Investigation of Various Novel Air-Breathing Propulsion Systems

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

MASTER OF SCIENCE

in the Department of Aerospace Engineering & Engineering Mechanics of the College of Engineering and Applied Science

2016

by Jarred M. Wilhite B.S. Aerospace Engineering & Engineering Mechanics University of Cincinnati 2016

Committee Chair: Dr. Ephraim Gutmark Committee Members: Dr. Paul Orkwis & Dr. Mark Turner Abstract

The current research investigates the operation and performance of various air-breathing propulsion systems, which are capable of utilizing different types of fuel. This study first focuses on a modular RDE configuration, which was mainly studied to determine which conditions yield stable, continuous rotating detonation for an ethylene-air mixture. The performance of this RDE was analyzed by studying various parameters such as mass flow rate, equivalence ratios, wave speed and cell size. For relatively low mass flow rates near stoichiometric conditions, a rotating detonation wave is observed for an ethylene-RDE, but at speeds less than an ideal detonation wave.

The current research also involves investigating the newly designed, Twin Oxidizer Injection Capable

(TOXIC) RDE. Mixtures of hydrogen and air were utilized for this configuration, resulting in sustained rotating detonation for various mass flow rates and equivalence ratios. A thrust stand was also developed to observe and further measure the performance of the TOXIC RDE. Further analysis was conducted to accurately model and simulate the response of thrust stand during operation of the RDE.

Also included in this research are findings and analysis of a propulsion system capable of operating on the Inverse Brayton Cycle. The feasibility of this novel concept was validated in a previous study to be sufficient for small-scale propulsion systems, namely UAV applications. This type of propulsion system consists of a reorganization of traditional gas turbine engine components, which incorporates expansion before compression. This cycle also requires a heat exchanger to reduce the temperature of the flow entering the compressor downstream. While adding a heat exchanger improves the efficiency of the cycle, it also increases the engine weight, resulting in less endurance for the aircraft. Therefore, this study focuses on the selection and development of a new heat exchanger design that is lightweight, and is capable of transferring significant amounts of heat and improving the efficiency and performance of the propulsion system.

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Acknowledgements

First and foremost, I would like to acknowledge and thank Dr. Ephraim Gutmark. He has been an excellent advisor who has provided me with meaningful and interesting research opportunities, which have funded me throughout my time as a graduate student. I would also like to thank Dr. Paul Orkwis and

Dr. Mark Turner for serving on my thesis committee. Each of my committee members are great professors. I really enjoyed their classes, and was able to learn a lot from both of them.

I would like to acknowledge Andrew St. George and Robbie Driscoll, who introduced me to detonation research, and gave me helpful advice to effectively conduct research and write research papers.

I would also like to thank my fellow detonation research team members, including Vijay Anand, William

Stoddard, Ethan Knight, and Justas Jodele for their encouragement, great advice and willingness to help me complete my experiments. I also thank Kranthi Yellugari for his assistance and willingness to work with me on heat exchanger design and analysis.

I am very grateful for the help and assistance from Ron Hudepohl whose guidance in the machine shop was very essential in machining parts for the thrust stand and RDE. I also appreciate the technical knowledge and support that I received from Mark Grooms and Curt Fox in the Gas Dynamics &

Propulsion Laboratory. I would also like to thank my fellow lab mates for their support and friendship throughout my time in graduate school.

I would also like to acknowledge Dr. Dunn, Mr. Simonson, Ms. Christine Johnson, Dr. Brandi Elliott and Dr. Eric Abercrumbie for their emotional support, encouragement and invaluable mentorship since my freshman year at the University of Cincinnati.

Lastly, I dedicate this thesis to my parents, Charles & Myrita, my brother, Justin, and the rest of my family for being an extremely positive influence in my life, and their genuine interest and constant encouragement to succeed and excel in all of my endeavors, especially academics. I also dedicate this to the love of my life, Devaki, who motivates and inspires me to pursue my dreams.

Table of Contents

Abstract ...... ii Acknowledgements ...... iv Table of Contents ...... v List of Figures...... vii List of Tables ...... x List of Symbols ...... xi Chapter 1: Introduction ...... 1 1.1 Rotating Detonation Engine (RDE) ...... 1 1.2 One-Dimensional Analysis ...... 3 a) Detonation Theory ...... 3 b) Hugoniot Curve ...... 5 c) ZND Theory ...... 8 1.3 Three-Dimensional Detonation Structure ...... 9 1.4 Thermodynamic Cycle Analysis ...... 12 a) The Detonation Cycle ...... 13 b) The Inverse Brayton Cycle ...... 15 1.5 RDE Literature ...... 17 1.6 Thrust in Detonation Engines...... 19 1.7 Research Objectives ...... 23 a) Rotating Detonation Engine ...... 23 b) Inverse Brayton Cycle Propulsion System ...... 24 Chapter 2: Experimental Methodology ...... 26 2.1 University of Cincinnati Detonation Test Facility ...... 26 a) Test Bunker & Safety Features ...... 26 b) Low Mass Flow System ...... 28 c) High Mass Flow System ...... 31 d) Data Acquisition (DAQ) and Control System ...... 33 2.2 Experimental Setup ...... 34

a) Instrumentation ...... 36 b) RDE Detonation Initiation ...... 37 2.3 Thrust Stand ...... 38 a) Structure...... 38 b) Linear Variable Different Transformer (LVDT) ...... 40 c) Signal Conditioning ...... 42 d) Calibration...... 44 e) Vibration Analysis ...... 50 2.4 Inverse Brayton Cycle Based Propulsion System...... 52 a) Heat Exchanger Design ...... 52 b) Inverse Brayton Cycle Simulation ...... 55 Chapter 3: Results & Discussion ...... 57 3.1 Ethylene-Air Modular RDE Study ...... 57 a) Operating Map ...... 57 b) Wave Speed Performance ...... 58 c) Detonation Cell Size, Fill Height and Pressure Ratio ...... 60 3.2 Inverse Brayton Cycle Turbojet Study ...... 62 a) Specific IBC Turbojet Case ...... 62 b) Various IBC Turbojet Cases ...... 66 c) Comparison to Similar Turbojets...... 73 3.3 Hydrogen-Air TOXIC RDE Thrust Study ...... 75 a) RDE Operation ...... 75 b) Simulation of Thrust Stand Response to RDE ...... 79 Chapter 4: Conclusions & Recommendations ...... 83 4.1 Ethylene-Air Modular RDE Study ...... 83 4.2 Inverse Brayton Cycle Turbojet Study ...... 84 4.3 Hydrogen-Air TOXIC RDE Thrust Study ...... 87 References...... 89

List of Figures Figure 1.1: PDE process [3] ...... 2 Figure 1.2: RDE process [3] ...... 3 Figure 1.3: Schematic diagram of a stationary, one-dimensional combustion wave [7] ...... 4 Figure 1.4: Rankine-Hugoniot curve (adapted from [8]) ...... 6 Figure 1.5: ZND detonation structure [7] ...... 9 Figure 1.6: Detonation wave structure obtained from smoked-foil technique [7] ...... 10 Figure 1.7: Triple point of a detonation wave [9] ...... 10 Figure 1.8: Cellular pattern of a detonation structure [7] ...... 11 Figure 1.9: Minimum cell size requirements for detonation in confined geometry [12] ...... 12 Figure 1.10: Ideal Thermodynamic Cycles on Temperature-Entropy (T-s) Diagram [1] ...... 14 Figure 1.11: Thermal Efficiency of each thermodynamic cycle vs. Compression static temperature-rise ratio [1] ...... 15 Figure 1.12: Schematic of the Inverse Brayton Cycle [13] ...... 16 Figure 1.13: T-s diagram of the ideal Inverse Brayton Cycle [13] ...... 16 Figure 1.14: Schematic of two-dimensional flow field within RDE [17] ...... 18 Figure 1.15: Thrust stand setup for PDE ejector experiment [20] ...... 20 Figure 1.16: Load cell response for one detonation run [24]...... 21 Figure 1.17: Thrust-time profile for methane-oxygen mixture at ϕ = 1.65 [5] ...... 22 Figure 1.18: Desired Power Density & SFC – Efficient Small-Scale Propulsion (ESSP) Vehicles [27].... 24 Figure 2.1: RDE contained within the UC Detonation Test Facility ...... 26 Figure 2.2: Schematic of the UC Detonation Facility [25] ...... 27 Figure 2.3: Last-chance valves for oxygen, fuel and nitrogen ...... 29 Figure 2.4: Gaseous fuel control panel ...... 30 Figure 2.5: High mass flow metering system ...... 33 Figure 2.6: SolidWorks Model of TOXIC RDE Assembly ...... 34 Figure 2.7: Schematic of the RDE Geometry & Instrumentation Layout [27] ...... 37 Figure 2.8: SolidWorks model of the thrust stand ...... 38 Figure 2.9: Interior view of the thrust stand model ...... 39 Figure 2.10: LVDT Placement inside Thrust Stand ...... 41

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Figure 2.11: Schematic of Internal Structure of LVDT [31] ...... 42 Figure 2.12: LDX-3A Signal Conditioner ...... 43 Figure 2.13: Thrust Stand Calibration Setup ...... 44 Figure 2.14: Calibration Curve for springs with k = 10 lbs/in without RDE apparatus ...... 46 Figure 2.15: Calibration Curve for springs with k = 35.6 lbs/in without RDE apparatus ...... 46 Figure 2.16: Calibration Curve for springs with k = 62.8 lbs/in without RDE apparatus ...... 47 Figure 2.17: Calibration Curve for springs with k = 10 lbs/in with RDE apparatus ...... 48 Figure 2.18: Calibration Curve for springs with k = 35.6 lbs/in with RDE apparatus...... 49 Figure 2.19: Calibration Curve for springs with k = 62.8 lbs/in with RDE apparatus...... 49 Figure 2.20: Simulink model used to simulate thrust stand operation ...... 50 Figure 2.21: System response with T= 300 lbs., m = 125 kg, k= 125.6 lbs/in and c = 12.8 lbs-s/in ...... 52 Figure 2.22: Heat exchanger variation chart [35] ...... 53 Figure 2.23: Single module of the microchannel heat exchanger [36] ...... 54 Figure 2.24: Simscape model of Inverse Brayton Cycle ...... 55 Figure 3.1: Pressure-time traces for successful test at ṁ = 0.2 kg/s: ...... 57 a) PCB pressure traces and b) Ion probe measurements ...... 57 Figure 3.2: Operating Map of Non-Premixed Ethylene-Air RDE ...... 58 Figure 3.3: Detonation wave speed vs. equivalence ratio ...... 59 Figure 3.5: Ratio of channel width to cell size for varying values ...... 61 Figure 3.6: Air injection pressure ratio ...... 62 Figure 3.7: Schematic of Heat Transfer through Recuperator and Ambient Heat Exchanger ...... 65 Figure 3.9: Specific thrust vs. Normalized compressor inlet temperature ...... 69 Figure 3.10: TSFC vs. Normalized compressor inlet temperature ...... 69 Figure 3.11: Thermal efficiency vs. Power output...... 71 Figure 3.12: Compressor inlet temperature vs. Power output ...... 71 Figure 3.13: Range of flight vs. Heat exchanger effectiveness...... 72 Figure 3.14: Pressure-time traces for successful test at ṁ = 0.47 kg/s and ϕ = 1.23 ...... 75 Figure 3.14: Thrust-time profile for successful test at ṁ = 0.2 kg/s and ϕ = 1 for k = 62.5 lbs/in ...... 76 Figure 3.15: Thrust-time profiles for two successful tests for k = 10 lbs/in: ...... 77

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Figure 3.16: Thrust-time profiles for two successful tests for k = 10 lbs/in: ...... 78 Figure 3.17: Simplified SolidWorks model of RDE stand and top plate of thrust stand ...... 80 Figure 3.18: Simulation results showing deflection of entire system with RDE thrust output of 300 lbs. . 80 Figure 3.19: Deflection of top plate of thrust stand with RDE thrust output of 300 lbs...... 81

List of Tables

Table 1.1: Data showing qualitative differences between detonation and deflagration [7] ...... 4 Table 3.1: Atmospheric Conditions defined for IBC Turbojet Simulation ...... 62 Table 3.2: Pressure Values for IBC obtained from Simscape Model ...... 63 Table 3.3: Heat Transfer Rates for Recuperator and Ambient Heat Exchanger ...... 65 Table 3.4: Inlet & Outlet Temperatures for IBC Turbojet Components ...... 66 Table 3.5: Performance Comparison of Turbojets ...... 73 Table 3.6: Thrust Produced During Combustion for Various Conditions ...... 79 Table 3.7: Deflection in Top Plate of Thrust Stand ...... 82

List of Symbols

Acronyms CEA Chemical and Equilibrium Analysis CMC Ceramic Matrix Composites CTAP Capillary Tube Averaged Pressure CCTV Closed-Circuit Television CFD Computational Fluid Dynamics C-J Chapman-Jouguet DDT Deflagration-to-Detonation Transition DoD Department of Defense ESSP Efficient Small-Scale Propulsion IP Ingress Protection IBC Inverse Brayton Cycle LRE Liquid-propellant Rocket Engine LVDT Linear Variable Differential Transformer MAV Micro Air Vehicles MSD Multiple Spark Ignition PDE Pulse Detonation Engine RBC Recuperated Brayton Cycle RDE Rotating Detonation Engine SFC Specific Fuel Consumption TSFC Thrust Specific Fuel Consumption TOXIC Twin OXidizer Injection Capable UAV Unmanned Aerial Vehicle ZND Zel’dovich-von Neumann-Döring

Variables a speed of sound

xi c damping constant C heat capacity rate cp specific heat at constant pressure D drag force F force f fuel-air ratio Fsp specific thrust fF force fraction g acceleration due to gravity gc proportionality constant h fill height Isp specific impulse k spring constant L lift force ṁ mass flow rate M Mach number P pressure

PRair air injection pressure ratio q heat release 푞̇ rate of heat transfer R individual gas constant for air s entropy T temperature T thrust u flow velocity W combustion wave speed w weight wch channel width

푊̇ 표푢푡 power output x displacement

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푥̇ velocity 푥̈ acceleration Greek Symbols γ ratio of specific heats for air 휀 heat exchanger effectiveness λ cell size

ηth thermal efficiency ρ density 1/ρ specific volume τ total temperature ratio ϕ equivalence ratio Ψ compression static temperature-rise ratio

Subscripts 0 flow properties of air at atmospheric conditions 1 flow properties upstream of detonation wave 2 flow properties downstream of detonation wave act actual c,in/out flow properties of cold side fluid entering/exiting heat exchanger c compressor d damper h,in/out flow properties of hot side fluid entering/exiting heat exchanger m RDE mass max maximum min minimum r freestream s spring t turbine tot total

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Chapter 1: Introduction

1.1 Rotating Detonation Engine (RDE)

Detonation research has recently begun to focus its efforts towards studying the Rotating Detonation

Engine (RDE). The RDE is a device that utilizes the detonation mode of combustion, which allows for increased thermal efficiency due to greater work availability, less entropy generation over the cycle and pressure gain combustion [1]. These are advantages that the RDE possesses over modern combustors, which operate by combusting mixtures at nearly constant pressure via deflagration. Countless experiments and studies have been focused towards determining how to best utilize this pressure gain to extract the theoretically higher work output by RDEs [2].

A pulse detonation engine or PDE is another device, which utilizes the detonation mode of combustion. Initially, a majority of detonation research focused on the PDE. However, this focus began to shift to the RDE when clear, significant advantages were discovered to using the RDE over the PDE. The

PDE operates with the following five distinct phases: Fill, Ignition, Deflagration-to-Detonation Transition

(DDT), Expansion & Exhaust, and Purge [3]. First, the detonation tube is filled with a reactive mixture of fuel and oxidizer, which is then ignited. The flame propagates down the tube at increasing speed, and transitions from a subsonic deflagration to a supersonic detonation wave (DDT). As the detonation propagates down the remainder of the tube, the products expand within the tube and exhaust out of the tube exit. Finally, the hot combustion products are purged out of the tube in order to prevent auto-ignition when the cycle is repeated. This last phase is not required if the temperature of the combustion products can be cooled down by an outside source. A schematic of this process is shown in Figure 1.

Figure 1.1: PDE process [3]

The maximum operating frequency of a PDE depends on cycle timing and is usually within the range of 100 Hz [2]. This low frequency can cause instabilities or high-amplitude pressure oscillations through the operating cycle, which can reduce the power extraction efficiency of the PDE [4]. Furthermore, the overall process of a PDE is very distinct and segmented, and must be constantly ignited from an outside source for each run.

The RDE typically uses an annular combustion chamber, which is a simpler design than the long detonation tube used for a PDE [3]. The operation of an RDE is similar to that of a PDE, which begins with filling and igniting the reactive mixture. As the flame propagates around the combustion chamber, it increases speed and transitions from a deflagration to detonation (DDT). Fresh reactants are continuously fed into the annular combustion chamber, which enables the detonation to continuously rotate circumferentially around the annulus. This results in steady operation with a sustained detonation wave traveling around the combustion chamber, while the products are exhausted out of the RDE exit. This process is shown schematically in Figure 1.2.

Figure 1.2: RDE process [3]

The continual process of an RDE results in higher operating frequencies (i.e. > 1000 Hz). The RDE is capable of operating at any flight velocity for very high frequency repetition, which produces quasi- steady exhaust and lower pressure fluctuations [3], and enables it to generate stable thrust [5]. These qualities make the RDE much more amenable for downstream components such as a turbine or nozzle

[6]. Thus, the RDE is a device that has the potential to achieve a great amount of specific impulse at very high operating frequencies, while having fewer moving parts than modern turbomachinery applications.

1.2 One-Dimensional Analysis

a) Detonation Theory

The structure of a detonation wave is highly three-dimensional. However, much knowledge and insight can be gained by conducting a one-dimensional analysis of a detonation wave. To help visualize this concept, consider a premixed, gaseous mixture in a very long constant-area duct. This mixture is a one-dimensional planar combustion wave that is moving within the duct shown in Figure 1.3 [7]. In a reference frame in which the combustion wave is in motion, the wave travels at a constant velocity while the duct is stationary. However, this analysis will assume that the wave is stationary. In Figure 1.3, the unburned gases upstream of the combustion wave contain properties, which are denoted by subscript 1,

3 while subscript 2 denotes the properties of the burned gases downstream of the combustion wave.

Velocities, u1 and u2 are defined with respect to the coordinate system fixed relative to the stationary combustion wave.

Figure 1.3: Schematic diagram of a stationary, one-dimensional combustion wave [7]

Given typical data on conditions upstream and downstream of the combustion wave, Figure 1.3 can provide a basic understanding of the physical situation regarding two types of combustion waves: deflagration and detonation. A deflagration wave propagates at subsonic speed, while a detonation wave propagates at supersonic speed. Table 1.1 compares data between typical deflagration and detonation waves [7].

Table 1.1: Data showing qualitative differences between detonation and deflagration [7]

Parameters Detonation Deflagration

u1/a1 5 – 10 0.0001 – 0.03

u2/a2 0.4 – 0.7 (deceleration) 4 – 6 (acceleration)

P2/P1 13 – 55 (compression) ≈ 0.98 (slight expansion)

T2/T1 8 – 21 (heat addition) 4 – 16 (heat addition)

ρ2/ρ1 1.7 – 2.6 0.06 – 0.25

Although the temperature ratio T2/T1 indicates that the amount of heat addition is similar for both detonation and deflagration, there are many differences between these two combustion waves. The main difference is the rise in density and pressure across the flame front for a typical detonation wave. The rise in pressure results in compression for detonation while the loss in pressure results in a slight expansion for deflagration. Thus, detonation is a process in which pressure gain combustion occurs, and ideally provides more extractable work than deflagration for a similar amount of heat addition. Although a detonation wave is composed of multiple three-dimensional structures, a simplified one-dimensional analysis can still provide useful insight into a detonation wave and allows for qualitative differences between a deflagration and detonation to be observed.

b) Hugoniot Curve

Equations that relate the initial and final conditions of a combustible gas that burns to completion can be derived from conservation equations [7]. These conservation equations are as follows, assuming steady, one-dimensional flow with no body forces under adiabatic conditions:

휌1푉1 = 휌2푉2 (1.1)

2 2 푃1 + 휌1푉1 = 푃2 + 휌2푉2 (1.2)

푉2 푉2 퐶 푇 + 1 + 푞 = 퐶 푇 + 2 (1.3) 푃 1 2 푃 2 2

The equations represent conservation of mass, momentum and energy, respectively. Eq. (1.1) states that mass over a given area is equal between initial and final conditions of the combustible gas.

Momentum is conserved assuming that pressure is the only force acting on the control volume [8]. Eq.

(1.3) includes terms for enthalpy, CPT assuming constant specific heat. By combining Eqs. (1.1) and

(1.2), the Rayleigh-line relation can be obtained as follows:

2 2 2 2 푃2−푃1 휌1 푉1 = 휌2 푉2 = (1.4) 1/휌1−1/휌2

The Rayleigh line can be obtained when plotting pressure, P vs. specific volume, 1/ρ for a fixed mass flow rate. The Rankine-Hugoniot curve can also be created on a P vs. 1/ρ plot; the solution of any steady- state deflagration and detonation waves are located on this curve. The Rankine-Hugoniot curve is obtained when the energy equation, Eq. (1.3) is satisfied in addition to the continuity and momentum [8].

By combining these equations Eqs. (1.1) – (1.3) and by applying the ideal gas law (푃 = 휌푅푇) to the combustion products, the Rankine-Hugoniot relation can be determined:

훾 푃2 푃1 1 1 1 ( − ) − (푃2 − 푃1) ( + ) = 푞 (1.5) 훾−1 휌2 휌1 2 휌1 휌2

The Hugoniot curve is shown in Figure 1.4, and includes a plot showing all of the possible values of the combustion products (1/ρ2, P2) for given properties of the reactants (1/ρ1, P1) and heat release, q [7].

The origin of the Rankine-Hugoniot curve is the point (1/ρ1, P1) and is considered the initial state of the reactants. The origin is labeled as “A” in Figure 1.4.

Figure 1.4: Rankine-Hugoniot curve (adapted from [8])

The curve is divided into five regions by drawing tangents to the curve through the origin A and vertical and horizontal lines through A. The two tangent points, B and E are considered the upper C-J point and lower C-J point, respectively for the combustion waves. The wave speed of the stable combustion wave (uB) can be determined at the C-J points via the Rayleigh-line relation:

1 푃2−푃1 푢퐵 = √[ ] (1.6) 휌1 1/휌1−1/휌2

Region C-D of the curve represents solutions that are physically impossible to attain. Based on the wave speed obtained from Eq. (1.6), section C-D implies that the velocity of the reactants, u1 is imaginary since P2 > P1 and 1/ρ2 > 1/ρ1. This yields solutions that are not valid for this section. The C-J points, B and

E correspond to the type of combustion wave at which the flame will stabilize. The upper C-J point, B corresponds to conditions for the wave speed of a stable detonation, while the lower C-J point, E corresponds to conditions for the wave speed of a stable deflagration.

The other sections of the curve represent physically valid solutions. The area above point B represents the strong detonation region. Solutions for this region require experimental setup for generating overdriven shock waves in very strong confinement [8]. This region is higher on the pressure axis than the upper C-J point, so it can be clearly seen that these overdriven detonations have pressures that are greater than that of a C-J detonation. Region B-C represents the weak detonation region. These pressure values are less than that of a C-J detonation. These weak detonations are rarely seen and typically stabilize to a stable deflagration in a short period of time [8].

Region D-E represents weak deflagrations, which are often observed. In passing through a weak deflagration, the gas velocity relative to the wave front is accelerated from a subsonic velocity to a greater subsonic velocity [7]. In most experimental conditions, the pressure in the burned-gas zone is less than the pressure of the unburned gases. Thus, solutions in this region are the most commonly observed form of deflagrations. The region below point E represents strong deflagrations. In passing through a strong deflagration, the gas velocity must be accelerated significantly from subsonic to supersonic. Since this

7 situation cannot occur in a duct of constant area, this solution is nearly impossible to observe due to the wave structures prohibiting a change from subsonic to supersonic speed [7].

c) ZND Theory

The classical C-J theory, which was developed and proposed by Chapman and Jouguet in the 19th century, was further extended in the 1940s. Zel’dovich, von Neumann and Döring are three scientists who independently proposed the modern detonation theory. The ZND detonation structure is a model that assumes steady, one-dimensional flow relative to the detonation front. It is based on the detonation theory postulated by these three scientists, and it is the most commonly used one-dimensional model that illustrates gaseous detonations [7]. The ZND detonation structure shows a variation of properties through a one-dimensional ZND detonation wave as shown in Figure 1.5.

A detonation wave can be described as a leading shock wave, which is tightly coupled to an exothermic chemical reaction. In the ZND model, the shock wave (red in Fig. 1.5) propagates at extremely high velocities through the reactants, which yields a net rise in pressure from the reactants to products. This process greatly increases temperature, pressure and density. The induction zone (blue in

Fig. 1.5) is a region that is immediately behind the shock wave. In this region, the rate of reaction slowly increases, which results in relatively constant, flat profiles for each of the properties. The reaction zone

(green in Fig. 1.5) immediately follows the induction zone in which the reaction rate sharply increases.

This results in a change in the properties including an increase in temperature. However, the density and pressure decrease due to an expansion of the flow. Each of the thermodynamic properties reaches their equilibrium values when the reaction is complete. It is important to note that the physical distance is very small between the shock wave front and the end of the reaction zone (~1 cm) [7].

Figure 1.5: ZND detonation structure [7]

1.3 Three-Dimensional Detonation Structure

As previously stated, the ZND model provides a one-dimensional illustration of the detonation structure, and it is an extension of the C-J theory, which assumes steady, one-dimensional flow. However, the real structure of a detonation is transient and highly three-dimensional. Over the years, methods have been developed to reveal the true structure of a detonation wave. One technique that has been extensively applied to the study of a detonation structure is the smoked-foil technique [7]. This technique involves coating the inner walls of the detonation tube with soot in order to record the path of the detonation. The detonation structure can then be studied by observing the imprint that the detonation leaves on the surface, as shown in Figure 1.6. Antolik first used the smoked-foil technique in 1875. However, this method was not applied to detonation research until much later when Denisov and Troshin used the smoked-foil technique to study an unstable detonation structure in 1959 [7]. The smoked-foil technique was an instrumental method to discovering a detonation wave’s real structure.

Figure 1.6: Detonation wave structure obtained from smoked-foil technique [7]

As can be seen in Figure 1.6, the detonation structure is comprised of a complex system of shock waves [7]. The local heat release rate determines the strength of the leading shock while the exothermic reaction time depends on the relative degree of shock heating and compression [9]. When the leading shock front and the reaction zone are coupled together, the coupling is usually unstable and nonlinear.

Instabilities within a detonation can either be seen as chaotic oscillations with varying frequencies or as simple oscillations observed in the induction length and the leading shock velocity [10]. As the leading shock wave propagates, transverse or reflected shock waves form behind it, which provide additional compression. These transverse waves periodically collide or intersect with the leading shock wave, forming a triple point as seen in Figure 1.7. The presence of triple points within a detonation wave is the reason that the propagating detonation wave is able to be recorded on a soot-covered surface.

Figure 1.7: Triple point of a detonation wave [9]

Triple points are the intersecting points of three shock waves: the Mach stem, the incident shock and reflected shock [7]. The Mach stem is the stronger part of the leading shock front while the incident shock is the weaker part. These three shock waves propagate throughout the reactive mixture, colliding with each other to form more triple points. As a result, these multiple curved shocks intersect to form a cellular pattern. Figure 1.8 shows a detailed schematic of the cellular pattern within a detonation structure.

Figure 1.8: Cellular pattern of a detonation structure [7]

The detonation cell size or width is determined by the spacing of the transverse waves. The cell size,

λ can provide information on the reactive mixture. Moreover, λ is a function of the thermodynamic state and composition of the mixture, and it can even be used to determine the detonation sensitivity of a mixture [11]. For instance, mixtures with smaller λ tend to have greater detonability. Parameters associated with macroscopic detonation behavior can be defined in terms of λ including critical initiation energy requirements, detonation propagation limits, and transmission limits [11].

For most mixtures, it is necessary to have collisions of transverse waves in order to sustain a detonation. In order for a detonation to propagate and be sustained throughout a confined geometry (i.e. tube, channel, etc.), the cell size must exceed a certain minimum diameter and channel width [12].

Otherwise, the detonation propagation will not be sustained as a result of an insufficient number of

11 transverse waves within the detonation front. Thus, if a detonation channel or tube is less than the minimum cell size, the detonation will not be sustained and will yield a deflagration.

Figure 1.9: Minimum cell size requirements for detonation in confined geometry [12]

A single-head spinning detonation consists of a single detonation cell propagating in a spinning mode

[7]. Since this is the smallest physically attainable detonation, the minimum diameter and circumference in a circular detonation tube can be determined based on this fact. Thus, the minimum diameter of a circular detonation tube must be 퐷푚𝑖푛 = 휆/휋. The minimum circumference of the detonation tube must be equal to the detonation cell width: 퐶𝑖푟푚𝑖푛 = 퐷푚𝑖푛 ∗ 휋 = 휆. The minimum width of the channel must be the width of the detonation cell, 푊푚𝑖푛 = 휆. This constraint is made since a detonation is unable to spin within a confined geometry with corner interactions [7].

1.4 Thermodynamic Cycle Analysis

A thermodynamic cycle is used to describe the process or sequence of states through which a working fluid passes within a propulsion system, such as a gas turbine engine. Two different thermodynamic cycles are used to represent two different types of propulsion systems that are investigated in the current study. This section provides a concise, detailed description of each thermodynamic cycle.

a) The Detonation Cycle

Thermodynamic cycles can be portrayed on a temperature-entropy, or T-s diagram. Modern gas turbine engines closely follow the Brayton thermodynamic cycle, which is used to characterize a constant pressure combustion system. Similarly, combustion in gas turbine engines occurs as deflagration at nearly constant pressure. The Brayton cycle can be seen in Figure 10 which shows the various steps of three different thermodynamic cycles. This process includes isentropic compression, heat addition by combustion, isentropic expansion, and finally heat rejection. The straight vertical lines shown in the diagram denote constant entropy or an isentropic process within the cycle.

The Humphrey cycle also involves isentropic expansion and compression. However, this cycle describes a constant volume combustion system, allowing for greater work to be produced by the

Humphrey cycle. This is indicated by the greater area enclosed by the curves for the Humphrey cycle in

Figure 1.10. Furthermore, the Humphrey cycle results in greater pressure and less entropy production than the Brayton cycle for the same amount of heat addition. Some previous studies have used constant volume combustion as a surrogate for the detonation process.

Heiser and Pratt were the first to present an ideal thermodynamic cycle that can be used to represent a

PDE [1]. The detonation cycle is based on the one-dimensional ZND model. Since an RDE also utilizes the detonation mode of combustion and can be approximated by the ZND model, this cycle can be used to represent both a PDE and an RDE. Thus, the cycle will simply be referred to as the detonation cycle in this study. In the detonation cycle, combustion takes place as a two-part process in which entropy is generated. First, compression occurs as a result of an adiabatic normal shock wave, followed by a constant-area heat addition process. At nearly sonic speed (M≈1), there is a slight downturn in the curve near point 4, which is a result of a drop in the static temperature caused by heat addition [1].

The detonation process causes an increase in pressure during combustion at nearly constant volume.

This pressure gain combustion contributes to a greater overall work availability of the engine. The area enclosed by the curves of the detonation cycle in Figure 1.10 is seen to be greater than both the Brayton

13 and Humphrey cycles. Figure 1.10 also shows that the detonation cycle results in less entropy generation than the other cycles.

Figure 1.10: Ideal Thermodynamic Cycles on Temperature-Entropy (T-s) Diagram [1]

Figure 1.11 compares the thermal efficiency of each thermodynamic cycle as a function of compression static temperature-rise ratio [1]. The plot shows that the detonation cycle has the greatest thermal efficiency for various amounts of heat added to the cycle. This thermodynamic cycle analysis by

Heiser and Pratt shows that PDEs and RDEs have the potential to produce greater work availability at greater thermal efficiencies than engines that are currently in use today. Thus, more research needs to be done to determine how to practically obtain the maximum possible work output from these engines.

Figure 1.11: Thermal Efficiency of each thermodynamic cycle vs. Compression static temperature- rise ratio [1]

b) The Inverse Brayton Cycle

This thesis also includes the investigation of a propulsion system that is designed to operate on the

Inverse Brayton Cycle. The Inverse Brayton Cycle is a thermodynamic cycle that incorporates expansion before compression, and is essentially a rearrangement of the traditional components of a gas turbine engine [13]. The operation of the Inverse Brayton Cycle includes the combustion of air (1-2), which enters the engine at atmospheric conditions. This is followed by isentropic expansion to sub-atmospheric pressure in the turbine (2-3). The recuperator (3-4) and the ambient heat exchanger (4-5) each work to extract a significant amount heat from the flow (4-5) before it enters the compressor (5-6) [13]. A schematic of the Inverse Brayton Cycle and its T-s diagram are shown in Figures 1.12 and 1.13, respectively.

Figure 1.12: Schematic of the Inverse Brayton Cycle [13]

Figure 1.13: T-s diagram of the ideal Inverse Brayton Cycle [13]

The recuperator is also designed to reclaim a portion of the heat that is exhausted by the turbine. The recuperator redirects this extracted heat to the combustor inlet, yielding greater cycle efficiency and greater work output from the system. In Figure 1.13, the dashed line in the T-s diagram is used to represent this process. The selection and design of the recuperator and ambient heat exchanger will be further discussed in the following chapter. The impact of the new heat exchanger design on a propulsion system based on the Inverse Brayton Cycle will also be covered later in this thesis.

1.5 RDE Literature

Over the past five decades, scientists around the world have focused their research efforts to study the function and operation of RDEs. Russian scientist, Voitsekhovskii was the first to conduct experimental research on RDEs [14]. In 1969, he ran experiments in which his RDE was able to sustain a continuous detonation wave by radially flowing a mixture of acetylene and oxygen into an annular combustion chamber. The flow velocity was nearly equal to the C-J velocity in one regime, but significantly less in the other regime, which may indicate that a detonation and deflagration were present within the chamber.

British scientist, Edwards later conducted an experiment nearly a decade later, in which he was able to achieve steady detonation with an RDE utilizing a mixture of ethylene, oxygen and nitrogen. The results from his experiment showed instances of double and triple waves moving counterclockwise within the annular combustion chamber, with detonation waves propagating at nearly C-J velocity [15].

The next significant experimental study on RDEs occurred much later in 2006, and was led and conducted by Russian scientist, Bykovskii [16]. Results from his experiment proved that continuous detonation could be achieved for nearly all hydrocarbon fuels (liquid or gaseous) mixed with gaseous oxygen in an annular combustion chamber. He also validated the feasibility of using different combustion chamber shapes to achieve detonation. Shortly thereafter, Polish scientists, Kindracki et al conducted an experiment, which investigated the feasibility of using an RDE in a rocket engine [5]. Using hydrocarbon fuels such as methane, ethane and propane, their experiment showed that rotating detonation could be established for these mixtures when mixed with gaseous oxygen. The results from their experiment further validated the findings from Bykovskii. The study also investigated how the changes in combustor length affected the operation of the RDE. Both configurations were able to sustain a rotating detonation wave. The experiment also included an investigation into the propulsive performance of the RDE, which will be discussed further in the following section.

Within the last decade, scientists have begun to carry out computational research to gain a better understanding of the operation and flow field within an RDE. Japanese researchers were among the first

17 to conduct a Computational Fluid Dynamics (CFD) analysis on an RDE [17]. Their two-dimensional model showed a detonation propagating continuously within the annular combustion chamber, but at a speed less than C-J velocity mainly due to insufficient mixing. Their study also defined criteria in which the flow field of an RDE can be approximated as two-dimensional rather than three-dimensional. This approximation can be made assuming that the distance between the inner and outer wall of the combustor is much smaller than their respective diameters. The diameter also needs to be large enough not to create a strong centrifugal force to the flow. Figure 1.14 shows a) a schematic of the flow field within an RDE and b) an approximation of the two-dimensional cylindrical flow field, in which the upstream and downstream conditions are identical to the cylindrical flow. Periodic boundary conditions connect the upper and lower sides [17].

Figure 1.14: Schematic of two-dimensional flow field within RDE [17]

There has been more computational analysis done in recent years including research from NRL scientists, Schwer and Kailasanath. These scientists developed three-dimensional computational models, which helped to more accurately simulate the real physical and chemical mechanisms in an RDE. Schwer and Kailasanath used their model to focus more on gaining a better understanding of the flow field within an RDE determined that the flow field closely follows the thermal detonation cycle [18].

1.6 Thrust in Detonation Engines

Previous detonation research has been carried out to determine which conditions yield optimal performance of a PDE and RDE by varying parameters including equivalence ratio, type of fuel used, combustion tube/chamber geometry, etc. However, there have been few experimental investigations that have focused on measuring the thrust and specific impulse of these detonation engines, especially in the case of RDEs.

The periodic operating characteristics of a PDE make it very difficult to measure time-resolved thrust outputs. Thus, the most effective way to determine the propulsive performance of a PDE is to measure the average thrust output. Various methods have been utilized to measure average thrust of PDEs including

Lu et al who obtained thrust measurements from a thrust stand system on which the PDE was placed [19].

From his experiment, he concluded that the equivalence ratio, ϕ has an effect on the thrust of the PDE.

Maximum thrust was reached at ϕ = 1.1, and a mixture that is too rich or too lean will cause reduced thrust in a PDE [19].

Santoro carried out an experiment, which focused on the feasibility of using a PDE driven ejector for applications to replace the high-pressure compressor and high-pressure turbine sections of a high bypass turbofan engine [20]. In order to do this, the experiment involved thrust augmentations of the PDE ejector, which would have the potential to reduce engine weight and specific fuel consumption. The 2.25- inch diameter detonation tube was mounted onto frictionless rails on a thrust stand, which was used to obtain average thrust measurements for multi-cycle operation. The thrust stand setup is shown in Figure

1.15 below, which shows a thrust block with a spring attached to the injector assembly end of the detonation tube. The displacement was measured for various applied forces in order to calibrate the thrust stand assembly. The force was applied using a force gage, while a linear variable differential transformer

(LVDT) measured the displacement. The calibration curve showed a linear relationship between force and displacement. A similar calibration technique was conducted in the current research, and will be described in the following chapter.

Figure 1.15: Thrust stand setup for PDE ejector experiment [20]

Average thrust was successfully measured using this setup. The results showed that average thrust for multi-cycle operation was reached within 2 seconds of the start of firing. The mixture-based specific impulse was 130 s based on average thrust measurements, which was consistent with a previous study that utilized the same ethylene-oxygen-nitrogen mixture. This study proved that steady state thrust could be accurately measured for multi-cycle operation of a PDE or PDE-ejector system.

Suchocki is one of the few researchers to conduct an experiment to investigate the thrust output of an

RDE [21]. His RDE operated with a mixture of hydrogen as fuel and oxygen-nitrogen oxidizer. He obtained thrust measurements using a 2000-pound load cell, which was attached to a rigidly mounted surface below the RDE. Because it was affixed underneath the RDE, the load cell measured the weight of the RDE in addition to the RDE’s thrust output. Thus, modifications were made to the raw data in order to obtain accurate thrust measurements. The load cell readings had four distinct regions as shown in Figure

1.16, which includes a plot of the load cell reading over the detonation run time.

Figure 1.16: Load cell response for one detonation run [24]

Region 1 records the response at the beginning and end of the run when no fuel or air was flowing through the engine. Thus, the load cell only read the weight of the engine (~60 lbs.) for Region 1. The reading in Region 2 starts at the point when air began flowing through the engine, and ends at the point when fuel began flowing through the engine. Region 3 starts at onset of fuel flowing into the engine and ends at ignition. Finally, Region 4 records ignition to shutdown, which is when the detonation propagated through the reactive mixture flowing into the RDE.

The readings from these four regions were modified in order to determine the gross thrust, thrust from combustion and the thrust from the air and fuel flow. Suchocki used the following equations to calculate the thrust:

푇퐺푟표푠푠 = 푅̅̅4̅ − 푅̅̅1̅ (1.7)

푇퐶표푚푏푢푠푡𝑖표푛 = 푅̅̅4̅ − 푅̅̅3̅ (1.8)

푇퐹푙표푤 = 푅̅̅3̅ − 푅3 (1.9)

Specific impulse, Isp and specific thrust, Fsp were also calculated in this experiment using the gross thrust, the thrust generated from combustion, and the mass flow rates of fuel and air.

One conclusion that Suchocki reached from his experiment was that the amount of thrust generated by the engine increased with greater airflow into the engine. This was true for both detonating and non- detonating cases. Another conclusion from his experiment is that the greater oxygen content in the air contributed to the engine being able to sustain detonations at higher mass flows. As a result, the maximum thrust output of the engine increased when more oxygen was added to the air. He also found that the specific impulse was greater with leaner equivalence ratios, with the maximum Isp as high as

4033 s at ϕ = 0.92 [21].

Kindracki also conducted an experimental investigation focusing on an RDE’s propulsive performance for rocket engine applications [5]. Thrust was measured using a 2 kN force transducer which was connected to a data acquisition system and computer. Average thrust values of 250-300 N were achieved for relatively low mass flow rates of fuel and oxygen (0.06 and 0.15 kg/s) at 0.1 bar chamber pressure. As seen in the aforementioned studies, the thrust-time profile in Figure 1.17 has many fluctuations and peaks when the mixture is ignited. The thrust generated before the ignition is very small due to the outflow of cold gases. The decrease at the end of the measurement was a result of the exhaust gases that filled up the dump tank and increased back pressure.

Figure 1.17: Thrust-time profile for methane-oxygen mixture at ϕ = 1.65 [5]

1.7 Research Objectives

The current study investigates two different types of propulsion systems: the RDE and a propulsion system based on the Inverse Brayton Cycle. The research objectives for each propulsion system are described in this section.

a) Rotating Detonation Engine

The current study will discuss an experiment involving the use of ethylene-air mixtures in a modular

RDE configuration. This experiment was conducted to determine which conditions yield steady, continuous rotating detonations for ethylene-air mixtures in an RDE. Previous experiments in the

University of Cincinnati Detonation Test Facility utilized hydrogen-ethylene fuel blends in an air- breathing RDE system [22], while this particular experiment utilized only ethylene as fuel, mixed with air. This research is significant, because it is essential for an RDE to be able to operate on hydrocarbon-air mixtures in order to be considered as a practical device for use in turbomachinery systems. Kerosene is a prevalent hydrocarbon fuel utilized in modern propulsion systems around the world. As a means to reach this goal, hydrocarbon fuels such as ethylene and propane can be used as logical steps to reach the final goal of a kerosene-air mixture in an RDE. This will also allow for the RDE to be more easily integrated into jet propulsion systems.

The experiments mentioned in the previous section prove that significant insight can be gained by determining the amount of thrust generated by detonation engines, especially RDEs. RDEs are capable of generating more stable thrust than PDEs due to their high operational frequency and quasi-steady exhaust

[5]. The method used to measuring thrust of an RDE in this current study differs from the aforementioned experiments. This thesis will discuss the design of the thrust stand system that was developed to obtain thrust measurements from the TOXIC RDE configuration. The next chapter will provide a detailed explanation of the components that make up the thrust stand, and the technique used to calibrate the thrust stand. The thrust stand was also modeled in order to simulate the thrust stand response to the RDE

23 operation. These simulations will also be discussed and analyzed. Furthermore, other parameters will be measured to determine the performance of the RDE, i.e. mass flow rate and equivalence ratio.

b) Inverse Brayton Cycle Propulsion System

The concept of a propulsion system that operates on the Inverse Brayton Cycle has been proposed as a solution to improve the efficiency of small-scale propulsion systems, such as those utilized in

Unmanned Aerial Vehicles (UAVs). The growing demand for UAVs, which are widely used for military combat and other purposes, has made it essential to develop propulsion systems that improve the supportability and efficiency of these vehicles. This necessity has been addressed as part of the Efficient

Small-Scale Propulsion (ESSP) Program, which was outlined by the U.S. Department of Defense (DoD)

[23]. ESSP aims to provide power for small-scale vehicles that range from 100 to 2500 lbs. A propulsion system that would be suitable for these vehicles would fall in the category between gas turbine technology and internal combustion engine technology as shown below in Figure 1.18.

Figure 1.18: Desired Power Density & SFC – Efficient Small-Scale Propulsion (ESSP) Vehicles [27]

ESSP seeks to find a propulsion system that fills the void between high power density and low specific fuel consumption (SFC), as denoted by the blue oval in Figure 20. The internal combustion engine provides less power density than the gas turbine engine [23]. Reducing the scale of the gas turbine engine to small sizes considered for a UAV results in greater viscous and tip clearance losses in the engine components. Also, the gas turbine suffers from increased SFC at small-scale power requirements for the UAV.

A previous study conducted by Grannan covers preliminary analysis and investigation of an Inverse

Brayton Cycle based UAV propulsion system [13]. The analysis proved that a propulsion system operating on the Inverse Brayton cycle can potentially result in significantly lower SFC for lower power outputs than the gas turbine engine, and can fulfill the requirement outlined by the ESSP. This study also proved the feasibility of such a propulsion system. As described earlier in this chapter, the recuperator works by reclaiming waste heat from flow exiting the turbine, and redirecting it to preheat the air entering the combustor. The ambient heat exchanger works to further reduce the temperature of flow entering the compressor, which improves the efficiency of the compressor and the overall cycle. The results from

Grannan’s study showed that while the addition of the heat exchanger elements improves the thermal efficiency of the cycle, it also greatly increases the weight of the engine (~70-130%). Greater engine weight results in shorter range and less endurance for the aircraft engine, which would be problematic if the UAVs were required for longer military missions [13].

This study will involve the investigation a turbojet operating on the Inverse Brayton Cycle. One objective of the current research is to compare the performance of this particular turbojet to other turbojets that utilize similar mass flow rates of fuel and air. Other objectives of the current research include developing a new heat exchanger design, which will be designed to weigh less but have similar effectiveness to the heat exchanger used in the previous study. Weight saving options for the recuperator will also be investigated and analyzed. Developing weight saving options for both heat exchanger elements is expected to increase the endurance, efficiency and improve the performance of the Inverse

Brayton Cycle based turbojet.

Chapter 2: Experimental Methodology

2.1 University of Cincinnati Detonation Test Facility

All of the experiments presented in this thesis were conducted in the University of Cincinnati (UC)

Detonation Test Facility. This facility is a part of the Gas Dynamics and Propulsion Laboratory (GDPL), and has been in use for nearly a decade since its design and construction by a previous research team [24].

This section will give a description of the facility as a whole, which includes the test bunker, air and fuel supply, safety system and the data acquisition system. This section heavily references literature written by

St. George [25] and Driscoll [26] who both conducted extensive research in this facility.

Figure 2.1: RDE contained within the UC Detonation Test Facility

a) Test Bunker & Safety Features

The test bunker contains two systems: the PDE turbine system and the RDE system. However, the experiments presented in this work utilize only the RDE system. The test bunker is located in a remote area, separate from the GDPL, and is connected to the main laboratory by an outdoor walkway. The remote location of the test bunker prevents the combustion exhaust products from entering the main

26 laboratory building, and simplifies exhaust and ventilation systems [25]. The test bunker measures about

5.3 m (17.4 feet) x 4.1 m (13.5 feet), providing sufficient space to operate and contain the RDE system

[25]. The walls of the test bunker are made of reinforced concrete that is 0.3 m thick [25]. The material and thickness of the walls makes them durable enough to provide protection from fires, and capable of fully containing any potentially disastrous failures.

Experiments are always run with operators stationed at the control area, which is located within the main part of the laboratory. The thick walls of the bunker and its remote location also provide adequate protection for the operators from the extremely high noise levels produced by the detonation experiments.

Noise produced by detonation combustion has been measured to reach levels greater than 160 dB, which can cause hearing loss [24]. The schematic of the UC Detonation Test Facility in Figure 2.2 shows the test bunker relative to the control area and other systems.

Figure 2.2: Schematic of the UC Detonation Facility [25]

The test bunker also includes an exhaust ventilation system, which operates at a high flow rate to remove any unburned reactants or exhaust products. In order to prevent various gases from accumulating, the ventilation ducts work to entrain airflow from the ceiling, floor and experimental levels. An RKI

Instruments gas detection system is also utilized and contained in the test bunker to detect levels of combustible gases, such as hydrogen and ethylene, in addition to carbon monoxide and oxygen [25].

The operators are given optical access to the test bunker before, during and after experiments via a closed-circuit television (CCTV) system. Four cameras are used and connected to the CCTV system to provide various viewing angles and digital video recording to replay and record footage of the detonation experiments. Experiments are generally conducted during late hours of the night when there is considerably less foot traffic past the walkway above the GDPL. In order to have a clear view of this walkway, two cameras are placed at ground level, above the GDPL before testing. Detonation tests are only run when the walkway is empty to ensure that non-laboratory personnel are not exposed to dangerous noise levels produced by the detonation, and to ensure that they are a safe distance away from hot fire testing.

b) Low Mass Flow System

The gaseous delivery system is located in the outdoor walkway outside of the test bunker, and is used to supply and control all low mass flow, reactive gases. The low mass flow, reactive gases are used for the pre-detonator, which will be explained in further detail later in this chapter. The location of this system is used as a safety precaution to separate the gaseous storage area from combustion processes within the bunker. This system includes a gaseous delivery cart and a gaseous control panel. The gaseous delivery cart system contains gaseous supply tanks for gases that are used in the experiments, such as nitrogen, oxygen and ethylene. The supply tanks contain regulators, which are used to regulate the tank pressure.

These regulators reduce the pressure from a range of 70-140 bar down to the supply pressure of the test bunker, which is approximately 18 bar [25, 26]. A series of measurement systems are also located on the delivery cart to monitor gaseous flow properties, including mass flow and static temperature & pressure.

The reactive gases then proceed through a series of safety features of the delivery cart, which includes a system of pneumatically controlled ball valves [26]. These valves are both controlled by compressed air.

One valve prevents the gases from entering the bunker until the experiment starts, and immediately stops any gaseous flow from entering the bunker in the event of an emergency. The other valve vents the supply lines. This allows for all reactive gases to be removed from the bunker supply lines, which occurs during normal shutdown, emergency stops or power outages.

Compressed air supply lines are normally pressurized when experiments are run, which enables the flow of reactive gases into the bunker. When an experiment is stopped, the air is evacuated from the supply lines, with the pneumatic valves returning to their initial positions. Manually operated shutoff valves can be used when it is necessary to change the supply tanks and for further gas relief. When these valves are opened, the experimental gases (oxygen, fuel and nitrogen) are able to pressurize the lines from the supply tanks to the injectors on the detonation tubes [26]. These valves are considered as the last chance valves in the delivery system, and are located inside the test bunker as shown in Figure 2.3.

Figure 2.3: Last-chance valves for oxygen, fuel and nitrogen

Operators in the control area are able to remotely control the gases used in the detonation experiments by using the gaseous control station. This station is used to control the pneumatic valves on the delivery cart through a system of relays, switches and solenoids. The system works by pressurizing air supply lines, which connect the control station to the delivery cart system. Each pneumatic valve on the delivery cart is actuated by the low-pressure laboratory “shop” air supply (~7 bar) [25, 26]. The control station also includes buttons on the front panel for functional control and indicator lights, which inform operators of the current condition of the gaseous flow. The front panel of the gaseous control station is shown in

Figure 2.4.

Figure 2.4: Gaseous fuel control panel

The operator starts the testing by pressing the “Operate – Start” button on the control panel. This causes the pneumatic valves to open or close, permitting reactant flow from the delivery cart to the detonation test rig. Similarly, the testing ceases when the operator presses the “Operate – Stop” button. Ending this process enables the pressurized air supply lines to vent, and the pneumatic control valves return to their initial positions. It also allows for reactants to be released from the test bunker, by venting the pressurized section of oxygen and ethylene lines to the atmosphere [26].

A nitrogen purge is another available feature, which allows nitrogen to flow into the reactant supply lines. This is done as a safety precaution to end all unwanted combustion in the test bunker by introducing nitrogen, a non-reactive gas into the system [26]. This operation involves the normal flow of reactants being stopped while nitrogen flows into the lines. The operator can control this process using the “Purge –

Start” and “Purge – Stop” buttons, which begin and end the nitrogen purge, respectively.

Ethylene and oxygen are also monitored as an additional safety precaution. For instance, the control station is programmed to trigger an emergency stop of gaseous flow if the flow of either of these gases were to fail. The nitrogen purge is also activated in such event, and runs uninterrupted until the issue is resolved. Also, the pressure of air supply lines that provide power to the pneumatic control valves at the delivery cart is released whenever a power outage occurs. When these control valves are released, they return to their initial positions, causing the reactive gases to vent from the test bunker. The control station is also digitally connected to the control computer, which ensures that the emergency stop is triggered if the computer were to fail or shut down. This emergency stop of gaseous flow is accompanied by the nitrogen purge, which continues until communication with the computer is restored.

c) High Mass Flow System

The gaseous delivery system used to supply and control all high mass flow gases is located in the outdoor walkway outside of the test bunker. Similar to the gaseous delivery system for low mass flow, this location is used as a safety precaution to separate the gaseous storage area from combustion processes

31 within the bunker. The high mass flow, reactive gases are used for the RDE supply, which will be explained in further detail in the following section of this chapter.

This system includes a gaseous cart delivery system, gaseous control system and nitrogen safety supply system. The main function of the delivery cart system is to prevent or allow gaseous fuel flow from the supply tanks to the test bunker. This system contains the gaseous supply tanks for all fuels that are used throughout the experiments, and is located at a distance of about 12 m away from the test bunker.

Similar to the low mass flow delivery system, regulators are used to regulate the tank pressure (70 – 140 bar) to a workable pressure of approximately 18 bar, the supply pressure of the test bunker [25, 26].

The reactive gases then proceed through a series of safety features of the delivery cart, which includes a system of pneumatically controlled shutoff valves. Each valve is controlled by the nitrogen system.

Before the experiment is ready to be started, one valve inhibits the reactive gases from entering the test bunker while the other valve vents the fuel supply lines. This feature ensures that fuel and combustion materials are removed from the test bunker supply line. The gaseous control system is a computer control system, which controls and monitors the delivery cart system, and it is located at the control station. The main function of the nitrogen safety supply system is to control the pneumatic valves that control the fuel supply. Air is provided by the GDPL air supply system, and can reach a maximum air supply pressure of

12.7 bar. Air enters the test bunker via a 50.8 mm schedule 40 pipe [25, 26]. Laboratory “shop” air is used to actuate a pneumatically actuated shutoff valve, which controls the flow of air into the facility [26]. For safety purposes, the control station contains features that are used to control the valves.

The final control and metering system of the high mass flow detonation facility is contained within the test bunker. Nitrogen-driven regulators are used to control the amount of reactant flow within the test bunker. These regulators are connected to the air and fuel supply lines. The control station delivers a current to actuate current-to-pressure (I-P) regulators, which provide a suitable nitrogen pressure to actuate the main supply regulators. Reactant flow rates are monitored by a set of Flomaxx sonic nozzles with different throat sizes, and are located downstream of the main supply regulators [26]. Choked

32 reactants flow through these sonic nozzles during normal operation. Accurate flow rates of reactants can be calculated when using pressure and temperature sensors that are placed on the supply lines. The control station produces a constant flow rate of reactants as the supply pressures are varied through test conditions [26]. Figure 2.5 shows a diagram of the choke-flow monitoring system.

Figure 2.5: High mass flow metering system

d) Data Acquisition (DAQ) and Control System

A high bandwidth National Instruments control and acquisition system is used to acquire data and control the facility. This system is an 18-slot, NI PXIe-1065 system, which is located inside the test bunker. This system is remotely operated through a fiber optic cable that allows for high-speed communication at a rate of up to 3 GB/s [25]. The data acquisition and system control includes multiple output and input channels with varying speeds. The output channels of the system include 16 channels of low-speed analog output (≤ 10 kHz), and 14 channels of counter/digital output (≤ 10 MHz). The input channels include 32 channels of low-speed analog input (≤ 10 kHz), and 24 channels of high-speed analog input (≤ 5 MHz) [25].

2.2 Experimental Setup

The RDE that is used in the experiments presented in this work was recently designed and constructed by former UC graduate student, Andrew St. George. It is known as the Twin Oxidizer

Injection Capable (TOXIC) RDE. Some features of the TOXIC RDE design are based on the modular

RDE developed by Shank at the Air Force Research Laboratory (AFRL) [3]. This RDE contains many components that can be interchanged to allow for modification of the combustor performance, including the center body, fuel plates, and air injection scheme. These variations of combustor geometry make it possible for various combustor configurations to be tested at very low cost. Each of the main RDE components, including those that are in direct contact with combustion is machined from aluminum.

Aluminum was chosen because it is lightweight, easy to machine, and can withstand extreme temperatures produced by detonation combustion. A SolidWorks model of the RDE assembly is shown in

Figure 2.6.

Figure 2.6: SolidWorks Model of TOXIC RDE Assembly

The numbers in parenthesis that are mentioned in this section refer to each component labeled in

Figure 2.6. The main component of the RDE is the combustor annulus, which consists of a center body

(1) and an outer body (2). These two parts make up the annulus walls, with fuel and oxidizer injection occurring upstream of the annulus. In this study, hydrogen will be used as fuel, while air will be used as oxidizer. This RDE configuration was designed so that air can be injected radially-inward or outward depending on the desired injection scheme. For instance, the outer air plenum (3) injects air radially- inward, while the inner air plenum (4) is only used when air is injected radially-outward. This experiment will involve using the outer air plenum for radially-inward injection through an air injection slot. Fuel is injected axially from the fuel plenum (5) through circular orifices in the fuel plate (6). This results in fuel being injected perpendicularly to the air stream, which generates crossflow mixing. This design enables the use of different fuel plates to be used, which provides the option to vary fuel injection schemes.

The apparatus that is directly upstream of the center body (7) is designed to control the airflow that is injected from the inner air plenum. Varying the size of the (dark blue) inner shim would change the height of the air injection slot. This apparatus will not be used for this experiment since air will only be injected radially-inward. However, this apparatus is available for future RDE experiments if radially-outward flow needs to be investigated. Instead, the configuration for this study will include the center body mounted onto a centering plate that is ½” thick at the upstream end. A retainer plate of the same thickness will be mounted to the center body at the downstream end (8).

The outer body is mounted onto the outer injector (9) at the upstream end, which controls the amount of air that is injected from the outer air plenum via the outer shim (10). Varying the size of the outer shim will change the height of the air injection gap. For instance, an outer shim with less thickness will decrease the air injection slot height, making the airflow more likely to choke. The outer body is also mounted to the outer retainer plate (11) at the downstream end, which helps to keep the boundaries for the air plenum intact. The outer retainer plate bolts into the outer plate (12), which keeps the entire RDE intact. A threaded rod is also bolted through the center of the RDE components down to the base plate

(13) to keep the structure intact. The base plate is bolted to steel unistruts, which enables the entire RDE assembly to be mounted horizontally onto a test stand. The test stand is placed on top of the thrust stand to enable thrust measurements.

Lastly, two different manifolds are included in the RDE configuration to supply either the inner or outer air plenum, depending on the injection scheme. The outer air plenum is radially supplied with air by four 1” pipes of the same length from an upstream manifold (14). The inner air plenum can be supplied similarly from the other manifold (15). The fuel plenum is supplied axially by a single, central inlet. A threaded rod is bolted into the RDE structure through the center of both plates and other RDE components to keep the engine components intact.

a) Instrumentation

The TOXIC RDE apparatus is comprised of twelve instrumentation ports on the outer wall, with four ports distributed into three azimuthal sections as shown in Figure 2.7 [27]. Each section is separated by

120°, with four equally spaced rows of measurement ports in each section. Three ionization sensors are placed in row 1 of the combustion annulus ports. These sensors are used to measure the burn time, or the duration of combustion within the annulus. There are three additional measurement ports for the air gap sensors located on the outer body, and flush mounted into the air injection slots. These ports are separated by 120°, and radially located 22 mm from the outer wall of the combustion annulus.

The air gap sensors are used to obtain time-accurate pressure fluctuations within the air injection slot using high-speed PCB pressure transducers. Since they are located close to the combustion annulus, these pressure transducers are also used to gather pressure fluctuations caused by combustion within the annulus. This data is used to make accurate operational frequency calculations. These pressure measurements gather fluctuations within the annulus while being safely separated from the extremely high temperatures within the combustion annulus. Capillary Tube Averaged Pressure (CTAP) sensors are also used in order to represent a quasi-time-averaged static pressure. These CTAP sensors are attached to the combustion annulus, and both the air and fuel supply plenums. The RDE is operated for a test length

36 of 1 second, and data from each sensor is acquired over that timeframe.

Figure 2.7: Schematic of the RDE Geometry & Instrumentation Layout [27]

b) RDE Detonation Initiation

A gaseous pre-detonator is used to initiate a detonation, and it exhausts tangentially into the annulus.

The pre-detonator for this experiment is designed to use oxygen and ethylene, as well as oxygen and hydrogen. The initiator tube can be seen in the schematic in Figure 2.7 on the far right. The tube is made of stainless steel, and has an inner diameter of 4 mm. This inner diameter reduces to 3 mm at the injection site in order to promote overdrive of the detonation upon entering the annulus. Reactants are injected into the pre-detonator at a delivery pressure that does not exceed 7.5 bar with a set of electrically-driven solenoid valves [28]. As mentioned in the previous section, a nitrogen purge feature is available for the pre-detonator in order to prevent auto-ignition of the reactants.

The pre-detonator is ignited by an automotive spark plug that is powered by an MSD aftermarket ignition system. This spark plug provides about 100 mJ of energy to ignite the pre-detonator. For mixtures that are highly detonable, this is sufficient to directly initiate detonation, or nearly instantaneous transition to detonation in some cases [28]. Wave speed is recorded using ionization probes that are installed within the pre-detonator. These probes are also used to verify nominal operation of the initiation system.

2.3 Thrust Stand

Previous studies utilized a load cell [21] or force transducer [5] to measure thrust generated by an

RDE. This study will instead utilize a thrust stand system to measure the thrust generated by the TOXIC

RDE. A thrust stand has been used in previous experiments to measure thrust, but mainly for PDE applications [19, 20]. This section outlines the thrust stand that was developed for this experiment, and includes detailed descriptions of the thrust stand structure, the LVDT, signal conditioner, calibration methods and vibration analysis

a) Structure

Figure 2.8: SolidWorks model of the thrust stand

Figure 2.8 shows a schematic of the thrust stand. The main parts of the thrust stand structure include the top plate and the base plate. These plates, along with the steel unistruts are used to hold the entire structure together. Both plates are 24” x 24” x ¼” aluminum sheets. The ¼” thickness of the plates is sufficient to support the RDE and other components. This thickness also allows for holes to be easily drilled through the plates to allow for various components to be attached to both plates. The pulleys that are mounted to the end of the thrust stand are used for holding a platform and weights, which will be used to calibrate the thrust stand.

Figure 2.9: Interior view of the thrust stand model

Another schematic of the thrust stand, which shows the internal components of the structure, is shown in Figure 2.9. Shock absorbers (1) are used to dampen the vibrations of the system. The linear variable differential transformer (LVDT) is used to measure displacement of the thrust stand. The LVDT (2) will be discussed in greater detail in the following section. Internal components also include the linear displacement block (3) and stationary contact block (4). Two rods, which are 0.3” in diameter, are connected to the linear displacement block. Each rod is equipped with a spring (5) in order to position the springs in between the two blocks. Two 1.25-inch diameter washers with a 0.3-inch inner diameter are also placed on the rods. This allows the rods to fit through the 1” holes in the side of the stationary contact block, enabling free motion of the rods, while the springs compress and expand between the two blocks. In addition to the shock absorbers, full compression of the springs results in complete dampening of motion of the system when the RDE is fired.

The pillow block fixed alignment bearings (6) are mounted to the top plate. These bearings are placed

39 onto support rails, enabling the top plate to slide back and forth. The ability of the top plate to slide in either direction on the support rails is essential for measuring displacement of the system.

b) Linear Variable Different Transformer (LVDT)

An LVDT is an electrical transducer that is used to measure linear position or displacement of an object. It functions by converting mechanical motion or vibrations into a variable electric voltage, signals or current [29]. The LVDT outputs a signal as the distance that the object has traveled in units of voltage, and has a negative or positive value.

The LVDT that is used in the current study is a High Accuracy AC LVDT Displacement Sensor, manufactured by Omega (LD320-50). The “50” in the part number denotes the ±50 mm (2”) measuring range in either direction [30]. This sensor consists of a tube-shaped body made of 300 stainless steel, and is 19 mm in diameter. This material makes the transducer durable, and protects the core within the body.

The Ingress Protection (IP) number is a two-digit rating that describes the degree of environmental protection of enclosures around an electronic device. The sealing of the outer body is rated at IP67, which means that the core inside the LVDT is completely protected against dust and foreign particles, and protected against the effect of immersion between 15 cm and 1 m [30].

The LVDT also has a movable member attached, which is a stainless steel rod surrounded by a spring. The rod is 6.5 inches in length, and its mobility makes it possible for the LVDT to measure the displacement. The LVDT will be mounted to the base plate of the thrust stand as shown in Figure 2.10.

Figure 2.10: LVDT Placement inside Thrust Stand

The internal structure of an LVDT is composed of three solenoid coils and a nickel-iron core [31].

The primary coil is in the center, and voltage is applied to it by an AC source with temperature-stable frequency and amplitude. The excitation frequency and amplitude for this particular LVDT are 5 kHz and

3 Vrms, respectively, which are typical for this type of sensor. Two secondary coils are designed to pick up the signal induced from the primary core based on the core’s linear position [31].

The core is attached to the movable rod whose displacement is measured. If the core position is in the middle of the LVDT, both secondary coils produce equal and opposite signals, which sum up to a null or zero voltage [31]. The polarity of the signal provides the direction of the displacement, and a voltage differential will result as the core is moved off center. This voltage is essentially a linear function of displacement.

Figure 2.11: Schematic of Internal Structure of LVDT [31]

This particular sensor was chosen because of its digital and mechanical interface (composition, dimensions, etc.), and the electrical input/output AC signal can be easily converted so that it is compatible with the DAQ system used during experiments. The latter quality makes it easier to incorporate the

LVDT into the LabVIEW computer program, which will be used to read and interpret various measurements. Furthermore, the core and inner components of the LVDT are very essential to the accuracy of the LVDT measurements. The sliding core does not touch the inside of the tube, which increases the accuracy and long-term reliability of the sensor, especially compared to other sensors and transducers [36]. Furthermore, the LVDT is placed inside of the thrust stand so that it is not directly exposed to the RDE during experiments. As a result, this position is expected to further increase the accuracy and the overall life span of the LVDT sensor.

c) Signal Conditioning

In this study, the Omega LDX-3A signal conditioner is used for conditioning the signal outputted by the LVDT sensor. Signal conditioning is a process that manipulates the signal of the sensor so that it can be effectively and accurately measured by the data acquisition system [32]. The LDX-3A signal conditioner was chosen for this experiment because it is compatible with the chosen Omega LVDT, and it is also AC powered. The LDX-3A amplifies the small voltage levels that are outputted by the LVDT so that they can be digitized and read by the DAQ system.

The LDX-3A is a compact conditioning unit housed in a die-cast aluminum box, which provides significant protection for the internal components [33]. It is powered from an external power supply unit, and is capable of providing outputs of up to ±10V and ±20 mA. As shown in Figure 2.12, the LDX-3A has three ports for connecting the LVDT (1), the output voltage (2), and the mains power supply (3).

Figure 2.12: LDX-3A Signal Conditioner

The LDX-3A requires a 5-Pin DIN connection for the LVDT port (1), which establishes the connection between the LVDT and the signal conditioner. A BNC connector cable is plugged into port

(2), which enables the connection between the signal conditioner and the DAQ system. It is important to note that the voltage enters the conditioner from the LVDT as AC voltage (red arrow in Fig. 30), and is manipulated to output a DC voltage through the BNC cable (blue arrow in Fig. 30). This is required since the DAQ system only reads DC voltage.

The settings also had to be modified inside the signal conditioner in order to set the LVDT output to the desired voltage range. For instance, the fine gain and fine offset were modified to vary the zero point and the voltage range, respectively. After setting up the LDX-3A, the range was set to vary from 0 V to ~

9.6 V, since the DAQ cannot read voltage measurements greater than 10 V.

d) Calibration

The thrust stand was calibrated in order to ensure that the measurements obtained during experiments are accurate. The calibration method involves using a platform made of unistruts. The platform weighs

26.8 lbs. with dimensions of 18.5” x 15.75” x 1.75”. The platform was hooked on to two wire ropes on each end, with the ropes positioned onto the pulleys of the thrust stand. Each wire rope has two loops on each end so that it can be attached to the hooks on the platform and around two eyebolts on the sides of the linear displacement block. Since the linear displacement block is mounted to the top plate, this will enable the top plate to slide when weights are added to the platform. The thrust stand calibration setup is shown in Figure 2.13.

Figure 2.13: Thrust Stand Calibration Setup

The LVDT will be used to measure the displacement of the thrust stand system. These displacement measurements will enable thrust to be calculated. As mentioned previously, two springs will be placed

44 between the linear displacement block and stationary contact block. These springs have a known k constant. When the top plate of the thrust stand moves, the LVDT will be able to measure displacement.

Thus, applying a spring force to the thrust stand system, which can be calculated via Hooke’s Law: 퐹 =

푘푥.

The shock absorbers in the thrust stand will also apply a damping force to the system, Fd. In addition to the spring force and the damping force, the mass of the RDE apparatus on top of the thrust stand will also apply a force to the system, Fm. The RDE apparatus includes the RDE, the RDE test stand and the pipes and tubes connected to the RDE. Each of these forces will be acting in the opposite direction of thrust. Thus, the sum of these forces can be used to calculate the thrust generated by the RDE as follows:

푇 = 퐹푠 + 퐹푑 + 퐹푚 (2.1)

Calibration of the thrust stand mainly involves ensuring that the displacement measurements from the

LVDT are accurate. In order to determine the accuracy of these measurements, the force applied to the thrust stand is plotted against the displacement, which is given as a voltage output. When the platform is attached to the wire ropes and pulleys on the thrust stand, it applies a known force (26.8 lbs.) to the thrust stand system. Large 34.5-lb weights are then added to the platform to apply even greater amounts of force to the system, as shown in Figure 2.13. Thus, when a force vs. voltage plot is created, it should result in a linearly increasing plot. This is very similar to the calibration technique used by Santoro in his experiment

[20]. The following calibration curves were plotted for springs with varying k constants as shown in

Figures 2.14-2.19.

100 90 y = 22.969x - 138.11 R² = 0.9734 80 70 60 50

Force(lbs) 40 30 20 10 0 7 7.5 8 8.5 9 9.5 10 Voltage (V)

Figure 2.14: Calibration Curve for springs with k = 10 lbs/in without RDE apparatus

200 y = 38.21x - 194.47 R² = 0.9845 150

100 Force(lbs)

0 5 6 7 8 9 10 Voltage (V)

Figure 2.15: Calibration Curve for springs with k = 35.6 lbs/in without RDE apparatus

350

y = 66.664x - 337.26 300 R² = 0.9881

250

200

150 Force(lbs)

100

0 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 Voltage (V)

Figure 2.16: Calibration Curve for springs with k = 62.8 lbs/in without RDE apparatus

Although each calibration curve slightly deviates from the trend line, each plot is linear, which validates the LVDT measurements. Calibration of the thrust stand was done with and without the RDE apparatus mounted on top of the thrust stand. The thrust stand was first calibrated without the RDE apparatus in order to determine the amount of damping force applied to the system. Figures 2.14 - 2.16 correspond to thrust stand calibration without the RDE apparatus for springs with k constants equal to 10,

35.6 and 62.8 lbs/in, respectively. The maximum load that the thrust stand could measure increased as springs with greater k constants were used. For instance, when two springs with k = 35.6 lbs/in were used, a maximum load of 183.8 lbs. was required for the springs to fully compress between the blocks.

However, when two springs with k = 62.8 lbs/in were used, it took a maximum load of 302.8 lbs. to fully compress the springs.

The measured displacement from the LVDT was interpolated in order to convert the displacement measurements from voltage to inches. Converting the displacement to inches allows for determining the spring force using 퐹 = 푘푥. The k constant for the spring was multiplied by the displacement to calculate

47 spring force, 퐹푠. The maximum spring force, 퐹푠 of the larger springs is calculated as follows:

푙푏 퐹 = 푘푥 = 2 ∗ 62.8 ∗ 2.1875 𝑖푛 = 274.75 푙푏푓 (2.2) 푠,푚푎푥 푚푎푥 𝑖푛

The maximum spring force, 퐹푠,푚푎푥 is less than the maximum load that was applied in the calibration technique when these springs were used (302.8 lbs.) as shown in Figure 2.16. This is because the shock absorbers apply a damping force, which also contributes to the capability of the thrust stand to withstand a greater load. The thrust stand reached its maximum displacement of 2.1875 in. when 302.8 lbs. were applied to the platform. The difference between the maximum spring force, 퐹푠,푚푎푥 and maximum load applied yields the maximum damping force applied by the shock absorbers:

퐹푑,푚푎푥 = 302.8 푙푏푓 − 274.75 푙푏푓 = 28.05 푙푏푓 (2.3)

140 y = 18.546x - 39.868 R² = 0.97 120

100

60 Force(lbs)

0 3 4 5 6 7 8 9 10 Voltage (V)

Figure 2.17: Calibration Curve for springs with k = 10 lbs/in with RDE apparatus

250 y = 37.091x - 114.39 R² = 0.9949 200

150

Force(lbs) 100

0 3 4 5 6 7 8 9 10 Voltage (V)

Figure 2.18: Calibration Curve for springs with k = 35.6 lbs/in with RDE apparatus

400

350 y = 62.258x - 249.67 R² = 0.9691 300

250

200 Force(lbs) 150

100

0 3 4 5 6 7 8 9 10 Voltage (V)

Figure 2.19: Calibration Curve for springs with k = 62.8 lbs/in with RDE apparatus

The thrust stand was also calibrated with the RDE apparatus mounted on top, as shown by the calibration curves in Figures 2.17-2.19. This calibration method is especially important since this is the actual setup used during experiments. It also allows for the force due to the mass of the RDE apparatus,

퐹푚 to be calculated. Both calibration curves are linear, with most of the points having minimal deviation from the trend line. The maximum load that the thrust stand can measure is 352.8 lbs. when the springs with k = 35.6 lbs/in are used. Using this value, 퐹푚 can be calculated by taking the difference between the maximum applied load and the maximum spring and damper forces:

퐹푚 = 352.8 푙푏푠 − 퐹푠,푚푎푥 − 퐹푑,푚푎푥 = 50 푙푏푠 (2.4)

Thus, a force 퐹푚 of 50 lbs. is applied to the thrust stand as a result of the mass of the RDE apparatus.

Since the RDE is expected to generate a maximum thrust of 300 lbs., using the springs with k = 62.8 lbs/in will be sufficient for this experiment.

e) Vibration Analysis

Vibration analysis was conducted as an additional method to determine whether the thrust stand structure can withstand the amount of thrust and vibration produced by the RDE. A Simulink model of the thrust stand was created to simulate the thrust stand system, and to determine the response of the system. A similar approach was used in a previous study to simulate the operation of a PDE ejector [20].

Figure 2.20: Simulink model used to simulate thrust stand operation

The current Simulink model, shown in Figure 2.20 was developed to account for the forces acting on the system. Based on these forces and Newton’s second law (F=ma), the following equation is used to describe the system:

−푘푥 − 푐푥̇ + 푇 = 푚푥̈ (2.7)

The spring force, 푘푥 and damping force 푐푥̇ oppose the direction of motion, while the external force is applied as thrust, T in the positive direction. These three forces are set equal to mass times acceleration, or 푚푥̈. In the Simulink model, thrust was modeled as a step function at 300 lbs. or 1344.4 N. The spring constant, k was set equal to 125.6 lbs/in, which is the total k value of the springs that will be used in the thrust stand. An extensive approach was taken to calculate the approximate mass of the RDE apparatus.

This included calculating the volume of each component, and using the density of various materials to obtain an estimated total mass of ~125 kg, which was used in the model.

The damping coefficient, c was not specified for the shock absorbers, but c can be estimated based on the damping force equation, 퐹푑 = 푐푥̇. In the previous section, it was mentioned that the shock absorbers provide 28.05 lbs. of maximum damping force to the system. Also, the maximum displacement of the thrust stand is 2.1875 inches in either direction. The RDE will run for about 1 second for each test.

Therefore, the velocity, 푥̇ of the system can be estimated to equal 2.1875 in/s, which results in a damping coefficient of c ≈ 12.8 lbs-s/in.

The system response is shown below in Figure 38, which uses this c value. It results in an underdamped system, which fully dampens the motion of the system within 0.57 seconds. Since each

RDE test is about 1 second long, this is a very favorable response for this system. The maximum displacement in the system response is ~2.5 inches, which is close to the maximum displacement that can be measured by the LVDT (2.1875 inches) in either direction. Due to the results from the Simulink vibration analysis, the shock absorbers and the springs will provide sufficient damping and spring force to effectively dampen the motion of the system during experiments.

Figure 2.21: System response with T= 300 lbs., m = 125 kg, k= 125.6 lbs/in and c = 12.8 lbs-s/in

2.4 Inverse Brayton Cycle Based Propulsion System

This section discusses the heat exchanger design that will be incorporated into the Inverse Brayton

Cycle based propulsion system. It also includes an explanation of the software used to simulate the propulsion system.

a) Heat Exchanger Design

A heat exchanger is a device that is capable of transferring thermal energy in one of three ways: between two or more fluids, between a solid surface and a fluid, or between solid particles and a fluid in thermal contact with each other at varying temperatures [34]. The current study focuses on designing a lightweight, ambient heat exchanger to incorporate into the Inverse Brayton cycle. The ambient heat exchanger is significant, because it is used along with the recuperator to reduce the compressor inlet temperature. The temperature at the compressor inlet has a direct impact on the thermal efficiency and power output of the system.

A great deal of research went into selecting the proper heat exchanger to implement into the Inverse

Brayton Cycle. Compact heat exchangers are designed to weigh less than typical heat exchangers, and are

52 capable of transferring a greater amount of heat over a given surface area (i.e. greater surface area density) [35]. The benefit of compact heat exchangers can be visualized in the chart shown in Figure 2.22.

Figure 2.22: Heat exchanger variation chart [35]

Due to its benefits over other compact heat exchangers, the microchannel heat exchanger was selected as the design for the ambient heat exchanger. A microchannel heat exchanger involves the flow of fluid in parallel confinements with hydraulic diameters that are less than 1 mm [35], which is significantly less than that of typical compact heat exchangers (1 mm – 6 mm). Smaller hydraulic diameter will help to reduce the weight of the heat exchanger, thus helping to solve the problem of engine weight increase due to the addition of the ambient heat exchanger. Microchannel heat exchangers also have greater surface area density than other typical heat exchangers, which results in a significant increase in heat transfer rate per unit volume.

Figure 2.23 shows a single module of the cross-flow microchannel heat exchanger. The entire ambient heat exchanger is composed of 100 modules to provide adequate heat transfer. The heat exchanger is designed to have offset microchannels and shorter fins, rather than continuous fins. These

53 shorter fins will reduce the thickness of thermal boundary layers that normally form on long, continuous fins, resulting in a greater amount of heat transfer on both the hot and cold sides of the heat exchanger

[35]. The material that was chosen for the microchannel heat exchanger was ceramic matrix composites

(CMC) because of its low material density (3-4 g/cm3), high thermal conductivity (250-400 W/m-K), and sufficient temperature limit (1650°C). In addition, CMC is relatively low in cost and high in strength when compared to other materials such as stainless steel, copper and ceramics [35].

Figure 2.23: Single module of the microchannel heat exchanger [36]

The hot fluid comes from the components upstream of the heat exchanger, while the cold fluid enters from the environment at atmospheric conditions. The hot fluid flows through the microchannels within the heat exchanger, while the cold fluid flows through the fins on top. This design enables both fluids to enter from different directions and facilitates the transfer of thermal energy. The maximum possible rate of heat transfer between both fluids through the heat exchanger is defined by the following equation:

푞̇푚푎푥 = 퐶푚𝑖푛 ∗ (푇ℎ,𝑖푛 − 푇푐,𝑖푛) (2.8)

where 퐶푚𝑖푛 is the minimum heat capacity rate and 푇ℎ,𝑖푛 and 푇푐,𝑖푛 denote the inlet temperatures from the hot fluid and cold fluid, respectively. The heat capacity rate is equal to the mass flow rate of the fluid multiplied by the specific heat of the fluid as follows:

퐶푚𝑖푛 = 푚̇ 푐푝 (2.9)

The equation for maximum heat transfer rate, 푞̇푚푎푥 implies that one fluid will experience the maximum possible temperature difference, 푇ℎ,𝑖푛 − 푇푐,𝑖푛. Thus, the actual heat transfer rate needs to be calculated to determine the true amount of heat that is transferred throughout the heat exchanger. This value is determined by the heat exchanger effectiveness (휀), which is the ratio between the actual heat transfer rate 푞̇푎푐푡 and the maximum heat transfer rate 푞̇푚푎푥 as follows:

푞̇ 휀 = 푎푐푡 (2.10) 푞̇푚푎푥

Further analysis of the microchannel heat exchanger design will be discussed in the following chapter.

b) Inverse Brayton Cycle Simulation

The Inverse Brayton Cycle was first modeled and simulated using Simscape, which is an extension of

MATLAB and Simulink. It is a physical systems simulation software that can be used to model a variety of systems. The Simscape model of the Inverse Brayton Cycle based turbojet engine is shown in Figure

2.23 below. Various parameters such as inlet Mach number, air and fuel flow rates, and atmospheric conditions can be defined for the model components. Each component includes an embedded MATLAB code, which defines inputs, outputs, and additional parameters that contribute to the simulation.

Figure 2.24: Simscape model of Inverse Brayton Cycle

This model contains both physical and thermal components. The atmosphere, intake, combustor, turbine, and compressor comprise the physical components. The thermal components include the recuperator, ambient heat exchanger and temperature source and sensor blocks. The latter two components were used to establish a connection between the physical and thermal components.

MATLAB codes were developed to verify the results obtained from the Simscape model. Similar to the Simscape model, the codes allow for various initial parameters to be defined. The codes also incorporate parameters from the microchannel heat exchanger design in order to determine the effect that the heat exchanger will have on the compressor inlet temperature and the overall engine. The codes are able to provide various outputs and plots, which will be discussed in the following chapter.

Chapter 3: Results & Discussion

3.1 Ethylene-Air Modular RDE Study

The results presented this section are from the investigation of an RDE, which utilized non-premixed ethylene-air mixtures. These results were previously presented as part of a conference paper that was written by the author of this thesis [27]. Included in this section are plots, which are used to measure and analyze the performance of the RDE under various conditions.

a) Operating Map

The modular RDE for this experiment was defined to function under two operating conditions: success or failure. A combustion front that continuously rotated within the combustion channel is considered a successful test. A failed test is defined as either a combustion event that never rotated within the channel (i.e., failure-to-initiate), or a rotating event that was propelled out of the channel (i.e. pop- out). Figure 3.1 shows measurements that are considered a successful test.

(a) (b)

Figure 3.1: Pressure-time traces for successful test at ṁ = 0.2 kg/s: a) PCB pressure traces and b) Ion probe measurements

Pressure feedback was measured using three PCB pressure transducers that were connected to the air injection slot as shown in Figure 3.1a. Three ionization sensors were attached to the outer body to indicate the passage of a combustion front. The traces for each ion probe measurement are shown to be out of

57 phase in Figure 3.2b, indicating a rotating event present within the combustion channel. The duration of each test was 1 second long, and continuous rotation was achieved for the entire testing period for each of the successful tests. For the successful tests shown in Figure 3.1, the mass flow rate is ṁ = 0.2 kg/s, and the equivalence ratio is ϕ = 1.25.

The operating map in Figure 3.2 shows the results from each test for various mass flow rates and equivalence ratios. There appears to be an established limit for successful cases in which continuous rotating detonation could be achieved. For instance, the range of mass flow rates for a successful test is ṁ

= 0.2–0.3 kg/s. Furthermore, two limits can be observed in Figure 3.2 for the successful cases, related to ϕ values. The lean limit, or minimum ϕ for successful operation was ϕ = 0.845, while the rich limit, or the maximum ϕ for successful operation was ϕ = 1.34. Any tests that were run below the lean limit or above the rich limit resulted in a failure. As mentioned earlier, this includes either a pop out or failure-to-initiate.

These results are consistent with the theory, which Lee proposed stating that detonation cannot propagate for ϕ < 0.5 due to an insufficient heat release behind the shock wave [9].

Figure 3.2: Operating Map of Non-Premixed Ethylene-Air RDE

b) Wave Speed Performance

Figure 3.3 shows the combustion wave speed, W plotted against the equivalence ratio, ϕ, which helps to further analyze and evaluate the RDE performance. The NASA Chemical Equilibrium and Analysis

(CEA) program was used to determine the speeds of the isobaric sound wave and ideal C-J detonation wave. These wave speeds were calculated assuming atmospheric conditions for the reactant pressure (1 bar) and temperature (300 K). Observing the plot, it can be seen that the speeds for each of the successful cases are significantly lower than the ideal detonation wave speed, WCJ. However, the successful cases with higher ϕ have wave speeds that are closer to the isobaric sound speed, and greater than the cases with lower ϕ. Overall, the combustion front travels approximately at the speed of sound in the combustion products (i.e. choked flame), which is a result that has been seen in a previous experiment for an ethylene- air RDE [22].

It is highly likely that the induced swirling velocity in the reactants caused the combustion front to propagate at a significant C-J deficit. The relatively low wave speed of the detonation could also be due to losses as a result of insufficient mixing. Since the wave speeds are significantly less than WCJ, and also less than isobaric speed of sound, it can be concluded that quasi-detonation occurred for each of the successful cases in this experiment.

Figure 3.3: Detonation wave speed vs. equivalence ratio

c) Detonation Cell Size, Fill Height and Pressure Ratio

Determining the size of the cells within the detonation wave structure as it rotates around the combustion chamber can be used to effectively measure the performance of an RDE. The online detonation database was used to find values for cell size, λ at atmospheric pressure of 1 bar for ethylene- air mixtures [38]. These values in particular were found since the combustion chamber was filled with ethylene-air mixture at atmospheric pressure of 1 bar. The fill height of the mixture, h was calculated using the following equation:

푚̇ ℎ = (3.1) 휌∙푊∙푤푐ℎ where ṁ represents mass flow rate, ρ represents reactant density, W represents combustion wave speed and wch represents combustion channel width. Figure 3.4 shows the ratio of fill height to cell size, h/λ plotted against the equivalence ratio, ϕ. The plot only shows successful cases for ṁ values of 0.2 and 0.3 kg/s. The curve for ṁ = 0.3 kg/s slightly increases near ϕ = 1.2, which is expected since the cell sizes are smallest when ϕ = 1.2, leading to greater h/λ ratios. Also the curve for ṁ = 0.3 kg/s is above the ṁ = 0.2 kg/s due to greater values of h/λ. This is expected since h is largely dependent on ṁ as shown in Equation

(3.1). In addition to nearly constant combustion wave speed, W, h is nearly constant for ṁ = 0.2 kg/s for higher equivalence ratios (ϕ > 1), which is the reason for minimal variation between h/λ values in the plot, resulting in a nearly flat curve.

Figure 3.4: Ratio of fill height to cell size for varying ϕ values

Figure 3.5: Ratio of channel width to cell size for varying values

The ratio of channel width to cell size, wch/λ was also investigated by plotting such values against ϕ as shown in Figure 3.5. The plotted curve shows the wch/λ for both mass flow rates, 0.2 and 0.3 kg/s. The size of the channel width was 13.1 mm for each of the tests, so the wch/λ values change with varying λ.

The curve peaks near ϕ = 1.2, which is similar to the previous plot in Figure 3.4 due to smaller cell size.

The air injection pressure ratio, PRAir was also investigated with varying ϕ values as shown in Figure

3.6. PRair is the ratio of air stagnation pressure to air static pressure. The choked limit of PRAir is 1.89, which is determined by the combustion chamber geometry. The plot shows that nearly each of the successful tests exceeds this calculated choked limit. This is due to multiple factors including the small air gap, the chamber pressure being kept constant at atmospheric pressure, and the lack of a nozzle attached to the center body while testing.

Figure 3.6: Air injection pressure ratio

3.2 Inverse Brayton Cycle Turbojet Study

a) Specific IBC Turbojet Case

This section discusses the results obtained from the Simscape model, which was developed to simulate an Inverse Brayton Cycle (IBC) based turbojet engine. Results from the simulations will determine the amount of power output that this type of engine is capable of generating. The parameters outlined in Table 3.1 were used to define atmospheric conditions at sea level.

Table 3.1: Atmospheric Conditions defined for IBC Turbojet Simulation Parameters Value Significance

g 9.81 m/s2 Acceleration due to gravity

R 287 J/kg-K Individual gas constant for air

γ 1.4 Ratio of specific heats for air

a0 340 m/s Speed of sound of air at atmospheric temperature

Mach, M 0.7 Inlet Mach number

The model was developed so that the turbojet engine components follow the same order as outlined in

Figure 1.12. As described in the Introduction, the combustor is the first component in the IBC. Thus, air enters the combustor at atmospheric conditions. Since sea-level altitude is assumed for this simulation, the inlet pressure is P0 = 101325 Pa. Similar to the ideal Brayton cycle, the ideal IBC assumes constant pressure combustion, so there is also atmospheric pressure at the combustor outlet. The flow is then expanded to sub-atmospheric pressure in the turbine. This model assumes constant pressure through both the recuperator and the ambient heat exchanger, which leads to sub-atmospheric pressure at the compressor inlet. The compressor then compresses the flow to higher pressure at the compressor exit.

Assuming isentropic compression and expansion, the Simscape model was simulated to obtain values for both the turbine exit and compressor exit pressures. These values are shown in Table 3.2.

Table 3.2: Pressure Values for IBC obtained from Simscape Model Component Inlet Pressure (Pa) Outlet Pressure (Pa)

Combustor 101,325 101,325

Turbine 101,325 67,280

Compressor 67,280 336,399

As previously mentioned, the IBC requires the pressure to be sub-atmospheric at the compressor inlet.

The model of the IBC turbojet was able to meet this requirement as shown in Table 3.2. A compressor pressure ratio of 5 was used to achieve adequate thrust output.

The Simscape model was also used to determine inlet and outlet temperatures for each component.

The temperature entering the combustor is initially T0 = 288.15 K since air enters the combustor at atmospheric conditions. Assuming atmospheric conditions, the model was simulated to determine the combustor exit temperature, and the inlet and outlet turbine temperatures.

The recuperator and ambient heat exchanger were modeled as thermal components. These thermal components include embedded MATLAB codes, which contain heat transfer equations that were used to find the inlet and outlet temperatures. The temperature exiting the recuperator is significant, because a portion of this heat will be transferred to the combustor, which will be used to define the combustor inlet temperature for the subsequent cycles. The following equations were used to determine the maximum and actual heat transfer rates through the recuperator and ambient heat exchanger:

푞̇푚푎푥 = 푚̇ 푐푐푝푐 ∗ (푇ℎ,𝑖푛 − 푇푐,𝑖푛) (3.1)

푞̇푎푐푡 = 푚̇ ℎ푐푝ℎ ∗ (푇ℎ,𝑖푛 − 푇ℎ,표푢푡) (3.2) where 푚̇ represents the mass flow rate, c represents the specific heat, and T represents temperature into or out of the heat exchanger elements for each fluid. The h subscript for each parameter signifies the hot fluid while the c subscript signifies the cold fluid. The hot fluid entering the recuperator is from the turbine exit, while the incoming cold fluid is air from the atmosphere. The mass flow rate of air for this particular case is 0.45 kg/s, while the mass flow of fuel is 0.01 kg/s. Since 푚̇ from the hot fluid includes air and fuel, 푚̇ ℎ= 0.46 kg/s, while 푚̇ 푐 = 0.45 kg/s since no fuel is included in the airflow from the cold fluid. Similarly, specific heat of the cold fluid, 푐푝푐 = 1.004 kJ/kg-K (from atmospheric conditions), while specific heat of the hot fluid 푐푝ℎ = 1.2541 kJ/kg-K (from air and fuel mixture). These values are then used to determine the temperature of both the cold fluid and the hot fluid as they exit the recuperator:

푞̇푚푎푥 푇ℎ,표푢푡 = 푇ℎ,𝑖푛 − 휀 ∗ ( ) (3.3) 푚̇ ℎ∗푐푝ℎ

푞̇푎푐푡 푇푐,표푢푡 = 푇푐,𝑖푛 + 휀 ∗ ( ) (3.4) 푚̇ 푐∗푐푝푐

Using these equations enables the function of a heat exchanger to be accurately simulated, yielding accurate results for exit temperatures of both the hot and cold fluids. Also, an effectiveness value, ε of

0.645 was used for both the recuperator and ambient heat exchanger.

After the simulation was run, the temperature exiting the recuperator was found to equal 995.2 K.

Thus, the Simscape model uses this temperature as the actual combustor inlet temperature for all subsequent cycles throughout the engine. The connection from the recuperator to the combustor is established using the temperature sensor as shown in Figure 2.24 in the previous chapter. Equations 3.1-

3.4 were again used to calculate values for heat transfer rates and both inlet and exit temperatures as indicated in Table 3.3 and Figure 3.7.

Table 3.3: Heat Transfer Rates for Recuperator and Ambient Heat Exchanger

Component 풒̇ 풎풂풙 (kW) 풒̇ 풂풄풕 (kW)

Recuperator 495.26 319.44

Ambient Heat 243.27 156.91 Exchanger

Figure 3.7: Schematic of Heat Transfer through Recuperator and Ambient Heat Exchanger

The recuperator and ambient heat exchanger both work to successfully extract heat from the flow before it enters the compressor, reducing the temperature from 1384.3 K to 552.6 K. The inlet and outlet temperature values for each component are outlined in Table 3.4. A MATLAB code was developed to

65 verify the calculations for the inlet and exit temperatures obtained by the Simscape model for each component to ensure the accuracy of the simulation results.

Table 3.4: Inlet & Outlet Temperatures for IBC Turbojet Components Component Inlet Temp (K) Outlet Temp (K)

Combustor 995.2 1457.2

Turbine 1457.2 1384.3

Recuperator 1384.3 826.6

Ambient Heat 871.22 552.6 Exchanger

Compressor 552.6 875.9

Finally, the power output for this specific case of an IBC based turbojet engine was calculated using the following equation from Mattingly’s Elements of Propulsion textbook [37]:

1 2 2 푊̇ 표푢푡 = [(푚̇ 0 + 푚̇ 푓) ∗ 푉푒 − 푚̇ 0푉0 ] (3.5) 2푔푐

where Ve and V0 are the exit and inlet flow velocities, respectively, which were obtained from the

Simscape results. The mass flow rates of air and fuel are denoted by 푚̇ 0 and 푚̇ 푓, respectively. gc is a proportionality constant which equals 1 when using SI units. For Ve = 600 m/s and V0 = 240 m/s, 푊̇ 표푢푡 =

69.84 kW. This power output is sufficient to power smaller UAVs, i.e. Micro Air Vehicles [39].

b) Various IBC Turbojet Cases

While the results from the previous section focused on one particular IBC case, this section focuses on results obtained when various IBC turbojet cases are investigated. This allows for a more in-depth analysis to observe the effect that certain conditions have on the performance of an IBC turbojet system.

Since compressor inlet temperature is such an integral factor to the efficiency of the IBC, parameters such

66 as specific thrust and thrust specific fuel consumption (TSFC) were compared over a range of compressor inlet temperatures. This was done to show the significance of the heat exchangers’ ability to extract heat from flow entering the compressor.

The compressor inlet temperatures were varied for two conditions: an IBC turbojet with two heat exchanger elements (recuperator and ambient heat exchanger), and an IBC turbojet with only a recuperator. The case with recuperation only was used as a comparison to further show the significance of using two heat exchanger elements as opposed to one. The range of compressor inlet temperatures, T6 for both conditions were chosen as follows:

IBC with 2 heat exchanger elements: 553 K ≤ T6 ≤ 840 K (3.6)

IBC with recuperation only: 830 K ≤ T6 ≤ 1115 K (3.7)

The minimum T6 value for each condition was found by simulating the IBC turbojet model for an effectiveness value of 0.645 for the heat exchanger elements, as defined in the previous section. The compressor inlet temperature for the case described in the previous section was ~553 K. When the same model was simulated with the exclusion of the ambient heat exchanger, the compressor inlet temperature was ~830 K. Using the values for T6, the model was able to determine the compressor outlet temperatures, T7 as follows:

IBC with 2 heat exchanger elements: 675 K ≤ T7 ≤ 957 K (3.8)

IBC with recuperation only: 947 K ≤ T7 ≤ 1232 K (3.9)

For each compressor inlet temperature (T6) within the given range, there is a corresponding compressor outlet temperature, T7 within the ranges shown in (3.8) and (3.9). The compressor inlet temperature values were normalized so that the range was from 0 to 1 for both cases. The lowest value in each compressor inlet temperature range corresponds to 0 while the highest compressor inlet temperature

67 in each range corresponds to 1. Normalizing the compressor inlet temperatures allows for a more direct comparison between the two cases since all of the values will fall within a range of 0 to 1.

MATLAB was also used to calculate various values that are utilized to conduct cycle analysis of an ideal turbojet including fuel-air ratio, f and ratios of exit total temperature to inlet total temperature (휏휆,

휏푟, 휏푐 and 휏푡) for various components in order to determine specific thrust, TSFC and thermal efficiency.

Equations for these ratios are defined in Mattingly’s Elements of Propulsion textbook, which can be used to calculate specific thrust, TSFC and thermal efficiency [37]. These are key parameters that can be used to effectively measure the performance of an engine. Equations (3.10) – (3.12) were used to calculate specific thrust, TSFC and thermal efficiency, respectively.

퐹 푎0 2 휏휆 = [√ ∗ (휏푟휏푐휏푡 − 1) − 푀0] (3.10) 푚̇ 0 푔푐 훾−1 휏푟휏푐

푓 푆 = (3.11) 퐹/푚̇ 0

1 휂푡ℎ = 1 − (3.12) 휏푟휏푐

The following plots in Figures 3.9 & 3.10 show the specific thrust and TSFC plotted over normalized ranges of compressor inlet temperatures. The two linear plots represent the IBC with two heat exchanger elements (blue) and IBC with recuperation only (red).

Figure 3.9: Specific thrust vs. Normalized compressor inlet temperature

Figure 3.10: TSFC vs. Normalized compressor inlet temperature

By observing the trends in each plot, it can clearly be seen that the engine performance suffers under higher compressor inlet temperatures. The IBC turbojet engine experiences a decrease in specific thrust and an increase in TSFC for greater compressor inlet temperatures. The increase in TSFC with compressor inlet temperature shows that a greater mass flow rate of fuel is required to generate sufficient thrust throughout the duration of the flight. Thus, the IBC turbojet engine is less efficient when flow enters the compressor at higher temperatures.

These plots also highlight the enormous benefit of implementing two heat exchanger elements in the

IBC rather than the recuperator alone. Using the recuperator along with the heat exchanger extracts a greater amount heat from the flow, which results in lower compressor inlet temperatures. Thus, using two heat exchanger elements results in improved efficiency and engine performance, i.e. greater specific thrust and less TSFC than with recuperation only.

Further analysis was conducted to investigate the performance of the IBC turbojet with two heat exchanger elements. The effectiveness, ε is a key parameter used to define the rate of heat transfer for the two heat exchanger elements. Thus, ε was varied to determine how it affects the thermal efficiency and power output of the IBC turbojet. Figure 3.11 shows the thermal efficiency, ηth plotted over varying power output values. Each curve on the plot represents varying ε values. Using Equation (3.5), the mass flow rate of air, 푚̇ 0 was varied in order to obtain values for power output within a range of 20-80 kW.

The thermal efficiency is shown to increase as power output increases. Since 푚̇ 0 was varied to obtain power output values within the desired range, it is expected for the power output to increase for higher air mass flow rates. Greater airflow through the engine will result in lower compressor inlet temperatures, thereby improving thermal efficiency. Figure 3.11 also shows an increase in thermal efficiency for greater

ε values. When ε is increased, a greater amount of heat is transferred and extracted from the flow, leading to lower temperatures at the compressor inlet. Therefore, the IBC turbojet is more efficient for greater heat exchanger effectiveness.

Figure 3.11: Thermal efficiency vs. Power output

Figure 3.12: Compressor inlet temperature vs. Power output

Figure 3.12 shows the compressor inlet temperature plotted against power output, with each curve representing varying ε values. This plot shows a decrease in compressor inlet temperature as power output and ε are increased. This plot further proves that increasing the flow rate of air through the engine, and increasing the effectiveness of the heat exchangers will result in lower compressor inlet temperatures and greater thermal efficiency. The blue dot in both Figures 3.11 & 3.12 denotes results from the specific IBC turbojet case, which was defined in the previous section. The thermal efficiency, ηth of the specific case is

0.372. Observing Figure 3.11, it can be seen that there is a small difference in ηth between the specific case and the most efficient case with ε = 0.7 (where ηth = 0.377). However, there is a noticeably greater difference between the compressor inlet temperatures for both cases, which can be seen in Figure 3.12.

Although the IBC turbojet experiences improved efficiency for greater ε values, there is a tradeoff between heat exchanger effectiveness and range of flight for the aircraft. This tradeoff is shown in Figure

3.13, which shows the flight range plotted against heat exchanger effectiveness.

Figure 3.13: Range of flight vs. Heat exchanger effectiveness

One of the outlined objectives of this research is to design an ambient heat exchanger that will not result in a considerable weight increase for the engine. The Brequet range equation was used to calculate the range of flight, which is dependent on the total engine weight as shown in the following equation:

퐿 푊𝑖 푅푎푛푔푒 = 휂푃 ∗ ( ) ∗ ln ( ) (3.14) 퐷 푊푓

where 휂푃 is the propulsive efficiency, L/D is the lift-to-drag ratio and Wi/Wf is the ratio of initial weight to final weight. Figure 3.13 shows that the range decreases significantly for greater ε values, which is directly related to an increase in the engine weight. Thus, an effectiveness value of 0.645 offers the best tradeoff between thermal efficiency, flight range and engine weight. This is the reason for setting the recuperator and heat exchanger effectiveness to ε = 0.645 for the IBC turbojet for the specific case.

c) Comparison to Similar Turbojets

The performance of the IBC based turbojet for the specific case was compared to similar turbojet engines. These turbojets are high-performance gas turbines and utilize similar mass flow rates of air and fuel. Table 3.5 shows a direct comparison of flow rates, thrust and SFC for each engine.

Table 3.5: Performance Comparison of Turbojets Engine Air Flow Fuel Flow Thrust SFC * 10-5 T/W Rate (kg/s) Rate (kg/s) (N) [kg/(N-s) (initial)

IBC Turbojet 0.45 0.01 314 3.180 3.65

Pegasus HP 0.375 0.008 167 4.036 8.15

Jetcat P-200 0.45 0.012 231 5.046 9.40

Olympus 0.45 0.011 230 4.640 9.57

Mercury 0.25 0.005 88 5.590 6.19

Titan 0.66 0.017 392 4.337 12.6

The other turbojets listed in Table 3.5 are produced by AMT Netherlands [x]. As can be seen from Table

3.5, the performance of the IBC turbojet is very comparable to these engines. The only turbojet that produces more thrust is the Titan, which is due to its slightly higher air and fuel flow rate through the engine, contributing to greater exhaust speed and thrust. The IBC turbojet has the least amount of SFC, which is due to the relatively low fuel flow rate. This is attributed to the recuperator, which reclaims a portion of the waste heat from the turbine, and uses it to preheat the air at the combustor inlet. As a result, less fuel (or heat input) is needed to obtain the same net work output.

However, the IBC turbojet also has the lowest initial thrust-to-weight ratio (T/W), which is due to the additional weight of the recuperator and ambient heat exchanger. These components add approximately 8 lbs. of additional weight to the engine. The relatively low thrust-to-weight ratio could also be due to the fact that the IBC turbojet uses a greater compressor pressure ratio than the other turbojet engines. Thus, reducing the compressor pressure ratio can further reduce the size of the compressor, thereby improving the thrust-to-weight ratio.

3.3 Hydrogen-Air TOXIC RDE Thrust Study

a) RDE Operation

This section covers results obtained when using the thrust stand to measure the thrust of the TOXIC

RDE configuration. A hydrogen-air mixture was utilized for this RDE. Each of the tests that were run for this configuration resulted in successful rotating detonation within the combustion chamber throughout the duration of the test (~1 second). This was expected since a hydrogen-air mixture has been proven to be a highly detonable mixture in past detonation experiments [11, 12]. A pressure vs. time profile of one test is shown in Figure 3.13. Similar to the ethylene-air RDE study, three PCB pressure transducers were used to measure the pressure feedback, and were connected to the air injection slot. The oscillations shown by each PCB trace indicates that a rotating event occurred within the combustion channel. This was the case for each of the tests that were investigated. For the pressure-time traces shown in Figure

3.14, the mass flow rate is ṁ = 0.244 kg/s, and the equivalence ratio is ϕ = 1.23.

Figure 3.14: Pressure-time traces for successful test at ṁ = 0.244 kg/s and ϕ = 1.23

For this study, the RDE stand was placed on top of the thrust stand to enable thrust measurements for the RDE. The thrust stand was designed to measure thrust based on the movement of the top plate of the

75 stand. The movement and vibrations of the RDE caused upon firing were thought to be sufficient for moving the top plate of the thrust stand, thus enabling a displacement reading by the LVDT. Two sets of springs were used in the thrust stand during experiments: the largest (k = 62.5 lbs/in) springs and the smallest (k = 10 lbs/in) springs. The LVDT was connected to the DAQ so that displacement measurements could be read and recorded via the LabVIEW program. The calibration curve corresponding to the springs used during each experiment was loaded into the LabVIEW program in order to directly calculate thrust based on the displacement readings of the RDE. A thrust vs. time plot obtained from one test is shown below.

Thrust (lbs) Thrust 8

0 0 1 2 3 4 5 6 7 8 9 Time (s)

Figure 3.14: Thrust-time profile for successful test at ṁ = 0.2 kg/s and ϕ = 1 for k = 62.5 lbs/in

The plot indicates that a maximum thrust value of about 19 lbs. of thrust was produced by the RDE for a test in which the mass flow rate is ṁ = 0.2 kg/s, and the equivalence ratio is ϕ = 1. This plot can be divided into four regions corresponding to various phases that take place during the test. The first region corresponds to the response when air began flowing through the engine. This region is immediately followed by the response due to the onset of fuel flowing into the engine, which can be seen by the first

76 peak in Figure 3.14. This region is followed by detonation combustion within the chamber, which begins with ignition of the reactive mixture denoted by the largest peak in the thrust-time trace. The final region records ignition to shut down at the conclusion of the test. This method of dividing the thrust-time trace into regions based on varying phases during testing is similar to the method used in Suchocki’s RDE thrust experiment [21].

The trends in the thrust-time profile in Figure 3.14 are similar to those obtained from other experimental investigations of thrust in RDEs [5, 21]. However, the actual thrust measurements are expected to be much greater than the readings in Figure 3.14. Previous RDE experiments utilized combustion chambers that were even smaller than the RDE in this experiment, and obtained thrust values of nearly 100 lbs. [20, 21]. Furthermore, the wave speed for each test ranges from about 1300 – 1350 m/s, which should result in greater thrust readings than shown in the thrust-time profile. Initially, the system was thought to be overdamped, which could have contributed to the lower thrust values. An overdamped system would also explain why the thrust stand did not slide when the RDE was fired. In order to solve this problem, the smaller (k = 10 lbs/in) springs were used instead of the larger (k = 62.5 lbs/in) springs to reduce the opposing spring force. The settings in the shock absorbers were also modified to reduce the amount of damping force.

Figure 3.15: Thrust-time profiles for two successful tests for k = 10 lbs/in: a) ṁ = 0.242 kg/s and ϕ = 1 and b) ṁ = 0.244 kg/s and ϕ = 1.23

Figure 3.16: Thrust-time profiles for two successful tests for k = 10 lbs/in: a) ṁ = 0.25 kg/s and ϕ = 0.86 and b) ṁ = 0.383 kg/s and ϕ = 0.86

With the reduced amount of spring and damping force, the thrust stand obtained new thrust measurements for multiple RDE tests. Results from these tests are shown in Figures 3.15 and 3.16.

Conditions were varied to determine which conditions would result in greater thrust measurements of the

RDE. For instance, Figure 3.15 shows two thrust-time profiles for varying equivalence ratios, while the mass flow rate of air is kept relatively constant. The peak due to ignition is seen to produce a greater amount of thrust for Figure 3.15b with a higher equivalence ratio. Another trend is observed in which the average thrust during combustion is greater for Figure 3.16b with higher mass flow rate of air. The average thrust produced during combustion was calculated for each test, by averaging the thrust values within the third region as defined in Figure 3.14. These average thrust values are outlined in Table 3.6 below. These trends show that the increase in airflow through the engine will result in greater thrust produced for the RDE, which is consistent with Suchocki’s findings [21].

Table 3.6: Thrust Produced During Combustion for Various Conditions

풎̇ ퟎ (kg/s) ϕ Average Thrust Produced During Combustion (lbs.)

0.242 1.02 3.35

0.244 1.23 3.78

0.25 0.86 3.59

0.383 0.86 4.09

b) Simulation of Thrust Stand Response to RDE

Although similar thrust-time profiles have been observed in previous research [5], the values for thrust in each of the plots is still much lower than expected. Another contributing factor to the low thrust measurements could be due to static friction forces between the fixed align bearings and the support rails due to the large mass of the RDE stand. Friction was not taken into account when the vibrational response in Simulink was modeled as shown in Fig. 2.21. Another very probable factor contributing to the low thrust measurements in the thrust-time profile is the possibility of torque produced by the RDE exerted on the thrust stand when it is fired. The RDE is about 1.5 feet above the thrust stand. Given the size and configuration, this particular RDE was expected to produce about 200 to 300 lbs. of thrust. This would result in a torque of about 300-450 ft-lb exerted on the RDE. If the force applied to the thrust stand is actually a rotational force, it would explain why larger thrust values are not observed in the plots. The thrust stand is designed to only measure force applied in a linear direction via the LVDT.

A SolidWorks model was created to effectively and accurately simulate the response of the thrust stand as the RDE is fired. This model is a simplified version of the top plate of the thrust stand situated under the RDE stand. A feature in SolidWorks called the Simulation Study Advisor was used to obtain deflection measurements throughout the entire model when thrust values of 200, 250 and 300 lbs. are generated by the RDE. The SolidWorks model and the simulation results are shown in Figures 3.17-3.18.

Figure 3.17: Simplified SolidWorks model of RDE stand and top plate of thrust stand

Figure 3.18: Simulation results showing deflection of entire system with RDE thrust output of 300 lbs.

When the simulation is animated, the horizontal unistruts of the RDE stand can be seen to deflect in a vertical direction. This same deflection can also be observed in the top plate of the thrust stand. This animation is very similar to the response that was shown during actual testing when the both the unistruts and thrust stand oscillated vertically. However, in Figure 3.18, the degree of deflection in the thrust stand cannot be observed due to the relatively greater magnitude of deflection in the RDE (red region). The plot in Figure 3.18 shows a better depiction of deflection variation for the top plate of the thrust stand.

Figure 3.19: Deflection of top plate of thrust stand with RDE thrust output of 300 lbs.

By observing Figure 3.19, it can be seen that maximum deflection occurs on edge of the top plate of the thrust stand. It is expected for this particular edge to have maximum deflection since it is directly underneath the RDE. The model was run to simulate various amounts of thrust being generated by the

RDE. These results are shown in Table 3.7, showing that the thrust stand experiences greater deflection due to torque as more thrust is applied by the RDE.

Table 3.7: Deflection in Top Plate of Thrust Stand

Deflection (mm) T = 200 lbs. T = 250 lbs. T = 300 lbs.

Average 6.13E-07 7.67E-07 9.20E-07

Maximum 1.02E-06 1.27E-06 1.53E-06

Minimum 4.61E-07 5.76E-07 6.91E-07

Chapter 4: Conclusions & Recommendations

4.1 Ethylene-Air Modular RDE Study

This study involved the observation of various parameters for measuring and analyzing the performance of a modular RDE operating on a mixture of ethylene and air. The operating maps showed conditions resulting in optimal performance for such an RDE configuration. By observing these operating maps, clear limitations can be seen for which successful rotating detonation was achieved within the combustion chamber. Successful tests, which constituted as continuous rotation achieved throughout the entire testing period, were seen to occur for mass flow rates of 0.2 and 0.3 kg/s. There was also a lean limit and rich limit of equivalence ratio, ϕ established during these tests. Successful tests were seen for equivalence ratios within the range of 0.85 < ϕ < 1.34. Thus, if relatively low mass flow rates are used in addition to nearly stoichiometric conditions, rotation will occur for an RDE utilizing an ethylene-air mixture.

The wave speed of the successful tests was also measured and analyzed, and was shown to be significantly less than the ideal C-J detonation wave speed. One reason for this is that the combustion front propagated at the isobaric speed of sound within the combustion products, which indicates that a choked flame rotated through the channel. The induced swirling velocity in the reactants also contributed to the combustion front propagating at a significant C-J deficit. Losses due to insufficient mixing of the reactants are another likely for the relatively low wave speed of the detonation. The detonations observed in the successful cases can be considered as quasi-detonating waves, because the detonations were shown to propagate at speeds much lower than C-J wave speed. This study also involved determining the cell size of the cells that compose the detonation wave. The ratio of fill height to cell size, h/λ exceeded 1, while the ratio of channel width to cell size, wch/λ exceeded 0.5 for nearly all of the successful tests.

The main objective of this experiment was to prove that rotation of a detonation wave can be sustained under certain conditions for a non-premixed ethylene-air RDE configuration. Although the detonation waves that were observed were quasi-detonations, the experiment was still a success because a

83 rotating detonation was achieved to some extent within the combustion chamber. Moreover, this was the first RDE experiment in the UC Detonation Test Facility to use solely ethylene as the fuel for the RDE. If mixing is improved, actual detonation waves can be observed in the next experiment utilizing ethylene-air mixtures. The newly designed TOXIC RDE configuration will be used for future RDE experiments in the

UC Detonation Test Facility, and its design enables combustor geometry and injection schemes to be easily modified. In future RDE experiments utilizing ethylene-air mixtures, various injection schemes can be explored to determine which conditions yield sufficient mixing of the reactants. This will result in successful rotating detonation when such a mixture is utilized.

Furthermore, it is important to investigate a given RDE configuration, which utilizes ethylene-air mixtures since ethylene is a hydrocarbon fuel. Advanced hydrocarbon fuels are utilized in modern turbomachinery applications. Therefore, successful operation of an RDE utilizing on hydrocarbon fuel will validate the potential to implement RDEs in future turbomachinery applications.

4.2 Inverse Brayton Cycle Turbojet Study

It is essential to develop propulsion systems that can improve the efficiency and supportability of

UAVs. Such propulsion systems that would be well suited for UAV applications lie in the category between gas turbine technology and internal combustion engine technology [27]. A propulsion system that operates on the Inverse Brayton Cycle can fulfill this requirement since it results in lower specific fuel consumption and higher power density for small-scale propulsion systems. This novel concept of the

IBC involves combustion of atmospheric air, followed by expansion in the turbine, heat extraction by the heat exchanger elements, and ending with compression at the exit. The feasibility of such a propulsion system was validated in a previous study [13], which showed the inclusion of an ambient heat exchanger to improve the thermal efficiency of the system. However, the addition of this heat exchanger also resulted in increasing the overall engine weight and reducing the range of the aircraft.

This study involved extensive research into selecting a heat exchanger design that would be suitable for a turbojet operating on the Inverse Brayton Cycle. Compact heat exchangers are lightweight and have a greater surface area density than conventional heat exchangers. It was determined that a microchannel heat exchanger would result in optimal performance of an IBC based turbojet engine. Its offset microchannels and shorter fins reduce the thickness of thermal boundary layers that normally form on long, continuous fins. This increases the amount of heat transfer on both the hot and cold sides of the heat exchanger [35]. CMC was chosen as the material for the microchannel heat exchanger due to significant benefits over other materials such as stainless steel, copper and aluminum. This type of heat exchanger addresses the problem of additional weight and decreased range as a result of using two heat exchanger elements (i.e. recuperator and ambient heat exchanger).

A Simscape model was developed to simulate a specific case of a turbojet engine operating on the

Inverse Brayton Cycle (IBC). The Simscape model effectively calculated the values for pressure and temperature at the inlet and exit for each component. Using multiple parameters and equations, the model was also able to accurately simulate the recuperator and ambient heat exchanger, which resulted in successfully extracting a considerable amount of heat from the flow entering the compressor (1384.3 K to

552.6 K). The calculations from the model were validated using a MATLAB code. Furthermore, the power output of the engine was calculated at ~70 kW, which is sufficient for providing power to small- scale UAV applications [39].

Various IBC turbojet cases were also studied in order to conduct further analysis on the IBC turbojet system. Specific thrust and TSFC were calculated and plotted over a normalized range of compressor inlet temperatures. Two curves were included in these plots to represent two different cases: IBC with two heat exchanger elements, and IBC with recuperation only. The plots showed greater specific thrust and less

TSFC for the turbojet utilizing two heat exchanger elements. These results were expected, because when the recuperator is used along with the heat exchanger, a greater amount of heat is extracted from the flow,

85 leading to lower compressor inlet temperatures. This results in improved performance of the engine and greater efficiency.

Thermal efficiency was also calculated and plotted over varying values of power output and heat exchanger effectiveness. Results from this plot showed that the thermal efficiency increases with greater power output values. The power output is directly proportional to the mass flow rate of air, 푚̇ 0. Thus, it can be concluded that as the airflow through the engine is increased, the engine becomes more thermally efficient. Thermal efficiency also increases with heat exchanger effectiveness, showing that greater heat transfer and extraction yields lower temperatures at the compressor inlet. This validates the results displayed in the TSFC vs. compressor inlet temperature plot, which shows less TSFC when two heat exchanger elements are used rather than one. Compressor inlet temperature was also plotted against power output, which further showed that increasing the flow rate of air leads to greater thermal efficiency.

A plot showing the range of flight in relation to the heat exchanger effectiveness shows that there is a tradeoff between thermal efficiency and flight range. When a heat exchanger has greater effectiveness, it will result in increased engine weight, which decreases the flight range. The main objective of this research is to develop weight saving options for the heat exchanger. The recuperator and heat exchanger effectiveness value of 0.645 offers the best tradeoff between flight range and thermal efficiency.

The performance of the IBC based turbojet for the specific case was compared to turbojet engines with similar sizes and mass flow rates. The IBC based turbojet was shown to generate a relatively high amount of thrust, and the lowest SFC value. The reason for the lowest SFC is that the IBC based turbojet utilizes a relatively low fuel flow rate, which is directly related to the effect of recuperation in the cycle.

The ability of the recuperator using waste heat from the turbine to preheat the air at entering the combustor results in less fuel required to get the same net work output.

Although extensive analysis and research was conducted to reduce the weight of the recuperator and ambient heat exchanger, the additional components still have a slight impact on the performance of the

86 engine. The thrust-to-weight ratio of the IBC turbojet is lower than the other turbojets due to the additional weight from the heat exchanger elements. The potential of using an IBC based turbojet for small-scale UAVs is validated by the comparable performance of such an engine to similar turbojets that are in use today validates the potential of the IBC turbojet. Further analysis should be conducted to improve the thrust-to-weight ratio of an IBC based turbojet. Reducing the heat exchanger effectiveness may solve this problem, but it can be only slightly reduced so that the flight range is not negatively impacted. Further parameters can be explored to further reduce the weight of the engine, such as reducing the size of other engine components.

Future experiments and analysis of the IBC will include developing and constructing a microchannel heat exchanger that is capable of being implemented into an IBC based propulsion system. Also, further simulations can be conducted to investigate how an IBC propulsion system performs at varying altitudes, and comparisons can be made to the RBC. If the results are favorable, this can encourage more extensive research to be conducted on the IBC, and perhaps lead to the actual development of improved propulsion systems that can power military for years to come.

4.3 Hydrogen-Air TOXIC RDE Thrust Study An experimental investigation of the newly designed TOXIC RDE configuration was conducted to observe and analyze its operation under certain conditions. Utilizing a mixture of hydrogen and air, the

RDE was able to successfully detonate for various tests with air mass flow rates ranging from about 0.2 –

0.6 kg/s. This investigation also involved the use of a thrust stand to obtain thrust measurements from the

RDE. The thrust stand design consists of multiple components, including an LVDT. The LVDT transducer is used to measure displacement as the top plate of the thrust stand slides along support rails within the structure.

Multiple thrust-time profiles were plotted for varying conditions, and the trends were similar to those obtained in previous RDE thrust experiments. For instance, a greater amount of average thrust was

87 measured when the air flow rate was increased. Increasing the equivalence ratio also resulted in a higher maximum thrust when the mixture was ignited. Although similar trends were observed in past RDE experiments, the measured values of thrust were much lower than expected. Even when both the spring and damping forces were reduced (i.e. reducing damping force of dampers and using smaller springs), thrust measurements were still very low.

A simplified model of the experimental setup, including the RDE stand and the top plate of the thrust stand was created in SolidWorks. This model was simulated to provide a more accurate depiction of the thrust stand system response to the force applied by the RDE. For varying thrust values, the simulation shows the model deflecting vertically in either direction. The animation is very similar to a recorded video of one of the RDE tests, which shows the thrust stand moving up and down when the RDE is fired.

It is highly probable that the force exerted by the RDE produces a torque which causes deflection in the thrust stand. The thrust stand is only designed to measure force applied in a linear direction via the

LVDT. Thus, the thrust was not able to be properly measured by the thrust stand since the force applied to the system is rotational.

However, it is also likely that improvements and modifications need to be made to the current thrust stand system to improve its ability to measure thrust. For instance, using ball bearing carriages along with guide rails instead of fixed align bearings may enable more movement of the top plate of the thrust stand.

Although the top plate was able to move easily along the support rails with the current design, it cannot easily slide when the RDE stand is placed on top of it. Ball bearing carriages can also result in reducing any static friction due to the additional weight of the RDE on top of the thrust stand. Although the current thrust stand configuration was unable to accurately measure thrust, lessons learned from this experiment can be used to make improved thrust stand designs for future RDE experiments.

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