhibited a transitional process of 4-80 ms duration, which was associated with the recovery of uniform air injection for detonation transmission, or the development of tangential instability and subsequent DDT when using the other ignition sources. A prior study by the current authors also strongly pointed towards the supply plenums as the primary reason for the onset times seen in RDCs [157]. We studied four different operating points ten times each to attain statistical rigidity (since the onset process is highly chaotic). By changing the air flow rates, the equivalence ratios and the backpressure, it was revealed that despite some variability between tests, the average onset time between the different cases was clearly distinguishable based on the operating conditions. For an air flow rate of 0.5 kg/s, the onset time was in tens of milliseconds, whereas 0.4 kg/s (at two different equivalence ratios) always tends to produce onset times that extend to hundreds of milliseconds. When the system is backpressurized, there is very low variability in onset times between the ten tests and stable detonation propagation always started within 6-7 ms.

The current study is the continuation of the prior one. Here, we once again study both atmospheric and backpressurized RDCs by varying the equivalence ratios and flow rates. Using multiple high-speed pressure sensors integrated into the combustor, air injector and the fuel plenum, along with ionization probes in the combustor, we ascertain the origins of the onset times in an RDC, in addition to chaotic behavior and wave directionality.

261

2. Experimental Methodology

Hydrogen-air mixtures are used to operate the RDC at air flow rates (ṁa) of 0.2, 0.3, 0.4 and 0.5 kg/s at different equivalence ratios (Φ). The air and fuel flow rates are controlled by a closed-loop system of nitrogen-driven pilot regulators and a set of Flowmaxx sonic nozzles. Norgren VP50 proportional control valves (pilot) are linked to Norgren pilot-operated regulators to isolate electrical components from the primary fuel supply. GE Unik 5000 sensors are linked to the choked- flow nozzle assemblies to monitor air and fuel flow rates. Fuel flow is administered to the rig through a pneumatically-actuated Bi-Torq isolation valve located just upstream of the fuel plenum, which allows fuel flow rates to stabilize within about 2 s of fuel introduction. The uncertainty in the pressure and temperature sensors (used in the reactants delivery) is ±0.069 bar and ±1 K, respectively. The linearized systematic error analysis of this uncertainty results in an estimate of

2.1% error in the air mass flow rate and 2.8% in fuel mass flow rate, which in turn results in a maximum error of 3.4% (seen for the lowest flow rates) in equivalence ratio. Experimentally, we test two different RDC geometries, by adding/removing a convergent-divergent nozzle at the RDC exit, to simulate backpressure by virtue of having a choked exit. This enables us to compare and contrast certain peculiarities of RDC operation at the two conditions, which is rather important since real-world applications of a combustor (in rocket engine or gas-turbines) seldom involves purely atmospheric operation. Both geometries, otherwise, have the same injector and annulus dimensions. Dimensions of the parts of interest are presented in Table 13 and the RDC geometry is shown in Figure 142. Air is injected radially inward through an annular slot, whereas fuel is injected through a row of orifices distributed circumferentially on the headwall exposed to the annulus. Both air and fuel plenums are instrumented with low-speed capillary tube averaged pressure (CTAP) sensors that measures the nominal averaged pressure (PA and PF respectively) inside the respective plenums [14,348].

262

There are multiple stations (azimuthal sectors) of instrumentation ports (I, II and III), with each station having a distribution of multiple rows of instrumentation (1,2,3 and 4) as can be seen in

Figure 142. Note that the time traces acquired from sensors in the stations I, II and III will, henceforth, be given by the coloring scheme of blue, red and black respectively. The stations are marked with respect to their angular difference from the predetonator (the tangential tube in the figure) entry plane and the ports with no sensors are grayed out. Three flush-mounted PCB piezoelectric sensors (blue tabs/ circles in the Figure 142a) are implemented in row 2 — 4.4 cm away from the headwall — of the three stations separated by 60o (see figure). In addition to this, an infinite tube pressure setup (ITP) with a Kulite piezoresistive sensor is integrated to the fourth row

(9.5 cm from headwall) of station +60o (orange circle in the figure). ITP-type pressure sensor mounting has been used to avoid damage of sensitive probes in extreme environments, such as

RDCs, to good effect [14,148]. By the usage of this current setup, we can not only accurately ascertain the mode of operation (rotating detonation vs. longitudinal pulsed detonation using the phase lag between the circumferentially distributed sensors [69]), but also estimate the low frequency changes in static pressure transients inside the device (since the piezoelectric sensors only record dynamic higher frequency variations in pressure). In addition to the three PCB sensors in the combustor, there are also three more mounted flush in the air inlet (blue tabs/ circles) and three in the fuel plenum at its base (green tabs/ circles in Figure 142). The air inlet sensors are 2.54 cm away from the combustor in the radial direction, and offset by 20o from the combustor sensors.

The fuel plenum sensors are in the same azimuth as the air inlet sensors as seen in Figure 142b, but are 6 cm away, radially (inward), from the combustor. This setup type was used to effectively determine the plenum dynamics in RDCs, where we determined the presence of both frequency modulated and amplitude modulated oscillations in the air injection [246,247]. Finally, three high- speed ionization probes (red circles/ tabs in the figure) are flush mount in row 1 of all three

263

stations to track the combustion activity, separately from the pressure dynamics. All the high speed sensors are sampled at 1 MHz by a National Instruments Data Acquisition device.

Predetonator Entry Plane Initiator -60 Tube Air Rows -80 Plenum RDC Channel θ III 1 2 3 4

+40 Fuel I Plenum +60

x RDC Channel II Converging Nozzle Initiator (removable) +180 Entry Height +160

(a) (b) (c)

Figure 142 Geometry and instrumentation schematic of the rotating detonation combustor,

showing (a) the front view, (b) side view, and (c) cut-section of side view showing the

plenums and mixing arrangement

Table 13 Dimension of interest in the RDC

Part Geometry measured Dimension

Individual fuel orifice length/ diameter ratio 12.8

Air injection slot width 1.02 mm

total slot area 490 mm2

Combustor annulus width 7.5 mm

inner diameter 139 mm

outer diameter 154 mm

length 125 mm

annulus exit area 3500 mm2

264

Convergent-Divergent annulus exit area 760 mm2

nozzle

3. Results and Discussions

3.1. Onset characteristics: atmospheric and backpressurized

The primary goal of this paper is to understand the cause behind onset time in an RDC. To do this, it is imperative to analyze this issue qualitatively first, and then quantitatively. Shown in Figure

143 are the ionization profiles from the three stations in the combustor (a), the pressure profiles from the same three stations in the combustor (b), and the pressure profile from one station in the air inlet (c). All three figures are from the same non-backpressurized operating point (ṁa = 0.5 kg/s and Φ = 1.03) and temporal range, showing the pressure and combustion dynamics from RDC ignition till the formation of stable detonation propagation (marked in the figures). The initial blast wave from the initiating predetonator is seen to make a significant impact on both the combustor and the air inlet, as seen by the sharp ionization and pressure spikes in the figure. After this ignition event, there is significant chaotic activity (both pressure and combustion) till t ≈ 0.023 s. During this period, there is no congruence between the different stations, i.e. there is no pressure or flame front motion from one sector of the RDC to the next. Instead, ionization and pressure peaks appear in a rather stochastic form with no peak-to-peak repeatability. Note that owing to the inherently strong coupling between the RDC and its supply plenums [171], a similar incongruence is also seen in the pressure dynamics in the air inlet. After t ≈ 0.023 s, however, stable detonation propagation begins and sustains till the fuel is shut off. Here, stability is defined as the characteristic of the detonation producing repeatable laps that can be tracked between the three stations. This behavior is better observable in Figure 144, which gives magnified profiles of pressure and ionization dynamics from the same operating point as Figure 143. Both ionization and pressure probes record

265

continual and sustained rotating detonation, as tracked by the excitation order of the three stations

— blue (I) -> red (II) -> black (III) — suggesting sustained counter-clockwise directionality. A similar periodicity is also observed in the pressure dynamics inside the air inlet, with periodic steep-fronted, shock-like profiles existing throughout. This is most probably due to the shock wave leakage into the air injector owing to the propagation of the detonation wave [179,184].

Ignition Onset period Stable Propagation

(a)

Stable Ignition Onset period Propagation

(b)

Ignition Stable Onset period

(c)

Figure 143 Atmospheric RDC ignition, onset and sustained stable propagation at ṁa = 0.5

kg/s and Φ = 1.03 — a) ionization probes in the combustor, b) pressure sensors in the

combustor, and c) pressure sensor in the air inlet

266

(a)

(b)

(c)

Figure 144 Stable detonation propagation at ṁa = 0.5 kg/s and Φ = 1.03 — a) ionization probes in the combustor, b) pressure sensors in the combustor, and c) pressure sensor in the

air inlet

Interestingly, backpressurized RDC operation exhibits significantly different characteristics pertaining to onset and stable propagation. First, when backpressurized, there is little to no ionization activity both before and after the onset period after ignition (Figure 145a). Second, the onset time is remarkably quicker in comparison to the atmospheric case as could be seen in Figure

145, which shows that stable propagation (Figure 145b) starts within 6 ms of ignition. Note that this operating point exhibits longitudinal pulsed detonation (LPD) as seen by the simultaneous excitation of all three azimuthal stations. This is known to occur at the lean limits of

267

backpressurized RDC operation [27,69]. It is stressed here that we also tested a backpressurized operating point with rotating detonations as well (discussed in the next section), and note a very similar behavior of highly curtailed combustion activity and onset time. The pressure dynamics inside the now-subsonic air inlet (due to choking at the RDC exit due to the CD nozzle) is also different from the atmospheric case. Here, while significant disturbance still remains in the air inlet at the same frequency of the detonation propagation, it is no longer steep-fronted, i.e. the rise and fall of the pressure oscillations in the air inlet is now smoothly sinusoidal. Both these observations

— of almost no ionization activity and acoustic-type oscillations in the air inlet — is suggestive of the notion that the detonation dynamics inside a backpressurized RDC is predicated more on acoustic modes inside the combustor and less on the flame fronts itself. In a prior study on LPD

[69], we theorized that the sustenance of LPD is due to detonation ignition produced by the reflected pressure waves from the choked exit, when it interacts with the fresh charge of mixture — a mechanism known as shock wave amplification by coherent energy release (SWACER) [21]. We shall not dwell further on the mechanism of stable detonation propagation in backpressurized RDC here, and leave it for a future discourse. For the current paper, we conclude that the onset time in such an RDC is considerably shorter and the combustor acoustics play a significant role in stable detonation propagation.

Ignition Onset period Stable Propagation

(a)

268

Ignition Onset period Stable Propagation

(b)

Stable Propagation Ignition Onset period

(c)

Figure 145 Backpressurized RDC ignition, onset and sustained stable propagation at ṁa = 0.3

kg/s and Φ = 0.93 — a) ionization probes in the combustor, b) pressure sensors in the

combustor, and c) pressure sensor in the air inlet

3.2. Air plenum dynamics and implications to onset time

This section of the paper deals with quantifying the air plenum dynamics after ignition from the predetonator. Before proceeding to that, it is essential to further qualify what a stable rotating detonation entails. By definition and its very structure, a conventional detonation wave consists of a shock wave preceding the flame front, which together maintains a feedback loop, causing and producing the other simultaneously [21]. Such a mechanism is also seen in RDCs when its operation is in the stable regime, as shown in Figure 146a. The shock waves (blue profiles) are seen to consistently precede the flame front (red profiles), lap to lap. Since the given pair of sensors

(pressure and ionization) are at the same station (same azimuth), it is possible to attain the time lag between the two. Positive time lag denotes proper detonations, whereas negative time lags should be taken to signify chaotic detonation events and not fully formed sustained propagations. The complete pressure and ionization trace of the same operating point is presented in Figure 146b.

269

The onset region that is distinguished by stochastic pressure and combustion activity is tagged by a blue arrow. To negate false positives, time lags greater/ lesser than 50 μs are neglected as non- physical events. The resulting plot of the lap-to-lap detonation-flame front time lags is presented in

Figure 146c, which shows that positive time lag is only present after the RDC operation surpasses its onset time. This supports our notion that the onset time is predicated by detonation “events” and not regular detonation sustenance. The fact that the air inlet sensors see a similar incoherent pressure activity during onset time augments the notion that this incoherence is plenum-induced.

The sheer number of the myriad of physical processes involved in RDCs render a first-principles approach towards understanding onset times improbable. Therefore, here, we use a “black-box” approach that has been highly successful in ascertaining physical mechanisms in the research of other combustors [349].

The RDC integrated with the air injector is assumed to be a single input-single output (SISO) linear time-invariant system (LTI) [349]. In short, for a system to be an LTI one, its input and output have to subscribe to algebraic linearity (superposition principle), while at the same time being an invariant function of time, i.e. the system will not respond differently to the same input if applied at different times [349]. By this definition, an RDC could be reasonably assumed to be an LTI system since the output would not change if the input series is applied at a different time (the moment of predetonator ignition does not alter the output). Since the impetus in this section is to ascertain the effect of plenum dynamics on the onset times, the input (x(n)) to the system is taken to be the pressure data obtained from the combustor, whereas the output is the pressure data recorded by the air inlet sensor (y(n)). With this construct, MATLAB’s system identification toolbox is used to evaluate and validate the defined system, using the transfer function model based on the ARX difference equation algorithm [350]. The first 0.2 s of both the pressure signals (x(n) and y(n)) are treated as the evaluation data to train the model, and the last 0.15 s of a given test is used to validate the trained model to ascertain its predictive quality (see Figure 146b and d). The goal here

270

is to test the hypothesis made by us [157] and Bykovksii et al. [161] that onset time in non- premixed RDCs is due to the air plenum settling time. This is to be done by extracting the impulse response time of the air inlet when disturbed by the initial blast wave from the predetonator used for RDC ignition. Impulse response is the output of a system when a unit magnitude is supplied to it at time, t = 0, and is used to find the settling time of a system [349].

Shock wave Flame front ∆t

(a)

x(n)

(b)

(c)

y(n)

(d)

271

Figure 146 Atmospheric RDC operation at ṁa = 0.5 kg/s and Φ = 1.03 — a) magnified

pressure (blue) and ionization (red) profiles of a stable rotating detonation, b) overall pressure and ionization time trace, c) lap-to-lap time lag between the shock wave and flame

front, and (d) overall pressure profile in the air inlet

Acquiring the proper impulse response and the associated settling time is predicated on proper identification of the system by the chosen transfer function model. Second-order systems lend themselves to a fairly simple analysis, but most real-world physical systems tend to be third-order

[351]. An iterative process, involving the alteration of the number of poles and zeros used to construct the transfer function, found that the RDC-air plenum system is best predicted by 3 poles and 2 zeros. Higher order prediction did not significantly alter the closeness of the predicted signal to the experimentally attained output (signal in the air inlet). As communicated previously, the current study is a continuation of our prior one where four different operation conditions

(atmospheric and backpressurized LPD operation) were tested experimentally, ten times each, to treat the inherently chaotic onset process in RDCs statistically rigorously [157]. Windowed cross- correlation of the pressure sensors in the three different stations (sectors) was performed to accurately estimate the onset duration. For the sake of brevity, we direct the readers towards our prior publications [157,290] for more information regarding this algorithm used to quantify onset times. In the present study, we add one more operating condition in addition to analyzing the previous four operating conditions — backpressurized RDC operation at ṁa = 0.3 kg/s and Φ = 1.25.

Note that this test condition tends to produce rotating detonations, thereby making the test matrix cover both LPD and the conventional rotating mode during backpressurized operation. The predicted output signal by the model is found to have a best fit to the actual, experimentally attained output (signal in the air inlet) ranging between 1% and 44.49% for the varied conditions.

This variance is to be expected considering the complexity of the process. To analyze the system dynamics properly, only those cases where the model predicts the system output behavior by more

272

than 20% is considered to attain the settling time of the impulse response. The median of the resulting values from the model, and the associated onset times along with its respective median time and standard deviation over the ten different tests for the five cases: A, B, C, D and E (the first four are from the prior study), are presented in Table 14.

Table 14 Onset times from experiments and model-predicted air plenum settling times

Case A B C D E

ṁa 0.5 0.4 0.4 0.3 0.3

Φ 1.03 1.43 1.04 0.93 1.25

Nozzle No No No Yes Yes

Test Onset Time (ms)

1 18 161 105 6 3

2 20 175 87 6 7

3 12 155 - 6 4

4 12 170 182 5 6

5 16 184 204 6 2

6 25 174 183 5 3

7 12 136 143 7 2

8 13 150 207 77 4

9 23 173 108 6 3

10 21 165 196 6 6

Standard deviation 4.7 13.4 44.4 21.3 1.7

Median Onset time (Expt) 17 167.5 182 6 3.5

Median Settling time 1 0.7 0.4 5 2.6 (Model)

273

It can be seen that the settling time obtained from the predictive model considerably under- predicts the onset time when the RDC exit is atmospheric. When the device is backpressurized, however, there is a striking congruence in the times predicted by the model with the onset time acquired experimentally, which supports the notion that for the tested conditions, the onset time of backpressurized RDCs is almost purely dependent on the impulse response of the air plenum. It is emphasized here that it is unlikely that the method of ignition itself has much import on the ignition time, as per the findings of Yang et al. [159] and Bykovksii et al. [161]. The formation of a detonation event of comparable peak pressure inside the combustor by any means (spark plug, blast wire, predetonator, etc.) is expected to produce comparable impulse response times in the air plenum. Sample impulse responses for the five cases are given in Figure 147. We note that the system is always slightly underdamped when the air flow rate is 0.5 kg/s (PA ≈ 3.6 bar) for all the tested cases. For 0.4 kg/s (PA = 3.05 bar), for both the equivalence ratios tested, the system varied between being underdamped and overdamped. We have provided an example each for the 0.4 kg/s cases (Figure 147b and c). This suggests that there is an inherent unpredictability in defining the system solely based on the interaction between the air plenum and the combustor, when the exit is atmospheric. When backpressurized, the system is highly underdamped, and could be attributed to the effect of having heightened pressure inside the combustor [43,69] by virtue of having a choked exit, which in turn tends to behave as a closed end in combustors [352].

To confirm that the attained impulse responses for the atmospheric cases are indeed physical, the predetonator was initiated with air flow through the RDC, but without any fuel flow to simulate an impulse loading on the air inlet. This is a valid assumption since the detonation wave speed in the predetonator used here is about 2500 m/s [156], and the method to attain the impulse response experimentally is not unlike that followed in analyzing auditorium acoustics [198]. Figure

148a shows the pressure trace from the air inlet during such a scenario of atmospheric cold-flow.

Figure 148b shows the impulse response attained from the model. One can see the qualitative and

274

quantitative similarities between the two traces, leading to the conclusion that the onset times seen for the atmospheric cases, which lasts up to hundreds of milliseconds, is not due to the air plenum as previously assumed. The latter is indeed responsible for the onset times seen in backpressurized

RDCs, but the attained evidence points towards fuel plenum as the cause of the onset duration seen in atmospheric RDCs, and will be treated in the next section.

(a) (b) (c)

(d) (e)

Figure 147 Normalized (by maximum value in the series) impulse response in the air inlet

after ignition estimated by the system prediction model, for atmospheric cases (a) ṁa = 0.5

kg/s and Φ = 1.03, (b) ṁa = 0.4 kg/s and Φ = 1.43, (c) ṁa = 0.4 kg/s and Φ = 1.04, and

backpressurized cases (d) ṁa = 0.3x kg/s and Φ = 0.93, (e) ṁa = 0.3 kg/s and Φ = 1.25

275

(a) (b)

Figure 148 Atmospheric RDC during cold-flow at ṁa = 0.5 kg/s — (a) experimentally acquired

air inlet response (normalized) after predetonator initiation, and (b) normalized impulse

response in the air inlet

3.3. Fuel plenum dynamics and implications to onset and stability

The three sensors at the base of the fuel plenum can be used in a way similar to the above discussion on RDC-air plenum coupling. A sample pressure-time trace attained from the base of the fuel plenum is shown in Figure 149. Overall, there is considerably more noise in the signal, in comparison to similar signals attained from the air inlet during RDC operation. A third-order system prediction of the nature performed previously did not return proper system identification results. The output signal predicted by the model in the fuel plenum barely exceeded a best fit of

1% with the original experimentally attained signal, leading to the conclusion that the RDC-fuel plenum system is of a significantly higher order than the RDC-air plenum system, and is composed of complex coupling dynamics. In fact, it was found iteratively that a 30 pole (order) system is required to attain a best fit of 5%. To analyze the process, ṁa = 0.4 kg/s is chosen and the RDC is tested at three different equivalence ratios, while maintaining the air flow constant. The resulting

Fast Fourier Transform (FFT) plots of the three operating conditions obtained from the fuel plenum pressure sensors is given in Figure 150. The following observations are evident: (i) the spectral content in the fuel plenum is distributed across a broad frequency range ranging from 1 Hz all the way up to 40 kHz, unlike the air plenum which is usually excited at frequencies only about the

276

operating frequency of the device [246], (ii) when the equivalence ratio is increased (read: the supply pressure of in the fuel plenum is increased), the higher frequencies of excitation are progressively reduced and the fuel plenum appears to be excited at the frequency of the propagating detonation wave (roughly 3800 Hz), with the harmonic vibrations notably dampened.

These results can be readily explained by considering the fuel plenum to be a chamber that is vulnerable to acoustic oscillations. In fact, all three FFTs are highly emblematic of the phenomenon of reflections and reverberations witnessed in acoustic chambers [198]. Reflections are produced due to a finite time delay echo production caused due to the initial sound wave reflecting from a solid non-absorbing boundary [198]. They appear as distinct spectral components in the FFT plot.

Reverberations, on the other hand, are produced due to higher order collection of multiple reflected sound waves and tend to decay exponentially after the removal of the initial sound source, and appear as high frequency broadband noise [198]. In the current study, a similar mechanism appears to occur inside the fuel plenum due to the acoustic excitation inside the plenum, due to detonation existence in the combustor [171,173,246,291]. Since increasing the pressure inside the plenum raises the pressure ratio across injection, the impedance across the injector increases [56], thereby producing markedly lower reflections and reverberations for Φ = 1.2, in contrast to Φ = 0.91.

Figure 149 Pressure dynamics in the fuel plenum during detonation propagation in an

atmospheric RDC at ṁa = 0.4 kg/s and Φ = 0.91

277

Reflections Reverberations Reflections Reverberations Φ = 0.91 Φ = 1.0 P = 3.26 bar PF = 3 bar F

(a) (b)

Reflections Reverberations Φ = 1.2

PF = 3.67 bar

(c)

Figure 150 FFT of pressure dynamics inside the fuel plenum for three cases at ṁa = 0.4 kg/s:

(a) Φ = 0.91, (b) Φ = 1.0, and (c) Φ = 1.2

Additional evidence for the proposition that fuel plenum dictates the onset time in atmospheric

RDCs is given in Figure 151. The pressure traces from the ITP-mounted, piezoresistive Kulite sensor in the combustor are given for four different equivalence ratios (incrementally higher pressures in the fuel plenum) at the same air flow rate of 0.4 kg/s. All four cases are ignited at t ≈ 0 s by the blast wave from the predetonator, which appears as an almost 2 bar pressure spike in all the plots. Fuel is supplied through the whole duration of 1 s of testing for these cases. However, for

Φ = 0.8, the detonation wave extinguishes at about 5 ms after the transient onset time. At Φ = 0.85, this transient onset time lasts for about 10 ms, after which the detonation once again fails.

Increasing the equivalence ratio to Φ = 0.9 still produces haphazard chaotic propagation that is highly transitory, but now failure occurs at about 640 ms. This type of RDC behavior —

278

characterized by initial successful detonation onset and propagation until a finite time after which failure occurs in the form of either an anchored deflagration or flame blow-out is called “pop-out”

— and is often seen at the lean limit of RDC operation [43]. At Φ = 1.0, we can see that there is a sustained rotating detonation throughout the 1 s duration of testing. One could also note that this condition tends to produce repeatable peak pressures devoid of the highly unstable behavior that is seen at Φ = 0.9. Thus, finally, we have the origins of onset times, and the phenomenon of chaotic detonation events and pop-outs seen widely in RDCs — improper fuel plenum recovery caused by highly pronounced acoustic oscillations inside the chamber that tend to shut off fuel supply due to strong subsequent reflections and reverberations. This discovery also explains why tests conducted in our facility at air flow rates of 0.2 kg/s and 0.3 kg/s are always unstable (unlike the 0.4 kg/s and

0.5 kg/s cases discussed here) despite the equivalence ratio being high [247]. Higher equivalence ratios (due to higher plenum pressures) at lower air flow rates still fall below the threshold of pressure that appears to be necessary to counteract the impact of the detonation wave onset. It is strongly emphasized here that this critical plenum pressure should not be construed as globally valid across facilities, since multiple variables could dictate the amount of reflections and reverberations seen in plenums, ranging from the shape of the plenum itself, size, injector hole sizing, etc. The fact that higher number of pop-out events is recorded at the lean limits when the individual fuel orifices are bigger when compared to smaller fuel orifices, despite both the injection schemes having the total injection area [43] suggests that viscous damping could also play a significant role in plenum designs. Chemiluminescence imaging of a transparent RDC of very similar geometry and dimensions to the current one shows that the rotating detonation wave structure is highly unrepeatable and unstructured at lower flow rates, despite the injectors being nominally choked [44]. The current findings may explain the origins of this observation as well.

279

Φ = 0.8, P = 3.15 bar F

(a)

Φ = 0.85, P = 3.24 bar F

(b)

Φ = 0.9, P = 3.33 bar F

(c)

Φ = 1.0, P = 3.42 bar F

(d)

Figure 151 Pressure-time traces acquired from ITP Kulite sensors for four atmospheric RDC

operating conditions at ṁa = 0.4 kg/s: (a) Φ = 0.8, (b) Φ = 0.85, (c) Φ = 0.9, and (d) Φ = 1.0

280

3.4. Wave directionality in RDCs

The above results and discussion merit a discussion on the widely observed stochastic wave directionality in RDCs. Using the windowed cross-correlation algorithm used to attain onset time, and discussed in detail in Ref [290], the atmospheric RDC is tested for four air flow rates of 0.2 kg/s,

0.3 kg/s, 0.4 kg/s and 0.5 kg/s, at the same equivalence ratio of 1.0. Since we have three sensors distributed equally among three sectors of the device, it is possible to predict with reasonable accuracy the direction of rotation of the wave within a given window (of three laps). We use a positive phase degree to denote clockwise propagation, whereas a negative phase represents counter-clockwise rotation. The resulting phase-dependent lag of the wave across three stations (I to II, II to III and III to I) throughout the 0.35 s duration of testing is shown in Figure 152. At once, the dependence of the wave directionality on the flow rates (and hence feed pressures) is clearly seen. For 0.2 kg/s and 0.3 kg/s, there is no preferred direction of the wave, and it flips back and forth (positive and negative phase) continually throughout the duration of testing. However, at 0.4 kg/s and 0.5 kg/s, after the initial chaotic onset time, the direction of the rotating detonation wave does not change and remains constant throughout the test. It could, therefore, be concluded that the random directionality of the detonation wave in RDCs is a function of the susceptibility of the supply plenums to be disturbed. Lower flow rates tend to produce detonation “events” rather than proper conventional detonations, and operate in a period of perpetual onset throughout. Hence, care should be taken to interpret RDC behavior at these conditions of improper plenum recovery by not attributing these system-level interactions to detonation-based physics.

281

200 200

150 I -> II 150 I -> II 100 II -> III 100 II -> III 50 III -> I 50 III -> I 0 0 -50 50 150 250 350 -50 50 150 250 350

-50 -50 Phase (degree) Phase (degree) -100 -100 -150 -150 -200 -200 Time (milliseconds) Time (milliseconds)

(a) (b)

200 200

150 I -> II 150 100 II -> III 100 50 III -> I 50 0 0 -50 50 150 250 350 -50 50 150 250 350 -50 -50

I -> II Phase (degree) -100 Phase (degree) -100 II -> III -150 -150 III -> I -200 -200 Time (milliseconds) Time (milliseconds)

Figure 152 Phase-lag of the wave between the three sectorally distributed combustor

pressure sensors for four operating points: (a) ṁa = 0.2 kg/s and Φ = 1.0, (b) ṁa = 0.3 kg/s

and Φ = 1.0, (c) ṁa = 0.4 kg/s and Φ = 1.0, and (d) ṁa = 0.5 kg/s and Φ = 1.0

4. Conclusions

The property of onset time in a rotating detonation combustor is studied at different flow rates and backpressures in the current paper. It is found that this highly incoherent and chaotic onset

282

time after ignition of an RDC is a function of the reactants supply plenums’ response to the formation of a detonation event from the initial condition of rest. The resulting feedback is modeled as a third order system using a black-box approach to reveal that the onset time during backpressurized operation is due to the settling time of the air plenum impulse response caused by the sudden formation of a detonation event. Atmospheric RDC operation, on the other hand, did not depend on the air plenum’s impulse response for the tested conditions. This necessitated a similar analysis of fuel plenum to reveal that the detonation formation and propagation inside the combustor produces significant disturbance of the fuel plenum characterized by strong reflections and reverberations at lower feed pressures and lower disturbances at higher feed pressures. This process of highly disturbed fuel plenum dynamics not only explains the onset times in atmospheric

RDC operation, but also explains the transient failure phenomenon of pop-outs at the lean limits of

RDC operation. It is pointed out here that the major takeaway from this study is that the plenum behavior – both air and fuel – dictates the duration of onset and the presence of chaotic detonation events in an RDC. For instance, if the current configuration is switched such that fuel is fed from the air plenum and vice versa, one should expect to see the same behavior hold (after accounting for the change in sound speed in the different gases). The current findings shed light on the importance of feed pressures and plenum design in an RDC, since improper design of either plenum results in highly chaotic operation throughout the duration of testing. This disturbance induced by the plenum is also found to be responsible for the widely observed phenomenon of apparently random changes in the wave’s directionality. When the proper conditions of air and fuel plenum pressures are met, there is stable, continuous, single-directional rotating detonation propagation. Moving forward, it is imperative to reconsider the interpretation of RDC mechanics at these conditions of inherent stochasticity. One should also expect similar chaotic behavior if the settling time of the two plenums are considerably different, which might once again lead to improper reactants supply due to destructive feedback. While the tested condition of backpressurized RDC operation were solely

283

dependent on the impulse response of the air plenum, it is possible that notably different supply pressures and injection areas might alter this factor. In short, we have shown here that proper RDC operation is predicated on proper plenum supply pressures and injection sizing. The result of this is to take a facility-specific approach to design the system in order to achieve stable rotating detonation waves in an RDC.

284

CHAPTER 8: ON MEAN PRESSURE SHIFTS AND CHUGGING OSCILLATIONS IN BACK-

PRESSURIZED ROTATING DETONATION COMBUSTORS

Chapter Abstract

The current manuscript deals with certain peculiarities observed in a back-pressurized rotating detonation combustor operation. The transient mean pressure shift to a higher value after ignition is analyzed to reveal that it is dependent on the mass flow rate and equivalence ratio due to the choked RDC exit. At certain operating conditions this transience causes strong chugging oscillations, which are characterized by low frequency modulation of the high frequency pressure signal produced by the detonation waves. Subsequently, this phenomenon is studied to reveal that it mostly presages a sudden mode shift in RDC operation. Numerical analysis suggests that the observed low frequency oscillation is caused due to acoustic modes, thereby making it the chugging instability that is widely witnessed in rocket engines.

Nomenclature

ṁa - mass flow rate of air (kg/s)

Φ - equivalence ratio f - operating frequency / detonation propagation frequency (Hz)

PI - initial pressure before ignition (bar)

PF - final plateaued pressure (bar)

PS-R - mean pressure shift ratio (PF/PI)

1. Introduction

Detonation waves are mostly distinguished by sonic to greater-than-sonic wave speeds, and is structured with a shock wave-chemical reaction zone coupling, with each entity sustaining the

285

other through a feedback loop [21]. This usually produces a pressure gain of 13-55 in gases [1] — a highly desirable characteristic due to a prospective increase in fuel efficiency since more work can obtained, in comparison to deflagrations [320]. Hence, detonation combustors are studied with increasing frequency and effort. The most promising of such devices is the rotating detonation combustor (RDC). It is characterized by an annulus (usually) that is fed reactants continuously and one or more detonation waves propagation circumferentially in the kilo-Hertz regime. Multiple factors like the reactants type, combustor geometry, thrust, oxidizer and fuel flow rates, and the detonation wave speed at these conditions have been studied in recent years [18,148]. Most of the experimental endeavors investigating RDCs utilize an atmospheric combustor without back- pressurization [3], and yet have revealed diverse propagation behaviors. This is, however, not representative of the actual environment that RDCs would be operating in, since both of its prospective applications — as rocket engine and in gas-turbines [3] — require the combustor to operate under significantly pressurized conditions. This is an area of active research since few campaigns [14,27,40,43,322] have addressed the peculiarities of RDC dynamics under pressurized operation. One such research noted that the static pressure of the combustor appeared to exhibit a highly transient increase when a backpressurized RDC is ignited, but eventually concluded that this observation might be the result of an improper sensor selection [230]. However, as noted in our study [43], there is indeed a physical, transient static pressure increase when a backpressurized

RDC is ignited; lasting about 0.95 s for the conditions we tested. Fotia et al. [14], subsequently, also noted the same transience in their RDC testing as well, but there it lasted between 0.75 s and 1.25 s, after which it plateaued to a steady-state pressure.

Our hypothesis of this pressure increase being the result of a choked RDC exit and detonative combustion (increased stagnation pressure) inside the annulus [43] was validated by Fotia et al. using an elegant mathematical approach combined with empirical results [14]. They showed using the fluid dynamic mass flow parameter (MFP) function, that for the flow to be choked (Mach

286

number of unity) at the exit nozzle (experimentally verified to be true) there has to be a stagnation pressure increase within the combustor that is the manifestation of the detonation processes itself.

Of course, the prospect of increased stagnation pressure across a detonation wave is not a new finding, and has been noted previously [353]. However, the relationship between this facet and a backpressurized RDC is a new-found phenomenon and deserves many more focused studies. Since the RDC is choked at the exit now, the injectors become unchoked leading to completely subsonic flowfield as the reactants enter into the combustor [14,43]. This should prospectively produce a prominent secondary effect of destabilized plenum dynamics, in addition to the primary effect of complicated detonation dynamics inside the combustor due to varying pressure inside the combustor. Considering the fact that longitudinal pulsed detonations (LPD) occur only when the exit is choked and the injection is subsonic [27,69,250], the implications of this effect become more pronounced. The current paper is one more step towards understanding some of the effects of this mean pressure shift and subsequent plateau in RDCs.

At this point, it is prudent to consider the claim made by us [32,69,354] and several other researchers over the years [18,31,52–55] that the high frequency tangential and longitudinal combustion instabilities, with “shock-fronted, detonation-like” waves, observed predominantly in rocket engines (and other combustors occasionally [355]) is a manifestation of detonation dynamics and not just the acoustic oscillations resulting from Rayleigh heat addition criterion. Since both RD and LPD share qualitative and quantitative similarities to these two combustion instabilities in other combustors [69,354], it is necessary to also consider, conversely, the possibility that other mechanisms seen in those combustors might manifest in RDCs. In this regard, qualitatively, the mean pressure shift in RDCs described above is similar to the “DC shift” seen in rocket engines [56,234–239,241,356]. The DC shift (derived from the electrical terminology of direct currents, owing to a net non-zero average in the obtained signal) is defined as an increase in the average static pressure of a rocket engine combustor that almost always accompanies the onset

287

and sustenance of high frequency combustion instabilities [63]. Another phenomenon of interest is the chugging instability that is characterized by acoustic coupling between the injector plenums and the combustor [56,57,243–245]. It is considered a type of low frequency instability (LFI) since the occurrence frequency is below 500 Hz [56]. Sometimes, this instability sets up “organ-pipe” oscillations throughout the entire reactants supply manifolds at distances significantly upstream of the combustor, as witnessed in F-1 engines [56]. While the exact cause of its onset is yet unknown, it appears that higher reactants feed pressures remove this instability due to increased fluidic impedance across the injectors that resist the feedback from the combustors [56]. Considering the severity of the both the above-mentioned issues in rocket engines, we investigate backpressurized

RDC operation to ascertain their effects. Two different geometries are tested — with and without a choked nozzle at the exit — to reveal observations that have not yet been reported in RDCs.

2. Methodology

2.1% error in the air mass flow rate and 2.8% in fuel mass flow rate, which in turn results in a maximum error of 3.4% (seen for the lowest flow rates) in equivalence ratio. The current study is

288

composed of results from three elements — two experimental campaigns and one numerical investigation. Experimentally, we test two different RDC geometries, with the first setup consisting of a convergent nozzle at the exit plane to enable choked RDC operation and the second setup using an atmospheric exit without the nozzle addition. This enables us to compare and contrast certain peculiarities of RDC operation at the two conditions. Since the same RDC is used for both the campaigns, both studies have the same injector and annulus dimensions, with the only difference in geometry being the addition of the nozzle at the back end. Dimensions of the parts of interest are presented in Table 11 and the two geometries are shown in Figure 153. Air is injected radially inward through an annular slot, whereas fuel is injected through three rows or orifices distributed circumferentially on the headwall exposed to the annulus. Both the plenums are instrumented with a low-speed capillary tube averaged pressure (CTAP) sensors that measures the nominal pressure

[14,348] inside the respective plenums.

The two campaigns also used two different instrumentation setups. There are multiple stations

(azimuthal sections) of instrumentation ports, with each station having a distribution of multiple rows of instrumentation as can be seen in Figure 153. The stations are marked with respect to their angular difference from the pre-detonator (the tangential tube in the figure) entry plane and the ports with no sensors are grayed out for a particular configuration. Shown in Figure 153a is the backpressurized RDC geometry with a nozzle at the exit plane. For this configuration, three flush- mounted PCB piezoelectric sensors (red tabs/ circles in the Figure 153a) are implemented in row 1

— 1.9 cm away from the headwall — of the three stations separated by 60o (see figure). In addition to this, an infinite tube pressure setup (ITP) with a Kulite piezoresistive sensor is integrated to the fourth row (9.5 cm from headwall) of station +60o (orange circle in the figure). ITP-type pressure sensor mounting has been used to avoid damage of sensitive probes in extreme environments, such as RDCs, to good effect [14,148]. By the usage of this current setup, we can not only accurately ascertain the mode of operation (rotating detonation vs. longitudinal pulsed detonation using the

289

phase lag between the circumferentially distributed sensors [69]), but also estimate the low frequency changes in static pressure transients inside the device (since the piezoelectric sensors only record dynamic higher frequency variations in pressure). The second campaign using an atmospheric RDC without a nozzle is shown in Figure 153b, and uses nine piezoelectric pressure sensors in total — three in the combustor, three in the air inlet and three at the base of the fuel plenum (see Figure 153b). The air inlet sensors are 2.54 cm away from the combustor in the radial direction, and offset by 20o from the combustor sensors. The fuel plenum sensors are in the same azimuth as the air inlet sensors as seen in Figure 153b, but are 6 cm away, radially (inward), from the combustor. This setup was used to effectively determine the plenum dynamics in RDCs, where we determined the presence of both frequency modulated and amplitude modulated oscillations in the air injection [246,247].

Approx. Initiator Entry Plane Initiator -60 Tube Air Rows -80 Plenum RDC Channel θ 1 2 3 4

+40 Fuel Plenum +60

x RDC Channel Converging Nozzle Initiator (removable) +180 Entry Height +160

(a)

290

Approx. Initiator Entry Plane -60 Rows -80 RDC Channel θ 1 2 3 4

+40

+60

+180 +160

(b)

Figure 153 Schematic of the geometry and associated instrumentations for – (a)

backpressurized RDC, and (b) atmospheric RDC

Table 15 RDC geometry across the two experiments

Part Geometry measured Dimension

Individual fuel orifice length/ diameter ratio 17

Air injection slot width 1.02 mm

total slot area 490 mm2

Combustor annulus width 7.5 mm

inner diameter 139 mm

outer diameter 154 mm

length 125 mm

Backpressurizing nozzle Area at RDC exit plane 760 mm2

The Modal Frequency sweep solver from the Pressure acoustics module of COMSOL 5.2 is used to obtain the Helmholtz resonance frequency of the slotted air inlet using an axisymmetric setup

(Figure 154a and b). A triangular mesh with a maximum element size of 0.00144m and a minimum element size of 5.42E-6m is used, after determining this grid assembly (“extra fine”) is sensitive

291

enough to capture the peak oscillating pressures as accurately as denser meshes. Maximum number of triangular elements is 2594 which includes 199 edge elements and 7 vertex elements. As explained earlier, multiple flow rates are tested experimentally, and hence the static pressure inside the plenum is input to be 2 bar, 2.85 bar and 3.65 bar in the numerical study. This represents the experimentally measured pressure values inside the plenum that produces air flow rates of 0.2 kg/s, 0.3 kg/s and 0.4 kg/s respectively, and provides a direct comparison between experiments and simulations. The first Eigen frequency of oscillation and the associated oscillation pressure magnitude is extracted to compare with the experimentally acquired values.

0.05

0.04

0.03

0.02

0.01

0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15

(a) (b)

Figure 154 (a) Axisymmetric view of the air plenum with the associated boundary conditions, and (b) Helmholtz resonance in the air plenum at the first Eigen frequency of 191

Hz (all dimensions are in meters)

3. Results and Discussion

3.1. Effect of back-pressurization

The foremost difference between an RDC operating in back-pressurized versus the atmospheric mode is in its averaged pressure behavior. This is clearly seen in Figure 155a (atmospheric exit)

292

and Figure 155b (back-pressurized), which shows the static pressure evolution before, during and after ignition in the air plenum (blue), fuel plenum (green) and the combustor (red) of the two geometries, for the same flow rates. When the combustor annulus is not converging (i.e. no nozzle), the CTAP sensors see a minimal increase in the average static pressure inside the combustor

(Figure 155a). This is to be expected since the low-speed pressure sensors (based on Wheatstone bridge circuit) is not responsive enough to capture the high frequency, strong pressure peaks of rotating detonations. A minimal uptick in pressure is also witnessed in the air plenum, owing to the back-pressurizing effects of the detonation dynamics inside the combustor [28]. The sudden increase in the static pressure in the fuel plenum at about -1 s is when the pneumatic valve is actuated to allow fuel flow into the plenum. When the combustor is back-pressurized, however, there is a considerable change in the pressure response as seen by the highly transient mean pressure rise in the combustor (red) after ignition (Figure 155b). Fuel injection is also seen to have a notable impact on the combustor pressure as seen by the minor uptick at about -2 s. This rise in the average static pressure after ignition will be defined as the ‘mean pressure shift’, as the pressure before ignition (PI) and after plateau (PF) is considerably different in a backpressurized

RDC. Note that, as explained in the introduction, a similar phenomenon is observed in rocket engine combustor (choked at the exit because of the C-D nozzle at the combustor exit) when there is an onset of high frequency combustion instabilities [63,239]. Of additional interest is that the air plenum pressure appears to be a function of this mean pressure rise as seen by the considerable increase in the static pressure in the plenum after ignition. A similar, but weaker, increase in fuel plenum pressure is also seen that appears to be due to the pressure transience in the choked combustor. For the tests performed here, this transience takes about 0.95 s to plateau, which is in contrast to the 0.75 s-1.25 s duration observed by Fotia et al. for a similar plateauing of pressure

[14]. Though they tested backpressurized configurations their analysis dealt with RDC dynamics after pressure plateauing, i.e. the pressure rise phenomenon immediately after ignition was not

293

considered. It is important to note here that there is a finite response delay in the air and fuel plenum pressure rise in relation to the combustor pressure rise (see Figure 155b). This is observed for all the experimental conditions performed with a convergent nozzle. This facet of backpressurized operation was also not noted by Fotia et al. since their air supply plenum appeared to not be instrumented (the supply lines were).

Response delay

Fuel Ignition Fuel injection injection Ignition

(a) (b)

Figure 155 Pressure-time traces at ṁa = 0.4 kg/s, Φ = 1.1 from (a) atmospheric RDC, and (b) back-pressurized RDC. Legend: combustor (red), air plenum (blue) and fuel plenum (green)

To understand the relevance of the pressure rise to RDC operation, it is imperative to quantify it at different operating conditions. Therefore, we introduce a parameter called the pressure shift ratio (PS-R) which is defined as the ratio of the initial static pressure before ignition (but after fuel injection) and the final static pressure during plateaued operation (the final 0.05 s of operation of the roughly 1 s operation):

푃퐹 푃푆−푅 = (1) 푃퐼

This ratio is plotted as a function of the air flow rate and equivalence ratio in Figure 156a, and can be seen to be strongly linked to the mass flow rate through the combustor and equivalence

294

ratio — higher air flow rates produce a higher mean pressure shift for all the four tested flow rates.

For a given air flow rate, however, the pressure shift ratio tends to be highest at an equivalence ratio of approximately 1.2 to 1.3. These results can be explained by considering the “equivalence ratio dependent stagnation pressure gain” in the combustor, as argued by Fotia et al. [14]. They found that the only way the Mach number across the choked RDC exit could be equal to unity is if there is actually a stagnation pressure increase inside the RDC due to detonative combustion — which is indeed the end goal of such pressure gain devices. Here, we take a similar approach using the mass flow parameter to ascertain the effects of stagnation pressure increase. However, the emphasis here is on the pressure shift phenomenon itself, and not on the steady-state operation analysis performed by the other research team. The mass flow parameter is defined as:

−ɣ+1 √푇 ɣ ɣ−1 푀퐹푃 = ṁ 표 = √ 푀 (1 + 푀2)2(ɣ−1) (2) 푃표퐴 푅 2

Assuming the flow to be choked across the RDC exit plane at the nozzle (which we know to be true, globally, from the experiments), and by equating the stagnation temperature at the exit to be a function of the static temperature of the products produced by the detonation wave, and substituting ɣ = 1.2 (for detonations) we get the stagnation pressure as:

ṁ 푇 푅 푃 ~ √ 푝 (3) 표 퐴

Where TP is the static temperature of the products after detonation. Finally, since the RDC exit is considerably choked, we approximate the stagnation pressure inside the combustor to be roughly equal to the static pressure owing to the subsonic flow profile that should be present in the device

(similar to Fotia et al.’s assumption). Thus, the equation for the pressure shift rise becomes:

푃표 푃푆−푅~ (4) 푃퐼

295

The specific gas constant (R), and the static temperature of the burnt products (TP) are functions of the global equivalence ratio tested experimentally, and subsequently are estimated from NASA Chemical Equilibrium and Applications (CEA) for a given equivalence ratio. The mass flow rate is input from the accurately measured values (using sonic nozzles), whereas the initial pressure value, PI, is found to be approximately equal to 2 bar across all experiments from the CTAP sensor. Thus, the semi-empirical values of the estimated pressure shift ratio are also plotted in

Figure 156a, which shows the trend line for a given air flow rate (since for a choked exit, Po depends on the flow rate, as can be seen in the above equations). It can be seen that, for 0.2 kg/s, the measured PS-R and the calculated PS-R are very close, both in quality and quantity. At 0.3 kg/s there is a higher disparity between the two values. This discrepancy increases considerably for 0.4 kg/s, and is the highest at 0.5 kg/s. Two inferences can be made: 1) the mean pressure shift appearing in

RDCs due to a choked exit seems to be due to the increase in stagnation pressure produced by the detonation wave inside the combustor, and 2) higher flow rates through an RDC with a choked exit appears to be operating at inefficient conditions, since there is a considerable mismatch between prediction and experiments for 0.4 kg/s and 0.5 kg/s. Intuitively, this appears to be obvious since incrementally higher flow rates should produce high amount of product gases upstream of the choked exit that would tend to reduce the combustion efficiency of the combustor (lower To). Fotia et al. note that stagnation temperature should not play a considerable role in a choked RDC, but our data suggests that this effect also has a significant role, but at higher flow rates.

This finding has implications to the detonation wave dynamics as well, since higher pressures prior to ignition produce stronger detonation waves for most mixtures [21]. Thus, one should expect to see a feedback loop, wherein the detonation events increase the stagnation pressure inside the RDC, and this consequently endorses a stronger subsequent detonation event. In Figure

156b, the root mean square (rms) of the pressure oscillations acquired from the piezoresistive sensor in the ITP configuration (after steady-state — last 0.05 s) are plotted as a function of PS-R.

296

Since each is a function of the other, it is difficult to clearly delineate the cause and effect, but the following inference can be made. The magnitude of the wave amplitude remains nominally the same (0.3 bar to 0.5 bar) as the flow rate is increased from 0.2 kg/s to 0.4 kg/s (1.3 ≤ PS-R ≤ 2.3).

However, at 0.5 kg/s, there is a significant increase in the oscillation magnitude, extending up to 0.9 bar, suggesting that higher pressure prior to ignition does indeed alter the detonation peak pressure. The fact that such a trend is not seen for the lower flow rates could perhaps be explained by studying that fundamental frequency of detonation wave propagation, which appears to be very complex when the RDC is backpressurized. As the pressure inside the combustor changes continually from ignition till plateau, most operating points exhibit two different modes of operation (two distinct detonation frequencies, f1 and f2) suggesting a fundamental change in the propagation of the detonation wave (which would alter the detonation peak pressure). Figure 156c shows the detonation wave frequencies observed for all the operating points. The red line denotes the Chapman-Jouguet (C-J) limit for the current RDC, assuming one detonation wave to propagate circumferentially (which we will show in the next section to not always be the case). From this global map, one could see that most operating points at most flow rates and equivalence ratios tend to have detonation propagation at frequencies significantly higher than the permissible C-J speed,

This cannot be readily explained by the usually observed RDC dynamics of one vs. two wave mode

— if such a bifurcation occurs in an RDC, the second fundamental frequency is always about twice the one wave frequency [3,27,250]. This is not the case here, as seen in the Figure 156c. For instance, at ṁa = 0.5 kg/s and Φ = 1, f1 ≈ 4.5 kHz and f2 ≈ 5.2 kHz. Similarly, for ṁa = 0.4 kg/s and Φ =

1.3, 1.4, 1.5, f1 ≈ 4.5 kHz and f2 ≈ 6 kHz.

297

4.0 1 0.5 kg/s 0.9

3.5

0.8

R -

S 0.4 kg/s

(bar) 0.7

3.0 rms 0.6

2.5 0.3 kg/s 0.5 0.4 2.0

0.3 Pressureshift ratio, P

Wave Wave amplitude,P 0.2 1.5 0.2 kg/s 0.1 1.0 0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 1 1.5 2 2.5 3 Equivalence ratio, Φ Pressure shift ratio, PS-R

(a) (b)

9000

8000

7000

6000

5000

4000

3000 Operatingfrequency, f 2000

1000

0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Equivalence ratio, Φ

(c)

Figure 156 (a) Equivalence ratio vs. pressure shift ratio, (b) Pressure shift ratio vs. detonation amplitude in rms, and (c) equivalence ratio vs. operating frequencies. Legend: ♦:

0.2 kg/s, ●: 0.3 kg/s, ▲: 0.4 kg/s, and ■: 0.5 kg/s

298

Pressure-time series, from the ITP sensor, of an operating point exemplifying such a fundamental mode change is shown in Figure 157. Four sections are marked: (I) ignition from the pre-detonator blast wave responsible for onset of detonations in the RDC, (II) detonation propagation with oscillations of 1 bar (and f1), (III) a distinct onset of low frequency modulation, and (IV) onset of a secondary propagation mode with oscillations of 2 bar (f2). It is emphasized here (and shown in the next section) that almost all the operating points exhibiting a sudden mode shift during the 1 s operation tend to exhibit a distinct period of low frequency modulated (FM) oscillation in the pressure trace. This oscillation always presages the mode shifts and is highly reminiscent of chugging oscillations seen in rocket engines, which is due to the pressure based coupling of the feed plenums with the combustor dynamics [56]. In the next section, analyze six arbitrary pressure traces to further understand RDC operation under back-pressurization.

299

II I III IV

I III IV

Figure 157 Pressure-time trace from the high speed piezoresistive sensor showing four

distinct segments of pressure dynamics, at ṁa = 0.5 kg/s and Φ = 0.92 a. Effect of mean pressure shift on operating modes

To analyze the effect of the mean pressure shift on the operating modes, two sets of operations are considered — the first set (Figure 158) contains sudden and seemingly random changes in mode (frequency of detonation wave), whereas the second set (Figure 159) is a collection of points with a gradual change in operating frequency throughout the 1 s duration of the test. Each set is composed of three operating points, and the associated air flow rate and equivalence ratio are given in the figure title. For this analysis, five plots are presented for each condition and are as follows: (i)

300

pressure vs. time trace acquired from air plenum (blue) and combustor (red) using the CTAP low speed sensors, (ii) pressure evolution acquired from the high speed Kulite piezoresistive ITP sensor, (iii) spectrogram of the high speed pressure recording, (iv) normalized (by the peak pressure during the initial ignition event) low-pass filtered ITP pressure data (below 500 Hz) and finally, (v) the time lag between the circumferentially distributed pair of PCB piezoelectric sensors obtained from cross-correlating the two signals. By segmenting the overall pressure trace from the

PCB sensors into windows of 5 ms, and then cross-correlating the windows, it is possible to ascertain the mode of RDC operation, as we have detailed previously [290]. When the cross- correlation gives a finite time delay that is recurring, the mode is deemed to be rotating detonations

(RD). When the time delay is zero, this signifies the existence of longitudinal pulsed detonations

(LPD) that produces azimuthally simultaneous explosions (and hence zero time delay between the circumferential sensors). Finally, when the time delay is finite, but lacks any coherent pattern and is significantly lower or higher than the C-J speed, the mode of operation is determined to be chaotic detonations (CD). We have addressed this mode to be a type of instability seen in an RDC — atmospheric [250] and backpressurized [69] — that is predicated on poor plenum recovery after detonation passage [127]. During chaotic detonations, there is no coherent wave motion in either the circumferential (RD) or the axial (LPD) direction, and this mode is marked by stochastic explosions at high frequencies. Chemiluminescence imaging of backpressurized RDCs tend to agree with our interpretation of pressure data, showing cycles of random failure and re-ignition of detonation events inside the pressurized combustor [254], which is similar to the images acquired during the operation of an atmospheric RDC with subsonic reactants injection [44].

The most important observation of backpressurized RDC operation is the tendency of the static pressure in the combustor to be higher than the air plenum static pressure for a finite duration of time after ignition (Figure 158-i). While a response delay (seen clearly in Figure 155b) is seen for all the tested operating points, only about half the tested points exhibit a higher combustor

301

pressure in comparison to the air plenum pressure. It is noted here that this adverse pressure gradient disappears by about 1.2 s, i.e. plateaued average pressure inside the combustor tends to always settle down to a value lower than the new plateaued value of the air plenum static pressure.

This facet of RDC operation has not been overserved elsewhere per the authors’ knowledge. It is inferred here that a tremendous feedback (pressure and mass) into the air plenum is an inherent part of a pressurized RDC start-up process, much more so than an atmospheric RDC due to the effect of MFP as discussed above. Black arrows are used to mark the onset of a different operating mode in Figure 158-iii and iv. There is a distinct demarcation in the operating frequency when there is an onset of a distinct oscillating pressure mode, as seen in the timewise changes. Just like the case discussed above in Figure 157, the sudden onset of a secondary operating mode is preceded in time by significant low frequency pressure oscillations as seen in Figure 158-iv. We theorize that this chugging oscillation is a primary cause of sudden detonation wave mode shifts. It appears that the chugging oscillation characterized by FM fluctuations (seen in Figure 158-iii below

500 Hz) are, on the other hand, the result of the mean pressure shift produced due to the increase in stagnation pressure. Finally, Figure 158-v shows that the change in frequency along with the accompanying change in pressure oscillation magnitude is indeed the result of the onset of a different operating mode, varying between RD, LPD and CD (marked appropriately in Figure 158- v).

A similar adverse pressure gradient between the air plenum and the combustor is observed even where there is no sudden mode shift (Figure 159-i) as well. Figure 159-ii shows that the pressure evolution during this operation is also gradual during the mean pressure transient shift after ignition. A similar behavior is exhibited by the frequency evolution for all the considered cases

(Figure 159-iii). Figure 159-iv reveals that for cases (a) and (b) there is no appreciable chugging oscillation in the combustor. However, case (c) exhibits significant frequency modulation throughout the tested duration. Hence, it is unsurprising that cases (a) and (b) do not exhibit any

302

change in operating mode, and exist throughout as rotating detonation. It is noted here that the observed time lag between two sensors dictates a frequency of about 5 kHz and 8 kHz, suggesting a complex two-wave operation (see Figure 159-v). However, it is not the intent of the study here to diagnose the modes themselves, and as such this investigation will be left for a future discourse. For the current study, these modes shall be called RD since there is a consistent and coherent time lag between the circumferential sensors. Observing case (c) in Figure 159-v, it is seen that there is no recognizable pattern in the detonation propagation, which once again suggests consistent chaotic failure and re-ignition. Since this is the only case where chugging was recorded throughout, and since this is the only case with CD throughout the duration of testing, it can be contended that plenum-combustor coupling has a significant role in detonation propagation. Of course, such an observation is not entirely new, but this study suggests that the coupled behavior is more intense in pressurized RDCs, since chaotic detonation is observed at a significant portion of the operating map, and not just at the lean limits of operation (and rather large injection holes allowing pressure feedback).

303

(a) (b) (c)

(i)

Ignition Ignition Ignition

(ii)

(iii)

(iv)

CD CD LPD RD RD LPD (v)

304

Figure 158 Three cases: (a) ṁa = 0.5 kg/s and Φ = 0.92, (b) ṁa = 0.2 kg/s and Φ = 0.71, and (c)

ṁa = 0.3 kg/s and Φ = 1, with five parameters plotted against time

(a) (b) (c)

(i)

Ignition Ignition Ignition

(ii)

(iii)

(iv)

(v)

RD CD

305

Figure 159 Three cases: (a) ṁa = 0.5 kg/s and Φ = 0.83, (b) ṁa = 0.3 kg/s and Φ = 1.64, and (c)

ṁa = 0.5 kg/s and Φ = 1, with five parameters plotted against time

3.2. Chugging oscillations

The preceding section detailed some of the aspects of mean pressure shift and its associated effects on RDC operating mode through the onset of chugging oscillation. In order to delineate the effect of chugging from the pressure shift, in this section of the paper, we resort to considering only the atmospheric RDC without back-pressurization that was detailed in the methodology section.

For the sake of brevity, in Figure 160 we only consider the azimuthally instrumented PCB piezoelectric pressure sensors in the air plenum, when there is rotating detonation wave propagation inside the combustor annulus. A detailed discussion on all the high frequency pressure coupling between the reactants plenum and the combustor is given in our prior publications

[246,247,290]. For the case presented in Figure 160, the detonation wave frequency is 3645 Hz. In such a scenario, despite the injector element being choked on an average, locally there is subsonic flow due to the backpressure provided by the detonation peak pressures [28]. Hence, the fundamental frequency in both the air and fuel plenum is observed to be equal to the detonation wave frequency in the combustor [246,291]. Figure 160a shows the pressure traces acquired from the three air inlet sensors during an entire duration of testing, and it can be seen that every lap of detonation produces about 1 bar of pressure feedback into the inlet. This behavior is better visualized in Figure 160b and c, which are magnified images of the same trace. One should also be able to notice the strong frequency modulation in the recorded pressure traces (Figure 160b and c).

It is emphasized here that this FM oscillation superimposed on the high frequency pressure oscillation of the detonation wave is seemingly the same phenomenon seen in backpressurized RDC in the actual combustor (III in Figure 157). Hence, one can conclude that chugging oscillations are

306

also present in an atmospheric RDC, but in the air inlet owing to locally subsonic flows. In a manner similar to before, we have also presented the low-pass filtered data showing strong low frequency modulations throughout the tested duration (Figure 160d). Note that this phenomenon appears to acoustic in nature (just as in rocket engines) since there is no time lag between the three sensors

(red, blue and black sensors are excited at the same time). Figure 161i, ii and iii show the spectrogram of pressure dynamics in the combustor, air inlet and fuel plenum respectively for three cases — (a), (b) and (c). It can be seen that there is no low frequency excitation in the combustor in the domain of interest below 500 Hz. However, there is considerable amplitude modulation of the detonation wave peak pressures (occurs as packets [247,250]), but this oscillation will not be seen as a separate frequency (AM frequency is offset from the fundamental frequency due to the mathematical formulation of FFT). Oscillation in the air inlet is always recorded to be 235 Hz in our

RDC irrespective of the flow rate and equivalence ratio [246], as seen in Figure 161-ii. No such low frequency oscillation is observed in the fuel plenum (Figure 161-iii), which is most probably the result of mostly sonic flows through the injector due to the viscous damping produced by the individual small holes, thereby considerably weakening the pressure feedback from the detonation wave [171].

The final point of interest is to confirm that the chugging oscillations seen in RDCs are produced due to the ‘organ-pipe’ acoustic standing modes inside the feed plenums [56]. Towards this endeavor, as explained before, the Helmholtz acoustic solver in COMSOL is used to numerically investigate the first acoustic Eigen frequency inside the air plenum. The static pressure inside the plenum is set to 2 bar, 2.85 bar and 3.6 bar respectively. These values are obtained from experimental measurements using the CTAP sensor, and represent air flow rates of 0.2 kg/s, 0.3 kg/s and 0.4 kg/s. The air temperature is set to 289 K, and the resulting parameters of interest are plotted in Table 16. It is seen clearly that for all three plenum pressures (read: flow rates), the oscillating frequency observed experimentally is in close agreement with the value of 191 Hz

307

attained numerically. The minor mismatch can be explained by considering the fact that there is a considerable backflow of hot combusted products into the air inlet [179], and therefore the actual sound speed would be higher than that dictated by 289 K. Also note that this frequency, just like experiments, does not vary with varying static plenum pressures, which is a given since the frequency of a classical Helmholtz resonator is only a function of the resonator geometry and sound speed [336]. Finally, there is qualitative congruence between experiments and simulation with respect to the oscillation magnitude, which increases with increasing plenum pressure (Table 16).

This finding once again supports the notion that the frequency modulation seen in RDCs, both pressurized and atmospheric, is due to the chugging oscillations widely reported in rocket engines and other combustors.

308

(a)

(b)

(c)

(d)

Figure 160 (a) Dynamic pressure oscillations in the air inlet from three air inlet sensors at

ṁa = 0.4 kg/s and Φ = 1, (b) magnified image showing the low frequency oscillation, (c) chugging oscillation superimposed on the pressure feedback from the detonation wave, and

(d) magnitude of chugging oscillation

309

(a) (b) (c) (i)

(ii)

(iii)

Figure 161 Spectrogram from the combustor (i), air inlet (ii) and fuel plenum (iii) for three cases: (a) ṁa = 0.2 kg/s and Φ = 1, (b) ṁa = 0.3 kg/s and Φ = 1, and (c) (a) ṁa = 0.5 kg/s and Φ

= 1

Table 16 Comparison of oscillation characteristics between experiments and simulation

Case Air Frequency Frequency Oscillation Oscillation

plenum from from from from

pressure experiments simulations experiments simulations

(bar) (Hz) (Hz) (bar) (bar)

a 2 235 191 0.56 0.16

b 2.85 235 191 1.24 0.23

c 3.6 235 191 2.04 0.29

310

4. Conclusions

Experimental investigation of back-pressurized RDC behavior is performed at diverse air flow rates and equivalence ratios. The mean static pressure shift observed in pressurized RDC operation is characterized to reveal that it is dependent on the stagnation pressure increase produced by detonative combustion, the mass flow rate through the device and inefficiency in combustion processes that could alter the stagnation temperature, i.e. pressure shift in RDCs is a function of the mass flow parameter across the choked RDC exit. This highly transient pressure behavior after ignition causes a wide range of variation in the operating mode of the device (rotating detonation vs. longitudinal pulsed detonation vs. chaotic detonation events), with the final steady-state mode usually being different from the initial mode of onset. The phenomenon of average pressure shift appears to be the similar to the highly detrimental “DC shift” phenomenon reported in rocket engines that exhibit high frequency combustion instabilities. Strong, low frequency modulated oscillations always predate the sudden mode shifts, which supports the notion that this type of chugging behavior — also seen widely in rocket engines — is an inherent part of a pressurized RDC operation, owing to the very strong coupling between the supply plenums and the combustor. To confirm that this is the same type of chugging seen elsewhere, numerical simulations were performed using acoustic solvers, with the resulting frequencies of Helmholtz acoustic modes being in close agreement with the experimental values. Thus, the current manuscript deals with the two important processes of pressure shift and chugging in RDCs, and establishes a link between this field and the considerably more mature field of rocket engine instabilities. We contend that some of the problems faced in the former could be solved by garnering the expertise gathered through the latter. As emphasized in the introduction, pressurized RDC behavior is still a field of nascent research. Moving forward, one needs to answer multiple questions pertaining to this in order to make RDCs a practical device, namely the effect of hysteresis of operating modes based on initial

311

pressurization, the optimum flow rates and mixing to enable highest stagnation pressure rise at the desired mode of operation, elimination of chugging during RDC operation, etc.

312

CHAPTER 9: ROTATING DETONATION WAVE MECHANICS THROUGH ETHYLENE-AIR

MIXTURES IN HOLLOW COMBUSTORS, AND IMPLICATIONS TO HIGH FREQUENCY

COMBUSTION INSTABILITIES

Chapter Abstract

Recent investigations into the rotating detonation phenomenon have involved its inception and sustenance in hollow combustors, in contrast to the traditional annular rotating detonation combustor (RDC) designs. Despite this proof-of-concept, the mechanism of propagation of detonation waves in hollow combustors is unclear. On the other hand, the decades-old issue of high frequency combustion instabilities, especially in rocket engines, has been known to produce distinct shock waves that are in-sync with regions of intense combustion, the reason for which is widely attributed to the Rayleigh criterion. In this paper, we argue that there is a considerable overlap in the physics behind the reported rotating detonations in hollow RDCs and the high frequency tangential combustion instabilities that are known to wreak havoc on engines. To support this notion, an atmospheric hollow combustor is experimentally tested to attain the baseline performance. It is then ‘transformed’ into a hollow RDC by the use of a flow-turning obstacle that diverts the combustible ethylene-air mixture towards the outer wall. Two distinct mechanisms are found to cause rotating detonations in a hollow combustor, and subsequently predicate its stability. The observed modes are analogous to the behavior exhibited by planar detonations at the near-limit. This explains not only the widely observed velocity and pressure deficits in rotating detonations, but also the “steep-fronted”, “detonation-like” behavior noted in high frequency combustion instabilities.

313

1. Introduction

Detonation is a supersonic combustion mode that produces a pressure gain [21] across the front due to the shock wave linked to the combustion behind it. This type of combustion can be activated in suitable mixtures in solid, liquid or gas phase [49]. The phenomenon was first discovered in the 19th century [49], and since then, considerable research has been directed towards understanding this phenomenon. Broadly, detonations can be stable or unstable [21].

Unstable detonations exhibit a highly time-dependent three-dimensional behavior and manifest as different peculiar phenomena. While their actual onset and exact physics are actively studied, there is common consensus that unstable detonations have a decoupled shock wave-reaction zone structure that is brought about due to the quality of reactants (high activation energy), boundary conditions, or both [21]. However, based on the mechanism of a coupled propagation, detonations exist in one of three sub-types: strong detonation, Chapman-Jouguet (C-J) detonation and weak detonation [21,49]. A strong detonation has a subsonic flow of products behind the detonation front, relative to it. As such, a strong detonation (“piston supported”) cannot sustain indefinitely, since the detonation wave weakens due to the expansion waves interacting with the reaction zone.

C-J detonations (“unsupported”), on the other hand, can be freely propagating (steady state), and most mixtures subscribe to the solutions obtained from the simple Rankine-Hugoniot relation with an additional energy release term. Here, the combusted products are sonic with respect to the detonation front, which means the detonation wave can be continually sustained, provided the upstream and boundary conditions are held constant. The third detonation type — weak detonation — is theoretically possible [49], but requires special conditions to exist. In fact, despite both Zel’dovich and Neumann showing the theoretical possibility of steady-state weak detonations

[21], notable apprehensiveness seemed to exist for some time among experimentalists regarding its possibility in the physical world. Weak detonations have a shock wave that is supersonic relative to the expanding products, and as a result have a comparatively (to C-J) higher propagation velocity

314

and lower peak detonation pressure [21,49]. It is at this juncture that we seek to divert the attention to the work of Adams [50], who tried to experimentally show that weak detonation waves can exist in gaseous mixtures, by varying the boundary conditions of the detonation tube. His work was partly motivated by the results of Voitsekhovskii, who was the first to show the possibility of having sustained and stably propagating rotating detonation waves in an annulus [51]. He observed detonation waves moving at half the C-J velocities of the mixture that was used. While the final conclusion of Adam’s investigation into weak detonations were ultimately inconclusive, the questions raised by him regarding the peculiarities observed by Voitsekhovskii in his rotating detonation combustor are of heightened significance, both from a fundamental physical inquiry and from an engineering perspective.

An intriguing facet of RDCs is the notably lower wave speed and peak detonation pressures relative to the solutions obtained for the ideal C-J conditions for the given mixture. To the authors’ knowledge the rotating detonation wave speed and peak pressure across all the facilities worldwide always exhibit varying levels of deficiencies from the expected ideal C-J values in an RDC

[36,48,51,69–71]. In this regard, rotating detonations differ from weak detonations since they actually exhibit lower wave speeds from C-J, which is in contrast to the higher wave speeds exhibited by weak detonations. Despite this unanimous RDC behavior, it is interesting to note that most researchers have refrained from addressing this velocity and pressure deficit; a trait in RDCs that was called out by Adams [50]. Such a deficit is also seen in a hollow RDC [32] . A hollow RDC is lighter than an annular combustor of similar dimensions, due to the absence of the RDC center wall.

It is emphasized that continuous detonation in a hollow combustor was first demonstrated by

Bykovskii et al. [33] using hydrogen, methane, kerosene and diesel with air in 1997. While these results from the literature forecast positive implications to the usage of a hollow rotating detonation combustor, we are left with an important unanswered question: if rotating detonation waves can be produced in both a hollow and an annular combustor, what is the physical mechanism

315

responsible for its production and continued sustenance? That is, under what conditions does an ordinary combustor become a rotating detonation combustor and vice versa, and is it something that can be controlled? In fact, if rotating detonation waves can be produced in a hollow combustor that are of equal strength (in terms of pressure and velocity) to the waves produced in an annular combustor, it would be logical to resort to the hollow combustor design, considering the heightened heat transfer to the annular walls. Since it is well known that a planar detonation in a tube with the same mixture concentration gets progressively weaker, and eventually fails when the tube diameter is reduced below a critical value of detonation cell size [21], logic dictates that we move away from the annular designs that have been the singular signature of rotating detonation combustors until now. In fact, the authors have shown a similar trend— of decreased operating regime, and increased failure to ignite detonation waves— when the annulus of the detonation combustor is reduced for a given hydrogen-air mixture composition [128].

A hollow RDC is, in essence, a basic cylindrical combustor that is widely prevalent in both gas- turbine and rocket engine combustors, and naturally, analyzing detonation propagation inside it has heightened significance for both the engines. While the previously discussed demonstration of continuous rotating detonation in a hollow combustor is voluntary, multiple researchers [31,52–

55] studying rocket engines (both liquid propellant engines and solid motors) have observed

“detonation-like” (because of the inability to explain large deviations in wave speed and pressure from the ideal C-J conditions, which has now been accepted as the standard operation in an RDC) waves spinning around the rocket combustion chamber at thousands of Hertz. This “high-frequency tangential instability” in rocket engines has been a source of constant adversity to the development of rocket engine programs, mainly due to the lack of understanding of the fundamental behavior of the complex combination of combustion and fluid dynamics. This had traditionally lead to the highly demanding and economically detrimental process of trying to treat the rocket-specific symptoms of the high-frequency instability by adopting a trial-and-error process of altering the

316

rocket geometry and mixing scheme, among other things, rather than addressing the nuclei of the issue [56]. For instance, the F-1 engines for the Saturn V program had to be subject to over 2000 full-scale test runs to detect and avoid the intrinsic (starts only after injection of reactants and subsequent ignition) instabilities, as it appeared to be highly sensitive to the injection scheme and flow rates used [57]. Of notable loss is the Ariane 4 rocket, which experienced a catastrophic explosion minutes after takeoff, due to one such high-frequency tangential instability event in its

Viking engines [56]. The high-frequency instabilities in rocket engines have been attributed to a variety of factors, some making more sense than others depending on the research facility [56]. A combustion-acoustic coupling in the form of an acoustic wave, conforming to the Rayleigh heat addition criterion [59–61], velocity fluctuations, entropy waves, “detonation-like” waves, liquid stream shattering and supercritical droplets explosion are some of the proposed theories [56]. It is to be emphasized that significant contention still exists among the researchers of rocket engine instabilities on the fundamental nature of the high-frequency tangential instability. Most studies still prescribe to the Rayleigh heat addition process through in-phase pressure and heat addition and explain the “steep-fronted, detonation-like” waves to be a kind of acoustic wave or a “heat wave” [75]. However, some other studies [31,52,62] have rightly pointed out the debilitating shortcomings, both logical and observational, of this theory. Flandro et al. [62], who are responsible for one of the most accurate analytical model on these high-frequency instabilities, go so far as to say that the theories that are purely based on the acoustic wave point of view have spent “much time and energy on attempts to correct deficiencies in the linear model by introduction of ad hoc fixes that are often based on guesswork, and misinterpretation and/or distortion of experimental evidence”. However, the physical mechanisms responsible for these instabilities have not yet been pinpointed, and as a result multiple unanswered questions remain. From the above information it can be ascertained that there seem to be two scientific communities operating rather independently of each other. The motivation for the current work is to ascertain if the physics

317

dictating the combustion dynamics in an RDC is the same as the one causing high frequency combustion instabilities in varied combustors. To investigate this, we resort to using a hollow atmospheric combustor, without backpressure, and ‘force’ it to sustain rotating detonations.

2. Methodology

2.1. Facility description

Ethylene-air mixtures are used to operate the hollow combustor at air flow rates (ṁa) of 0.2,

0.3, and 0.4 kg/s (pressure ratio across injection is 2, 2.7 and 3.2 respectively) at different equivalence ratios (Φ), for a time period of about 0.43 s. Air and fuel flow rates (ṁf) are controlled by a closed-loop system of nitrogen-driven pilot regulators and a set of Flowmaxx nozzles. Norgren

VP50 proportional control valves (pilot) are linked to Norgren pilot-operated regulators to isolate electrical components from the primary fuel supply. GE Unik 5000 sensors are linked to the choked- flow nozzle assemblies to monitor air and fuel flow rates. Fuel flow is administered to the rig through a pneumatically-actuated Bi-Torq isolation valve located just upstream of the fuel plenum, which allows fuel flow rates to stabilize within 2 s of fuel introduction. The uncertainty in the pressure and temperature sensors (used in the reactants delivery) is ±0.069 bar and ±1 K, respectively. The linearized systematic error analysis of this uncertainty results in an estimate of

2.1% error in the air mass flow rate and 2.8% in fuel mass flow rate, which in turn results in a maximum error of 3.4% (seen for the lowest flow rates) in Φ.

2.2. Combustor

As explained earlier in the introduction, we are concerned about inducing rotating detonations in a hollow combustor. To effect this, two different geometric variations/ schemes are utilized to change the degree of mixing inside the combustor, since global equivalence ratio should be

318

markedly different from the local equivalence ratio in a hollow combustor, unlike the conventional annular RDC geometries. The generic combustor geometry is shown in Figure 162a. The first scheme only has a single row of fuel injection orifices. The individual orifices have a length-to- diameter ratio of 17. The second scheme uses an additional obstacle on the headwall (maroon slot in Figure 162a). This obstacle is a circular plate with a thickness of 3 mm and a diameter of 142 mm

(Figure 162a). The motivation behind this is to divert the mixture of the radially inward air flow and axial fuel flow towards the combustor wall, thereby increasing the local mixture quality at the combustor wall in comparison to Scheme I. It will be shown posteriori, from experimental findings, that this obstacle-induced variation in equivalence ratio dictates the onset of rotating detonations.

The current study utilizes a single air injection area for all the tested points. The geometric parameters of interest for the combustor are listed in Table 17. A two-dimensional axisymmetric analogue of the combustor is simulated under cold-flow conditions for the two schemes, to confirm the efficacy of this obstacle. Since the air inlet in the actual RDC is a slot, the same width is used in the numerical analysis. However, the fuel inlet is multi-holed, and circumferentially arranged.

Hence, fuel injection is modeled as a slot with a thickness (wfo) that would give an area equivalent to the total area of injection. Note that the fuel slot is placed right at the exit of the air inlet. The nominal cell-length is based on the Taylor micro-scale λT, which is assumed to be the intermediate length scale at which the size of eddies has a significant impact on the turbulence dissipation rate

[357]. The domain is thus discretized into 159,106 quad cells. The solver used is the pressure-based formulation of the Spalart-Allmaras turbulence model, as available in the commercial solver Fluent

(ANSYS Fluent, Release 15.0, Ansys Inc., 2013). The velocity and pressure equations are coupled, and the spatial discretization is computed to the second order on pressure, density, and momentum. A multi-phase mixture of air and ethylene is defined as the operating flow, and the mass fraction of air and ethylene at the mass flow inlet boundaries are defined based on the equivalence ratio.

319

As could be expected, a 2D cold-flow simulation of the RDC channel with equivalent fuel injection areas would by no means capture the complete physics of the process. But, that is not our aim here. The intent here is to attain an approximate trend in the radial variation of the local equivalence ratio, thereby ascertaining if the obstacle satisfies its required role of producing a higher fuel composition (and thus, a more energetic mixture) for Scheme II, in comparison to

Scheme I. The resultant mass fraction variations of ethylene are shown in Figure 162b for Schemes

I and II, respectively. This 3 mm thick circular obstructing plate causes a drastic change in the local equivalence ratio inside the hollow combustor, as seen in the radial distance vs. Φ plot given in

Figure 162c. Near the wall, the obstacle (Scheme II) produces considerable equivalence ratio, whereas without the obstacle, the radially-inward air injection scheme pushes the fuel inwards thereby having negligible fuel content near the walls.

Outer wall

Scheme I Scheme II

Scheme II

Scheme I Obstacle

Figure 162 (a) Hollow RDC geometry, (b) ethylene mass fraction variation for the two

Schemes (2D cold-flow simulation), and (c) equivalence ratio fluctuation with radius at an

axial distance of 1.9 cm

320

Table 17 Hollow RDC geometric dimensions of interest

Combustor geometric parameters Dimension

Combustor diameter 154 mm

Combustor length 131 mm

Air injection slot width 1 mm

Length-to-diameter ratio of fuel orifices 17

Diameter of the outermost row of fuel orifices 151 mm

Diameter of the circular obstacle 142 mm

Thickness of the circular obstacle 3 mm

2.3. Instrumentation and data acquisition

A tangential pre-detonator utilizing a rich mixture of ethylene-oxygen is used to ignite the reactants (Figure 163). A detailed presentation of our ignition system is given in Ref [156]. The location of the predet entering the combustor is marked as the predet entry plane (Figure 163), and all the other stations are referenced relative to it in terms of the angular displacement. Three different types of sensors are instrumented in the combustor setup: PCB piezoelectric pressure sensors, ion probe sensors and piezoresistive capillary tube average pressure (CTAP) Omega pressure sensors. Of the three, the CTAP sensors [345] are sampled at 1 kHz, whereas the other two sensors are sampled at 1 MHz. The frequency resolution for the high speed acquisition is ±2.85 Hz, since the testing duration is around 0.45 s and the sampling rate is 1 MHz (frequency resolution = sampling rate / acquired samples). Three CTAP sensors are used, with one each in the air plenum, fuel plenum and the combustor respectively. They provide an averaged value of the static pressure inside different subsections of the combustor from which the reactants injection pressure ratio is determined.

321

Instrumented ports are referred by their station (designated by their azimuthal degree from the pre-detonator plane) and row number (ascending order from the RDC headwall). The combustor has six stations of instrumentation ports with five of the six stations having four rows of ports each

(the pre-detonator plane station only has three rows to allow entry into the combustor – see Figure

163). The first row of instrumentation ports is 1.9 cm away from the headwall, whereas the other rows are spaced 2.54 cm from each other. Three piezoelectric sensors (yellow tabs/ circles) are instrumented in row 1 of stations +30o (green pressure traces), +180o (blue pressure traces) and -

60o (red pressure traces). There are also three ion probes (blue tabs/ circles) in the second row of stations +60o, -180o and -60o. The ionization probe circuit used here [323] gives a negative voltage that correlates with the strength of ionization present. We shall henceforth use the color scheme of red, green and blue for presenting pressure traces from the stations -60o, +30o and +180o, respectively. The same color scheme is used to present ionization traces from the stations -60o, +60o and +180o (see figure for clarity).

Station +30o, in addition to having a piezoelectric sensor in the first row, also has three more piezoelectric sensors distributed axially in the second, third and fourth rows. Thus, there are a total of six piezoelectric sensors, and are instrumented as per the color-schematic shown in Figure 163.

This azimuthal and axial distribution of the pressure sensors enables the determination of the combustion instability mode (transverse/ rotating/ longitudinal). To elaborate, if the pressure phenomenon is rotating, there is a clear phase-lag between the individual azimuthally distributed sensors in row 1. In the following sections, sensor -180o (blue) is used when the analysis pertains to pressure magnitudes. As will be explained in the next section, we observe both transverse and rotating combustion phenomena in the hollow combustor at specific operating conditions and geometries. We did not observe the longitudinal pulsed detonation [69] during the current study, which can be attributed to the absence of a choked exit. In addition to the above, a closed circuit television (CCTV) camera is also used to observe the combustor in real time.

322

Pre-detonator Red plane Pre-detonator

Green +60o

Blue

Figure 163 Instrumentation schematic of the hollow rotating detonation combustor

3. Results and discussion

3.1. Effect of obstacle on operation

In this section, we demarcate the fundamental differences in operation induced by adding the obstacle at the headwall. For Scheme I (without the obstacle), rotating detonations are not observed in the regimes of ṁa and Φ tested. Operating points that are prone to an anchored deflagration flame throughout the test duration or those points that did not exhibit any combustion initiation at all are defined as failure points and are presented as blue markers in Figure 164a.

When ‘rough’ combustion (notable activity in the piezoelectric pressure sensors) is observed, the operating points are differentiated between rotating oscillations (red markers) and transverse oscillations (orange markers). For Scheme I, high frequency transverse combustion instability is observed for all three air flow rates, only at Φ = 1.4. When two of the three azimuthally distributed pressure sensors in row 1 exhibit in-phase pressure oscillations it is inferred that transverse instabilities (radial oscillations) are set up inside the combustor. Two arbitrary pressure traces from two operating points exhibiting transverse HFI are shown in Figure 165. Sensors in station

+30o and -60o show in-phase pressure oscillation, whereas the sensor in station +180o oscillates out of phase. The pressure magnitude does not exceed 0.2 bar and appears as well-defined sine waves.

The frequency of the instability decreases from 2939 Hz to 2848 Hz as ṁa increases from 0.2 kg/s

323

to 0.4 kg/s. Assuming crude hot flow conditions having a heat capacity ratio of 1.2, “average” gas temperature inside the combustor of 3000 K, and specific gas constant of 287 J/(kg-K), we get a sound speed of 1016 m/s. This, in turn generates a half-wave frequency for the transverse instability to be 3300 Hz, which is close to the recorded values. Since the first transverse mode between two walls is a half-wave eigenmode [358], one could contend that the transverse HFI produced with Scheme I at Φ = 1.4 is due to an acoustic standing wave that is set up inside the hollow combustor. The fact that the station +180o sensor records comparable peak overpressures and underpressures (0.15 bar and -0.15 bar, respectively) augments the claim that the rough combustion witnessed for Scheme I is due to standing acoustic modes. This equal strength in compression and expansion further strengthens the claim that the transverse HFI is caused due to standing acoustic waves that are intertwined with combustion, similar to the process seen in other hollow combustors [78,358,359].

A drastic variation in the hollow combustor operation is produced when the 3mm thick obstacle is mounted at the headwall (Scheme II). First, rough combustion is observed for all but one operating point tested (ṁa = 0.4 kg/s and Φ = 0.8 only supports anchored deflagration). All points tested at the lowest ṁa of 0.2 kg/s had two of the three row 1 pressure sensors exhibiting in-phase pressure oscillations that are illustrative of transverse HFI. Here however, two distinct bands of transverse HFI are observed — one in the same range as before at about 3000 Hz, and the other at a notably higher range at about 5000 Hz. The transverse HFI high frequency band occurs at Φ < 1.3, whereas the low frequency band occurs at Φ > 1.3. Sinusoidal pressure oscillations, not exceeding

0.6 bar is observed at the high frequency band. Additionally, the operating points in this band exhibit a distinct two-peak (black arrows in Figure 166a) behavior characterized by two of the three sensors in row 1 recording distinct two pressure peaks, whereas the third sensors exhibits only a single peak. As before, pressure sensor in station +180o records equal overpressures and underpressures (+/- 0.6 bar). These observations suggest that, once again, standing transverse

324

acoustic modes are responsible for the rough combustion produced when Φ < 1.3. However, unlike the prior cases with Scheme I, higher modes at around 5000 Hz seem to be excited when Scheme II is used, which might be due to the different modes and orientations of the standing wave transverse instability, a phenomenon observed in hollow combustors [358,359]. This explains the double peaking behavior, the higher oscillation frequencies and equal overpressure and underpressure magnitudes. While it may be tempting to attribute the standing acoustic wave mechanism to the low frequency transverse HFI operation observed here at Φ > 1.3, it is imperative to note that such a scenario is unlikely because of the vast discrepancy between the peak overpressure and underpressure, as seen in Figure 166b. For these operating cases, a peak pressure is always around

1 bar or greater, whereas the negative pressure does not fall below 0.5 bar, for all the operating cases investigated.

Additionally, the pressure signals are no longer sinusoidal, but are now characterized by very sharp rise-times characteristic of shock waves inside the combustor. It is this type of sharp rising pressure signals that have been attributed to the “shock-fronted” behavior of high frequency combustion instabilities seen in rocket engines (as detailed in the introduction). For ṁa of 0.3 kg/s and 0.4 kg/s, and Φ > 0.9, we no longer observe any in-phase pressure oscillations. For these operating points with Scheme II, continual rotating pressure waves are observed. This is verified by a time-of-flight algorithm that captures the subsequent (temporally) peak pressures across all the three pressure sensors in the first row, and using the obtained time interval to divide the sectoral distance between the stations the sensors are instrumented in. To further expand, we confirm that what we observe is indeed rotating by ensuring that: 1) the three sensors are phase-lagged, and 2) the speed of occurrence of the phenomenon is uniform and relatively constant across the three sensors distributed azimuthally. Note that, at this point, we call it pressure waves and not detonations, the reasons for which are given in the next section. Both stable and unstable rotating pressure wave propagations are observed. exceed 20 bar. An example for unstable rotating

325

pressure waves is seen in Figure 166d, where until time, t = 0.285 s, there is considerable scatter in the propagation speed and peak pressures, but after t = 0.285 s, there is a stability onset. We define stability based on the scatter in wave speed and peak pressure of subsequent laps of the rotating pressure wave. If the wave speeds are highly repeatable and without much scatter (in a manner similar to Lee’s definition of detonation wave stability [21]) the operating points are deemed to be stable. An example of stable rotating pressure waves, propagating inside the hollow combustor, is seen in Figure 166c, where the wave rotates in the clockwise direction (blue → green → red pressure signals). As can be seen from the sensor in station +180o, the peak pressures, at certain laps even exceed 20 bar. An example for unstable rotating pressure waves is seen in Figure 166d, where until time, t = 0.285 s, there is considerable scatter in the propagation speed and peak pressures, but after t = 0.285 s, there is a stability onset.

0.5 0.5 Rotating detonations

0.4 2848 Hz 0.4 (kg/s)

(kg/s) 4894 Hz

a a 0.3 2895 Hz 0.3 5109 Hz 3175 Hz 3179 Hz 0.2 2939 Hz 0.2 4933 Hz 5175 Hz 3242 Hz

0.1 Failure Transverse Failure 0.1 Ai f f Ai ṁ ,

Ai f f Ai ṁ , HFI 0 0 0.7 0.9 1.1 1.3 1.5 1.7 1.9 0.7 0.9 1.1 1.3 1.5 1.7 1.9 Equivalence ratio, Φ Equivalence ratio, Φ

(a) (b)

Figure 164 Hollow combustor operating regime for (a) Scheme I and (b) Scheme II. Legends:

◇-0.2 kg/s, □-0.3 kg/s, △-0.4 kg/s, with colors: blue (deflagration/blow-out failure), yellow

(transverse HFI), and red (Rotating waves)

326

(a) (b)

Figure 165 Pressure traces showing high frequency transverse instability with

Scheme I at Φ = 1.4 for (a) ṁa = 0.3 kg/s, and (b) ṁa = 0.2 kg/s

(a) (b)

327

(c)

(d)

Figure 166 Pressure traces with Scheme II showing (a) transverse HFI for ṁa = 0.2

kg/s at Φ = 1.2 (b) transverse HFI for ṁa = 0.2 kg/s at Φ = 1.6 , (c) stable rotating

pressure wave propagation for ṁa = 0.4 kg/s at Φ = 1.4, and (d) unstable rotating

pressure wave propagation for ṁa = 0.4 kg/s at Φ = 1.6

Having determined that these operating points exhibit rotating combustion, henceforth, for the remained of the paper, we are more vested in this phenomenon. It is not the aim of the current paper to dissect the high frequency transverse instability, and it is only discussed when it pertains to this rotating combustion phenomenon. The average wave speeds of the rotating pressure wave for the different operating points are given in Figure 167a. The ideal C-J wave speed (red curve) is acquired from NASA Chemical Equilibrium with Applications, for a given global equivalence ratio.

Upstream conditions are assumed to be atmospheric pressure and temperature, while conceding the difficulty in knowing the exact effect / presence of burnt gases in the combustor, upstream of the wave. Figure 167b shows the averaged peak pressures (for a given operating point) of the rotating pressure waves acquired from the sensor in station +180o. When the rotating pressure waves are stable, they also propagate very close to the C-J wave speed (95% of the ideal C-J speed) and the average peak pressure values for these operating points range between 4 bar and 12 bar. At certain laps, the pressure peaks even reach pressures greater than 20 bar (as shown above), which

328

is physically impossible for an acoustic wave as this violates the isentropy requirement [103].

Hence, we deem these stable rotating pressure waves to be stable rotating detonations travelling around the hollow combustor with minimal velocity deficit but notable peak pressure deficits. To the best of our knowledge, this is the first time rotating detonations have been attained in a non- premixed mixture of ethylene-air. A previous study by the authors utilizing multiple annular channel widths in a conventional RDC failed to produce detonations, but exhibited rotating waves at sub-isobaric sound speeds [134]. Other studies have used ethylene-air-oxygen mixtures in a large combustor (around 500 mm diameter), but still failed to achieve the steep-fronted, high wave speed that is required of detonations [54,71]. A major part of this shortcoming could be attributed to the probable quenching effect of the narrow annular walls; a predicament that is removed in the current paper. For those operating points with unstable rotating pressure wave propagation, the peak pressures barely reach a 2 bar maximum, and on an average stay around 1 bar. The pressure waves travel at speeds greater than 80% of the ideal C-J speed for the given mixture, while the peak pressures are lower than 5% of the ideal C-J pressure.

There are significant implications to the above-discussed data. First, we have shown that a minor change in geometry — of adding a 3 mm thick headwall obstacle — has transpired a change in operation of a hollow combustor from exhibiting minimal rough combustion (< 0.2 bar transverse oscillations) to housing very strong rotating detonation waves (> 20 bar oscillations).

Second, air flow rate has a strong impact on the mode of operation, since no rotating pressure waves are observed for 0.2 kg/s with Scheme II, whereas no transverse HFI is observed at 0.4 kg/s.

Third, equivalence ratio at a given air flow rate appears to dictate the stability of the rotating pressure waves. We discuss this issue in the next section. But, at this point, we once again invoke the idea of the “high frequency tangential instability” in rocket engine and other combustors.

Despite some researchers recognizing its “detonation-like” behavior, most ascribe it the Rayleigh heat addition criterion. While such a sentiment— of in-phase heat and pressure oscillation— does

329

indeed answer some of the many complexities of these crippling instabilities, it does not explain the shock wave profiles that are concomitant to these instabilities. The Rayleigh heat addition principle which theorizes sustained acoustic wave propagation cannot explain either the speeds or the peak pressure magnitudes observed here, as that would violate the isentropy required across a sound wave [103]. However, the Rayleigh criterion does explain the standing transverse modes seen with

Scheme I. In light of this evidence, perhaps it is prudent to consider the possibility that high frequency combustion instabilities in conventional combustors (and by extension, rotating detonations in hollow combustors) are dependent on both of the proposed theories — detonation- like behavior and Rayleigh criterion, i.e. there is a gray region connection both the theories. This is evident in the gradual change in operation and behavior exhibited by the hollow combustor, depending on a variety of parameter as we move from Scheme I to Scheme II.

3 20 18 2.5 16 Stable

(km/s) 2 14 S 12 1.5 10 8 1 6 Stable Unstable 4

0.5 Peakpressure, P (bar) Wave speed,W 2 Unstable 0 0 0.7 0.9 1.1 1.3 1.5 1.7 1.9 0.7 0.9 1.1 1.3 1.5 1.7 1.9 Equivalence ratio, Φ Equivalence ratio, Φ

(a) (b)

Figure 167 (a) Wave speed of rotating pressure waves with Scheme II, and (b) average peak

pressure of the waves obtained from Sensor +180o. Legends: □-0.3 kg/s, △-0.4 kg/s.

3.2. Propagation behaviors

The remainder of the paper is focused on identifying keys aspects of select operating points that shed further insight into the phenomena. As described earlier, both stable and unstable rotating

330

pressure waves are observed. To analyze the difference between both, we first qualitatively analyze an operating point that exhibits both behaviors. Shown in Figure 168a are the pressure traces (from the pressure sensor in row 1, station +180o) and the ionization traces (from the ionization sensor in row 2, station +180o), for one such test point. This gives us the ability to track the relative changes between pressure and ionization since both sensors are at the same azimuth. Note that data acquisition is simultaneous and hence the data — pressure (blue) and ionization (red) — are time- synced, and since they are at the same station, they give the pressure and ionization behavior of the detonation wave as it passes through that point in the circumference. As noted earlier, our ionization probe circuit outputs negative voltage drops, the magnitude of which depends on the strength of the ionization passing the probe. However, to better represent the coupling between pressure and ionization, the ion probe data is multiplied by negative unity. This is just a cosmetic change for the sake of the readers. Upon ignition (t ≈ 0 s), it is seen from Figure 168a, that initially there is no pressure activity; just ionization activity. At t ≈ 0.02 s, rotating pressure waves with considerable peak pressure magnitudes (and hence rotating detonations) appear. However, at t ≈

0.05 s, the rotating detonation wave seemingly descends into highly unstable propagations that are characterized by “packets” of subsequent laps that have amplitude modulated (AM) sinusoidal component. This AM fluctuation is characteristic of all the unstable rotating pressure wave propagations observed in this study. This unstable behavior extends till t ≈ 0.28 s, after which there is, once again, sustained periodic rotating detonations without the packets of instability. Of interest is the fact that, for a given packet of instability, ionization (red) is recorded for only about roughly the first half of the sinusoidal packet, whereas the second half is composed of just pressure activity

(Figure 168a). Figure 168b shows pressure and ionization data from an arbitrary duration from the same test point when there is stable rotating detonation wave propagation. It can be seen that the shock wave precedes the ionization (combustion) peak, as is to be expected in a detonation wave. A further magnified image of this snippet (Figure 168c) shows this distinction — pressure peak

331

preceding the ionization peak — better. The black circles denote the peak pressure and ionization values, and are acquired by a time-of-flight algorithm that captures peak values, for a given lap.

Figure 168d contains pressure and ionization data during two subsequent packets of unstable operation, from the same test case. As explained earlier, for a given amplitude modulated packet of subsequent rotating pressure waves, ionization activity exists for roughly the first half of the packets. Periods between the two packets do not exhibit any ionization, but do exhibit very weak rotating pressure waves that do not exceed 0.5 bar. It is once again emphasized here that even during this very low amplitude unstable, AM behavior, the pressure waves are confirmed to be rotating (since we have three circumferentially distributed sensors in row 1). A striking difference from the pressure-ionization coupling behavior seen during stable operation (Figure 168c) is evident in Figure 168e, during unstable behavior. During unstable propagation, most laps in a given cycle have the peak pressure succeeding the ionization / combustion peak. This is, in fact, observed for all unstable propagations. Hence, it is imperative to quantify the time lag, ∆t, between the peak pressure event and the peak ionization event to ascertain the difference between the two propagation mechanisms. We use the system of positive ∆t if the peak pressure precedes the peak ionization and negative ∆t if it succeeds it.

Figure 169a to f gives the pressure trace (3 sensors in row 1), ionization trace (3 sensors in row

2), wave speed (from time-of-flight algorithm used on station +180o sensor) and time lag between pressure peak and ionization peak (negative value if ionization peak precedes pressure peak) for six different test points. Figure 169a and b are representative of stable operation, whereas Figure

169c to f are cases that exhibit unstable propagation. Note that all plots presented are for the whole duration of testing. The following observations can be readily made. During stable operation, there is continual ionization activity throughout the duration of the test as witnessed by the three ion probes in row 2. Once rotating detonation starts, it sustains at highly steady speeds until fuel supply is stopped. When the propagation is unstable, there are packets of rotating pressure waves with

332

very low peak pressure magnitudes. The corresponding ionization traces reveal a similar packet- type behavior (Figure 169c to f). The sinusoidal oscillation evident in the peak pressure magnitudes of subsequent laps also results in sinusoidal oscillations in the lap-to-lap wave speeds, when the propagation is unstable. This is suggestive of a periodically strengthening and weakening rotating wave. It is imperative to note that during stable propagation the wave speed of each lap is about

95% of the C-J speed (red dotted line), whereas during unstable propagation, the wave speed is highest at the highest pressure point of the packet and is about 90% of the C-J speed. The average wave speed, however, is considerably lower due to the waxing and waning on either sides of the maximum pressure value. Additionally, for the highly unstable cases shown in Figure 169e and f

(here, the degree of instability is defined based on the period between subsequent packets — larger duration between packets are assumed to denote highly unstable behavior) the piezoelectric sensors do not record any pressure revolutions during the period between the unstable packets.

For instance, it can be seen in Figure 169f, that between t = 0.27 s and t = 0.36 s, there is no pressure oscillations or ionization activity. In this time duration of 0.09 s, it is unlikely that the burnt gases are anchored inside the combustor, since the bulk axial fluid velocity is estimated to be about 100 m/s, from the cold-flow simulation. Since heat transfer from the combustor wall is known to augment the detonation wave speed [311], it is possible that this mechanism is responsible for re-ignition of rotating pressure waves. Of heightened importance are the time lag characteristics across the different test cases. It is seen that when the propagation is stable, the time lag is predominantly positive across the approximately thousand laps, i.e. peak pressure precedes ionization. Initially, after ignition, combustion wave precedes the pressure wave (region indicated by blue arrow). However, after this initial period, the shock wave supersedes ionization events, thereby exhibiting the commonly known behavior of stable detonation wave propagation. When the propagation is unstable, such an observation is not seen. In fact, during unstable propagation, for a given packet of instability, the number of laps with ionization preceding the pressure wave is

333

almost equal to the number of laps with the opposing trend. A maximum of ± 50 μs is set to remove fallacious values that are an artifact of the algorithm.

334

(a) Unstable Stable

(b) Continual ionization activity

(d) Initial ionization Only pressure onset revolutions

No ionization activity

(e) Combustion wave Ionization onset leading pressure wave

∆t (negative)

No ionization activity

335

Figure 168 Pressure and ionization traces at 0.4 kg/s and Φ = 1.6: (a) complete traces, (b)

stable propagation, (c) magnified traces during stable propagation, (d) unstable

propagation, and (e) magnified traces during unstable propagation

While this result is seemingly contradictory at first glance, it can be readily explained to be due to the flame acceleration and transition to detonation phenomenon, most commonly observed in ducts with deflagration-to-detonation inducing obstacles [82]. In their comprehensive review of the said phenomena, Ciccarelli and Dorofeev state that “flame propagation in an enclosure generates acoustic waves that, after reflections from walls and obstacles, can interact with the flame front and develop flame perturbations through a variety of instability mechanisms” and say that if such a flame propagation is fast enough, it “can result in severe flame distortion which can induce flame acceleration and, in extreme cases, cause transition to detonation” [82]. One could thus postulate that the concave surface of the RDC outer wall acts like a reflecting obstacle thereby sustaining the propagation process. It is a well-known property of detonations in curved channels to have pronounced collision and subsequently stronger ignitions at the outer concave wall [83,84]. This hypothesis also explains the effect of the obstacle. As shown in our cold-flow simulations, the obstacle considerably alters the mixture composition near the RDC outer wall, making the region more energetic (low activation energy due to higher equivalence ratio of ethylene-air mixtures

[360]), and hence more prone to ignition by the flame acceleration mechanism.

Rotating detonations are not seen in Scheme I because the radially-inward air injection forces the combustible mixtures away from the wall. Thus, finally we can attribute the low magnitude rotating pressure waves to be a type of unstable detonation wave propagation, where ignition seems to be continual and caused due to a probable flame acceleration mechanism sustained by the concave wall. Of course, such a claim is a preliminary theory and needs to be validated through focused, future studies. At present, however, it seems reasonable to attribute two different

336

propagation mechanisms — conventional detonation propagation / flame acceleration causing DDT

— to stable / unstable propagation. While we have not come across any literature that has made similar observations in combustors, Seo [361], in his parametric investigation of high frequency tangential rocket engine instabilities has presented pressure traces with a very similar sinusoidal instability, with waxing and waning, that travels tangentially at very high frequencies. Interestingly, for a given air flow rate, increasing Φ leads to inception of instability. For instance, at 0.4 kg/s, the propagation is stable for Φ = 1.4 (Figure 169a). When Φ = 1.6, there is a sudden onset of instability midway during the test (Figure 169c). When the equivalence ratio is further increased to Φ = 1.8, the complete duration of the test is unstable. A similar trend is seen for 0.3 kg/s as well, with increasing Φ, resulting in increased instability (Figure 169b, d and e). The trend is as follows: stable rotating detonation devolves into unstable weak rotating detonation with high frequency of packets

(similar to galloping detonation [21]). Further increase in Φ produces unstable packets that are separated by prolonged durations during seemingly no pressure or ionization activity (similar to stuttering detonations [21]). We are not able to explain this observation at present. It seems unlikely that this is purely due to chemistry, since these near limit unstable behaviors are observed in planar detonations at very lean equivalence ratios [21]. An analogous behavior to this would be the change from steady propagation to galloping and eventually stuttering detonations, in planar detonations in tubes [21]. One needs to consider the possibility that higher Φ, and hence higher fuel injection velocities, cause higher axial momentum loss [337], thereby pronouncing the decoupling between the weak pressure wave and the combustion wave, which would explain why we see this behavior occurring in our hollow combustor at higher flow rates. This will be tested in a future discourse.

337

ṁa = 0.3 kg/s, Φ = 1.4 ṁa = 0.4 kg/s, Φ = 1.4

(a) (b)

ṁa = 0.3 kg/s, Φ = 1.6 ṁa = 0.4 kg/s, Φ = 1.6

338

ṁa = 0.3 kg/s, Φ = 1.8 ṁa = 0.4 kg/s, Φ = 1.8

(e) (f)

Figure 169 Pressure traces (first row), Ionization traces (second row), wave speed

(third row) and time lag between pressure and ionization wave (fourth row)

4. Conclusion

The motivation behind the current work was the question: what makes a hollow combustor a rotating detonation combustor? Towards this goal, two geometric variations (which produces drastic changes in mixing) of a hollow combustor with ethylene-air mixtures were tested, by using a

3 mm thick circular plate that was added to the RDC headwall to serve as an obstacle, thereby diverting the fresh follow towards the combustor wall. A stark difference in the hollow combustor operation was observed depending on the scheme used. With the first scheme (no obstacle), the majority of the points tested either did not light-off or were prone to an anchored smooth deflagration flame, interspersed by standing acoustic modes — a well-known cause of high frequency combustion instabilities. With the second geometric scheme (with obstacle), high

339

frequency transverse instabilities were observed at low flow rates. The other test points exhibit tangential instabilities exhibiting steep-fronted, shock-like behavior characterized by overpressures easily exceeding 1 bar, with underpressure not falling below -0.5 bar. These rotating pressure waves exhibited both stable and unstable behavior. During stable propagation, at times, the peak pressures exceeded even 20 bar and the wave speed was about 95% of the ideal C-J wave speed of the mixture, which is only possible if the rotating pressure wave is a stable detonation wave. During unstable propagation, distinct “packets” are noted with subsequent laps of the rotating pressure wave getting sinusoidal stronger and weaker (in terms of peak pressure), with a similar waxing and waning in wave speeds. Here, the average peak pressure barely exceeded 2 bar, while the average wave speed was about 80% of the C-J speed. An operating point that exhibited both stable and unstable operation was chosen for a focused study to reveal that during stable operation, the pressure wave (shock wave) preceded the ionization wave (combustion), as is to be expected of conventional detonation waves. However, during unstable propagation, for the majority of the laps, the opposite was observed — combustion waves preceded the weak pressure pulses.

The fact that both these propagation behaviors are observed within one combustor at slightly different conditions is highly suggestive of the notion that high frequency combustion instabilities observed in rocket engines and other combustors could be because of detonation phenomena, and not purely due to the Rayleigh criterion. Further experimentation is required to understand this complex phenomenon. In light of the above evidence, it is likely that rotating detonation propagations are a type of near-limit detonation propagation. This explains why there is a deficit in both pressure and velocity (from C-J theory), which would not be the case if rotating detonations were weak detonations — a question first put forth by Adams [50]. Knowing this distinction can perhaps help in designing combustors that work with the preferred type of combustion mode — either the conventional deflagration, or the more efficient, but prohibitive detonations.

340

CHAPTER 10: ROTATING DETONATIONS AND SPINNING DETONATIONS: SIMILARITIES AND

DIFFERENCES

Chapter Abstract

Rotating Detonation Combustors are studied with increasing interest worldwide, and are seen as the most promising of the available pressure gain (stagnation) combustion concepts. The dynamics and structure of the rotating detonations are an area of active interest owing to their sensitivity to a wide range of factors, which have been hard to predict. In the current manuscript, we argue that rotating detonations share a considerable number of quantitative and qualitative properties with spinning detonations, which is a well-known near-limit phenomenon in fundamental detonation studies. We show that the fill height in rotating detonations play the same role as the pitch length inscribed by spinning detonations. While the pitch-to-hydraulic diameter ratio of spinning detonations is known to range from 2 to 6 across a wide range of conditions, it is shown here, from literature, that the fill height-to-hydraulic diameter of rotating detonations also extends across a similar range — between 1 and 5 across diverse facilities and conditions.

Nomenclature

P perimeter of transverse detonation wave [mm] p pitch of spin detonation [mm] d diameter of a circular tube [mm]

dH hydraulic diameter of an annular tube [mm]

λ detonation cell height [mm]

341

h fill height in RDC / rotating detonation wave height [mm]

wch channel width of RDC [mm]

vfill bulk reactants injection velocity in an RDC [m/s]

ṁt total mass flow rate through an RDC [kg/s]

Φ global equivalence ratio n number of rotating detonation waves in an RDC simultaneously

1. Introduction

The analysis of rotating detonation combustors has considerably matured in recent years, worldwide [3]. A streamlined, multifaceted, experimental and numerical approach has shed significant insight into the rather complex physico-chemical process of rotating detonations (which is different from spinning detonations in a stationary mixture – [129]). Nevertheless, to achieve the final goal of using this process to generate pressure gain reliably in rocket engines and gas-turbines, considerable challenges still need to be overcome. Perhaps, the most important challenge is the issue of understanding the rotating detonation wave’s dynamics. All the experimental campaigns on rotating detonation combustors (RDCs), done by diverse facilities, have shown that the rotating detonation wave (RD) propagates with a significant velocity deficit, when compared to the ideal

Chapman-Jouguet (C-J) detonation. The exact reason behind this deficit is unknown, as of yet. It is emphasized here that for detonation propagation along a curved boundary, as in the case of RD, the

‘true’ detonation velocity is given by the normal velocity component to the outer wall [83].

However, all experimental studies on RDCs to date resort to presenting and analyzing the detonation wave in terms of the tangential velocity, and not the normal velocity. This is due to the

342

extreme difficulty is acquiring the angular inclination of RDs on the combustor walls, experimentally [188]. While numerical simulations have shown that channel width has a significant impact on this orientation angle (with no inclination when the width is very small, to very high inclination at higher widths [125]), this is yet to be validated experimentally. However, since the normal velocity of RD would always be the product of the tangential velocity and the cosine of an acute angle, the former would always be smaller in magnitude than the latter [132]. Hence, when resorting to describing RDs with normal velocities, it is expected to see higher velocity deficits from the C-J conditions, than when we only compare the tangential velocities. Additionally, it has also been revealed that more than a single rotating detonation wave exists at a given instance inside the combustor annulus. The common finding among these studies is that increasing the flow rates seemingly increments the number of RDs [27,40,43,48,256,257]. RDC operation with one wave

[27,51,70,151,259], two [10,27,43,256], three [10,27,39,40], four [46,48], five [46], six [24,46], seven [47], eight [46] and even nine waves [260] have been observed. In the last two cases of seven and eight waves, it was contemplated that they could be ‘acoustic waves’ instead of Chapman-

Jouguet detonations, owing to the very high wave speed deficit (about 50%). In fact, the reduction in wave speed with increasing number of waves has been a recurring theme about rotating detonation waves [27,129].

A recent study by the current authors showed that the number of RDs in an RDC can also be controlled by altering the channel width and the mixture reactivity while maintaining the air flow rate and equivalence ratio approximately constant [39]. Increasing the oxygen percentage (of the enriched air oxidizer) at a given channel width caused a shift from one wave, to two wave, and finally three RDs, for a given channel width. A similar multiplicity behavior was also observed when the channel width is reduced for a given oxygen percentage and equivalence ratio. The tangential speed of the individual detonation waves decreases every time a new wave is spawned. Assuming

343

the cross-sectional area of the rotating detonation to be a rectangle (dimensioned by the RDC channel width and the detonation wave height [39]), we recognized that these two apparently independent factors — channel width and mixture reactivity— could be linked together by normalizing the calculated detonation wave height and the channel width by the cell size, λ, of the global mixture. A new detonation wave spawned when the ratio of the perimeter of the individual

RD cross-section and the cell size (P/λ) exceeds 7.4. To elaborate, one wave operation transcends to two wave operation when P/λ (a function of mixture reactivity and channel width) exceeds 7.4, for the given conditions of geometry and flow rate. Another divergence from two waves to three waves occurred when the normalized perimeter of the newly formed waves increases above 7.4. Thus, it is apparent that detonation scaling that has been so successful in characterizing the diverse behaviors seen in conventional detonation wave propagation [21] is also useful in ascertaining rotating detonation wave dynamics.

The current paper is, hence, an exercise in the endeavor of drawing parallels between the two connected, yet unresolved, fields. To do this, we resort to viewing rotating detonations through the lens of fundamental gaseous detonation wave physics — a field that has been studied intensively since its inception in 1883, when two French engineers discovered the phenomenon of detonations in coal mines [21]. Detonation was widely regarded as a one-dimensional combustion wave even after almost half a century after its discovery as the Chapman-Jouguet theory of modified Rankine-

Hugoniot equations with ‘zero reaction width thickness’ was able to accurately predict the peak pressures and wave speeds of the phenomenon. This perception, however, was shattered in 1926 when Campbell and Woodhead [22] reported the entirely three-dimensional phenomenon of spinning detonations (SD), which move helically in a tube with stationary mixture [23]. Since then, and due to intense research over the next several decades, several discoveries were made, the most important of which is the true nature of detonations — the complex three-dimensional interaction

344

between Mach wave, incident wave, transverse wave and the reaction zone that together form what is now called the ‘detonation cell’ [21]. Thus, spinning detonations were responsible for the new outlook on detonation waves, and naturally have been researched extensively, in spite of which there are still outstanding issues and questions to be answered. One such researcher that investigated the complex phenomenon was Voitsekovskii [24]. Since a comprehensive analysis of spinning detonations required detonation tubes of considerable length, depending on the mixture used (even up to 10 m [24]), Voitsekovskii proposed “fixing” the detonation wave in a stationary frame of reference, which could potentially alleviate the demanding facility requirements. He reasoned that a premixed mixture of the required reactants, when fed into an annular chamber at the required inlet velocity (so as to balance the spinning detonations’ axial velocity in a stationary premixed tube) the transverse waves composing the detonation wave could be fixed in the laboratory frame, thereby lending it to be studied more easily. However, since such a premixed injection was prone to intense flash back events, he resorted to experimentally testing the next best configuration — a non-premixed injection that is continually fed into an annular chamber; or, in other words, what we now know to be a rotating detonation combustor. Voitsekovskii’s intention seems to not have been to create a pressure gain device, but rather to efficiently study spinning detonations. Over the next several decades, RDCs have been recognized as a device with very high potential, but the origins of its inception and its strong links to spinning detonations have apparently been overlooked for the most part. In the next few sections, we investigate the quantitative and qualitative relationships between rotating and spinning detonations, through a comprehensive review of both.

2. Parallels to Spinning Detonation

As explained in the introduction, the origins of rotating detonations lie in the phenomenon of spinning detonations. The fundamental difference between the two mechanisms is that RD is

345

axially fixed at a given point in space whereas the spinning detonation moves helically in an enclosed structure, and therefore has an axial velocity component [22]. SD has a leading shock front

(incident wave) that is coupled to the transverse wave [26]. The secondary difference is that SD travels in premixed stationary reactants [21], whereas RD moves through non-stationary reactants

[3]. A comprehensive explanation of spinning detonations is provided in Lee’s monograph [21] and will not be dealt with here, for the sake of brevity. An image acquired from axially-compensated photography [24] of four laps of spinning detonations is given in Figure 170a. Figure 170b shows four laps of rotating detonations, once again acquired from open-shutter photography [27].

Immediately, the commonality in the structures is evident. Highest heat release (deciphered by the brightness) occurs at the transverse detonation wave (TDW), at the bottom of which is attached a

Mach stem (in case of spinning detonations) [21] or an oblique shock wave (in case of rotating detonations) [28]. A simplified schematic of spinning detonation motion is presented in Figure

171a. The axial direction of motion of the planar detonation wave is marked, along with the locus of the triple point path (helical structure marked on the tube wall in gray) by the TDW (red tab). Note that the axially moving shock structure only marginally coincides with the cross-sectional plane of the tube, whereas the other regions of the front (composed of the incident wave and Mach stem circumferentially and a Mach leg extending radially inwards towards the tube axis) are warped downstream in conjunction with the TDW structure. This is better visualized when the TDW and the associated structures on the tube wall are unwrapped along the circumference, with TDW placed at 0o (Figure 171b). It can be seen that the incident wave pre-compresses and causes some contact surface burning of the mixture upstream of the TDW. The intersection of the three waves

(triple point) is thought to produce the fine helical striations seen on soot foil records in detonation tubes during spinning detonations [21]. One of the most interesting and important characteristics of spinning detonations is that the ratio of the pitch of this helix traced by the transverse wave composing the detonation wave and the diameter of the enclosure is, for the most part,

346

independent of the mixture used [21]. That is, the pitch-to-diameter ratio (p/d) of spinning detonations is notionally constant across a rather extensive spectrum of conditions, and is usually about 3 [26].

We have also presented a simple schematic of rotating detonations (composed of the TDW and the attached oblique shock wave) in an annular space, with channel width wch, in Figure 172a.

Here, the detonation wave is fixed in the laboratory frame at a given axial location, unlike spinning detonations, while the reactants are injected at a velocity denoted by vfill. Thus, a single complete lap of rotating detonation entails that there be a column of fresh mixture before the start of the second lap of height, h, which is called the fill height in RDC literature [27]. Once again, an unwrapped projection of the rotating detonation wave structure along the combustor circumference is given in

Figure 172b, showing the TDW, the oblique shock attached downstream to it, and the region of contact surface burning behind the oblique shock wave. We claim here that this fill height is to a rotating detonation what the pitch is to a spinning detonation. That is, if one were to “untangle” the rotating detonation wave spatially (in the axial direction) by taking into account the velocity of injected reactants it would result in a helical path, the pitch of which is dependent on vfill, and is equal in magnitude to the fill height, h.

(a) (b)

Figure 170. (a) Spinning detonations [24], and (b) Rotating detonations [27]

347

Detonation direction Detonation front 180o Mach Transverse stem 270o detonation wave

TDW Mach o

leg Tube 0 mixture

Stationary Stationary Incident

diameter, d diameter, Rotation o wave 90 Contact surface burning Pitch, p Cross-section 180o

(a) (b)

Figure 171 (a) Three-dimensional spinning detonation structure in a tube with the important elements marked, and (b) Unwrapped spinning detonation structure showing the

TDW, incident wave and Mach stem. The sketches are adopted from Refs [21,26,362].

180o Channel Contact surface width, w burning ch 270o TDW 0o Fill height, h Rotation Oblique 90o Transverse shock detonation wave Injected mixture, v 180o fill

(a) (b)

Figure 172 (a) Three-dimensional rotating detonation structure in an annulus with the important elements marked, and (b) Unwrapped rotating detonation structure showing the

TDW and oblique shock wave. The sketches are adopted from Refs [27,28].

With the theoretical congruence between pitch and fill height established, it is now necessary to ascertain if rotating detonation mechanics is dictated by the physical processes controlling spinning detonations. To do this, we resort to comparing the analogous terms in the two processes that define each of the process. For spinning detonations, the defining term, as noted earlier, is p/d. For rotating detonations, the term analogous to this would be h/d. It is imperative to note here that p/d

348

is to be construed as the ratio of the pitch to hydraulic diameter (dH) and not the geometric diameter. This effect of hydraulic dimension on SD in geometries other than a circular cross- sectional tube was established by analyzing the process in rectangular cross-sectional tubes [29] and annular tubes [30]. For annular cross-sections (RDCs), the term analogous to the diameter length is equal to twice the annular width [30], and hence dH = 2wch. To further elaborate, our previous claim holds credence if p/d (spinning detonations in circular tubes) ≈ h/dH (rotating detonations in annular combustors). The pitch of spinning detonations is usually acquired with relative ease using compensated video imaging of transparent tubes [21], and there are well- documented values for different mixtures, and they are on an average equal to 3, but have been known to range between 2 and 6 [26]. However, video imaging of an RDC is a lesser developed field owing to the complexity of the setup, and few studies exist that have carried out such an endeavor.

A comprehensive literature review is performed to collect the detonation height (≈ fill height) and the associated operating conditions. The result of this review, along with the source citation, is presented in Table 18. Record of the rotating detonation wave height is available for three mixtures

(acetylene-air, acetylene-oxygen and hydrogen-air). Three methods have been used in literature to obtain the same: (a) ordinary high-speed imaging, (b) gray-scale interpolation of detonation structure using densely packed ion probes, and (c) chemiluminescence imaging of a transparent

RDC. These detonation wave recordings span a myriad of conditions like diverse ṁa and ṁf (and hence Φ), wch and outer diameter (d), and supersonic and subsonic (superscript *) reactants injection. The number of rotating detonation waves existing simultaneously (mode number, n) in the combustor is also given, when such information is available. Not all the studies included detailed description of the flow rates and the mode number, and hence when this information is not available the corresponding cell is left blank. Since the fuel flow rate is an order of magnitude smaller than the air flow rate, the total reactants flow rate (ṁt) is approximately equal to ṁa.

349

Demarcation of the table is done first based on the fuel used, and then on the oxidizer used. A

similar system of demarcation, based on the fuel, is performed for spinning detonations as well.

The h/dH of RD through C2H2-air mixtures is about 5, whereas for C2H2-O2 mixtures it varies

from 1 to 1.2. When the injection is subsonic, h/dH falls below 0.56. This is most probably an artifact

of strong plenum-combustor coupling due to the RD’s propensity to disturb the plenum dynamics

due to lower impedance brought about by the decreased pressure ratio across the injection [174].

For SD, p/d for acetylene mixtures at different dilutions extends between 2.73 and 2.92. When

hydrogen-air mixtures are used, p/d extends from 2.93 to 3.37 for spinning detonations, whereas

h/dH ranges from 1 to 5.2 for rotating detonations. Considering the complexity of the different

processes at play here, the propinquity of the two values obtained from the two detonation

phenomena is quite remarkable, and quantitatively substantiates the claim about the relationship

between fill height in rotating detonations and pitch length in spinning detonations. This implies

that, at least on a macroscopic scale rotating detonations seem to behave similar to spinning

detonations, as was the initial intention of Voitsekhovskii et al. 16.

Table 18: Quantitative comparison of rotating detonations with spinning detonations

Rotating Detonations Spinning detonations

Fuel Ox Refs ṁt Φ n h, wch, d, h/dH Reactants (demarcated p/d

(kg/ cm cm cm based on fuel)

C2H2 Air [27]a 23 2.3 30.6 5 C2H2+Air (Φ=1) [363] 2.92

O2 [260 0.06 1- 1-4 1 0.5 10 1

]a – 1.18 2-9 1.2 0.5 10 1.2

350

0.08

[174 1 1.2 0.05 4 0.12 C2H2 + 1.5O2 + 12.5Ar 2.73

]a * [364]

3 4 0.04 10 0.44

5 * C2H2 + 7.58O2 + 34.3Ar 2.76

1 5 0.04 10 0.56 [365]

5 *

H2 Air [48]b 6.7 2 10 2.5 40.6 2 H2-Air (Φ=1) [363] 2.97

6.7 2 13 2.6

6.8 1 20 4

[44]c 0.15 1 1 2 0.76 15.4 1.3 H2+O2 (Φ=0.5-1.5) [366] 3.03

0.33 1 1 3 2 -

0.63 1 1 4 2.6 3.37

0.86 1 2 3 2 2H2+O2 [364] 2.93

0.32 0.7 1 4 2.6

0.32 1 1 5 3.3

0.32 1.3 2 4 2.6 2H2 + O2 + 3Ar [364] 3.03

[161 4 6 2.3 30.6 1.3

]a 3 8 1.7

2 12 2.6 1.5H2 + 1.5O2 + 7Ar [365] 2.95

1 24 5.2

[206 1 20 2.3 30.6 4.3

]a 2 12 2.3 30.6 2.6

351

The above result spawned another comprehensive review of literature; this time oriented towards comparing the qualitative similarities (or differences) between RD and SD. We are able to identify twelve properties peculiar to the two processes, and have tabulated them in Table 19. There is an uncanny similarity in the observed characteristics of the processes (properties: 2-6, 8 and 9), with regard to the higher modes of onset and sustenance, and the velocity deficits. This qualitative confluence of different traits furthers the notion that the underlying physics is common to both RD and SD. Of the listed traits, the last (perturbation of shock front by downstream combustion) is the most important. If a detonation wave travels at C-J speed, then by definition, the products expand at a sonic speed relative to the upstream shock front [21]. However, considerable velocity deficit is observed in TDWs in spinning detonations. Consensus regarding this is that spinning detonations are not C-J detonations and the continual propagation of TDW is due to the strong coupling of the shock wave with the products downstream which is only possible if the products are subsonic with respect to the shock wave. Such a condition normally only occurs in an overdriven detonation wave, which is not steadily propagating and fails after a finite time [21], unlike a spinning detonation. Lee attributes this “paradox” [21] to strong boundary layer effects and two-dimensionality of TDW, which is not captured in the ideal C-J theory. In light of this finding — of rotating detonation wave’s quantitative and qualitative similarity to spinning detonations — it is essential to consider the possibility that rotating detonations might be a type of near limit propagation of detonation waves.

Note that, in gaseous detonations near limit is defined not only by chemical limits imposed by equivalence ratio, but also by physical limits that are dependent on the boundary conditions [21].

Table 19: Qualitative comparison of rotating detonations with spinning detonations

NO. Property Rotating detonations Spinning detonations

1 Regime Observed at wide ranges of Observed at near limits of

352

detonable mixtures with a motionless detonable mixtures in

subsonic or supersonic tubes with circular, annular,

injection velocity relative to rectangular, triangular cross-

the RD, in hollow, annular, section, etc. [21,29,30]

oblong and disk-shaped

combustors. [27,32–36]

2 Cross-current Pressure difference across the Pressure difference across the

/ swirl transverse wave causes high transverse wave causes high

positive fluid swirl (in the positive fluid swirl (in the

direction of the TDW). The direction of the TDW). The same

same pressure difference pressure difference causes low

causes low negative fluid swirl negative fluid swirl (in the

(in the opposite direction of opposite direction of the TDW),

the TDW), such that the such that the angular momentum

angular momentum is is conserved. [38]

conserved. [37]

3 Multiplicity More than one TDW ‘wave’ is More than one TDW ‘head’ is

possible [27] possible. [21]

4 Mixture Increase in reactivity spawns Increase in reactivity spawns

reactivity more ‘waves’. [39] more ‘heads’. [21,24,367]

5 Pressure Increase in pressure spawns Increase in pressure spawns more

dependence more ‘waves’. [40] ‘heads’. [21,367]

6 Unreacted Pockets of unreacted mixtures Pockets are formed near the inner

pockets are formed when there is an wall when there is an annulus.

annulus. [41] [42]

353

7 Co-rotating Observed at heightened flow Not observed; though theorized to

waves/heads rates and pressures. be possible. [23,24]

[27,39,40,43]

8 Counter- Observed when there are Observed when there are multiple

rotating multiple ‘waves’. [44,45] ‘heads’. [21]

waves/heads

9 TDW velocity Lower than C-J speed [43]. The Lower than C-J speed [21]. The

individual speed of the TDW individual speed of the TDW

decreases when the number of decreases when the number of

‘waves’ increases. At a very ‘heads’ increases. At a very high

high number of waves, each number of heads, each head is

head is almost an “acoustic almost an “acoustic wave”.

wave”. [46,47]

10 Symmetricity It has been noted that when Two heads are unsymmetrical

(property of there are two waves, the when there is no axial insert

multiplicity of distance between them is (when the tube is circular), i.e. one

waves/heads) lesser than half the head is stronger than the other.

circumferential distance of the Two heads are symmetric when

RDC. [48] Hence, the multi- there is an axial insert with

wave modes are not diameter that is 20% - 50% the

symmetric. tube diameter. [24]

11 Pre- There is no leading shock A strong leading shock front pre-

compression wave, and hence no such pre- compresses the upstream fresh

of mixtures compression aiding the TDW. reactants before it is consumed by

[16] the TDW. [24]

354

12 Perturbation Not yet addressed / reported. There is unanimous contention

of shock front that spinning detonation is

by sustained due to acoustic

downstream perturbations from the

combustion downstream products interacting

with the upstream detonation

front [21]. The frequency and

pitch angle of spinning

detonations can be rather

accurately explained using

acoustic theory, by considering

pressure antinodes to exist in the

product gases behind the

detonation fronts [24]. For high

frequency spins away from the

operational limits, acoustic theory

breaks down in describing the

frequency. When the cell size is

small compared to the tube

diameter / annulus width, the

sustenance seems not to be due to

the acoustic eigen-mode but due

to chemistry [21]. This “paradox”

of the downstream products

interacting with the upstream

355

shockwave suggests that these

detonations do not behave like C-J

detonations, despite travelling

steadily (in laboratory frame).

3. Conclusions

The motivation behind the current paper was to address the origins of rotating detonations, which lies in the study of spinning detonations. We subsequently compared and contrasted the two phenomena through a comprehensive literature review. This led to the discovery of the quantitative and qualitative congruence of rotating detonations with spinning detonations, which is a type of near-limit detonation behavior. While the pitch-to-hydraulic diameter ratio of spinning detonations is known to range from 2 to 6 across a wide range of conditions, it is shown here, from literature, that the fill height-to-hydraulic diameter of rotating detonations also extends across a similar range — between 1 and 5 across diverse facilities and conditions. The findings herein suggests that a promising venue of future research is in further analysis of rotating detonation waves through the known physics of near-limit planar detonation wave behavior. On the corollary, perhaps rotating detonation waves could help us understand the yet-poorly understood behavior of spinning detonations, which was the original motivation behind the production of rotating detonation waves by Voitsekhovskii.

356

CHAPTER 11: SUMMARY AND FUTURE OUTLOOK

1. Summary

The preceding sections dealt with the investigation of rotating detonation waves in annular and hollow combustors. Several modes of operation (chaotic, co-rotating, longitudinal pulsed detonation and low frequency oscillations) were identified and subsequently discussed. The importance of mixing, injection elements and pressurization in determining these modes were also elaborated upon. The most important takeaways from the current thesis are listed below, and are described in detail after the list:

 Air and fuel injection sizing has a significant impact on RDC behavior. Higher pressure

ratios and closer orifice arrangement, in general, predicate proper operation (higher

wave speeds and stable behavior).

 Four types of off-design modes are observed.

 The first type, multiplicity, is seen to occur at higher flow rates and at smaller fuel injection

holes.

 Chaotic detonation wave propagation is essentially an RDC is “perpetual onset” period.

Both the air and fuel plenum pressure dynamics (settling time) predicate this instability

depending on the exit conditions: atmospheric vs. backpressurized.

 Three types of low frequency instabilities are observed. The first two are linked to

plenum coupling through acoustic resonance and probable pressure beatings, respectively.

The third is combustion induced (alternate coupling and decoupling of combustion and

pressure front)

357

 Longitudinal pulsed detonation instability has a “sweet spot” in terms of subsonic

pressure ratios to occur. Within this range, backpressure and equivalence ratio dictates the

frequency of LPD operation.

 When backpressurized, there is also a strong transient increase in the mean static

pressure inside the combustor. This is linked to the pressure increase incurred due to

detonative combustion.

 Mixing conditions near the outer wall dictates the mode of operation of a hollow

combustor. A 3mm plate is enough to produce a drastic change in operation of an

atmospheric hollow combustor with ethylene-air mixtures.

 All of the observations are in essence, a rediscovery of the crippling issue of low and high

frequency instabilities in rocket engines.

Chaotic detonation propagation was identified as a mode which is in a perpetual onset phase, where the detonation wave causes considerable disturbance of the injectors thereby causing an inherent stochasticity to the process of detonation formation and reactants recovery. This was identified to be the cause of having random switches in rotating detonation wave’s directionality.

For RDCs to be integrated with turbines, this mode has to be dealt with since drastically different pressure dynamics has been observed in the combustor based on the wave’s direction and its angular inclination with turbine stages. The duration of the onset phase after ignition is linked to the settling time of the impulse response function of the air plenum when the RDC is backpressurized. When the exit is atmospheric it is linked to the reverberations that are set up inside the fuel plenum, which produces transient failure operations and considerably longer onset durations. Multiplicity of co-rotating waves is linked to higher flow rates, which is line with the findings of other researchers. It was also found to be dependent on the fuel injection hole sizing, with smaller holes producing two-wave mode despite having the same flow rates and total injection area. These observations suggest fluidic impedance across individual holes to contribute to the

358

formation of multiple waves. Addition of a CD nozzle increased the backpressure of the device, which in turn lowered the fill height of reactive mixtures. This had the effect of transferring the rotating detonation mode to an azimuthally simultaneous, axially moving event, known as longitudinal pulsed detonations. Pressure ratios between 1.4 and 1.85 supported this mode suggesting a criticality of fill height in determining its existence. A mechanism based on shock wave amplification by coherent energy release (SWACER) and reflected pressure waves was proposed to explain its sustenance.

Three types of low frequency oscillations were observed at various conditions of operation.

The first one is characterized by base-pressure oscillations at locked-in frequencies at the air inlet which causes an amplitude oscillation in an atmospheric RDC. When the RDC was backpressurized this type of “chugging” was observed in the actual combustor as well. Results from numerical acoustic modeling suggested this type of overall pressure oscillation to be due to Helmholtz resonance occurring in the air inlet (atmospheric) or the combustor itself (backpressurized).

Significant mode changes were produced by the occurrence or stoppage of chugging in pressurized

RDC, indicating a fundamental shift in reactants supply characteristics during the transient onset phase in pressurized RDC operation. The second type of oscillation is characterized by a rotary amplitude modulation in the air inlet and the combustor where there is a sinusoidal variation in- built on the peak detonation wave pressures. This low frequency rotating was observed to move in a direction opposite to the direction of the rotating detonation wave suggesting its origins might be linked to pressure beating phenomenon in the supply plenums where the reflected waves move in an opposite direction to the detonation wave. The last type of low frequency oscillation was discovered to be combustion-linked. It occurred in hollow RDCs and is distinguished by the alternate coupling and de-coupling of the pressure wave and the combustion front, which is suggestive of near-limit detonation propagation behavior. The origins of the transient mean pressure rise in RDCs when it is backpressurized was also investigated. Evidence was gathered to

359

indicate that this increase is the result of detonation activity inside the combustor, which tends to produce a stagnation pressure gain (and hence pressure gain combustion).

Finally, the question of what constitutes a rotating detonation combustor was dealt with. A

3mm plate was mounted to the RDC headwall to effect flow-turning inside a hollow RDC, thereby producing a reactive mixture near the concave combustor. This geometry was found to produce strong rotating detonation waves, in contrast to the hollow setup without the thin obstacle which only produced acoustic radial oscillations throughout. For the first time in published literature, rotating detonations with wave speeds upwards of 95% of the Chapman-Jouguet speed and sometimes even 15 bar peak pressures were produced in ethylene-air mixtures. Increasing the equivalence ratio (fuel injection velocity) further caused the formation of instability where packets of detonation waves were produced with a sinusoidal oscillation in peak pressures, ionization and wave speed. Alternative coupling and decoupling between the pressure and combustion fronts were also recorded, as discussed above, suggesting the presence of a flame-acceleration mechanism that causes deflagration-to-detonation transition. Thus, one could contend that any converter could be converted into an RDC, if the reactants quality near the combustor wall and the injection velocities are satisfied to promote detonation formation. Finally, to address the near-limit-type behavior of rotating detonations, an extensive literature review was performed spanning the two fields of rotating detonations and spinning detonations. This led to the identification of several qualitative similarities behind the two detonation phenomena. Additionally, it was shown from varied facilities and mixtures that fill height is to a rotating detonation what pitch is to a spinning detonation, i.e. the ratio of fill height to hydraulic diameter is of the same order and similar range as the ratio of pitch length to hydraulic diameter (1-5 and 2-6, respectively). It was posited that rotating detonations may actually be a type of near-limit detonation propagation behavior due to these overlaps in characteristics.

360

2. Future Outlook

As detailed in the introductory chapter, the benefits of RDCs in increasing the thermal efficiency of rocket engines and gas-turbine combustors are no longer a promise based solely on theoretical models. Multiple research groups have provided experimental evidence that pressure gain combustion is realizable through RDCs. While undoubtedly there are numerous challenges to overcome, it is important at this juncture for engine manufacturers and policy makers to realize the step-change performance increase offered by this class of combustors in general, and RDC in particular. Though many “green” energy prospects have been proposed to overcome the challenges pertaining to emissions and energy efficiency as humanity refocuses its attention on the coming decades, the fact remains that the more “traditional” power generation and propulsion systems like gas-turbines and rocket engines are a necessity to support the demanding missions of the present and future. Cases in point are the SpaceX’s Falcon Heavy rocket engines and GE’s Harriet and 9X gas-turbine engines. It should also be noted that about 10% of the energy consumed in the US is by gas-turbines (2.5% from aviation and 6.9% from power generation). A 1% improvement in the thermodynamic efficiency of these devices would be tantamount to removing 1,360,000 cars off the roads, as pointed out by Paxson (Pressure-Gain Combustion for the Gas Turbine, University Turbine

Systems Research Workshop, 2010). It is thus self-evident that, moving forward, rotating detonation combustors will need to occupy a significant portion of the efforts related to reducing emissions and increasing systems efficiency.

On the other hand, in the author’s opinion, the more important take-away from the present thesis is that the modes of operation of RDCs share numerous striking similarities with combustion instabilities observed in rocket engines, both qualitatively and quantitatively. These overlaps, listed and discussed above, are one too many to be a result of mere coincidence. Not surprisingly, the field of RDCs has started “looking back” into the issue of high and low frequency combustion instabilities

361

that have plagued many a rocket engine development program (Blomshield, Historical perspective of combustion instability in motors - Case studies, 2001). While some of the programs were able to overcome these crippling instabilities, which usually tend to destroy engines within seconds, some have not been as fortunate, as discussed in the reference cited above. In this regard, the author contends that research into RDCs has a two-pronged merit — one is its offer of increased efficiency, and the other is the treatment of combustion instabilities that plague conventional engines using detonation physics. Needless to say, the latter should be construed to be as important as the former considering the lack of “first-principles” understanding of why, when and how the crippling instabilities form. Though the thrust in this thesis has been on establishing the overlaps in RDC mechanics and rocket engine physics, it is emphasized that many other combustion systems

(afterburners, premixed burner, etc.) are also susceptible to very similar destructive phenomena

(Barrère and Williams, Comparison of combustion instabilities found in various types of combustion chambers, 1969). The issue of demarcating these off-design behaviors based on an engine “type” is one stemming from the human need for classification and not of an inherent difference in physico- chemical processes occurring therein. In this vein, studying RDCs is theorized to have a tremendous impact on understanding the physics of deflagrative combustors due to the essence of what an RDC is: a hollow or annular geometry that is fed reactants continuously, which at certain conditions, tends to produce strong, shock-fronted, high-frequency, combustion-coupled oscillations that produce notably higher heat transfer, erosion rates and thrust compared to normal operation.

Additionally, as seen by the similarities between rotating detonations and spinning detonations

(discussed above), one should view the tertiary benefit of RDCs to be its prospective application in answering some of the many unknowns in fundamental detonation physics. This, once again, is important in the engineering-sense in order to avoid explosions in industries where reactive mixtures need to be moved in tubes or stored in tanks — understanding the onset of spinning detonations in tubes is instrumental in avoiding unnecessary explosions.

362

Finally, it should be agreed that some of the shortfalls that have led to inaccurate descriptions of the observed RDC-related phenomena are due to the lack of appropriate sensing techniques. For instance, the current need of the hour is to have a high-frequency pressure sensor that does not degrade within a second of being exposed to the RDC environment. To measure the operation of a pressure gain combustion system, this is a rather critical shortcoming. The same issue holds true for high-frequency heat flux sensors as well, which have been known to disintegrate within a second (see introduction). Finally, current technology also appears to be insufficient in clearly visualizing the inherently three-dimensional phenomenon of gaseous detonations. It is apparent that the advancement and subsequent application of RDCs requires a commensurate development in the field of fluid and combustion dynamic instrumentation. The last point of required future focus according to the current author is the need to develop materials and structures that can withstand the extreme heat, pressure and frequency loading produced during

RDC operation. Indeed, if structural limitations weren’t the primary bottleneck faced by rocket engines during HFI, it would a reasonable assumption that rocket engine researchers would have preferred to operate in this mode that produces higher efficiency and thrust (as some have pointed out). Unfortunately, such an operation has mostly been linked with catastrophic structural failures after a finite time. RDC implementation, thus, requires heighted concentration on these elements as well, along with a focus on active and/or passive cooling systems.

363

REFERENCES

[1] Stephen Turns. An Introduction to Combustion. Singapore: McGraw-Hill International; 2006.

[2] Roy GD, Frolov SM, Borisov AA, Netzer DW. Pulse detonation propulsion: challenges, current status, and future perspective. Prog Energy Combust Sci 2004;30:545–672. doi:10.1016/j.pecs.2004.05.001.

[3] Wolański P. Detonative propulsion. Proc Combust Inst 2013;34:125–58. doi:10.1016/j.proci.2012.10.005.

[4] Yi T-H, Lou J, Turangan C, Choi J-Y, Wolanski P. Propulsive Performance of a Continuously Rotating Detonation Engine. J Propuls Power 2011;27:171–81. doi:10.2514/1.46686.

[5] Wintenberger E, Sheperd JE. Thermodynamic Cycle Analysis for Propagating Detonations. J Propuls Power 2006;22:694–7. doi:10.2514/1.12775.

[6] Jones S, Paxson D. Potential Benefits to Commercial Propulsion Systems from Pressure Gain Combustion. Jt. Propuls. Conf., San Jose, CA,: 2013.

[7] Frolov, Dubrovskii A V., Ivanov VS. Three-Dimensional Numerical Simulation of Operation Process in Rotating Detonation Engine. Prog Propuls Phys 2013;4:467–88. doi:10.1051/eucass/201304467.

[8] Sousa J, Paniagua G, Collado Morata E. Thermodynamic analysis of a gas turbine engine with a rotating detonation combustor. Appl Energy 2017;195:247–56. doi:10.1016/j.apenergy.2017.03.045.

[9] Strakey P, Ferguson D, Sisler A, Nix A. Computationally Quantifying Loss Mechanisms in a Rotating Detonation Engine. 54th AIAA Aerosp Sci Meet 2016:1–14. doi:10.2514/6.2016- 0900.

[10] Sonwane C, Clafli S, Lynch ED, Stout J. Recent Advances in Power Cycles Using Rotating Detonation Engines with Subcritical and Supercritical CO2. 4th Int. Symp. - Supercrit. CO2 Power Cycles, Pittsburgh, Pennsylvania: 2014. doi:10.1017/CBO9781107415324.004.

[11] Frolov SM, Aksenov VS, Ivanov VS. Experimental proof of Zel’dovich cycle efficiency gain

364

over cycle with constant pressure combustion for hydrogen-oxygen fuel mixture. Int J Hydrogen Energy 2015;40:6970–5. doi:10.1016/j.ijhydene.2015.03.128.

[12] Wolański P. Application of the Continuous Rotating Detonation to Gas Turbine. Appl Mech Mater 2015;782:3–12. doi:10.4028/www.scientific.net/AMM.782.3.

[13] Naples A, Hoke J, Battelle R, Wagner M, Schauer F. Rotating Detonation Engine Implementation into an Open- Loop T63 Gas Turbine Engine. 55th AIAA Aerosp. Sci. Meet., Grapevine, Texas: n.d. doi:10.2514/6.2017-1747.

[14] Fotia ML, Schauer F, Kaemming T, Hoke J. Experimental Study of the Performance of a Rotating Detonation Engine with Nozzle. J Propuls Power 2016;32:674–81. doi:10.2514/6.2015-0631.

[15] Paxson DE, Naples A. Numerical and Analytical Assessment of a Coupled Rotating Detonation Engine and Turbine Experiment. 55th AIAA Aerosp. Sci. Meet., Grapevine, Texas: 2017. doi:10.2514/6.2017-1746.

[16] Kailasanath K. The Rotating-Detonation-Wave Engine Concept: A Brief Status report. 49th AIAA Aerosp. Sci. Meet. Incl. New Horizons Forum Aerosp. Expo., Orlando, FL: 2011. doi:10.2514/6.2011-580.

[17] Kailasanath K. Recent Developments in the Research on Rotating-Detonation-Wave Engines. 55th AIAA Aerosp. Sci. Meet., Grapevine, Texas: AIAA; 2017.

[18] Lu FK, Braun EM. Rotating Detonation Wave Propulsion: Experimental Challenges, Modeling, and Engine Concepts (Invited). J Propuls Power 2014;30:1125–42. doi:10.2514/6.2011- 6043.

[19] Kailasanath K, Schwer DA. High-Fidelity Simulations of Pressure-Gain Combustion Devices Based on Detonations. J Propuls Power 2017;33:153–62. doi:10.2514/1.B36169.

[20] Jodele JB, Zahn A, Knight E, Anand V, Gutmark E. Quantifying chaotic operation in rotating detonation combustors using high speed chemiluminescence. Scitech 2019, San Diego, CA: 2019.

[21] Lee JHS. The Detonation Phenomenon. Cambridge University Press; 2008. doi:10.1017/CBO9780511754708.

365

[22] Campbell C, Woodhead DW. The ignition of gases by an explosion-wave. Part I. Carbon monoxide and hydrogen mixtures. J Chem Soc 1926;129:3010–21. doi:10.1039/JR9262903010.

[23] Vasil’ev AA. Some aspects of recording and interpretation of rotating detonation waves. Combust Explos Shock Waves 2015;51:710–6. doi:10.1134/S001050821506012X.

[24] Voitsekhovskii BV, Mitrofanov V V., Topchian ME. Structure of Detonation Front in Gases. Izd Sib Branch Acad Sci USSR (English Transl by Air Force Syst Command FTD-MT-64-527) 1963.

[25] Anand V, Gutmark E. Rotating Detonations vs. Spinning Detonations: Similarities and Differences. AIAA J 2018.

[26] Kasimov AR, Stewart DS. Spinning instability of gaseous detonations. J Fluid Mech 2002;466:179–203. doi:10.1017/S0022112002001192.

[27] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous Spin Detonations. J Propuls Power 2006;22:1204–16. doi:10.2514/1.17656.

[28] Schwer D, Kailasanath K. Fluid dynamics of rotating detonation engines with hydrogen and hydrocarbon fuels. Proc Combust Inst 2013;34:1991–8. doi:10.1016/j.proci.2012.05.046.

[29] Vasil’ev AA. Near-limiting regimes of gaseous detonation. Combust Explos Shock Waves 1987;23:358–64. doi:10.1007/BF00748799.

[30] Gao Y, Ng HD, Lee JHS. Near-limit propagation of gaseous detonations in narrow annular channels. Shock Waves 2017;27:199–207. doi:10.1007/s00193-016-0639-y.

[31] Ar’kov OF, Voitsekhovskii, B. V., Mitrofanov V V., Topchiyan ME. On the Spinning-Detonation- Like Properties of High Frequency Tangential Oscillations in Combustion Chambers of Liquid Fuel Rocket Engines. J Appl Mech Tech Phys 1970;11:159–61.

[32] Anand V, St. George A, Gutmark E. Hollow Rotating Detonation Combustor. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: 2016. doi:10.2514/6.2016-0124.

[33] Bykovskii FA, Mitrofanov V V., Vedernikov EF. Continuous detonation combustion of fuel-air mixtures. Combust Explos Shock Waves 1997;33:344–53. doi:10.1007/BF02671875.

366

[34] Lin W, Zhou J, Liu S, Lin Z. An experimental study on CH4/O2 continuously rotating detonation wave in a hollow combustion chamber. Exp Therm Fluid Sci 2015;62:122–30. doi:10.1016/j.expthermflusci.2014.11.017.

[35] Nakagami S, Matsuoka K, Kasahara J, Kumazawa Y, Fujii J, Matsuo A, et al. Experimental Visualization of the Structure of Rotating Detonation Waves in a Disk-Shaped Combustor. J Propuls Power 2016;33:80–8. doi:10.2514/1.B36084.

[36] Gawahara K, Nakayama H, Kasahara J, Matsuoka K, Tomioka S, Hiraiwa T, et al. Detonation engine development for reaction control systems of a spacecraft. AIAA Jt. Propuls. Conf., San Jose, CA: 2013. doi:10.2514/6.2013-3721.

[37] Nordeen CA, Schwer D, Corrigan AT, Cetegen B. Radial Effects on Rotating Detonation Engine Swirl. 51st AIAA/SAE/ASEE Jt. Propuls. Conf., Orlando, FL: 2015. doi:10.2514/6.2015-3781.

[38] Kurosaka M, Tsuboi N. Spinning detonation, cross-currents, and the Chapman–Jouguet velocity. J Fluid Mech 2014;756:728–57. doi:10.1017/jfm.2014.460.

[39] St. George A, Driscoll R, Anand V, Gutmark E. On the existence and multiplicity of rotating detonations. Proc Combust Inst 2017;36:2691–8. doi:10.1016/j.proci.2016.06.132.

[40] Roy A, Ferguson DH, Sidwell T, O’Meara B, Strakey P, Bedick C, et al. Experimental Study of Rotating Detonation Combustor Performance under Preheat and Back Pressure Operation. 55th AIAA Aerosp. Sci. Meet., Grapevine, TX: 2017. doi:10.2514/6.2017-1065.

[41] Yao S, Tang X, Luan M, Wang J. Numerical study of hollow rotating detonation engine with different fuel injection area ratios. Proc Combust Inst 2016;0:1–7. doi:10.1016/j.proci.2016.07.126.

[42] Tsuboi N, Daimon Y, Hayashi AK. Three-dimensional numerical simulation of detonations in coaxial tubes. Shock Waves 2008;18:379–92. doi:10.1007/s00193-008-0152-z.

[43] Anand V, St. George A, Driscoll R, Gutmark E. Investigation of rotating detonation combustor operation with H2-Air mixtures. Int J Hydrogen Energy 2016;41:1281–92. doi:10.1016/j.ijhydene.2015.11.041.

[44] Rankin BA, Richardson DR, Caswell AW, Naples AG, Hoke JL, Schauer FR. Chemiluminescence imaging of an optically accessible non-premixed rotating detonation engine. Combust Flame

367

2016;176:12–22. doi:10.1016/j.combustflame.2016.09.020.

[45] Wang C, Liu W, Liu S, Jiang L, Lin Z. Experimental investigation on detonation combustion patterns of hydrogen/vitiated air within annular combustor. Exp Therm Fluid Sci 2015;66:269–78. doi:10.1016/j.expthermflusci.2015.02.024.

[46] Stechmann D, Heister SD, Sardeshmukh S. High-Pressure Rotating Detonation Engine Testing and Flameholding Analysis with Hydrogen and Natural Gas. 55th AIAA Aerosp. Sci. Meet. AIAA, Grapevine, Texas: 2017. doi:10.2514/6.2017-1931.

[47] Lentsch A, Bec R, Serre L, Falempin F, Daniau D, Piton D, et al. Overview of Current French Activities on PDRE and Continuous Detonation Wave Rocket Engines. AIAA/CIRA 13th Int. Sp. Planes Hypersonics Syst. Technol. Conf., Capua, Italy: 2005. doi:10.2514/6.2005-3232.

[48] Frolov SM, Aksenov VS, Ivanov VS, Shamshin IO. Large-scale hydrogen-air continuous detonation combustor. Int J Hydrogen Energy 2015;40:1616–23. doi:10.1016/j.ijhydene.2014.11.112.

[49] Dremin AN. Toward Detonation Theory. New York, NY: Springer New York; 1999. doi:10.1007/978-1-4612-0563-0.

[50] Adams TC. Do Weak Detonation Waves Exist? AIAA J 1978;16:1035–40. doi:10.2514/3.61001.

[51] Kindracki J, Wolański P, Gut Z. Experimental research on the rotating detonation in gaseous fuels-oxygen mixtures. Shock Waves 2011;21:75–84. doi:10.1007/s00193-011-0298-y.

[52] Clayton RM, Rogero RS. Experimental measurements on a rotating detonation-like wave observed during liquid rocket resonant combustion. 1965.

[53] Levine RS. Experimental status of high frequency liquid rocket combustion instability. Symp Combust 1965;10:1083–99. doi:10.1016/S0082-0784(65)80248-X.

[54] Edwards BD. Maintained detonation waves in an annular channel: A hypothesis which provides the link between classical acoustic combustion instability and detonation waves. Symp Combust 1977;16:1611–8. doi:10.1016/S0082-0784(77)80440-2.

[55] Male T, Kerslake R, Tischler AO. Photographic study of rotary screaming and other oscillations in a rocket engine. Cleveland, OH: 1954.

368

[56] Harrje DT, Reardon FH. Liquid propellant rocket combustion instability. vol. NASA SP-19. Washington D.C.: 1972.

[57] Oefelin JC, Yang V. Comprehensive review of liquid-propellant combustion instabilities in F-1 engines. J Propuls Power 1993;9:657–77. doi:10.2514/3.23674.

[58] Culick FEC. Combustion Instabilities in Solid Propellant Rocket Motors 2002:27–31.

[59] Crocco L. Aspects of combustion instability in liquid propellant rocket motors. Part {II.}. \Jars 1952;22:7–16.

[60] Putnam AA. Combustion Driven Oscillations in Industry. New York: Elsevier; 1971.

[61] Knapp B, Oschwald M. High Speed Visualization of Flame Response in a LOX/H2 Combustion Chamber during external Excitation. 12th Int. Symp. Flow Vis., Göttingen, Germany: 2006.

[62] Flandro G, Sims J, Majdalani J. On Nonlinear Combustion Instability in Liquid Propellant Rocket Engines, Fort Lauderdale, Florida: 2004. doi:10.2514/6.2004-3516.

[63] Flandro GA, Fischbach SR, Majdalani J. Nonlinear rocket motor stability prediction: Limit amplitude, triggering, and mean pressure shift. Phys Fluids 2007;19. doi:10.1063/1.2746042.

[64] Flandro G, Perry E, French J. Nonlinear Rocket Motor Stability Computations: Understanding the Brownlee-Marble Observations. 44th AIAA Aerosp. Sci. Meet. Exhib., Reno , NV: 2006. doi:10.2514/6.2006-539.

[65] Jacob EJ, Flandro GA, Gloyer PW, French JC. Nonlinear Liquid Rocket Combustion Instability Behavior using UCDS TM Process. 46th AIAA/ASME/SAE/ASEE Jt. Propuls. Conf. Exhib., Nashville, TN: 2010. doi:10.2514/6.2010-6800.

[66] Flandro GA, Majdalani J, Sims JD. Nonlinear Longitudinal Mode Instability in Liquid Propellant Rocket Engine Preburners. AIAA/ASME/SAE/ASEE Jt. Propuls. Conf. Exhib., Fort Lauderdale, Florida: 2004. doi:10.2514/6.2004-4162.

[67] Flandro G a., Majdalani J, Sims JD. On Nonlinear Combustion Instability in Liquid Propellant Rocket Motors. 40th AIAA/ASME/SAE/ASEE Jt Propuls Conf 2004.

[68] Clayton R, Rogero R, Sotter J. An experimental description of destructive liquid rocket

369

resonant combustion. AIAA J 1968;6:1252–9. doi:10.2514/3.4730.

[69] Anand V, St. George A, Driscoll R, Gutmark E. Longitudinal pulsed detonation instability in a rotating detonation combustor. Exp Therm Fluid Sci 2016;77:212–25. doi:doi:10.1016/j.expthermflusci.2016.04.025.

[70] Yang C, Wu X, Ma H, Peng L, Gao J. Experimental research on initiation characteristics of a rotating detonation engine. Exp Therm Fluid Sci 2016;71:154–63. doi:10.1016/j.expthermflusci.2015.10.019.

[71] Dyer R, Naples A, Kaemming T, Hoke J, Schauer F. Parametric Testing of a Unique Rotating Detonation Engine Design. 50th AIAA Aerosp. Sci. Meet. Incl. New Horizons Forum Aerosp. Expo., Nashville, Tennessee: 2012.

[72] Bellman DR, Humphrey JC, Male T. Photographic investigation of combustion in a two- dimensional transparent rocket engine. Cleveland, OH: 1953.

[73] Jr K, H.C. Tangential Mode of Combustion Instability. Prog Astronaut Rocket 1962;6:339–66.

[74] Anderson WE, Yang V, editors. Liquid Rocket Engine Combustion Instability. Washington DC: American Institute of Aeronautics and Astronautics; 1995. doi:10.2514/4.866371.

[75] Lubarsky E, Hadjipanayis M, Shcherbik D, Bibik O, Zinn BT. Control of tangential instability by asymmetric baffle. 46th AIAA Aerosp. Sci. Meet. Exhib., Reno , NV: 2008.

[76] Bennewitz JW, Frederick R a. Overview of Combustion Instabilities in Liquid Rocket Engines - Coupling Mechanisms & Control Techniques. 49th AIAA/ASME/SAE/ASEE Jt. Propuls. Conf. Exhib., San Jose, CA: 2013. doi:10.2514/6.2013-4106.

[77] Popov PP, Sideris A, Sirignano W a. Stochastic modelling of transverse wave instability in a liquid-propellant rocket engine. J Fluid Mech 2014;745:62–91. doi:10.1017/jfm.2014.96.

[78] Bennewitz J, Lubarsky E, Shcherbik D, Bibik O, Zinn B. Asymmetric Injector Distribution for Passive Control of Liquid Rocket Engine Combustion Instabilities. 48th AIAA Aerosp. Sci. Meet., Orlando, FL: 2010.

[79] Brownlee WG, Marble FE. An experimental investigation of unstable combustion in solid propellant rocket motors. AIAA Prog Astronaut Rocket Solid Propellant Rocket Res 1960;1:455–94.

370

[80] Freeman RH. Understanding Space Launch Vehicle Complexity : A Case Study in Combustion Instabilities. AIAA Sp. Conf. Expo., Pasadena, California: 2015. doi:10.2514/6.2015-4550.

[81] Anand V, St. George A, Farbos de Luzan C, Gutmark E. Rotating detonation wave mechanics through ethylene-air mixtures in hollow combustors, and implications to high frequency combustion instabilities. Exp Therm Fluid Sci 2018;92:314–25. doi:10.1016/j.expthermflusci.2017.12.004.

[82] Ciccarelli G, Dorofeev S. Flame acceleration and transition to detonation in ducts. Prog Energy Combust Sci 2008;34:499–550. doi:10.1016/j.pecs.2007.11.002.

[83] Nakayama H, Moriya T, Kasahara J, Matsuo A, Sasamoto Y, Funaki I. Stable detonation wave propagation in rectangular-cross-section curved channels. Combust Flame 2012;159:859– 69. doi:10.1016/j.combustflame.2011.07.022.

[84] Pan Z, Fan B, Zhang X, Gui M, Dong G. Wavelet pattern and self-sustained mechanism of gaseous detonation rotating in a coaxial cylinder. Combust Flame 2011;158:2220–8. doi:10.1016/j.combustflame.2011.03.016.

[85] Blomshield F. Historical perspective of combustion instability in motors-Case Studies. 37th Jt. Propuls. Conf. Exhib., Salt Lake City, UT: 2001. doi:10.2514/6.2001-3875.

[86] Flandro GA. Nonlinear Combustion Instability. Tech. Interchang. Meet. Part 1 - Case Stud., 2005.

[87] Fujiwara T, Hishida M, Kindracki J, Wolanski P. Stabilization of Detonation for Any Incoming Mach Numbers. Combust Explos Shock Waves 2009;45:603–5. doi:10.1007/s10573-009- 0072-y.

[88] Nordeen CA, Schwer D, Schauer F, Hoke J, Barber T, Cetegen BM. Role of inlet reactant mixedness on the thermodynamic performance of a rotating detonation engine. Shock Waves 2016;26:417–28. doi:10.1007/s00193-015-0570-7.

[89] Schwer D, Kailasanath K. Numerical investigation of the physics of rotating-detonation- engines. Proc Combust Inst 2011;33:2195–202. doi:10.1016/j.proci.2010.07.050.

[90] Ishihara K, Kato Y, Matsuoka K, Kasahara J. Performance Evaluation of a Rotating Detonation Engine with Conical-shape tail. 53rd AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2015.

371

[91] Radulescu M. I, Lee JHS. The Failure Mechanism of Gaseous Detonations: Experiments in Porous Wall Tubes. Combust Flame 2003;131:29–46.

[92] Mehrjoo N, Gao Y, Kiyanda CB, Ng HD, Lee JHS. Effects of porous walled tubes on detonation transmission into unconfined space. Proc Combust Inst 2015;35:1981–7. doi:10.1016/j.proci.2014.06.031.

[93] Fay JA. Two dimensional gaseous detonations: Velocity deficit. Phys Fluids 1959;2:283–9. doi:10.1063/1.1705924.

[94] Dabora EK, Nicholls JA, Morrison RB. The influence of a compressible boundary on the propagation of gaseous detonations. Symp Combust 1965;10:817–30. doi:10.1016/S0082- 0784(65)80225-9.

[95] Paxson DE. Examination of Wave Speed in Rotating Detonation Engines Using Simplified Computational Fluid Dynamics. 2018 AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2018. doi:10.2514/6.2018-1883.

[96] Paxson DE. Impact of an Exhaust Throat on Semi-Idealized Rotating Detonation Engine Performance. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: 2016. doi:10.2514/6.2016-1647.

[97] Nordeen CA, Schwer D, Schauer F, Hoke J, Cetegen B, Barber T. Thermodynamic Modeling of a Rotating Detonation Engine. 49th AIAA Aerosp. Sci. Meet., San Diego, CA: 2011. doi:10.2514/6.2011-803.

[98] Nordeen C, Schwer D, Schauer F, Hoke J, Barber T, Cetegen B. Divergence and Mixing in a Rotating Detonation Engine. 51st AIAA Aerosp. Sci. Meet., Grapevine, Texas: 2013. doi:10.2514/6.2013-1175.

[99] Nordeen CA, Schwer DA, Corrigan AT. Area Effects on Rotating Detonation Engine Performance. 50th AIAA/ASME/SAE/ASEE Jt. Propuls. Conf., Cleveland, OH: 2014. doi:10.2514/6.2014-3900.

[100] Nordeen CA, Schwer DA, Schauer FR, Hoke JL, Barber T, Cetegen B. Energy Transfer in a Rotating Detonation Engine. 47th AIAA/ASME/SAE/ASEE Jt. Propuls. Conf. Exhib., San Diego, CA: 2011.

[101] Cho KY, Codoni JR, Rankin BA, Hoke J, Schauer F. Effects of Lateral Relief of Detonation in a

372

Thin Channel. 55th AIAA Aerosp. Sci. Meet., Grapevine, Texas: 2017, p. 1–9. doi:10.2514/6.2017-0373.

[102] Houim RW, Fievisohn RT. The influence of acoustic impedance on gaseous layered detonations bounded by an inert gas. Combust Flame 2017;179:185–98. doi:10.1016/j.combustflame.2017.02.001.

[103] John Anderson. Modern Compressible Flow: With Historical Perspective / Edition 3 by John Anderson, John Anderson | | 9780072424430 | Hardcover | Barnes & Noble. 3rd ed. McGraw-Hill Higher Education; 2002.

[104] Wu D, Liu Y, Liu Y, Wang J. Numerical investigations of the restabilization of hydrogen-air rotating detonation engines. Int J Hydrogen Energy 2014;39:15803–9. doi:10.1016/j.ijhydene.2014.07.159.

[105] Fievisohn RT, Yu KH. Steady-State Analysis of Rotating Detonation Engine Flowfields with the Method of Characteristics. J Propuls Power 2017;33:89–99. doi:10.2514/1.B36103.

[106] Hishida M, Fujiwara T, Wolanski P. Fundamentals of rotating detonations. Shock Waves 2009;19:1–10. doi:10.1007/s00193-008-0178-2.

[107] Li Q, Liu P, Zhang H. Further investigations on the interface instability between fresh injections and burnt products in 2-D rotating detonation. arXiv Prepr 2017.

[108] Liu P, Li Q, Huang Z, Zhang H. Interpretation of wake instability at slip line in rotating detonation. arXiv Prepr 2018.

[109] Schwer DA, Kailasanath K. Numerical Study of the Effects of Engine Size on Rotating Detonation Engines. 49th AIAA Aerosp. Sci. Meet., Orlando, FL: 2011. doi:10.2514/6.2011- 581.

[110] Uemura Y, Hayashi AK, Asahara M, Tsuboi N, Yamada E. Transverse wave generation mechanism in rotating detonation. Proc Combust Inst 2013;34:1981–9. doi:10.1016/j.proci.2012.06.184.

[111] Davidenko DM, Gökalp I, Kudryavtsev AN. Numerical modeling of the rotating detonation in an annular combustion chamber fed with hydrogen-oxygen mixture. THIRD Eur. Combust. Meet., Dubrovnik, Croatia: 2007.

373

[112] Zhdan SA, Bykovskii FA, Vedernikov EF. Mathematical modeling of a rotating detonation wave in a hydrogen-oxygen mixture. Combust Explos Shock Waves 2007;43:449–59. doi:10.1007/s10573-007-0061-y.

[113] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous Spin Detonation of Hydrogen – Oxygen Mixtures. 3 . Methods of Measuring Flow Parameters and Flow Structure in Combustors of Different Geometries. Combust Explos Shock Waves 2008;44:150–62. doi:10.1007/s10573- 008-0021-1.

[114] Edwards D, Jones T, Price B. Observations on oblique shock waves in gaseous detonations. J Fluid Mech 1963;17:21. doi:10.1017/S0022112063001075.

[115] Zhdan SA. Mathematical model of continuous detonation in an annular combustor with a supersonic flow velocity. Combust Explos Shock Waves 2008;44:690–7. doi:10.1007/s10573-008-0104-z.

[116] Zhdan SA, Syryamin AS. Numerical Modeling of Continuous Detonation in Non- Stoichiometric Hydrogen-Oxygen Mixtures. Combust Explos Shock Waves 2013;49:69–78. doi:10.1134/S0010508213010085.

[117] Gaillard T, Davidenko D, Dupoirieux F. Numerical optimisation in non reacting conditions of the injector geometry for a continuous detonation wave rocket engine. Acta Astronaut 2015;111:334–44. doi:10.1016/j.actaastro.2015.02.006.

[118] Dubrovskii AV, Ivanov VS, Frolov SM. Three-dimensional numerical simulation of the operation process in a continuous detonation combustor with separate feeding of hydrogen and air. Russ J Phys Chem B 2015;9:104–19. doi:10.1134/S1990793115010157.

[119] Nakayama H, Kasahara J, Matsuo A, Funaki I. Front shock behavior of stable curved detonation waves in rectangular-cross-section curved channels. Proc Combust Inst 2013;34:1939–47. doi:10.1016/j.proci.2012.06.012.

[120] Schwer DA, Kailasanath K. Effect of low pressure ratio on exhaust plumes of rotating detonation engines. 47th AIAA/ASME/SAE/ASEE Jt. Propuls. Conf. Exhib., Cleveland, OH: 2014. doi:10.2514/6.2011-6044.

[121] Tsuboi N, Watanabe Y, Kojima T, Hayashi AK. Numerical estimation of the thrust performance on a rotating detonation engine for a hydrogen-oxygen mixture. Proc Combust

374

Inst 2015;35:2005–13. doi:10.1016/j.proci.2014.09.010.

[122] Sharpe GJ. The effect of curvature on pathological detonations. Combust Flame 2000;123:68– 81. doi:10.1016/S0010-2180(00)00156-5.

[123] Oran ES. Understanding explosions – From catastrophic accidents to creation of the universe. Proc Combust Inst 2015;35:1–35. doi:10.1016/j.proci.2014.08.019.

[124] Meng L, Shuang Z, Jianping W, Yifeng C. Parallel three-dimensional numerical simulation of rotating detonation engine on graphics processing units. Comput Fluids 2015;110:36–42. doi:10.1016/j.compfluid.2014.11.017.

[125] Zhou R, Wang JP. Numerical investigation of shock wave reflections near the head ends of rotating detonation engines. Shock Waves 2013;23:461–72. doi:10.1007/s00193-013-0440- 0.

[126] Zhang H, Liu W, Liu S. Effects of inner cylinder length on H2/air rotating detonation. Int J Hydrogen Energy 2016;41:13281–93. doi:10.1016/j.ijhydene.2016.06.083.

[127] Kindracki J, Kobiera a., Wolański P, Gut Z, Folusiak M, Swiderski K. Experimental and numerical study of the rotating detonation engine in hydrogen-air mixtures. Prog Propuls Phys 2012;2:555–82. doi:10.1051/eucass/201102555.

[128] Driscoll RB, Anand V, St. George AC, Gutmark EJ. Investigation on RDE Operation by Geometric Variation of the Combustor Annulus and Nozzle Exit Area. 9th U.S. Natl. Combust. Meet., Cincinnati, OH: 2015.

[129] Bykovskii FA, Zhdan SA. Current Status of Research of Continuous Detonation in Fuel – Air Mixtures ( Review ). Combust Explos Shock Waves 2015;51:21–35. doi:10.1134/S0010508215010025.

[130] Frolov SM, Aksenov VS, Ivanov VS, Shamshin IO. Continuous detonation combustion of ternary “hydrogen-liquid propane-air ” mixture in annular combustor. Int J Hydrogen Energy 2017:1–13. doi:10.1016/j.ijhydene.2017.05.138.

[131] Zhang H, Liu W, Liu S. Experimental investigations on H 2 /air rotating detonation wave in the hollow chamber with Laval nozzle. Int J Hydrogen Energy 2017;42:3363–70. doi:10.1016/j.ijhydene.2016.12.038.

375

[132] Tang XM, Wang JP, Shao YT. Three-dimensional numerical investigations of the rotating detonation engine with a hollow combustor. Combust Flame 2015;162:997–1008. doi:10.1016/j.combustflame.2014.09.023.

[133] Yao S, Tang X, Wang J. Numerical Study of the Propulsive Performance of the Hollow Rotating Detonation Engine with a Laval Nozzle. Int J Turbo Jet-Engines 2015;34:49–54. doi:10.1515/tjj-2015-0052.

[134] Wilhite J, Driscoll RB, St. George AC, Anand V, Gutmark EJ. Investigation of a Rotating Detonation Engine using Ethylene-Air Mixture. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: 2016. doi:10.2514/6.2016-1650.

[135] Andrus IQ, King PI, Polanka MD, Schauer FR, Hoke JL. Design of a Premixed Fuel–Oxidizer System to Arrest Flashback in a Rotating Detonation Engine. J Propuls Power 2017;33:1063– 73. doi:10.2514/1.B36259.

[136] Stoddard WA, St. George A, Driscoll R, Anand V, Gutmark EJ. Experimental validation of expanded centerbodiless RDE design. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: 2016.

[137] Stoddard W, Anand V, Driscoll R, Dolan B, St. George A, Villalva R, et al. Experimental characterization of centerbodiless RDE emissions. 55th AIAA Aerosp. Sci. Meet., Grapevine, Texas: 2017. doi:10.2514/6.2017-0788.

[138] Stoddard WA, Gutmark EJ. Numerical Investigation of Centerbodiless RDE Design Variations. 53rd AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2015. doi:doi:10.2514/6.2015-0876.

[139] Stoddard W, Gutmark EJ. Numerical Investigation of Expanded and Stepped Centerbodiless RDE Designs. 51st AIAA/SAE/ASEE Jt. Propuls. Conf., Orlando, FL: 2015.

[140] Yao S, Ma Z, Zhang S, Luan M, Wang J. Reinitiation phenomenon in hydrogen-air rotating detonation engine. Int J Hydrogen Energy 2017;42:28588–98. doi:10.1016/j.ijhydene.2017.09.015.

[141] Kerslake WR, Male T. A Method for Prevention of Screaming in Rocket Engines. NACA RME54F218a 1954.

[142] Liu Y, Wang Y, Li Y, Li Y, Wang J. Spectral analysis and self-adjusting mechanism for oscillation phenomenon in hydrogen-oxygen continuously rotating detonation engine.

376

Chinese J Aeronaut 2015;28:669–75. doi:10.1016/j.cja.2015.03.006.

[143] Ishiyama C, Miyazaki K, Nakagami S, Matsuoka K, Kasahara J, Matsuo A, et al. Experimental Study of Research of Centrifugal-Compressor-Radial-Turbine Type Rotating Detonation Engine. 52nd AIAA/SAE/ASEE Jt. Propuls. Conf., Salt Lake City, UT: 2016. doi:10.2514/6.2016-5103.

[144] Kindracki J. Experimental research on rotating detonation in liquid fuel–gaseous air mixtures. Aerosp Sci Technol 2015;43:445–53. doi:10.1016/j.ast.2015.04.006.

[145] Le Naour B, Falempin FH, Coulon K. MBDA R&T Effort Regarding Continuous Detonation Wave Engine for Propulsion - Status in 2016. 21st AIAA Int. Sp. Planes Hypersonics Technol. Conf., Xiamen, China: 2017. doi:10.2514/6.2017-2325.

[146] Daniau E, Falempin F, Zhdan S. Pulsed and rotating detonation propulsion systems: First step toward operational engines. AIAA, Capua, Italy: 2005.

[147] Bykovskii FA, Zhdan SA, Vedernikov EF, Zholobov YA. Detonation burning of anthracite and lignite particles in a flow-type radial combustor. Combust Explos Shock Waves 2016;52:703– 12. doi:10.1134/S0010508216060101.

[148] Rankin BA, Fotia ML, Naples AG, Stevens CA, Hoke JL, Kaemming TA, et al. Overview of Performance, Application, and Analysis of Rotating Detonation Engine Technologies. J Propuls Power 2017;33:131–43. doi:10.2514/1.B36303.

[149] George AS, Driscoll R, Anand V, Munday D, Gutmark EJ. Fuel Blending as a Means to Achieve Initiation in a Rotating Detonation Engine. 53rd AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2015. doi:doi:10.2514/6.2015-0633.

[150] Stechmann D, Heister SD, Sardeshmukh S. High-Pressure Rotating Detonation Engine Testing and Flameholding Analysis with Hydrogen and Natural Gas. 52nd AIAA/SAE/ASEE Jt. Propuls. Conf., Grapevine, TX: 2016. doi:10.2514/6.2016-5099.

[151] Shank JC, King PI, Karnesky J, Schauer FR, Hoke JL. Development and Testing of a Modular Rotating Detonation Engine. 50th AIAA Aerosp. Sci. Meet. Incl. New Horizons Forum Aerosp. Expo., Nashville, Tennessee: 2012.

[152] Miller SJ, King PI, Schauer FR, Hoke JL. Ignition Design for a Rotating Detonation Engine. 51st

377

Aerosp. Sci. Conf., Grapevine, Texas: 2013.

[153] Brophy C, Dvorak T, Dausen D, Myers CB. Detonation Initiation Improvements Using Swept- Ramp Obstacles. 48th AIAA Aerosp. Sci. Meet. Incl. New Horizons Forum Aerosp. Expo., Orlando, FL: 2010. doi:10.2514/6.2010-1336.

[154] Driscoll R, Randall S, St. George A, Anand V, Gutmark EJ. Shock-Initiated Combustion in an Airbreathing, Pulse Detonation Engine-Crossover System. AIAA J 2015;54:936–49. doi:10.2514/1.J054571.

[155] Fotia ML, Hoke J, Schauer F. Study of the ignition process in a laboratory scale rotating detonation engine. Exp Therm Fluid Sci 2017. doi:10.1016/j.expthermflusci.2017.11.002.

[156] St. George A, Randall S, Anand V, Driscoll R, Gutmark E. Characterization of initiator dynamics in a rotating detonation combustor. Exp Therm Fluid Sci 2016;72:171–81. doi:10.1016/j.expthermflusci.2015.11.002.

[157] St. George AC, Driscoll RB, Anand V, Gutmark EJ. Starting Transients and Detonation Onset Behavior in a Rotating Detonation Combustor. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: American Institute of Aeronautics and Astronautics; 2016. doi:10.2514/6.2016-0126.

[158] Peng L, Wang D, Wu X, Ma H, Yang C. Ignition experiment with automotive spark on rotating detonation engine. Int J Hydrogen Energy 2015;40:8465–74. doi:10.1016/j.ijhydene.2015.04.126.

[159] Yang C, Wu X, Ma H, Peng L, Gao J. Experimental research on initiation characteristics of a rotating detonation engine. Exp Therm Fluid Sci 2016;71:154–63. doi:10.1016/j.expthermflusci.2015.10.019.

[160] Teodorczyk A, Drobniak P, Dabkowski A. Fast turbulent deflagration and DDT of hydrogen- air mixtures in small obstructed channel. Int J Hydrogen Energy 2009;34:5887–93. doi:10.1016/j.ijhydene.2008.11.120.

[161] Bykovskii FA, Zhdan SA, Vedernikov EF. Initiation of detonation of fuel-air mixtures in a flow-type annular combustor. Combust Explos Shock Waves 2014;50:214–22. doi:10.1134/S0010508214020130.

[162] Anand V, St. George A, Jodele J, Knight E, Gutmark E. The Origins of Wave Directionality,

378

Chaotic Propagation and Onset Time after Ignition in a Rotating Detonation Combustor 2018.

[163] Andrus IQ, Polanka MD, Schauer FR, Hoke J. Further Experimentation of a Premixed Rotating Detonation Engine. 55th AIAA Aerosp. Sci. Meet., Grapevine, Texas: 2017. doi:10.2514/6.2017-0786.

[164] Andrus IQ, King P, Polanka MD, Schauer F, Hoke JL. Design of a Premixed Fuel-Oxidizer System to Prevent Flashback in a Rotating Detonation Engine. 54th AIAA Aerosp Sci Meet 2016:1–15. doi:10.2514/6.2016-0127.

[165] Andrus IQ, King P, Polanka MD, Schauer F, Hoke J. Experimentation of a Premixed Rotating Detonation Engine Utilizing a Variable Slot Feed Plenum. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: 2016. doi:10.2514/6.2016-1404.

[166] Li J-M, Chang P-H, Li L, Yang Y, Teo CJ, Khoo BC. Investigation of Injection Strategy for Liquid- Fuel Rotating Detonation Engine. 2018 AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2018. doi:10.2514/6.2018-0403.

[167] Lim D, Heister S, Stechmann D, Kan B. Transient response of a liquid injector to a steep- fronted transverse pressure wave. Shock Waves 2017:1–14. doi:10.1007/s00193-017-0787- 8.

[168] Schwer D, Kailasanath K. Fluid dynamics of rotating detonation engines with hydrogen and hydrocarbon fuels. Proc Combust Inst 2013;34:1991–8. doi:10.1016/j.proci.2012.05.046.

[169] Liu M, Zhou R, Wang J-P. Numerical Investigation of Different Injection Patterns in Rotating Detonation Engines. Combust Sci Technol 2015;187:343–61. doi:10.1080/00102202.2014.923411.

[170] Cocks PA, Holley AT, Rankin BA. High Fidelity Simulations of a Non-Premixed Rotating Detonation Engine. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: 2016. doi:10.2514/6.2016- 0125.

[171] Schwer D, Kailasanath K. Feedback into Mixture Plenums in Rotating Detonation Engines. 50th AIAA Aerosp. Sci. Meet. Incl. New Horizons Forum Aerosp. Expo., Nashville, TN: 2012. doi:10.2514/6.2012-617.

[172] Schwer DA, Kailasanath K. On Reducing Feedback Pressure in Rotating Detonation Engines.

379

51st AIAA Aerosp. Sci. Meet., Grapevine, Texas: 2013. doi:10.2514/6.2013-1178.

[173] Sun J, Zhou J, Liu S, Lin Z, Cai J. Effects of injection nozzle exit width on rotating detonation engine. Acta Astronaut 2017;140:388–401. doi:10.1016/j.actaastro.2017.09.008.

[174] Bykovskii FA, Vedernikov EF. Continuous detonation of a subsonic flow of a propellant. Combust Explos Shock Waves 2003;39:323–34. doi:10.1023/A:1023800521344.

[175] Yao S, Liu M, Wang J. Numerical Investigation of Spontaneous Formation of Multiple Detonation Wave Fronts in Rotating Detonation Engine. Combust Sci Technol 2015;187:1867–78. doi:10.1080/00102202.2015.1067202.

[176] Stoddard W, Gutmark E. Numerical Study of Obstacles in Rotating Detonation Engines. 51st AIAA Aerosp. Sci. Meet. Incl. New Horizons Forum Aerosp. Expo., Grapevine, Texas: American Institute of Aeronautics and Astronautics; 2013. doi:10.2514/6.2013-1031.

[177] Liu S-J, Lin Z-Y, Sun M-B, Liu W-D. Thrust Vectoring of a Continuous Rotating Detonation Engine by Changing the Local Injection Pressure. Chinese Phys Lett 2011;28:1–4. doi:10.1088/0256-307X/28/9/094704.

[178] Schwinn KS, Kan B, Sardeshmukh S V., Gejji RM, Heister SD, Slabaugh CD. Self-Excited, Multi- kHz Dynamics in a Linear, Semi-Bounded Detonation Channel. 55th AIAA Aerosp. Sci. Meet., Grapevine, Texas: 2017. doi:10.2514/6.2017-0375.

[179] Bedick C, Sisler A, Ferguson D, Strakey P, Nix A, Billips D. Development of a Lab-Scale Experimental Testing Platform for Rotating Detonation Engine Inlets. 55th AIAA Aerosp. Sci. Meet., Grapevine, TX: 2017. doi:10.2514/6.2017-0785.

[180] Fujii J, Kumazawa Y, Matsuo A, Nakagami S, Matsuoka K, Kasahara J. Numerical investigation on detonation velocity in rotating detonation engine chamber. Proc Combust Inst 2017;36:2665–72. doi:10.1016/j.proci.2016.06.155.

[181] Paxson DE, Matthew L. Fotia, Hoke J, Schauer F. Comparison of Numerically Simulated and Experimentally Measured Performance of a Rotating Detonation Engine. 53rd AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2015. doi:10.2514/6.2015-1101.

[182] Deng L, Ma H, Xu C, Zhou C, Liu X. Investigation on the propagation process of rotating detonation wave. Acta Astronaut 2017;139:278–87. doi:10.1016/j.actaastro.2017.07.024.

380

[183] St. George A, Driscoll R, Anand V, Gutmark E. Chemical kinetic analysis of detonability- enhancing strategies for ethylene–oxidizer mixtures. Acta Astronaut 2016;128:194–202. doi:10.1016/j.actaastro.2016.07.015.

[184] Fotia M, Hoke J, Schauer F. Propellant Plenum Dynamics in a Two-dimensional Rotating Detonation Experiment. 52nd Aerosp. Sci. Meet., National Harbor, Maryland: American Institute of Aeronautics and Astronautics; 2014. doi:10.2514/6.2014-1013.

[185] Mikoshiba K, Sardeshmukh S V., Stechmann DP, Heister SD. On the Response of Annular Inlets Feeding a Rotating Detonation Combustor. 2018 AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2018. doi:10.2514/6.2018-0885.

[186] Driscoll R, Aghasi P, St George A, Gutmark EJ. Three-dimensional, numerical investigation of reactant injection variation in a H2/air rotating detonation engine. Int J Hydrogen Energy 2016;41:5162–75. doi:10.1016/j.ijhydene.2016.01.116.

[187] Bohon MD, Bluemner R, Paschereit CO, Gutmark EJ. Experimental study of reactants mixing in model rotating detonation combustor geometries. Int. Conf. Jets, Wakes Separated Flows, Cincinnati, OH: 2017.

[188] Rankin BA, Fugger CA, Richardson DR, Cho KY, Hoke J, Caswell AW, et al. Evaluation of Mixing Processes in a Non-Premixed Rotating Detonation Engine Using Acetone PLIF. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: 2016. doi:10.2514/6.2016-1198.

[189] Narayanaswamy V, Raja LL, Clemens NT. Control of unsteadiness of a shock wave/turbulent boundary layer interaction by using a pulsed-plasma-jet actuator. Phys Fluids 2012;24. doi:10.1063/1.4731292.

[190] Semlitsch B, Mihaescu M, Gutmark EJ. Flow Structure Generation By Multiple Jets in Supersonic Cross-Flow 2013.

[191] Génin F, Menon S. Dynamics of sonic jet injection into supersonic crossflow. J Turbul 2010;11:1–30. doi:10.1080/14685240903217813.

[192] Mahesh K. The Interaction of Jets with Crossflow. Annu Rev Fluid Mech 2013;45:379–407. doi:10.1146/annurev-fluid-120710-101115.

[193] Sutton GP. History of Liquid Propellant Rocket Engines. Reston ,VA: American Institute of

381

Aeronautics and Astronautics; 2006. doi:10.2514/4.868870.

[194] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous Spin Detonation of Hydrogen – Oxygen Mixtures. 1 . Annular Cylindrical Combustors. Combust Explos Shock Waves 2008;44:150– 62. doi:10.1007/s10573-008-0021-1.

[195] Gaillard T, Davidenko D, Dupoirieux F. Numerical simulation of a Rotating Detonation with a realistic injector designed for separate supply of gaseous hydrogen and oxygen. Acta Astronaut 2017;141:64–78. doi:10.1016/j.actaastro.2017.09.011.

[196] Osborn JR, Davis LR. Effects of injection location on combustion instability in premixed gaseous bipropellant rocket motors. Lafayette, Indiana: 1961.

[197] Osborn JR, Rahon JR. Effects of Radial Energy Release Variations on Transverse Combustion Pressure Oscillations. Lafayette, Indiana: 1962.

[198] Everest FA, Pohlmann KC. Master Handbook of Acoustics. McGraw-Hill Professional Publishing; 2009.

[199] Bykovskii FA, Vedernikov EF. Continuous detonation combustion of an annular gas-mixture layer. Combust Explos Shock Waves 1996;32:489–91.

[200] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous spin detonation of a hydrogen-air mixture with addition of air into the products and the mixing region. Combust Explos Shock Waves 2010;46:52–9. doi:10.1007/s10573-010-0009-5.

[201] Bykovskii FA, Zhdan SA, Vedernikov EF, Samsonov AN. Effect of combustor geometry on continuous spin detonation in syngas–air mixtures. Combust Explos Shock Waves 2015;51:688–99. doi:10.1134/S0010508215060106.

[202] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous spin detonation of synthesis gas-air mixtures. Combust Explos Shock Waves 2013;49:435–41. doi:10.1134/S0010508213040060.

[203] Braun J, Saracoglu BH, Paniagua G. Unsteady Performance of Rotating Detonation Engines with Different Exhaust Nozzles. J Propuls Power 2016;33:121–30. doi:10.2514/1.B36164.

[204] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous Spin Detonation of Hydrogen – Oxygen Mixtures. 2 . Combustor with an expanding annular channel. Combust Explos Shock Waves

382

2008;44:150–62. doi:10.1007/s10573-008-0021-1.

[205] Dubrovskii A V, Ivanov VS, Zangiev AE, Frolov SM. Three-dimensional numerical simulation of the characteristics of a ramjet power plant with a continuous-detonation combustor in supersonic flight. Russ J Phys Chem B 2016;10:469–82. doi:10.1134/S1990793116030179.

[206] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous detonation in the air ejection mode. Domain of existence. Combust Explos Shock Waves 2010;47:330–4. doi:10.1007/s10573- 010-0047-z.

[207] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous detonation in the regime of self- oscillatory ejection of the oxidizer. 1. Oxygen as a oxidizer. Combust Explos Shock Waves 2010;46:344–51. doi:10.1007/s10573-010-0047-z.

[208] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous detonation in the regime of self- oscillatory ejection of the oxidizer. 2. Air as an oxidizer. Combust Explos Shock Waves 2010;47:217–25. doi:10.1007/s10573-010-0047-z.

[209] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous Detonation in the Regime of Nonstationary Ejection of the Oxidizer. Combust Explos Shock Waves 2009;424:40–2. doi:10.1007/s10573-010-0047-z.

[210] Yetao S, Meng L, Wang J. Continuous detonation engine and effects of different types of nozzle on its propulsion performance. Chinese J Aeronaut 2010;23:647–52. doi:10.1016/S1000-9361(09)60266-1.

[211] Smith RD, Stanley S. Experimental Investigation of Continuous Detonation Rocket Engines for In-Space Propulsion. 52nd AIAA/SAE/ASEE Jt. Propuls. Conf., Salt Lake City, UT: 2016. doi:10.2514/6.2016-4582.

[212] Tsuboi N, Jourdaine NH, Watanabe T, Hayashi AK, Kojima T. Three-dimensional Numerical Simulation on Hydrogen-Oxygen Rotating Detonation Engine with Unchoked Aerospike Nozzle. 2018 AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2018. doi:10.2514/6.2018-1885.

[213] Stechmann D. Experimental study of high-pressure rotating detonation combustion in rocket environments. Purdue University, 2017.

[214] Ivanov VS, Aksenov VS, Frolov SM, Shamshin IO. Operation and performance of rotating

383

detonation rocket engine fueled by natural gas : experimental studies. 11th Int. Colloq. Pulsed Contin. Detonations, St. Petersburg, Russia: n.d., p. 121–35.

[215] Fotia ML, Kaemming T, Schauer F, Hoke JL. Study of the Experimental Performance of a Rotating Detonation Engine with Nozzled Exhaust Flow. 53rd AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2015. doi:10.2514/1.B35913.

[216] Kato Y, Ishihara K, Matsuoka K, Kasahara J, Matsuo A, Funaki I. Study of Combustion Chamber Characteristic Length in Rotating Detonation Engine with Convergent-Divergent Nozzle. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: 2016. doi:10.2514/6.2016-1406.

[217] Eto S, Tsuboi N, Kojima T, Hayashi AK. Three-Dimensional Numerical Simulation of a Rotating Detonation Engine: Effects of the Throat of a Converging-Diverging Nozzle on Engine Performance. Combust Sci Technol 2016;188:2105–16. doi:10.1080/00102202.2016.1213990.

[218] Anand V, Farbos De Luzan C, Babu L, St. George A, Driscoll R, Gutmark E. On Mean Pressure Shifts and Chugging Oscillations in Back-pressurized Rotating Detonation Combustors n.d.

[219] Braun EM, Lu FK, Wilson DR, Camberos JA. Airbreathing rotating detonation wave engine cycle analysis. Aerosp Sci Technol 2013;27:201–8. doi:10.1016/j.ast.2012.08.010.

[220] Fotia ML, Hoke J, Schauer F. Experimental Performance Scaling of Rotating Detonation Engines Operated on Gaseous Fuels. J Propuls Power 2017;33:1–10. doi:10.2514/1.B36213.

[221] Codoni JR, Cho KY, Hoke JL, Rankin BA, Schauer FR. Simultaneous mid-IR and OH chemiluminesence measurements within a RDE operating with and without backpressure. 2018 AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2018. doi:10.2514/6.2018-1882.

[222] Schwer DA, Corrigan AT, Kailasanath K. Towards Efficient, Unsteady, Three-Dimensional Rotating Detonation Engine Simulations. 52nd AIAA Aerosp Sci Meet 2014:1–17. doi:10.2514/6.2014-1014.

[223] Braun J, Saavedra Garcia J, Paniagua G. Evaluation of the unsteadiness across nozzles downstream of rotating detonation combustors. 55th AIAA Aerosp. Sci. Meet., Grapevine, Texas: 2017. doi:10.2514/6.2017-1063.

[224] Kindracki J. Temperature Measurements in the Detonation Chamber Supplied by air from

384

Centrifugal Compressor and Gaseous Hydrogen. Trans Inst Aviat 2017;3:7–23.

[225] Knowlen C, Wheeler E, Mendez D, Kurosaka M. Supersonic Exhaust Velocity in a Rotating Detonation Engine with constant area annulus. 2018 AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2018. doi:10.2514/6.2018-0884.

[226] Frolov SM, Zvegintsev VI, Ivanov VS, Aksenov VS, Shamshin IO, Vnuchkov DA, et al. Tests of the Hydrogen-Fueled Detonation Ramjet Model in a Wind Tunnel with Thrust Measurements. AIP Conf. Proc., vol. 20003, Novosibirsk, Russia: 2017.

[227] Frolov SM, Zvegintsev VI, Ivanov VS, Aksenov VS, Shamshin IO, Vnuchkov DA, et al. Wind tunnel tests of a hydrogen-fueled detonation ramjet model at approach air stream Mach numbers from 4 to 8. Int J Hydrogen Energy 2017;42:25401–13. doi:10.1016/j.ijhydene.2017.08.062.

[228] Frolov SM, Zvegintsev VI, Ivanov VS, Aksenov VS, Shamshin IO, Vnuchkov DA. Demonstrator of Continuous-Detonation Air-Breathing Ramjet : Wind Tunnel Data 2017;474:75–9. doi:10.1134/S0012501617050013.

[229] Tellefsen JR, King PI, Schauer FR, Hoke JL. Analysis of an RDE with Convergent Nozzle in Preparation for Turbine Integration. 50th AIAA Aerosp. Sci. Meet. Incl. New Horizons Forum Aerosp. Expo., Nashville, Tennessee: 2012. doi:10.2514/6.2012-773.

[230] DeBarmore ND, King PI, Schauer FR, Hoke JL. Nozzle Guide Vane Integration into Rotating Detonation Engine. 51st AIAA Aerosp. Sci. Meet. Incl. New Horizons Forum Aerosp. Expo., Grapevine, Texas: 2013.

[231] Zel’dovich Y. To the Question of Energy Use of Detonation Combustion. J Propuls Power 2006;22:588–92. doi:10.2514/1.22705.

[232] Knowlen C, Wheeler E, Mendez D, Kurosaka M. Supersonic Exhaust Velocity in a Rotating Detonation Engine. AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2018. doi:10.2514/6.2018- 0884.

[233] Anand V, St. George A, Driscoll R, Gutmark E. Investigation of rotating detonation combustor operation with H2 -Air mixtures. Int J Hydrogen Energy 2016;41:1281–92. doi:10.1016/j.ijhydene.2015.11.041.

385

[234] Arves J, Jones H, Arves J, Jones H. Explanation of the “DC shift” in hybrid motors. 33rd Jt. Propuls. Conf. Exhib., Seattle, Washington: 1997. doi:10.2514/6.1997-2938.

[235] Karabeyoglu A, Dyer J. Nonlinear Combustion in Hybrid Rockets – Explanation of Spontaneous Shifting in Motor Operation. 45th AIAA/ASME/SAE/ASEE Jt Propuls Conf Exhib 2009:AIAA 2009-5218. doi:10.2514/6.2009-5218.

[236] Greatrix D, Harris P. Structural vibration considerations for solid rocket internal ballistics modeling. 36th AIAA/ASME/SAE/ASEE Jt Propuls Conf Exhib 2000. doi:10.2514/6.2000- 3804.

[237] Malhotra S, Flandro G. On the origin of the DC shift. 33rd Jt. Propuls. Conf. Exhib., Seattle, Washington: 1997. doi:10.2514/6.1997-3249.

[238] Karnesky AL, Coluccif SE. Recent Occurrences of Combustion Instability in Solid Rocket Motors — An Overview. J Spacecr 1975;12:33–8. doi:doi:10.2514/6.1973-1296.

[239] Blomshield FS. Lessons Learned In Solid Rocket Combustion Instability. 43rd AIAA/ASME/SAE/ASEE Jt. Propuls. Conf., Cincinnati, OH: 2007.

[240] Baum JD, Levine JN, Lovine RL. Pulsed instability in rocket motors - A comparison between predictions and experiments. J Propuls Power 1988;4:308–16. doi:10.2514/3.23068.

[241] Jacob EJ, Flandro G a, Banuti D. Forced Resonant Shock Waves and Mean Pressure Shift in a Closed Tube. AIAA Pap 2007-5806 2007:3–8. doi:10.2514/6.2007-5806.

[242] Stechmann D, Lim D, Heister SD. Survey of Rotating Detonation Wave Combustor Technology and Potential Rocket Vehicle Applications. 50th AIAA/ASME/SAE/ASEE Jt. Propuls. Conf., Cleveland, OH: 2014. doi:10.2514/6.2014-3902.

[243] An S, Jin J, Lee J, Jo S, Park D, Kwon S. Chugging Instability of H2O2 Monopropellant Thrusters with Reactor Aspect Ratio and Pressures. J Propuls Power 2011;27:422–7. doi:10.2514/1.48939.

[244] Wood DJ, Dorsch RG. Effect of Propellant-Feed-System Coupling and Hydraulic Parameters on Analysis of Chugging. vol. NASA TN D-. Cleveland, Ohio: 1967.

[245] Wenzel LM, Szuch JR. Analysis of Chugging in Liquid-Bipropellant Rocket Engines Using Propellants with Different Vaporization Rates. 1965.

386

[246] Anand V, St. George A, Driscoll R, Gutmark E. Analysis of air inlet and fuel plenum behavior in a rotating detonation combustor. Exp Therm Fluid Sci 2016;70:408–16. doi:10.1016/j.expthermflusci.2015.10.007.

[247] Anand V, St. George A, Gutmark E. Amplitude modulated instability in reactants plenum of a rotating detonation combustor. Int J Hydrogen Energy 2017;42:12629–44. doi:10.1016/j.ijhydene.2017.03.218.

[248] Levin VA, Manuylovich IS, Markov V V. Numerical Simulation of Rotating Detonation under Variable Conditions. 26th ICDERS, Boston, MA: 2017.

[249] Li B, Wu Y, Weng C, Zheng Q, Wei W. Influence of equivalence ratio on the propagation characteristics of rotating detonation wave. Exp Therm Fluid Sci 2018;93:366–78. doi:10.1016/j.expthermflusci.2018.01.014.

[250] Anand V, St. George A, Driscoll R, Gutmark E. Characterization of instabilities in a Rotating Detonation Combustor. Int J Hydrogen Energy 2015;40:16649–59. doi:10.1016/j.ijhydene.2015.09.046.

[251] Anand V, George AS, Driscoll R, Randall S, Gutmark EJ. Statistical Treatment of Wave Instability in Rotating Detonation Combustors. 53rd AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2015. doi:doi:10.2514/6.2015-1103.

[252] Russo R. Operational characteristics of a rotating detonation engine using hydrogen and air. Air Force Institute of Technology, 2011.

[253] Hayashi AK, Kimura Y, Yamada T, Yamada E, Tangirala VE. Sensitivity Analysis of Rotating Detonation Engine with a Detailed Reaction Model. 47th AIAA Aerosp. Sci. Meet., Orlando, FL: 2009.

[254] Cho K, Codoni J, Rankin BA, Hoke J, Schauer F. Chemiluminescence Imaging of a Rotating Detonation Engine with Back Pressure. Int. Constant Vol. Detonation Combust. Work., Chasseneuil Du Poitou, France: 2017.

[255] Zhou S, Ma H, Li S, Liu D, Yan Y, Zhou C. Effects of a turbine guide vane on hydrogen-air rotating detonation wave propagation characteristics. Int J Hydrogen Energy 2017. doi:10.1016/j.ijhydene.2017.06.115.

387

[256] Suchocki JA, John Yu S-T, Hoke JL, Naples AG, Schauer FR, Russo R. Rotating Detonation Engine Operation. 50th AIAA Aerosp. Sci. Meet. Incl. New Horizons Forum Aerosp. Expo., Nashville, Tennessee: 2012. doi:10.2514/6.2012-119.

[257] Lin W, Zhou J, Liu S, Lin Z, Zhuang F. Experimental study on propagation mode of H2/Air continuously rotating detonation wave. Int J Hydrogen Energy 2015;40:1980–93. doi:10.1016/j.ijhydene.2014.11.119.

[258] Liu S-J, Lin Z-Y, Liu W-D, Lin W, Zhuang F-C. Experimental Realization of H 2 /Air Continuous Rotating Detonation in a Cylindrical Combustor. Combust Sci Technol 2012;184:1302–17. doi:10.1080/00102202.2012.682669.

[259] Liu S, Liu W, Lin Z, Lin W. Experimental Research on the Propagation Process of Continuous Rotating Detonation Wave. Combust Sci Technol 2015;187:1790–804. doi:10.1016/j.dt.2013.11.003.

[260] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous Spin Detonation in Annular Combustors. Combust Explos Shock Waves 2005;41:449–59. doi:10.1007/s10573-005-0055-6.

[261] Deng L, Ma H, Xu C, Liu X, Zhou C. The Feasibility of Mode Control in Rotating Detonation Engine. Appl Therm Eng 2018;129:1538–50. doi:10.1016/j.applthermaleng.2017.10.146.

[262] Han SYX, Wang YLJ. Numerical study of rotating detonation engine with an array of injection holes. Shock Waves 2016;27:467–76. doi:10.1007/s00193-016-0692-6.

[263] Yao S, Wang J. Multiple ignitions and the stability of rotating detonation waves. Appl Therm Eng 2016;108:927–36. doi:10.1016/j.applthermaleng.2016.07.166.

[264] Bluemner R, Bohon MD, Paschereit CO, Gutmark EJ. Single and Counter-Rotating Wave Modes in an RDC. 56th AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2018. doi:10.2514/6.2018-1608.

[265] Meholic G. MHD Power Generation Based on Pressure Gain Combustion Systems. DoE/NETL Magnetohydrodyn. Power Gener. Work., Arlington, VA: 2014.

[266] Canteins G. Etude de la detonation continue rotative - Application ’a la propulsion. University of Poiters, 2007.

[267] Wang Y. Rotating detonation in a combustor of trapezoidal cross section for the hydrogen-air

388

mixture. Int J Hydrogen Energy 2016;41:5605–16. doi:10.1016/j.ijhydene.2016.02.028.

[268] Lietz C, Mundis NL, Schumaker SA, Sankaran V. Numerical Investigation of Rotating Detonation Rocket Engines. AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2018. doi:10.2514/6.2018-0882.

[269] Theuerkauf SW, Schauer F, Anthony R, Hoke J. Experimental Characterization of High- Frequency Heat Flux in a Rotating Detonation Engine. 53rd AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2015. doi:10.2514/6.2015-1603.

[270] Knight E, Anand V, Jodele J, Malla B, Zahn A, St. George A, et al. Effect of corrugated outer wall on operating regimes of rotating detonation combustors. Int. Conf. Jets, Wakes Separated Flows, Cincinnati, OH: 2017.

[271] Zahn A, Knight E, Anand V, Jodele J, Gutmark E. Examination of Counter-Rotating DetonationWaves Using Cross-Correlation. Jt. Propuls. Conf., Cincinnati, OH: 2018.

[272] Wolf P, Staffelbach G, Balakrishnan R, Roux A. Azimuthal instabilities in annular combustion chambers. Proc. Summer Program, Cent. Turbul. Res. NASA AMES, Stanford University, USA: 2010, p. 259–69.

[273] Poinsot T. Prediction and control of combustion instabilities in real engines. Proc Combust Inst 2017;36:1–28. doi:10.1016/j.proci.2016.05.007.

[274] Sensiau C, Nicoud F, Poinsot T. A tool to study azimuthal standing and spinning modes in annular combustors. Int J Aeroacoustics 2009;8:57–67.

[275] Wolf P, Staffelbach G, Gicquel LYM, Müller J, Poinsot T. Acoustic and Large Eddy Simulation studies of azimuthal modes in annular combustion chambers. Combust Flame 2012;159:3398–413. doi:10.1016/j.combustflame.2012.06.016.

[276] Bykovskii F a, Zhdan S a, Vedernikov EF. Continuous Spin Detonation of Fuel – Air Mixtures. Combust Explos Shock Waves 2006;42:463–71. doi:10.1007/s10573-006-0076-9.

[277] Lee JH, Knystautas R, Yoshikawa N. Photochemical initiation of gaseous detonations. Acta Astronaut 1978;5:971–82. doi:10.1016/0094-5765(78)90003-6.

[278] Berndt P, Klein R. Modeling the kinetics of the Shockless Explosion Combustion. Combust Flame 2017;175:16–26. doi:10.1016/j.combustflame.2016.06.029.

389

[279] Anand V, Jodele J, Knight E, Prisell E, Lyrsell O, Gutmark E. Dependence of Pressure , Combustion and Frequency Characteristics on Valved Pulsejet Combustor Geometries. Flow, Turbul Combust 2018;100:829–48.

[280] Lores ME, Zinn BT. Lonlinear longitudinal combustion instability in rocket motors. 11th Aerosp. Sci. Meet., Washington D.C.: 1973.

[281] Berman K, Cheney Jr SH. Combustion Studies in Rocket Motors. J Am Rocket Soc 1953;23:89– 96. doi:10.2514/8.4549.

[282] Berman K, Logan SE. Combustion studies with a rocket motor having a full length observation window. J Am Rocket Soc 1952;22:78–85.

[283] Wang C, Liu W, Liu S, Jiang L, Lin Z. Experimental verification of air-breathing continuous rotating detonation fueled by hydrogen. Int J Hydrogen Energy 2015;40:9530–8. doi:10.1016/j.ijhydene.2015.05.060.

[284] Peng L, Wang D, Wu X, Ma H, Yang C. Ignition experiment with automotive spark on rotating detonation engine. Int J Hydrogen Energy 2015;40:8465–74. doi:10.1016/j.ijhydene.2015.04.126.

[285] Anand V, Gutmark E. Types of low frequency instabilities in rotating detonation combustors. Adv. Flow Combust. Control, 2018.

[286] Muralidhar K, Biswas G. Advanced Engineering Fluid Mechanics. Alpha Science International, Ltd; 2nd edition; 2005.

[287] Polifke W, Paschereit CO, Döbbeling K. Constructive and Destructive Interference of Acoustic and Entropy Waves in a Premixed Combustor with a Choked Exit. J Acoust Vib 2001;6:135– 46.

[288] Leonardi M, Nasuti F, Di Matteo F, Steelant J. A methodology to study the possible occurrence of chugging in liquid rocket engines during transient start-up. Acta Astronaut 2017;139:344– 56. doi:10.1016/j.actaastro.2017.07.027.

[289] Hulka JR, Jones GW. Performance and Stability Analyses of Rocket Thrust chamber with Oxygen/Methane Propellants. 46th AIAA/ASME/SAE/ASEE Jt. Propuls. Conf., Nashville, TN: 2010.

390

[290] St. George AC, Anand V, Driscoll RB, Gutmark EJ. A Correlation-Based Method to Quantify the Operating State in a Rotating Detonation Combustor. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: American Institute of Aeronautics and Astronautics; 2016. doi:10.2514/6.2016-1402.

[291] Naples A, Hoke J, Schauer F. Experimental Investigation of a Rotating Detonation Engine Fuel Injector Temporal Response. 53rd AIAA Aerosp Sci Meet 2015:1–7.

[292] Randall S, Anand V, St. George AC, Gutmark EJ. Numerical and Experimental Study of Heat Transfer in a Rotating Detonation Engine. 53rd AIAA Aerosp. Sci. Meet., Kissimmee, Florida: American Institute of Aeronautics and Astronautics; 2015. doi:10.2514/6.2015-0880.

[293] Bykovskii FA, Vedernikov EF. Heat fluxes to combustor walls during continuous spin detonation of fuel-air mixtures. Combust Explos Shock Waves 2009;45:70–7. doi:10.1007/s10573-009-0010-z.

[294] Falempin F, Daniau E. A Contribution to the Development of Actual Continuous Detonation Wave Engine. 15th AIAA Int. Sp. Planes Hypersonic Syst. Technol. Conf., Dayton, Ohio: 2008. doi:10.2514/6.2008-2679.

[295] Ishihara K, Nishimura J, Goto K, Nakagami S, Matsuoka K, Kasahara J, et al. Study on a Long- time Operation Towards Rotating Detonation Rocket Engine Flight Demonstration. 55th AIAA Aerosp. Sci. Meet., Grapevine, Texas: 2017. doi:10.2514/6.2017-1062.

[296] Theuerkauf S, King PI, Schauer FR, Hoke JL. Thermal Management for a Modular Rotating Detonation Engine. 51st AIAA Aerosp. Sci. Meet. Incl. New Horizons Forum Aerosp. Expo., Grapevine, Texas: 2013.

[297] Clafli S. Recent progress in continuous detonation engine development at Pratt and Whitney Rocketdyne. Int. Work. detonation Propuls., Tsukaba, Japan: 2012.

[298] Goldenstein CS, Almodóvar CA, Jeffries JB, Hanson RK, Brophy CM. High-bandwidth scanned- wavelength-modulation spectroscopy sensors for temperature and H2O in a rotating detonation engine. Meas Sci Technol 2014;25:1–11. doi:10.1088/0957- 0233/25/10/105104.

[299] McGahan CJ, Tom BA, Caswell AW, Gord JR, Schauer FR, Hoke JL. Exhaust gas analysis of a rotating detonation engine using tunable diode laser absorption spectroscopy. 52nd AIAA Aerosp. Sci. Meet. - AIAA Sci. Technol. Forum Expo. SciTech, National Harbor, Maryland:

391

2014.

[300] Rein KD, Roy S, Sell B, Hoke JL, Caswell AW, Schauer FR. Time-Resolved In-Situ Absorption Spectroscopy of a Hydrogen-Air Rotating Detonation Engine using a Fiber- Coupled Tunable Laser System, San Diego, CA: 2016. doi:10.2514/6.2016-1199.

[301] Rein KD, Roy S, Hoke J, Caswell AW, Schauer F, Gord JR. Multi-beam Temperature Measurements in a Rotating Detonation Engine Using H 2 O Absorption Spectroscopy. 55th AIAA Aerosp. Sci. Meet., Grapevine, Texas: 2017. doi:10.2514/6.2017-1064.

[302] Roy A, Strakey P, Sidwell T, Ferguson D. Unsteady Heat Transfer Analysis to Predict Combustor Wall Temperature in Rotating Detonation Engine. 51st AIAA/SAE/ASEE Jt. Propuls. Conf. AIAA, Orlando, FL: 2015.

[303] Rankin BA, Codoni JR, Cho KY, Hoke J, Schauer FR. Mid-Infrared Imaging of an Optically Accessible Non-Premixed Hydrogen-Air Rotating Detonation Engine. 55th AIAA Aerosp. Sci. Meet., Grapevine, TX: 2017. doi:10.2514/6.2017-0370.

[304] Stevens CA, Fotia M, Hoke J, Schauer F. Quasi Steady Heat Transfer Measuments in an RDE. 2018 AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2018. doi:10.2514/6.2018-1884.

[305] Meyer SJ, Polanka MD, Schauer F, Anthony RJ, Stevens CA, Hoke J, et al. Experimental Characterization of Heat Transfer Coefficients in a Rotating Detonation Engine. 55th AIAA Aerosp. Sci. Meet., Grapevine, Texas: American Institute of Aeronautics and Astronautics; 2017. doi:10.2514/6.2017-1285.

[306] Theuerkauf SW, Schauer FR, Anthony R, Hoke JL, Engine D, Engine PD, et al. Average and Instantaneous Heat Release to the Walls of an RDE. 52nd Aerosp. Sci. Meet., National Harbor, Maryland: 2014.

[307] Theuerkauf SW, Schauer F, Anthony RJ, Paxson DE, Stevens CA, Hoke J. Comparison of Simulated and Measured Instantaneous Heat Flux in a Rotating Detonation Engine. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: 2016. doi:10.2514/6.2016-1200.

[308] Meyer SJ, Polanka MD, Schauer FR, Hoke JL. Parameter Impact on Heat Flux in a Rotating Detonation Engine. 2018 AIAA Aerosp. Sci. Meet., Kissimmee, Florida: 2018. doi:10.2514/6.2018-0400.

392

[309] Schwer DA, Kailasanath K. Physics of Heat-Release in Rotating Detonation Engines. 53rd AIAA Aerosp. Sci. Meet., Reston, Virginia: American Institute of Aeronautics and Astronautics; 2015. doi:10.2514/6.2015-1602.

[310] Cho KY, Codoni JR, Rankin BA, Hoke JL, Schauer FR. High-Repetition-Rate Chemiluminesence Imaging of a Rotating Detonation Engine. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: 2016. doi:10.2514/6.2016-1648.

[311] Wang Y, Wang J, Qiao W. Effects of thermal wall conditions on rotating detonation. Comput Fluids 2016;140:59–71. doi:10.1016/j.compfluid.2016.09.008.

[312] Schwer DA, Kailasanath K. Characterizing NOx Emissions for Air-Breathing Rotating Detonation Engines. 52nd AIAA/SAE/ASEE Jt. Propuls. Conf., Salt Lake City, UT: 2016. doi:10.2514/6.2016-4779.

[313] Jachimowski CJ. An Analytical Study of the Hydrogen-Air reaction Mechanism with Application to Scramjet Combustion. Hampton, Virginia: 1988.

[314] Yungster S, Radhakrishnan K, Breisacher K. Computational and Experimental Study of NOx Formation in Hydrogen-Fueled Pulse Detonation Engines. 40th AIAA/ASME/SAE/ASEE Jt Propuls Conf Exhib 2004:1–17. doi:10.2514/6.2004-3307.

[315] Correa SM. A review of NOx formation under gas-turbine combustion conditions. Combust Sci Technol 1993;87:329–62. doi:10.1080/00102209208947221.

[316] Pandiya N, St. George AC, Driscoll RB, Anand V, Malla B, Gutmark EJ. Efficacy of Acoustics in Determining the Operating Mode of a Rotating Detonation Engine. 54th AIAA Aerosp. Sci. Meet., San Diego, CA: 2016. doi:10.2514/6.2016-1649.

[317] Bykovskii FA, Vedernikov EF, Polozov S V. Noise and vibrations in a combustor with continuous spin detonation combustion of the fuel. Combust Explos Shock Waves 2006;42:582–93. doi:10.1007/s10573-006-0090-y.

[318] Frolov SM, Aksenov VS, Dubrovskii A V., Zangiev AE, Ivanov VS, Medvedev SN, et al. Chemiionization and acoustic diagnostics of the process in continuous- and pulse-detonation combustors. Dokl Phys Chem 2015;465:273–8. doi:10.1134/S0012501615110019.

[319] Lighthill MJ. On Sound Generated Aerodynamically. I. General Theory. Proc R Soc A Math

393

Phys Eng Sci 1952;211:564–87. doi:10.1098/rspa.1952.0060.

[320] Heiser WH, Pratt DT. Thermodynamic Cycle Analysis of Pulse Detonation Engines. J Propuls Power 2002;18:68–76.

[321] Schwer DA, Kailasanath K. Numerical Investigation of Rotating Detonation Engine. 46th AIAA/ASME/SAE/ASEE Jt. Propuls. Conf. Exhib., Nashville, TN: 2010. doi:10.1080/00102202.2010.497316.

[322] Frolov SM, Aksenov VS, Ivanov VS, Shamshin IO. Large-scale hydrogen–air continuous detonation combustor. Int J Hydrogen Energy 2015;40:1616–23. doi:10.1016/j.ijhydene.2014.11.112.

[323] St. George AC, Driscoll RB, Munday DE, Gutmark EJ. Development of a Rotating Detonation Engine Facility at the University of Cincinnati. 53rd AIAA Aerosp. Sci. Meet., Kissimmee, Florida: American Institute of Aeronautics and Astronautics; 2015. doi:10.2514/6.2015- 0635.

[324] Ciccarelli G, Ginsburg T, Boccio J, Economos C, Finfrock C, Gerlach L, et al. High-Temperature Hydrogen-Air- Steam Detonation Experiments in the BNL Small-Scale Development Apparatus. Nureg/Cr-6213 Bnl-Nureg-42414 1994.

[325] Nordeen C. Thermodynamics of a Rotating Detonation Engine. Univ Connect Dr Diss 2013:201. doi:oai:digitalcommons.uconn.edu:dissertations-6482.

[326] Wang J-P, Shao Y-T. Rotating Detonation Engine Injection Velocity Limit and Nozzle Effects on Its Propulsion Performance. Comput. Fluid Dyn. 2010, Berlin, Heidelberg: Springer Berlin Heidelberg; 2011, p. 789–95. doi:10.1007/978-3-642-17884-9_100.

[327] Tellefsen J. Build up and operation of an axial turbine driven by a rotary detonation engine. Air Force Institute of Technology, 2012.

[328] Ng HD. The effect of chemical reaction kinetics on the structure of gaseous detonations. vol. 68. 2005.

[329] Ng HD, Ju Y, Lee JHS. Assessment of detonation hazards in high-pressure hydrogen storage from chemical sensitivity analysis. Int J Hydrogen Energy 2007;32:93–9. doi:10.1016/J.IJHYDENE.2006.03.012.

394

[330] Welsh DJ, King PI, Debarmore ND, Schauer FR, Hoke JL, Engineer M, et al. RDE Integration with T63 Turboshaft Engine Components. 52nd Aerosp Sci Meet 2014:1–10.

[331] Wang YH, Wang JP. Rotating Detonation Instabilities in Hydrogen-Oxygen Mixture. Appl Mech Mater 2014;709:56–62. doi:10.4028/www.scientific.net/AMM.709.56.

[332] Anand V, Driscoll R, George AS, Gutmark E. Experimental investigation of H2-Air mixtures in a rotating detonation combustor. Proc. ASME Turbo Expo, vol. 4B, 2015. doi:10.1115/GT201543614.

[333] Rankin BA, Fotia ML, Paxson DE, Hoke JL, Schauer FR. Experimental and Numerical Evaluation of Pressure Gain Combustion in a Rotating Detonation Engine. 53rd AIAA Aerosp Sci Meet 2015:1–17.

[334] Naples A, Hoke J, Schauer F. Rotating Detonation Engine Interaction with an Annular Ejector. 52nd Aerosp. Sci. Meet., National Harbor, Maryland: American Institute of Aeronautics and Astronautics; 2014. doi:10.2514/6.2014-0287.

[335] Stevens CA, Fotia M, Hoke J, Schauer F. Comparison of Transient Response of Pressure Measurement Techniques with Application to Detonation Waves. 53rd AIAA Aerosp. Sci. Meet., Reston, Virginia: American Institute of Aeronautics and Astronautics; 2015. doi:10.2514/6.2015-1102.

[336] Alster M. Improved calculation of resonant frequencies of Helmholtz resonators. J Sound Vib 1972;24:63–85. doi:10.1016/0022-460X(72)90123-X.

[337] Paxson DE. Numerical Analysis of a Rotating Detonation Engine in the Relative Reference Frame. 52nd Aerosp. Sci. Meet., National Harbor, Maryland: American Institute of Aeronautics and Astronautics; 2014. doi:10.2514/6.2014-0284.

[338] Kuznetsov MS, Alekseev VI, Dorofeev SB, Matsukov ID, Boccio JL. Detonation propagation, decay, and reinitiation in nonuniform gaseous mixtures. Symp Combust 1998;27:2241–7. doi:10.1016/S0082-0784(98)80073-8.

[339] Bartenev AM, Gelfand BE. Spontaneous initiation of detonations. Prog Energy Combust Sci 2000;26:29–55. doi:10.1016/S0360-1285(99)00007-6.

[340] Kuznetsov MS, Dorofeev SB, Efimenko a. a., Alekseev VI, Breitung W. Experimental and

395

numerical studies on transmission of gaseous detonation to a less sensitive mixture. Shock Waves 1997;7:297–304. doi:10.1007/s001930050084.

[341] Voitsekhovskii BV. Maintained Detonations. Sov Phys Dokaldy 1959;129:1254–6.

[342] Li Y, Wang Y, Wang J, Li Y. Detonation Instability of Continuously Rotating Detonation Engines for H 2 -Air mixture. Int Invent J Eng Sci Technol 2014;1:1–7.

[343] Boshoff-Mostert L, Viljoen HJ. Analysis of combustion-driven acoustics. Chem Eng Sci 1998;53:1679–87. doi:10.1016/S0009-2509(98)00015-3.

[344] Randall S, Anand V, St. George AC, Gutmark EJ. Numerical Study of Heat Transfer in a Rotating Detonation Combustor. 53rd AIAA Aerosp Sci Meet 2015:1–12. doi:10.2514/6.2015-0880.

[345] Stevens CA, Fotia ML, Hoke JL, Schauer FR. Comparison of Transient Response of Pressure Measurement Techniques with Application to Detonation Waves. AIAA Aerosp Sci Meet 2015;5:2015–1102. doi:10.2514/6.2015-1102.

[346] MARIAPPAN S, SUJITH RI. Thermoacoustic instability in a solid rocket motor: non-normality and nonlinear instabilities. J Fluid Mech 2010;653:1–33. doi:10.1017/S0022112010000133.

[347] Gruber S. Weak shock wave reflection from concave surfaces 2013. doi:10.1007/s00348- 013-1571-x.

[348] Stevens CA, Fotia ML, Hoke JL, Schauer FR. Comparison of Transient Response of Pressure Waves. 53rd AIAA Aerosp Sci Meet 2015:1–10.

[349] Polifke W. Black-box system identification for reduced order model construction. Ann Nucl Energy 2014;67:109–28. doi:10.1016/j.anucene.2013.10.037.

[350] Zouak M, Mechaqrane A. A comparison of linear and neural network ARX models applied to a prediction of the indoor temperature of a building. Neural Comput Appl 2004;13:32–7. doi:10.1007/s00521-004-0401-8.

[351] Eager D, Pendrill A-M, Reistad N. Beyond velocity and acceleration: jerk, snap and higher derivatives. Eur J Phys 2016;37:65008. doi:10.1088/0143-0807/37/6/065008.

[352] Barrére M, Williams FA. Comparison of combustion instabilities found in various types of

396

combustion chambers. Symp Combust 1969;12:169–81. doi:10.1016/S0082- 0784(69)80401-7.

[353] Zeldovich YB. To the Question of Energy Use of Detonation Combustion. J Propuls Power n.d.;22:1453–61. doi:10.2514/1.22705.

[354] Anand V, George AS, Farbos De Luzan C, Gutmark E. Rotating detonation wave mechanics through ethylene-air mixtures in hollow combustors, and implications to high frequency combustion instabilities. Exp Therm Fluid Sci 2018;92:314–25.

[355] Barrère M, Williams FA. Comparison of combustion instabilities found in various types of combustion chambers. Symp Combust 1969;12:169–81. doi:10.1016/S0082- 0784(69)80401-7.

[356] Baum JD, Levine JN, Force A, Afb E, Lovine RL, Systems AT, et al. Pulse Triggered Instability in Solid Propellant Rocket Motors AIAA / SAE / ASME 18th Joint Propulsion Conference 1982.

[357] Taylor GI. Statistical theory of turbulence. Proc R Soc London A Math Phys Eng Sci 1935;151:421–44.

[358] Selle L, Benoit L, Poinsot T, Nicoud F, Krebs W. Joint use of compressible large-eddy simulation and Helmholtz solvers for the analysis of rotating modes in an industrial swirled burner. Combust Flame 2006;145:194–205. doi:10.1016/j.combustflame.2005.10.017.

[359] Ghani A, Poinsot T, Gicquel L, Staffelbach G. LES of longitudinal and transverse self-excited combustion instabilities in a bluff-body stabilized turbulent premixed flame. Combust Flame 2015;162:4075–83. doi:10.1016/j.combustflame.2015.08.024.

[360] Kumar K. Global Combustion Responses of Practical Hydrocarbon Fuels: n-Heptane, iso- Octane, n-Decane, n-Dodecane and Ethylene 2007:195.

[361] S. Seo. Investigation of Self-Excited Combustion Instabilities in Two Different Combustion Systems. KSME Int J 2004;18:1246–57.

[362] Sugiyama Y, Matsuo A. Numerical study of acoustic coupling in spinning detonation propagating in a circular tube. Combust Flame 2013;160:2457–70. doi:10.1016/j.combustflame.2013.06.003.

397

[363] Ul’yanitskii VY. Experimental investigation of the volumetric structure of a spinning detonation. Combust Explos Shock Waves 1980;16:99–103. doi:10.1007/BF00756251.

[364] Nikolaev YA, Topchiyan ME, Ul’yanitskii VY. Experimental investigation and calculation of triple configurations of spin detonation. Combust Explos Shock Waves 1978;14:790–3. doi:10.1007/BF00786114.

[365] Huang ZW, Lefebvre MH, Van Tiggelen PJ. Experiments on spinning detonations with detailed analysis of the shock structure. Shock Waves 2000;10:119–25. doi:10.1007/s001930050185.

[366] Kitano S, Fukao M, Susa A, Tsuboi N, Hayashi AK, Koshi M. Spinning detonation and velocity deficit in small diameter tubes. Proc Combust Inst 2009;32 II:2355–62. doi:10.1016/j.proci.2008.06.119.

[367] Kasimov AR, Stewart DS. Spinning instability of gaseous detonations. J Fluid Mech 2002;466:179–203. doi:10.1017/S0022112002001192.

398