Autoignition Dynamics and Combustion of N-Dodecane Droplets Under Transcritical Conditions

Home , Dodecane

AUTOIGNITION DYNAMICS AND COMBUSTION OF N-DODECANE DROPLETS UNDER TRANSCRITICAL CONDITIONS

EVAN NOAH ROSE

Submitted in partial fulﬁllment of the requirements

For the degree of Master of Science

Department of Mechanical and Aerospace Engineering

CASE WESTERN RESERVE UNIVERSITY

May, 2019 Autoignition Dynamics and Combustion of n-Dodecane Droplets

under Transcritical Conditions

Case Western Reserve University Case School of Graduate Studies

We hereby approve the thesis1 of

EVAN NOAH ROSE

for the degree of

Master of Science

Dr. Vedha Nayagam

Committee Chair, Adviser Date Department of Mechanical and Aerospace Engineering

Dr. Daniel Dietrich

Committee Member Date NASA Glenn Research Center

Dr. Ya-Ting Liao

Committee Member Date Department of Mechanical and Aerospace Engineering

Dr. Fumiaki Takahashi

Committee Member Date Department of Mechanical and Aerospace Engineering

March 18, 2019

1We certify that written approval has been obtained for any proprietary material contained therein. Dedicated to my family Table of Contents

List of Tables vi

List of Figures vii

Acknowledgements xii

Abstract xiii

Chapter 1. Introduction 1

Chapter 2. Literature Review 3

Droplet Ignition 3

Two-stage Ignition 6

Droplet Burning Characteristics 11

Present Work 13

Chapter 3. Experimental Apparatus and Procedure 14

Experimental Apparatus 14

Diagnostic Equipment 20

Experiment Procedure 23

Data Analysis 24

Chapter 4. Results 31

Homogeneous Two-stage Ignition 32

Droplet Two-stage Ignition in Normal Gravity 35

Cool Flame Ignition Behavior 43

Hot Flame Ignition Behavior 46

iv Two-Stage Ignition Delay Times 49

Other Aspects of Droplet Combustion in Normal Gravity 53

Chapter 5. Preliminary Microgravity Results 58

Experimental Conditions 58

Experimental Procedure 58

Microgravity Experimental Results 59

Comparison with Normal Gravity Results 62

Chapter 6. Conclusions 65

Chapter 7. Suggested Future Research 67

Appendix A. Data 69

Appendix B. Experimental Apparatus 109

Appendix C. Property values of n-Dodecane 117

Appendix D. Ignition Flame Propagation Data 120

Appendix. Complete References 123

v List of Tables

3.1 Spatial optical resolution testing results. 25

4.1 Time scales of relevant processes in droplet two-stage ignition. 36

4.2 Burning rates of selected temperature and pressure cases. 54

5.1 Comparison of ignition dynamics between microgravity and normal

gravity. 63

A.1 Test conditions for summary plots of included results. 69

C.1 Table of relevant property values for n-dodecane. 118

vi List of Figures

2.1 Ignition regions for n-dodecane droplets with D 0.7 0.8.8 0 = −

3.1 Schematic of the experimental apparatus with selected components

labeled. The same apparatus is used for both normal and microgravity

testing. TC 1, TC 2, and TC 3 are thermocouples, labeled in the order

in which they are described in Section 3.2.2. 16

3.2 Schematic showing fuel and gas line piping and instrumentation. 18

3.3 Schematic showing experimental control system, with outputs to

imaging and instrumentation data acquisition. 19

3.4 A top view schematic of the pressure chamber, showing the position

of diagnostic instrumentation around the high-temperature region. 20

3.5 Comparison of unprocessed and processed image data used to

identify the ignition location for cool (a) and hot (b) ﬂames. The

propagating waves are visible in white. The image containing the

cool-ﬂame front is cropped to make it easier to identify. The droplet

is out of frame, centered directly above the front. 27

4.1 Test matrix showing ambient pressure and temperature conditions

for each test in normal gravity. 32

4.2 Ignition delay times shown for n-dodecane in a perfectly premixed

reactor at relevant pressures. The times were calculated with the

Cantera software. An NTC region, where ignition delay increases with

temperature, is clearly evident. 33

vii 4.3 Temperature shown as a function of time for homogeneous gas

mixtures at P = 1 atm for various initial temperatures. The time of

thermal runaway at each temperature demonstrates the NTC for

n-dodecane. 34

4.4 Induction times shown as a function of temperature for P = 1 atm.

The opposing behavior of ﬁrst and second induction times gives rise

to the NTC region. 35

4.5 Image sequence showing a representative case of two-stage ignition

in grayscale and color. Test conditions are 3 atm and 622 K. 37

4.6 Image sequences showing ﬂame front initiation and propagation for

both the cool and hot ﬂame. The ﬁeld of view is smaller in (a) to focus

on the cool-ﬂame front; the droplet is centered directly above each

image. 39

4.7 Square of droplet diameter, temperature measurement below the

droplet, and PMT output shown with respect to time. 40

4.8 Area of interest in Figure 4.7 expanded to mark the occurrence of

relevant processes. 40

4.9 Image of droplet showing hot ﬂame ignition starting from behind a

propagating cool ﬂame. The experimental conditions are 10 atm and

571 K. 42

4.10 Droplet history and temperature data at 2 atm and 600 K. The droplet

burns to completion with a cool ﬂame, without transitioning to a hot

ﬂame. 42

viii 4.11 Cool ﬂame ignition distance to droplet shown as a function of

temperature for several pressure cases. The temperature range is

different for each pressure case. 44

4.12 Cool ﬂame propagation speed shown as a function of temperature for

several pressure cases. 46

4.13 Hot ﬂame ignition kernel distance to droplet shown as a function

of temperature for several pressure cases. The temperature range is

different for each pressure case. 48

4.14 Hot ﬂame propagation speed shown as a function of temperature for

several pressure cases. 48

4.15 Total induction time, or ignition delay time, as a function of

temperature for several pressure cases. D 1.1 1.3 mm. 50 0 = − 4.16 First induction time as a function of temperature shown for all

ambient pressures where a cool ﬂame is observed, so the ignition

delay can be divided into two stages. D 1.1 1.3 mm. 51 0 = − 4.17 Second induction time as a function of temperature shown for all

ambient pressures where a cool ﬂame is observed. D 1.1 1.3 mm. 51 0 = − 4.18 First and total induction times are shown as a function of pressure

from 2 – 25 atm. The ignition delay times reach a minimum near the

critical pressure. T 603 K, D 1.0 1.1 mm. 52 0 = 0 = − 4.19 Second induction time is shown as a function of pressure from 2 –

25 atm. The second induction time decreases as pressure increases,

even past the critical point. T 603 K, D 1.0 1.1 mm. 53 0 = 0 = −

ix 4.20 Total induction time for selected pressure cases compared for two

rounds of testing. 55

4.21 Second induction time for selected pressure cases compared for two

rounds of testing. 55

4.22 Comparison of background density variation at various pressures. 57

5.1 Image sequence showing representative case of two-stage ignition in

microgravity. Test conditions are 3 atm and 623 K. Initial diameter is

1.07 mm. 60

5.2 Image sequences showing ﬂame kernel initiation and spherical front

propagation for both the cool ﬂame and hot ﬂame. Test conditions

are 3 atm and 623 K. 61

5.3 Square of droplet diameter shown as a function of time from

autoignition. Circular markers denote points measured manually.

P = 3 atm, T = 623 K, D 1.07 mm. 62 0 =

B.1 Engineering drawing showing full assembly with both high-

temperature and deployment regions. 110

B.2 Engineering drawing of pressure chamber. 111

B.3 Engineering drawing of electrically heated oven assembly. 112

B.4 Engineering drawing showing schematic of gas and liquid plumbing. 113

B.5 Temperature proﬁles in the chamber at atmospheric pressure for

several temperature cases are compared. The largest increase

x in temperature per unit distance occures at the entrance to the

high-temperature region. 114

B.6 Comparison of the temperature proﬁle in the chamber for several

ambient temperatures at 1 and 5 atmospheres of pressure. Increased

convection at higher pressures raises the temperature near the

droplet above the setpoint temperature. 115

B.7 Velocity proﬁle of the droplet translation mechanism. 116

C.1 Binary diffusivity of n-dodecane in air as a function of temperature

for various pressures. 117

C.2 Boiling point temperature, latent heat of vaporization, and liquid

density at the boiling point as a function of pressure. 118

C.3 Enthalpy, speciﬁc heat, thermal conductivity and density as a

function of temperature for several pressure cases. 119

D.1 Demonstrative image of the ﬂame front position measurement. The

position of the ﬂame front, depicted by the horizontal line, is tracked

over time along the vector shown in red. 120

D.2 Cool ﬂame position shown as a function of time. 121

D.3 Hot ﬂame position shown as a function of time. 122

xi Acknowledgements

I would like to express my gratitude to my adviser, Dr. Vedha Nayagam, for guiding me through this process and introducing me to the vast ﬁeld of combustion. This work would not have been possible without his high standards and attention to detail.

I would also like to thank Dr. Daniel Dietrich, Dr. Michael Hicks, Dr. Uday Hegde, and Dr. Rosa Padilla. Their support, suggestions, and advice, both scientiﬁc and general, has been invaluable.

The dedicated assistance of the engineers and technicians of the Zero Gravity Re- search Facility, especially Eric Neumann, Luke Ogorzaly, and Vittorio Valletta, was vital in ensuring the successful operation of the experiment, as was the expert design knowl- edge of Daniel Gotti.

I would like to acknowledge the members of the NASA LTX branch for their willing- ness to share their unparalleled experience and insight with me. I am proud to have been part of this esteemed group.

Funding for this work was provided by NASA’s Space Life and Physical Sciences Re- search and Applications (SLPSRA) program.

xii Abstract

Autoignition Dynamics and Combustion of n-Dodecane Droplets under Transcritical Conditions

Abstract

EVAN NOAH ROSE

Understanding the spontaneous ignition and burning behavior of liquid fuels is critical to improving the performance of modern combustion devices. This work examines the effects of varying ambient temperature and pressure on the autoignition and burning characteristics of fiber-supported n-dodecane fuel droplets in normal gravity and in microgravity. Ambient temperatures and pressures were 500 to 1000 K and 1 to 25 atm, respectively, encompassing the transcritical region for n-dodecane. The results show the dynamics of ignition with the formation of a cool-flame front and a hot-flame front prior to the final establishment of a diffusion flame surrounding the droplet. These phenomena are observed for both normal gravity and microgravity environments. Measurement of two-stage ignition delay times shows qualitative agreement with previous research.

xiii 1

1 Introduction

Hydrocarbon petroleum products comprise one of the largest sources of energy in the world. The United States alone consumed 7.26 billion barrels of petroleum products in 2017 at a total cost of over $365 billion. By this reasoning, any marginal increases in combustion efﬁciency will have major economic impacts. Understanding liquid fuel combustion in its most basic form — in a droplet — provides useful information for other more complex combustion processes.

The study of droplet combustion is one of the most widespread methods of examining the burning parameters of liquid fuels. This type of combustion closely matches the characteristics of many types of combustion devices, including automobile, aircraft, and rocket engines. Combustion inside the aforementioned combustion devices, such as the cylinder of a diesel engine or the combustion chamber of a liquid rocket engine, often takes place at supercritical temperatures and pressures. To better understand ﬂame behavior in those conditions, it is necessary to study hydrocarbon fuels as supercritical

ﬂuids. As compression-ignition engines move to pressures 30 atm and above1 to increase volumetric efﬁciency, the necessity to understand the varying ignition behavior of fuels at these pressures increases. Optimizing every part of the combustion process leads to a more complete reaction with fewer unburnt particles released as particulate Introduction 2

matter. Previous studies have shown that the burning rate of liquid fuel droplets reaches a maximum at the respective fuel’s critical pressure2. Maximizing the burning rate leads to a more complete combustion process, with higher energy release and fewer unburnt reactants.

But higher engine pressures increase the autoignition tendency of the fuel. Under- standing the chemical and physical behaviors that cause autoignition can reduce knock in spark-ignited engines and improve the efficiency of modern homogeneous charge compression ignition (HCCI) engines. While most combustion applications rely on a fuel spray instead of a liquid fuel, the simplicity afforded by a spherical droplet improves the experimental analysis. For this reason, hydrocarbon fuel droplet combustion experiments have been conducted since 1963 with varying fuel types and experimental condi- tions3. The body of work detailing the combustion of hydrocarbon fuels at high temperatures and pressures is well established, but the details of the droplet ignition process are not well understood. Many of the ignition processes take place at time scales on the order of milliseconds, which until now have not been visible with traditional imaging. New imaging technology enables the observation of low-temperature cool flames in the droplet ignition process. Better understanding the low-temperature chemistry that takes place during the ignition period will further improve the efficiency of the combustion engine.

Performing experiments in microgravity further simpliﬁes the combustion analysis.

Reducing the force of gravity on combustion eliminates the presence of convection in the system, removing convective effects from the chemical kinetics and heat transfer of the ﬂame. 3

2 Literature Review

Chapter2 covers relevant published research to the study of both the autoignition

and burning characteristics of n-alkane fuel droplets in high-pressure conditions.

2.1 Droplet Ignition

Aggarwal4 has produced an extensive review of droplet ignition, discussing many as-

pects of the problem including both theoretical and experimental studies, some of which

is discussed further in this work.

The classical problem of droplet autoignition involves a spherical single-component,

cold liquid droplet instantaneously introduced into an inﬁnite hot quiescent medium.

It is a non-homogeneous, two-phase problem that is ideal for research due to the rela-

tive simplicity of the domain. Behavior of the droplet prior to and during ignition are of

particular practical concern for engine development.

The prevailing theories regarding droplet ignition were formulated by Law5, who examined the impact of droplet heating on ignition delay. He stated that ignition occurred in a vaporizing droplet when it exceeded a certain ignition Damköhler number, and identiﬁed the existence of a minimum temperature beyond which ignition is not possible. Literature Review 4

Replicating the instantaneous introduction of a spherical droplet into a hot ambient requires the rapid translation of a suspended droplet into a heated region. Faeth et al.6 were the first to study droplet autoignition, followed by Long and Grens7, using a high-speed (500-1000 frames/sec) camera to show that ignition times decreased with increasing temperature. Kadota et al.8 extended the scope of autoignition studies by measuring the impact of pressure, temperature, and ambient oxygen concentration on the ignition delay time using a moving electric oven for n-alkane droplets at elevated pressures up to 40 atm. Further research uncovered more of the components that comprise the overall droplet autoignition process. Bergeron and Hallet9 first observed significa- tion fuel vapor leaving the droplet in their studies of two-component fuel droplets, con-

firming previous theoretical results. Nakanishi et al.10 defined the ignitable limits of fuel droplets based on minimum diameter and ambient temperature, where complete evaporation occured before ignition. For all pressure cases, the ignition delay time increased as it approached this minimum temperature where it increased asymptotically. Many studies encompassed both autoignition and steady burning, including Kadota et al.11, who showed minima at the critical pressure for both ignition time and droplet lifetime for octodecanol. Ghassemi et al.12 also used a moving electric heater to examine fuel evaporation at high ambient pressure, observing significant thermal expansion followed by quasi-steady evaporation. A second study by the same authors13 involved kerosene autoignition, showing that the ignition kernel location formed closer to the droplet as ambient pressure increased. Nakaya et al.14 examined the impact of fuel vapor in the ambient, showing that low-reactivity fuels such as methane increase the ignition delay, while high-reactivity fuels such as n-heptane promote spontaneous ignition. Literature Review 5

A number of other publications use a heated gas flow to induce autoignition in the droplet while simplifying droplet deployment, but this approach removes the aspect of the quiescent ambient. Faeth and Canada15 first approximated this problem by simu- lating a droplet with a porous sphere at pressures up to 40 atm. Whang et al.16 examined the ignition behavior of larger-diameter droplets, visually identifying the existence of an initial premixed flame that propagates to surround the droplet. The flame propagation speed was found to increase with gas flow temperature.

Kim et al.17 took a different approach to the problem, suspending an n-heptane droplet from a thermocouple inside a rapid compression machine (RCM), which more closely approximates the conditions of a compression-ignition engine. A high-speed color camera was able to capture the ignition of the hot ﬂame close to the droplet. Test- ing at approximately 30 bar and 350◦C for varying droplet diameters and two compression times showed that ignition delay increases with droplet diameter. The droplet ignited during the heating process even before it reached the boiling point, and ignition occurred during thermal expansion.

The case of spherical droplet being instantly exposed to a high-temperature ambient in microgravity has been well-explored numerically, due to the one-dimensionality of the problem. Shaygan and Prakash18 computed the droplet heating and transport that occurs before and after ignition, showing that fuel vapor buildup in the ignition zone is a controlling process for the chemical reactions to take place, and that ignition occurs when fuel vapor forms a critical concentration at a sufﬁciently high-temperature point near the droplet. The ignition delay can be divided into two clearly-deﬁned parts, as proposed by Chen and Peng19: temperature-dominated physical delay and reaction- dominated chemical delay. Literature Review 6

All the ignition studies outlined in this section describe only the single-stage ignition process, where the droplet ignites immediately with a hot ﬂame. This neglects important chemical kinetic processes, however, in which low-temperature reactions known as cool ﬂames cause a two-stage temperature rise during the droplet ignition.

2.2 Two-stage Ignition

The premixed batch reactor is one the simplest experimental systems that allows the study of chemical kinetic mechanisms involved in autoignition process. In this reactor, air and gaseous fuel form a homogeneous mixture, maintained at a specific temperature with no heat transfer to the surroundings. The air and fuel begin reacting until ignition, where thermal runaway occurs and the temperature of the system rapidly increases. In general, the ignition delay time for the mixture decreases as temperature increases. Some hydrocarbons exhibit a negative temperature coefficient (NTC) region where the overall reaction rate decreases with increasing temperature. This phenomenon is explained by the two-stage ignition process, where intermediate reactions pro- duce a low-temperature cool flame that precedes the hot flame.

Peters20,21 described the existence of three temperature regimes for higher hydrocarbon fuel droplets: the high- and low-temperature regimes, where ignition delay time increases with decreasing temperature, and the intermediate-temperature regime, where the ignition delay time decreases with decreasing temperature. This behavior occurs due to reverse reactions that become faster at approximately 800 K. Speciﬁcally, the ketohydroperoxide dissociation reaction is critical for the low-temperature chemistry regime. While reduced chemical mechanisms have been shown to be sufﬁcient for calculating ignition delay, Sarathy et al.22 developed a comprehensive set of 7200 species Literature Review 7

and 34100 reactions for long-chain n-alkanes with carbon numbers 8 to 16, with a spe- ciﬁc focus on low-temperature reactions.

Pearlman23 identiﬁed the need for microgravity test conditions to more accurately measure two-stage ignition and cool ﬂame burning. His investigation of propane-air mixtures at subatmospheric pressures and temperatures from 300–600◦C observed cool

flame formation using intensified cameras. Cool flame formation began at the top of the vessel and propagated downward in normal gravity, but began in the middle of the vessel and propagated spherically outward in microgravity. The first induction time decreases as pressure increases, and is shorter under microgravity conditions. Fairlie et al.24 validated the experimental results with numerical analysis using a skeletal chemical kinetic scheme, and showed that oscillatory cool flames could exist in both microgravity and, in a highly damped manner, normal gravity.

Zhao et al.25 studied the two-stage ignition of premixed flames using dimethyl ether numerically. They calculated the first and second induction times as a function of temperature, showing that the ignition delay time is dominated by the first induction time in the low-temperature regime and the second induction time in the intermediate- temperature regime. Above the NTC region, single-stage ignition occurs.

A series of experiments and numerical analyses carried out over a period of about 15 years at the Center of Applied Space Technology and Microgravity (ZARM) at the Univer- sity of Bremen are considered the principal reference for high pressure droplet autoignition, due to the comprehensive range of fuels, temperatures, and pressures examined.

Tanabe et al.26–28 employed droplet diameters of 0.7–0.8 mm to determine the existence of a two-stage ignition with both cool and hot ﬂames at elevated pressures for certain hydrocarbon fuel droplets. The experiment used a horizontal ﬁber to support the droplet, Literature Review 8

and a mechanism that could rapidly insert it into a high-temperature chamber. Density

field visualization and interferometry made visible the elevated temperature regions of both the cool flame and hot flame. The experiment measured first, second, and total induction times for temperatures between 550 and 1100 K and pressures up to 2 MPa. The results showed distinct regions of temperature and pressure where each type of ignition; single stage, two-stage, or cool flame only, occurred, pictured in Figure 2.1. For droplets, the first induction time is mostly dependent on physical processes, such as droplet heating and fuel evaporation, so is very temperature dependent. The negative temperature coefficient (NTC) region found in premixed flames, where low-temperature chemistry reduces the reaction rate, was correlated with a zero temperature coefficient (ZTC) region for droplets. Experiments performed in the microgravity environment of the ZARM drop tower showed a minor decrease in ignition delay time in the absence of gravity.

1000

2 900

800 4 1. Two-stage ignition 1 2. Single-stage ignition 3. Cool flame only 4. No ignition 700 Temperature (K) 3

2 600

4 500 0.1 1 10 Pressure (MPa)

Figure 2.1. Ignition regions for n-dodecane droplets with D 0.7 0.8. 0 = − Literature Review 9

Eigenbrod et al.29 showed the effectiveness of laser-induced ﬂuorescence to detect formaldehyde emissions, a common indicator of cool-ﬂame reactions in microgravity.

Schnaubelt et al.30 also supported the earlier findings for n-heptane droplets with experimental and numerical results. A thermocouple positioned near the droplet identified a gas-phase temperature rise associated with the cool flame. Another paper by the same authors31 identified the distance from the ignition point to the droplet in microgravity, termed the ignition radius, for both cool-flame and hot-flame ignition. Microgravity testing and numerical simulations at an ambient pressure of 5 bar showed that the cool

ﬂame formed closest to the droplet at an ambient temperature of 700 K, and that the hot

ﬂame ignited in approximately the same place above 640 K. Moriue et al.32 continued the experimentation using the same experimental design26 for n-alkane fuels with larger molecular weights up to n-hexadecane, showing two-stage ignition for each. Fuels with lower volatility exhibited longer induction times.

Due to the difficulty of observing the cool flame, many studies of two-stage ignition analyze the problem numerically. For numerical models, removing the effects of gravity greatly simplifies the problem by suppressing natural convection. In addition to the extensive experimental results, researchers at ZARM investigated droplet autoignition numerically in detail. Several papers by Schnaubelt et al.30 expanded on the prior numerical models27 to find good agreement with experimental results, specifically comparing temperature rise near the droplet with the experimental temperature measurement data of Tanabe et al.28. Additionally, the authors compared the experimental results of n-decane with numerical data to demonstrate the presence of the ZTC region. The second induction time depends on the cool flame temperature; a higher temperature favors high-temperature reactions over low-temperature reactions and shortens the cool Literature Review 10

flame burning time. Further numerical analysis33 qualitatively describes the two-stage ignition process in more detail for n-heptane. After inserting the droplet, evaporation and Stefan flow introduce a species and temperature gradient from the droplet to the ambient air. An elevated temperature zone caused by the cool flame forms and moves over time to the droplet surface, increasing droplet evaporation until the hot-flame ignition occurs. This process occurs both numerically and experimentally for all researched ambient conditions. Parallel burning was observed numerically, where the cool flame persisted even after hot-flame ignition. The simulations examined the problem from a

finite domain as well as an infinite one: Moriue et al.34,35 simulated fuel droplet ignition for small droplets (<0.1 mm) in a finite domain for closer comparison to the behavior of spray combustion. The ignition process behavior was markedly different for small system equivalence ratios compared to unity equivalence ratios.

A number of other authors examined the experimental results performed at ZARM with additional numerical analyses. Stauch and Maas36 used a reduced mechanism for n-heptane to further analyze the ignition regions of Tanabe et al28. At lower pressures between 750–900 K, both sets of reactions are too low, and the droplet does not ignite.

For the case of cool ﬂame burning only, if physical transport is faster than chemical kinetics, the second ignition does not appear. The temperature near the droplet will decrease, re-enabling the low-temperature reactions and in turn increasing the temperature once more. As transport decreases with pressure, increasing the pressure then leads to a two-stage ignition. Additionally, increasing the ambient temperature and pressure moves the location of cool-ﬂame ignition closer to the droplet. Cuoci et al.37,38 validated the experimental measurements of Xu et al.39 and Tanabe et al.27 with numerical models Literature Review 11

for both droplet ignition and burning. Their first study used a chemical kinetic mechanism including both low- and high-temperature reactions to show hot-flame ignition, two-stage ignition, and oscillatory cool flame behavior. At the same ambient pressure and droplet diameter, an autoignition case exhibited cool flame burning, while a spark- ignited case ignited straight to a hot flame. The addition of low temperature chemistry to the mechanism also improved the agreement of burning rates with experimental results. A later study examined a temperature range of 600–1100 K and a pressure range of 1–20 bar, comparing experimental results to a detailed chemical kinetic scheme. Nu- merical models showed agreement with the ignition regions of Tanabe et al.28, but un- derestimated the total ignition time at high temperatures.

2.3 Droplet Burning Characteristics

In the area of droplet combustion, understanding the burning process is of equal impor- tance to the ignition process. Both hot and cool ﬂames are present in burning droplets under certain ambient conditions. Williams40, described the well-known problem of droplet burning, including quasi-steady burning governed by the d 2-law, where the square of the droplet diameter decreases linearly over time. Faeth et al.41 described the burning characteristics of hydrocarbon fuel droplets at pressures as high as 136 atm, measuring their temperatures and burning rates. These studies were the ﬁrst to demonstrate the need for a microgravity environment to study supercritical droplet combustion, to eliminate droplet falloff due to the reduction in surface tension as the droplet temperature increases. Literature Review 12

Further investigation of droplet burning by Sato et al.2 and Mikami et al.42 shows that the maximum burning rate occurs slightly above the critical pressure and is temperature dependent in this region. Improved diagnostic equipment was used to show the change in shape of the droplet at supercritical pressures. The droplet surface becomes wrinkled as the outer layer ignites and reaches the critical temperature. They also observed ejection of material starting near the fiber and moving to the droplet equator, suggesting a natural convection- and fiber heating-driven thermocapillary flow. Xu et al.39 performed experiments with n-decane droplets at atmospheric pressure using both an oven igniter and hot-wire igniter configuration to examine the influence of initial diameter on the burning-rate constant. The initial diameter was varied from 0.8–1.6 mm, and the burning rate was found to increase with droplet diameter. Bae and Avedisian43 confirmed the observation that soot formation increases with pressure, and discussed the impact of pressure on flame and soot shell shape and luminosity.

Space-based microgravity experiments provide a long-term microgravity environment suitable for extended experimentation. Droplet combustion on the space shut- tle with freely ﬂoated droplets in different ambient oxygen concentrations44,45 showed quasi-steady burning following the d-square law, as well as both radiative and diffusive

flame extinction. Microgravity droplet combustion on the International Space Station through the Flame Extinguishment (FLEX) Experiments revealed the presence of long- duration cool flames for n-alkane droplets using free-floating droplets ignited by a hot wire. Nayagam et al.46–48 showed that for n-heptane, after radiative extinction of the hot

flame, cool-flame burning continued consistently with the quasi-steady approximation until a second extinction. Further research quantitatively identified the cool flame for n-heptane, n-octane and n-decane using a radiometer and determined that the cool Literature Review 13

ﬂame extinction diameter decreases with increasing ambient oxygen concentration. In addition, a model of quasi-steady droplet combustion with fuel thermal expansion after ignition was developed and compared with existing models. The new model showed better agreement with experimental data early in the droplet burning lifetime.

2.4 Present Work

While the two-stage ignition process has been studied in the past, no theoretical, numerical, or experimental studies have fully captured the detailed dynamic aspects of the ignition process for n-alkane droplets.

The present work expands on prior research by way of an extended pressure range and improved diagnostics. High-speed backlit and color imaging capture ignition processes with a timescale on the order of milliseconds, such as the initiation and propagation of a premixed ignition kernel. The present work verifies the presence of a low- temperature "cool flame" that propagates toward the droplet prior to hot-flame ignition.

The present work uses n-dodecane fuel due to its two-stage ignition behavior and its extensive use in prior research. Additionally relevant is its use as a surrogate fuel for diesel and jet engine testing. The ignition and burning behaviors below and above the critical point are observed. 14

3 Experimental Apparatus and Procedure

The experimental design and procedure are described in this section. The experiments were carried out using a specially designed high pressure combustion apparatus capable of being dropped in the Zero Gravity Facility at the NASA Glenn Research Cen- ter. The system is composed of a pressure chamber with an electric furnace, plumbing for fuel and gas delivery, electromechanical control elements and diagnostics. A droplet of fuel is suspended on a thin ﬁlament, and rapidly raised into a high-temperature environment. This process approximates the injection of a cold droplet in a hot ambient observed in practical devices. The entire process takes place within the pressure vessel.

The hardware is designed for operation in both in normal gravity and in microgravity environments, and is controlled remotely.

3.1 Experimental Apparatus

The various components of the experiment are: the pressure chamber, fuel and gas supply systems, control system, and diagnostic instruments. Each aspect of the overall experimental system is described below. Experimental Apparatus and Procedure 15

3.1.1 High Pressure Chamber

The pressure chamber is constructed of Inconel 625 superalloy, used for its resistance to stress and elevated temperatures, with a cylindrical interior volume measuring 4.345 ∗ 3 3 10− m . The chamber is divided into two regions: the deployment region at the bot-

tom and the electrically heated oven section on the top. The droplet is dispensed on

a thin ﬁber in the deployment region before it is raised into the oven. The oven is ca-

pable of heating the upper chamber’s temperature to 1000◦C, and has a usable volume

4 3 of 7.301 10− m . It is lined with a Morgan Advanced Materials Thermal Ceramics Cer- ∗

ablanket ceramic ﬁber insulation with a maximum use temperature of 1177◦C to prevent

heat damage to the mechanical and electronic components in the deployment region.

The temperature inside the heater is measured with a K-type thermocouple (accuracy

2.2◦C) and regulated with a PID controller. The temperature inside the deployment ± region is measured with a K-type thermocouple to show that the electronics stay within

the recommended temperature conditions during deployment. The pressure chamber

includes six sapphire windows for diagnostic purposes. Four larger windows, 32 mm

in diameter, and two smaller ones in the deployment region provide a view inside the

chamber during an droplet deployment.

3.1.2 Droplet Suspension and Movement

Fiber suspension is a commonly used method for positioning the fuel droplet within

the combustion chamber. The droplet is suspended on a 250 µm spherical bead melted

onto the end of a 125 µm quartz ﬁlament. This material has a thermal conductivity of

W 0.05 m K , minimizing the heat transfer from the filament to the droplet. Unlike previous ∗ works in which the fiber is positioned horizontally26, the filament in this experiment Experimental Apparatus and Procedure 16

Electric heater Insulation

Backlight High Speed Camera

TC 1 Sapphire TC 2 windows Fuel syringe

Grayscale Backlight Camera

Droplet Droplet deployment suspension system

TC 3

Figure 3.1. Schematic of the experimental apparatus with selected components labeled. The same apparatus is used for both normal and microgravity testing. TC 1, TC 2, and TC 3 are thermocouples, labeled in the order in which they are described in Section 3.2.2. is oriented vertically. This allows a more even heat distribution to the droplet, as the heaters are positioned axially. Additionally, it produces an axisymmetric droplet in both the normal and microgravity cases.

Droplet insertion into the electric oven is driven by a stepper motor. The model used was an H2W Technologies single-axis linear stepper forcer traveling on roller bearings along a 30.75 mm wide nickel-plated steel platen over a distance of 670 mm. Pulse- width modulation determines the acceleration of the motor during its travel. An s-curve trajectory for displacement is used to reduce jerk; its velocity proﬁle is shown in Figure

B.7. A minimally short insertion time is preferable to approximate the instantaneous Experimental Apparatus and Procedure 17

insertion of the droplet into the hot-air ambient. The droplet travel time in the electric furnace was initially 800 ms but was reduced in later tests to 200 ms.

3.1.3 Fuel Supply System

In order to maintain a consistent fuel droplet diameter, a syringe-pump driven system is used to deploy a droplet onto the fiber. A New Era NE-1000 syringe pump with an 8 mL reservoir is able to dispense 65 µL of fluid at one actuation, and operate at pressures higher than the maximum testing pressure. Its dispensing accuracy is 1% The fuel ± travels through the fuel line as shown in Figure 3.2, and is dispensed via a fine 0.010" diameter needle positioned close to the fiber. This needle can be retracted from the fiber using a linear solenoid to protect both the needle and fiber during droplet insertion. A combination of check valves and a burst disk are used to reduce the safety concerns of highly pressurized liquid fuel.

3.1.4 Gas Supply System

The ambient gas is dry air supplied from a gas cylinder, brought through the gas line as shown in Figure 3.2. Solenoid valves in conjunction with a mass ﬂow controller limit the gas ﬂow into and out of the pressure chamber. The air cylinder is pressurized prior to testing with an external gas cylinder. Of note in the gas supply design is the presence of a pressure regulator in the outlet line, that maintains constant chamber pressure by vent- ing air as the chamber temperature increases. As ambient pressure is a major parameter in this experiment, pressure is measured using transducers in the chamber, inlet line, and outlet line. Experimental Apparatus and Procedure 18

Figure 3.2. Schematic showing fuel and gas line piping and instrumentation.

3.1.5 Control System

The control system incorporated into this experiment consists of one main input channel and two output channels. Figure 3.3 shows a schematic of the control system.

The experiment receives input from a human-machine interface (HMI), which is capable of setting the test parameters and triggering the experiment sequence. A pro- grammable logic controller (PLC) converts the input into instructions for the electrical and mechanical components, including valves, diagnostics, and temperature controls. Experimental Apparatus and Procedure 19

More information regarding the electrical and mechanical components can be found in sections 3.1.3 and 3.2.

The ﬁrst output channel converts the visual observation of the experiment into digital images. An onboard video data acquisition system (VDAQ) receives and stores direct video data from the cameras. The color and deployment camera outputs are recorded directly to the VDAQ, and can be downloaded directly or accessed via a remote desktop connection. The high speed camera output is recorded to an NAC storage system, and can be downloaded via GigE ethernet connection to the VDAQ.

An additional output channel records the measurements from the instrumentation during the experiment. A National Instruments CompactDAQ (CDAQ) reads from the

1 pressure transducers, thermocouples and PMT at a sampling rate of 3000 s− . This data

is accessible in the same manner as the visual data.

NAC

HS ETHERNET CDAQ INSTR CAM COLOR, DEPL.

VDAQ

ELEC/ MECH

HMI PLC

Figure 3.3. Schematic showing experimental control system, with outputs to imaging and instrumentation data acquisition. Experimental Apparatus and Procedure 20

3.2 Diagnostic Equipment

3.2.1 Optical Diagnostics

Figure 3.4 shows the placement of the optical diagnostic equipment around the high- temperature region.

Color Camera

Collimated High-speed Backlight Camera

PMT

Figure 3.4. A top view schematic of the pressure chamber, showing the position of diagnostic instrumentation around the high-temperature region.

A NAC MEMRECAM HX-7 high-speed digital camera with a telecentric lens was used to record 12-bit grayscale images of the droplet during the combustion reaction. The camera was set up as a shadowgraph, an optical system similar to Schlieren that reveals variation in the ﬂuid density gradients inside the chamber. Shadowgraphy is sensitive to the second derivative of the index of refraction, while Schlieren is sensitive to the ﬁrst Experimental Apparatus and Procedure 21

derivative of the index of refraction49. The high-speed camera was able to record the droplet size and soot formation in a ﬁeld of view of 30 mm by 30 mm around the droplet

1 with a frame rate of 3000 s− . It provided the combination of spatial and temporal resolution necessary to examine the ignition process in more detail than previous studies.

Images captured by the camera were clear enough to visualize the propagation of an ignition kernel near the droplet on a time scale of less than 10 ms. An Opto Engineering

Core LTCLCR048-G illuminator backlight with a central wavelength of 520 nm provided collimated light to the high-speed camera. The backlight strobing is synchronized with the camera shutter and precisely controlled the amount of light reaching the camera’s sensor per exposure.

An Allied Vision Prosilica GT 1290 monochrome camera was used during testing.

1 The camera had a frame rate of 30 s− recording 2.8 megapixel images. It recorded in conjunction with a Thorlabs M530L3 collimated backlight with a central wavelength of

530 nm to record 8-bit grayscale images of a ﬁeld of view measuring 6.8 mm by 6.8 mm in the deployment region, aiding in droplet placement and test setup.

Two color cameras were used at different points in testing. Initially, an Allied Vision

1 Prosilica GT 1930C camera, with a frame rate of 30 s− and a resolution of 2.35 megapix- els, recorded color images of the ﬂame at an angle normal to the high-speed camera.

Later, a FLIR Grasshopper3 2.3 megapixel high-speed color camera with a frame rate of

1 180 s− was substituted to view the high-temperature region at a higher frame rate to better identify ignition. Both cameras were able to record color images of the ﬂame with a ﬁeld of view of 18 mm by 18 mm.

A photomultiplier tube (PMT) was used to precisely determine the instant of ignition. The PMT used in this experiment was a metal package Hamamatsu H10722-110 Experimental Apparatus and Procedure 22

with a low-noise ampliﬁer. The short response time of the PMT was used to record the ignition time of the droplet, and to attempt to identify two-stage ignition. Light emission from the cool ﬂame was so small, however, that the PMT could not identify it through the windows of the pressure chamber. Data was collected from the PMT at a

1 rate of 3000 s− . An Andover Corporation 442HC150-12.5 bandpass ﬁlter with a bandwidth of 355–495 nm was used with the PMT. This bandwidth captured light emission

from formaldehyde species released by the cool ﬂame ignition, as shown in studies by

Nayagam et al.47. The model used in this experiment was an Andover 442HC150-12.5 hard-coated broadband ﬁlter, which provided 80% transmission at the desired wave- lengths. Additionally, an Edmund Optics 48-622 ultraviolet-visible wavelength neutral density ﬁlter with an optical density of 1.5 reduced the incidence of light to the PMT, improving the signal quality.

3.2.2 Temperature Measurement

Three thermocouples were used to measure temperature inside the pressure chamber during the experiment. For some tests, an Omega SCASS-010E-6 K-type thermocouple was used to measure the temperature near the droplet over time. The bare wire thermocouple with a wire diameter of 0.0015" was positioned on the suspender hook less than 1 cm from the droplet. It was also used to validate the ignition detection of the high-speed camera and PMT, conﬁrming the presence of an intermediate temperature region during two-stage ignition. This thermocouple had a response time smaller than the 10 ms capture time of the temperature data acquisition system, allowing it to detect rapid changes in temperature.

A larger thermocouple with a 1.64 mm sheath diameter was positioned inside the high-temperature region to measure the electric heater temperature. It is located 24.8 mm Experimental Apparatus and Procedure 23

radially from the droplet and extends 40 mm above the insulation. It was connected to a PID controller to regulate the heater temperature once it reached the desired test setpoint. The third, beaded-type thermocouple with a bead diameter of 0.43 mm was positioned inside the deployment region to provide an approximate temperature in that region and prevent damage to heat-sensitive components. All thermocouples were type-

K. Figure 3.1 shows the placement of the thermocouples within the pressure chamber.

3.3 Experiment Procedure

To prepare for testing, the chamber is sealed and pressurized to 5 atm through the intake valve with zero air. The heaters are turned on until condensation forms on the chamber walls, and the exhaust valve is opened to remove residence air from the chamber. This removes any moisture present in the chamber that could condense on the windows and obscure the camera view, and is only performed when the chamber is initially sealed.

Once moisture is effectively removed from the pressure chamber, the chamber is pressurized and heated to the desired pressure and temperature set points. The heating process has a typical duration of 5 minutes. Once the chamber reaches the test temperature, the temperature is held constant for an additional 5 minutes until the chamber walls can approach a thermal steady state. A droplet measuring 1.0–1.3 mm in diameter is dispensed onto the ﬁber and quickly raised into the high-temperature region, approx- imating a stepwise temperature increase in the ambient gas.

The fuel used in the experiments was Sigma-Aldrich anhydrous n-Dodecane with a purity of more than 99%. Appendix C lists relevant property values of the fuel. The ambient environment is zero air with a low moisture content. The air had a 21% oxygen Experimental Apparatus and Procedure 24

concentration and less than 0.1 ppm of hydrocarbon impurities. The ambient temperature ranged from 500 to 1000 K and ambient pressure ranged from 0.1 to 25.0 MPa.

The experiment was recorded through windows on the pressure chamber by a three- instrument setup, as shown in Figure 3.4. A high-speed black and white camera, a color camera, and a PMT were used to gather data during testing.

3.3.1 Normal Gravity and Microgravity Testing

When the experiment is conﬁgured for normal gravity testing, multiple test sequences can be run in succession. The test sequence is carried out manually using controls on the experiment. Between tests, the exhaust valve is opened, and the chamber is allowed to depressurize. The exhaust valve is then closed, and the chamber is re-pressurized.

This process is repeated at least 3 times to ensure that the combustion products are cleared from the chamber. The minimum time interval between tests is 5 minutes. Re- sults are collected from the data acquisition system and stored on an external hard drive.

The experiment apparatus was designed for use in both normal gravity and microgravity conditions. Microgravity experiments are conducted using the 5.2s drop tower at the NASA Glenn Research Center Zero Gravity Research Facility.

3.4 Data Analysis

3.4.1 Droplet Burning History

ImageJ50,51 was used to process the digital images obtained from the high speed camera with an automated routine, in order to quantify the droplet diameter as a function of time. Both the thermal expansion that occurs before ignition and burning rate after ignition are calculated from this data. Experimental Apparatus and Procedure 25

The droplet diameter was calculated from the high-speed camera images by deﬁning the diameter as that of a sphere with the same projected area as that of the droplet52.

The droplet does not form a spherical shape due to the inﬂuence of the ﬁber — and of gravity for the normal gravity tests — and assumes an ellipsoidal or lemon-shaped form instead. The effective droplet diameter is expressed as:

s 4 Ap de ∗ (3.1) = π k2 ∗ where "Ap " is the projected area of the droplet onto the image and "k" is the spatial optical resolution of the camera. The optical resolution of the high-speed camera was measured using a Edmund Industrial Optics distortion target, and those of the normal grayscale camera and color cameras were measured by comparing to a known object for reference. The results are shown in Table 3.1.

Table 3.1. Spatial optical resolution testing results.

Camera Spatial resolution (pix/mm) Uncertainty (pix) NAC MEMRECAM HX-7 34 1 Prosilica GT 1290 140 5 Prosilica GT 1390C 68 1 FLIR Grasshopper3 58 2

Full droplet burning history until extinction was attainable for only some test cases.

As soot formation increased with increasing pressure, in accordance with the ﬁndings of

Bae and Avedisian43, the projected area of the droplet could not be reliably measured. Experimental Apparatus and Procedure 26

Soot production occurred so close to the droplet that the boundary was not reliably dis- tinguishable. For this reason, droplet diameter measurement after ignition is only reliable at pressures less than 3 atm. Similarly to previous ﬁber-supported droplet experi- ments2, the droplet fell off the ﬁber easily at high pressures and temperatures under normal gravity conditions. For these tests, droplet diameter was measured until the droplet fell out of view of the camera. Appendix A contains droplet diameter measurements for all tests.

3.4.2 Identiﬁcation of Ignition

Correctly identifying the instant of ignition is critically important to measuring the induction times and droplet burning lifetime.

Cool flame ignition is measured from the appearance of a clearly visible front in the shadowgraph. As the heat release of a cool flame is low, the density gradient caused by the cool-flame front is difficult to observe without additional image processing50,51.

An image processing technique, where a previous image frame is differenced from the current image to remove background noise, provided a better visualization as shown in

Figure 3.5.

Hot flame ignition takes place with the appearance of a hot-flame ignition kernel marked by its higher density gradient in the shadowgraph. Hot flame ignition can be observed on the high-speed and color cameras, and in the rapid response of the PMT and the thermocouple. The instant of ignition is defined as the time at which the PMT voltage measurement differs by more than five standard deviations from the background level. Experimental Apparatus and Procedure 27

(a) Cool ﬂame

(b) Hot ﬂame

Figure 3.5. Comparison of unprocessed and processed image data used to identify the ignition location for cool (a) and hot (b) ﬂames. The propagating waves are visible in white. The image containing the cool-ﬂame front is cropped to make it easier to identify. The droplet is out of frame, centered directly above the front.

3.4.3 Timing Synchronization and Induction Times

A Meinberg IRIG (Inter Range Instrumentation Group) timing system synchronizes time measurement for all diagnostic devices in the experiment. Every temporal measurement during the experiment refers to a consistent trigger time, which allows data to be reliably compared. Experimental Apparatus and Procedure 28

As in Tanabe et al.27, ﬁrst induction time is deﬁned as the time from when the droplet

first enters the high-temperature region until the appearance of a cool-flame kernel. To- tal induction time is defined as the time from droplet exposure to the high-temperature region to the appearance of the hot-flame ignition kernel. Second induction time is defined as the difference between the first and total induction times, and denotes the length of cool flame burning time.

3.4.4 Flame Propagation Speed

The propagation speed of the cool ﬂame and hot ﬂame are measured manually using

ImageJ software50,51. The image processing method is the same as that described above to visually enhance the cool flame. The position of the flame is approximated by measuring the position of a constant-brightness pixel on the leading edge of the premixed wave along a profile normal to the wave’s velocity vector at several different times. The speed is calculated from a linear fit of the position data.

3.4.5 Ignition Location

Previous studies13,16 have measured the distance from the location of ignition to the droplet. In this work, the vertical distance from the ignition point is measured for both cool and hot flame ignition. For the cool flame, the distance is measured at the first visual appearance of a front, from the point on the leading edge of the propagating flame closest to the droplet to the lowest point on the droplet itself. If the cool flame initiation occurs so far from the droplet that it is out of the field of view of the high-speed camera, the distance is recorded as the distance from the edge of the field of view to the lowest point on the droplet. For the hot flame, the distance is measured from the center of the ignition kernel. As the camera is telecentric, and therefore cannot indicate Experimental Apparatus and Procedure 29

the radial distance from the ﬂame to the droplet, vertical distance is the most reliable measurement.

3.4.6 Accuracy of Measurements

The accuracy of ambient pressure is 2.5 psi or 0.18 atm; as the pressure transducers ± ± are intended to accurately measure pressures over 100 atm, sacriﬁcing accuracy at lower

pressures. Additionally, the position of the thermocouple regulating the temperature in

the chamber is lower and radially outward from the position of the droplet, introducing

ambient temperature measurement error. Figures B.6 and B.5 show the difference in

temperature between the location of the chamber thermocouple and the location of the

droplet.

The droplet translation time has the greatest inﬂuence on the accuracy of the induc-

tion times. As the entrance of the droplet into the high-temperature region cannot be a

step function, some variability is introduced as to the exact time the droplet enters the

region. For initial experimentation, the droplet move time in the high-temperature re-

gion was 800 ms, so the minimum measurable induction time was 800 ms. The droplet

move time was reduced to 200 ms, allowing an according minimum measurable induc-

tion time.

The instant of hot ﬂame ignition is accurate to within the frame rate of the high-

speed camera, or 1/3000 s. As the instant of cool ﬂame ignition less readily apparent, its

measurement is slightly less accurate. The error in measurement of the instant of cool

flame formation is 30 ms. The accuracy of identification of cool flame ignition is larger

for higher pressures, as the cool ﬂame front is darker and more evident. Experimental Apparatus and Procedure 30

The location of ignition for both low- and high-temperature cases is accurate within one pixel at the start and end point of measurement. The estimated error for these measurements is 0.06 mm. ± 31

4 Results

The experimental results will be presented below, in the following order: First, the two-stage ignition process is examined numerically for the case of a homogeneous premixed system. Next, the two-stage ignition process for droplets is explained qualitatively using experimental results in normal gravity. The dynamics involved in the ignition process are analyzed, including cool and hot ﬂame initiation and propagation. The experimental ignition delay times, comprised of ﬁrst, second, and total induction times, are presented as a function of ambient temperature and pressure. Finally, other relevant aspects of the experiment, including droplet burning rates, initial droplet size and droplet thermal expansion are discussed.

The test matrix of temperature and pressure conditions for each experimental test point is shown in Figure 4.1. The lower dashed line corresponds to the lowest temperature for which the droplet ignites before evaporating completely due a long ignition delay time. The higher dashed line corresponds to the limit imposed by the rapidity with which the droplet can be inserted and brought to rest into the oven before ignition occurs. An asterisk marks the critical point of the fuel n-dodecane. Results 32

1000 P : 17.9 atm, T : 658.1 K c c 950

900 Ignition occurs before insertion 850

800

750 Evaporation-limited

700 Temperature (K) 650

600

550

500 0 5 10 15 20 25 Pressure (atm)

Figure 4.1. Test matrix showing ambient pressure and temperature conditions for each test in normal gravity.

4.1 Homogeneous Two-stage Ignition

Autoignition of homogeneous mixtures does not involve transport aspects and only the chemical kinetics are at play. This allows us to delineate the effects of thermal and mass transport from the purely chemical aspect of ignition. The ignition delay times for a homogeneous n-dodecane-air mixture were calculated using Cantera53, an open-source

software for chemical kinetics, thermodynamic and transport calculations. The simula-

tion setup was a perfectly premixed adiabatic batch reactor at constant volume with a

mixture fraction of unity. The initial temperature varied from 550 K to 1200 K in order to

show the three temperature regimes described by Peters20. The calculations used a sub-

set of the comprehensive chemical kinetic mechanism created by Lawrence Livermore

National Laboratories (LLNL)22. Speciﬁcally, the mechanism included n-alkanes up to

n-dodecane, with 2755 species and 14314 reactions. Results 33

Figure 4.2 shows the ignition delay time of a homogeneous dodecane-air mixture at atmospheric pressure, an elevated subcritical pressure, and a supercritical pressure.

Ignition delay times are typically shown as a function of 1000 divided by the ambient temperature, with a logarithmic secondary axis. This method is similar to an Arrhenius plot, as ignition delay is inﬂuenced by chemical kinetics. The ignition delay time is linear at high and low temperatures, with the slope representing the activation energy of the high- and low-temperature reactions, respectively. A region exists at any pressure, however, where the ignition delay time increases with temperature. This is known as the negative temperature coefﬁcient (NTC) region.

Temperature (K) 1200 1000 800 600 1000

100

10 Ignition delay time (ms) 1

1 atm 10 atm 20 atm 0.1 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1000/T

Figure 4.2. Ignition delay times shown for n-dodecane in a perfectly premixed reactor at relevant pressures. The times were calculated with the Cantera software. An NTC region, where ignition delay increases with temperature, is clearly evident.

A series of simulations at atmospheric pressure, shown in Figure 4.3, illustrate the

NTC region graphically. The longest ignition delay time occurs for the lowest ambient Results 34

3000 950 K

2500

2000

1500 Temperature (K)

750 K

1000

850 K 650 K 550 K 500 0 100 200 300 400 500 600 700 800 900 1000 Time(ms)

Figure 4.3. Temperature shown as a function of time for homogeneous gas mixtures at P = 1 atm for various initial temperatures. The time of thermal runaway at each temperature demonstrates the NTC for n- dodecane.

temperature case, Tamb = 550 K. As temperature increases by increments of 100 K, the ignition delay time decreases, increases, then decreases again. Additionally, the two- stage temperature rise that indicates a cool ﬂame increases in duration from 550–750 K.

The NTC region can be better visualized by examining the first and second induction times of the mixture as a function of temperature25. In the low-temperature stage below the NTC region, the first induction time is almost equal to the total induction time; the second induction time is close to zero. As temperature increases to the intermediate- temperature stage, as does the second induction time, so the cool flame burns for longer before the hot flame ignition. This temperature region favors the cool flame and reverse reactions described by Peters20, and temporarily inhibits the hot flame reactions. Results 35

1000

100

10 Ignition delay time (ms)

First induction Second induction Total induction 1 550 600 650 700 750 800 Temperature (K)

Figure 4.4. Induction times shown as a function of temperature for P = 1 atm. The opposing behavior of ﬁrst and second induction times gives rise to the NTC region.

Past the NTC region in the high-temperature stage, the two-stage ignition is replaced by single-stage ignition, where only the high-temperature chemistry leads to thermal runaway. Figure 4.4 shows this behavior for atmospheric pressure.

While two-stage ignition is described by the same terms for homogenous mixtures and liquid droplets, many of the mechanisms that govern the process are different in each case. Unlike the chemically driven premixed gas ignition, droplet ignition is controlled in large part by heat and mass transfer, as will be shown in the following subsec- tions.

4.2 Droplet Two-stage Ignition in Normal Gravity

This section discusses the phenomenon of two-stage ignition, first identified in droplets by Tanabe et al.26 In the two-stage ignition process, a cool flame first forms in the vicinity Results 36

of the droplet and propagates toward it, later followed by a hot flame. Conversely, in the single-stage ignition process a hot flame forms without being preceded by a cool flame, observed in this experiment at atmospheric pressure. The single-stage ignition process has been studied extensively theoretically and experimentally, so this work focuses on describing two-stage ignition both qualitatively and quantitatively. The approximate time scales of the processes involved in two-stage ignition are listed in Table 4.1.

Table 4.1. Time scales of relevant processes in droplet two-stage ignition.

Process Time scale (s) Heating and diffusion 100 1 Cool ﬂame burning 10− 3 Hot ﬂame ignition 10− Burning lifetime 100

When the droplet enters the heated chamber as described in Chapter 3, multiple processes occur simultaneously leading up to autoignition. The droplet is initially colder than its surroundings, being closer in temperature to the insulated deployment region.

As the droplet heats up, it experiences both thermal expansion and increased evaporation. Fuel vapor begins to diffuse from the droplet, driven downward by convection due to its higher density in the presence of gravity. The vapor temperature increases from conduction and oxygen mixes with the fuel.

The first ignition stage occurs when a location in the air-fuel mixture reaches a certain critical temperature and mixture fraction favorable to the low-temperature reactions, known as a cool flame. This flame is invisible to the naked eye, but its density gradient is visible in the high-speed shadowgraph camera images in Figure ??. The shadowgraph is not capable, however, of measuring the flame thickness. The cool-flame Results 37

A. 880 ms before ignition: Droplet is stationary in the high-temperature chamber. Droplet heating and fuel evaporation are oc- curing simultaneously but a cool ﬂame has not yet formed.

B. 322 ms before ignition: A cool ﬂame, outlined in the grayscale image and invisible in the color image, has formed below the droplet and is propagating toward it.

C. 1 ms after ignition: A hot flame ignition kernel, clearly visible in both images, forms in the region of fuel vapor below the droplet. The premixed flame propagates toward and establishes a diffusion flame around the droplet.

D. 436 ms after ignition: Midway through the burning process, a buoyant ﬂame has formed around the droplet, carrying soot upward away from it. Soot- ing propensity increases with pressure.

Figure 4.5. Image sequence showing a representative case of two-stage ignition in grayscale and color. Test conditions are 3 atm and 622 K. Results 38

front propagates upward toward the droplet through the unburnt gas mixture, and reactions continue to occur behind the front. Once the front reaches the droplet, the droplet swells rapidly due to the sudden temperature increase. Droplet evaporation continues during cool flame burning, until a hot-flame ignition kernel develops at a location previ- ously traversed by the cool flame — the second ignition stage. Unlike the cool flame, the hot flame is spherical and propagates radially in all directions, surrounding the droplet before dissipating. The fuel vapor below the droplet slows down the flame locally, forming a cone around the colder, richer mixture as observed by Whang et al.16 Figure 4.6b shows the formation and propagation of the hot flame. A diffusion flame forms around the droplet, quickly assuming the teardrop shape characteristic of buoyant flames. The droplet continues to burn with a hot diffusion flame until completion. Figure 4.5 shows the process graphically.

This process can also be shown quantitatively by examining the square of the droplet diameter over time, as depicted in Figure 4.7. The case shown is a different test under similar conditions to the image sequence in Figure 4.5. The droplet enters the field of view and begins to heat up and thermally expand while the fuel vapor diffuses downward due to buoyancy. A cool flame forms, visible in the shadowgraph images, but is not initially recorded by the thermocouple or PMT. When the cool flame propagates past the thermocouple, the heating rate increases, and the temperature increases past the ambient setpoint temperature. Characteristic of the cool flame is a temperature of about

750 K. Further sudden thermal expansion of the droplet about 200 ms prior to hot-flame ignition indicates the time at which the cool flame reaches the droplet. Rapid spikes on both the PMT and thermocouple readings represent the hot-flame ignition. As the thermocouple is positioned below the droplet, it is able to measure the temperature increase Results 39

(a) Cool ﬂame. Images shown 100 ms apart.

(b) Hot ﬂame. Images shown 1 ms apart.

Figure 4.6. Image sequences showing flame front initiation and propagation for both the cool and hot flame. The field of view is smaller in (a) to focus on the cool-flame front; the droplet is centered directly above each image.

from the initial premixed flame, but not the buoyant flame closer to the droplet. The droplet size increases with the hot-flame ignition, then decreases rapidly as the burning process continues. At a certain point in the hot-flame burning process, the droplet becomes small enough that surface tension moves it higher up on the fiber (not seen Results 40

3 atm, 623 K, D0 = 1.02 mm 900 5 1.6

1.4 800 Temperature near droplet (K) 4 1.2 700 PMT Output (V)

) 3

2 1.0 600

(mm 0.8 2

D 2 0.6 500

0.4 1 400 0.2

0.0 300 0 -1500 -1000 -500 0 500 Time relative to hot-flame ignition (ms) Droplet Temperature PMT Output

Figure 4.7. Square of droplet diameter, temperature measurement below the droplet, and PMT output shown with respect to time.

700 1.7

1.6 Temperature below droplet (K) 650

1.5 ) 2 Cool flame passes Hot flame ignition 600 (mm thermocouple 2 1.4 D

1.3 550

Cool flame 1.2 reaches droplet

500 -500 -400 -300 -200 -100 0 100 200 Time relative to hot-flame ignition (ms)

Figure 4.8. Area of interest in Figure 4.7 expanded to mark the occurrence of relevant processes. Results 41

in microgravity, as described in the next section). The droplet size measurement is dis- turbed at that point, and the burning rate slightly increases due to increased conduction from the ﬁber. Both the droplet size and PMT output fall to zero at the time of extinction.

4.2.1 Low-temperature Ignition at High Pressures

Tanabe et al.28 described two regions in the temperature and pressure domain where single-stage ignition occurred: one at high temperatures and one at low temperatures.

In the low-temperature region, they hypothesized that the low-temperature reactions immediately activated the high-temperature reactions, causing an infinitesimally short second induction time. The wider field of view and increased temporal resolution of the current experiment allows for clarification of this phenomenon. At high pressures and low temperatures, cool-flame formation occurs far away from the droplet. As shown in Figure 4.9, the hot-flame ignition occurred immediately behind the cool-flame front before it reaches the droplet, and propagated past it in less than 1 ms. Therefore, Tanabe et al’s assertion may be limited by their limited diagnostic capabilities.

4.2.2 Cool-Flame Only Combustion

Also notable was a region at ambient pressure and temperature where the droplet burned only with a cool ﬂame. In this case, the droplet entered the chamber and evaporated approximately with the d 2-law for more than two seconds, as one would expect. The cool

flame formed well below the droplet and propagated towards it. Color camera images were unable to capture the cool flame, but the high-speed camera showed a noticeable disturbance to the droplet when the cool flame reached it. Figure 4.10 shows that the rate of change of droplet size increased from an evaporation rate of 0.258 mm2/s to a Results 42

Figure 4.9. Image of droplet showing hot flame ignition starting from behind a propagating cool flame. The experimental conditions are 10 atm and 571 K. cool flame burning rate of 0.815 mm2/s. The second induction time was longer than the droplet lifetime, so the droplet burned with a cool flame until extinction.

2 atm, 603 K, D = 1.06 mm 1.2 0

700 1.0 Temperature near droplet (K)

0.8 600 ) 2 0.6 (mm 2 500 D

0.4

400 0.2 Droplet Temperature Rate calculation bounds 0.0 300

-3000 -2000 -1000 0 1000 Time relative to cool-flame ignition (ms)

Figure 4.10. Droplet history and temperature data at 2 atm and 600 K. The droplet burns to completion with a cool ﬂame, without transitioning to a hot ﬂame. Results 43

4.3 Cool Flame Ignition Behavior

This section focuses on the initiation of the cool flames, and their propagation toward the droplet. Measurement of both the vertical distance from the ignition point to the droplet and the average speed at which the flame propagates provide insight to the phenomena occurring during droplet ignition. The high-speed shadowgraphy used in this experiment provided, for the first time, visual observation of the formation and propagation of a cool flame during droplet autoignition.

4.3.1 Location of Ignition

Ignition of both cool flame and hot flame takes place below the droplet due to the downward convection of fuel vapor under normal gravity. Figure 4.11 shows the location of cool flame ignition versus temperature for several ambient pressures. While the temperature range differs for each pressure case, cool flame ignition generally occurs closer to the droplet as temperature increases, due to the increased reactivity of the low- temperature reactions. Cool flame ignition location is both temperature- and pressure- dependent. At lower ambient pressures, the cool flame initiation occurs so far from the droplet that it is out of the field of view of the high-speed camera. In this case, the location of ignition is recorded as the distance from the droplet to the edge of the field of view. At any given temperature, the cool flame ignites closer to the droplet as pressure increases.

Of note is the cool ﬂame formation behavior at 10 atm ambient pressure. The cool

ﬂame forms farther away from the droplet as temperature decreases from 650 K to 550 K.

Yet at 525 K ambient temperature, cool ﬂame formation occurs closer to the droplet. Results 44

2 atm 3 atm 5 atm 10 10 10

5 5 5

0 0 0 600 700 800 600 700 800 550 600 650 700 750 Distance from droplet (mm) Distance from droplet (mm) Distance from droplet (mm) Temperature (K) Temperature (K) Temperature (K) 10 atm 15 atm 10 10

5 5 L

0 0 500 550 600 650 500 550 600 Distance from droplet (mm) Distance from droplet (mm) Temperature (K) Temperature (K)

Figure 4.11. Cool ﬂame ignition distance to droplet shown as a function of temperature for several pressure cases. The temperature range is different for each pressure case.

This results from a change in ignition regime at that temperature, from two-stage ignition to the high-pressure, low-temperature single stage ignition ﬁrst described by Tan- abe et al.27 and discussed in Section 4.2.1.

4.3.2 Propagation Speed

Lewis and Von Elbe54 defined the burning velocity of a propagating flame as the velocity of unburnt fuel traveling in a direction normal to the the flame front. The velocity of the

ﬂame can therefore be described with respect to either the unburnt fuel or the burnt fuel. The unburnt and burnt velocities are related using the following equation:

µ ¶ ρb su sb (4.1) = ρu where s represents flame speed and ρ represents gas density of the unburnt and burnt fuel, respectively. Zhao et al.25 described the unburnt flame speed of cool flames for Results 45

premixed dimethyl ether at atmospheric pressure and 750 K ambient to be on the order of 1 cm/s.

For the current case, small convective flows are present in the unburnt fuel, due to buoyancy effects which are not well characterized. Therefore the cool-flame front velocity cannot be strictly defined with respect to either the unburnt or burnt mixture. The front velocity here is measured in the reference frame of the laboratory environment. It is measured relative to the solid mechanical components of the system, rather than the unburnt or burnt mixtures, both of which are fluids. The cool flame propagates through an opposed flow of fuel vapor v f , so its observed speed v f ,0 can be approximately related to the cool flame propagation speed su as

s v v (4.2) u = f ,0 − f

The unburnt ﬂow velocity is small, on the order of 1 mm/s, but is non-negligible compared to the cool ﬂame propagation speed.

Cool ﬂame propagation speed generally increases as pressure increases, which re-

ﬂects the increased reactivity at elevated pressure. There appears to be a minimum cool

ﬂame propagation speed at approximately 625 K at lower pressures as seen in Fig. 4.12.

The measurement procedure to calculate the ﬂame-front velocity is described in

Section 3.4.4. Typically, the cool ﬂame propagates toward the droplet at an approximately linear rate. Appendix D shows the measured ﬂame-front position as a function

of time from which the velocities are obtained by linear curve-ﬁts. Results 46

60 2 atm 3 atm 50 5 atm 10 atm 15 atm

10 Cool flame propagation speed (mm/s)

0 550 600 650 700 Temperature (K)

Figure 4.12. Cool ﬂame propagation speed shown as a function of temperature for several pressure cases.

4.4 Hot Flame Ignition Behavior

This section focuses on the initiation and propagation of hot-ﬂame fronts. Measure- ment of both the vertical distance from the ignition kernel to the droplet and the average speed at which the ﬂame propagates are provided.

The relatively high propagation speeds of these hot-ﬂame fronts have historically made it difﬁcult to observe and measure. Imaging devices have only recently become fast enough to reliably capture the location of ignition near the droplet. The high-speed camera used in this experiment can identify the ignition point with a time resolution of

0.33 ms.

4.4.1 Location of Ignition

Figure 4.13 shows the location of the hot ﬂame ignition kernel versus temperature for several ambient pressures. Results 47

The influence of temperature on ignition location for hot flames has been studied in the past: Whang et al.16 using a post-burner gas flow setup, showed that ignition moved closer to the droplet as temperature increased. Khan et al.13 measured the location of hot-flame ignition versus pressure at several ambient temperatures. The effect of temperature on ignition kernel location, however, varies in a non-monotonic fashion with pressure as described below.

The location of autoignition varies signiﬁcantly with temperature at different ambient pressures. Although the temperature range was different at each ambient pressure, the ignition location changed linearly with respect to temperature. At low ambient pressures, ignition begins close to the droplet at low temperatures, and moves away as temperature increases. As the pressure increases, however, the slope of the trend line decreases; at 10 atm ignition begins far from the droplet at low temperatures and moves closer to the droplet as temperature increases.

4.4.2 Propagation Speed

Turns55 describes the laminar flame speed as a function of temperature and pressure for premixed flames. Laminar flame speed increases as temperature increases and decreases as pressure increases. In comparison with the cool flame speed, the measured hot flame propagation speeds are higher due to increased reaction rate and heat release which leads to significant thermal expansion.

The hot flame propagation speed, shown in Figure 4.14, is generally higher than typical laminar flame speeds, and is on the order of 100 cm/s. The hot flame speed shows a similar trend to the laminar flame speed, clearly increasing as temperature increases, and decreasing as pressure increases, though not as steeply. Like the cool flame, the hot

ﬂame propagates toward the droplet at a constant velocity. Results 48

2 atm 3 atm 5 atm

10 10 10

5 5 5

0 0 0 600 700 800 600 700 800 550 600 650 700 750 Distance from droplet (mm) Distance from droplet (mm) Distance from droplet (mm) Temperature (K) Temperature (K) Temperature (K) 10 atm 15 atm

10 10

L 5 5

0 0 500 550 600 650 500 550 600 Distance from droplet (mm) Distance from droplet (mm) Temperature (K) Temperature (K)

Figure 4.13. Hot ﬂame ignition kernel distance to droplet shown as a function of temperature for several pressure cases. The temperature range is different for each pressure case.

4000

3500

3000

2500

2000

1500 2 atm 3 atm Hot flame propagation speed (mm/s) 1000 5 atm 10 atm 15 atm 500 500 550 600 650 700 750 800 850 Temperature (K)

Figure 4.14. Hot ﬂame propagation speed shown as a function of temperature for several pressure cases. Results 49

4.5 Two-Stage Ignition Delay Times

Testing at ambient pressures ranging from atmospheric to supercritical shows the temperature and pressure dependence of the ﬁrst, second, and total induction times. The minimum temperature for which ignition is observed (before the droplet completely evaporates), and the maximum temperature at which the droplet becomes stationary prior to ignition, bound the temperature range at each pressure as described earlier.

This temperature range narrows at higher pressures.

Ignition delay times for droplets are presented in the same style of plot as for homogeneous systems. However, the physical processes involved in droplet ignition obfus- cate the trends observed in premixed gases.

Figure 4.15 shows total induction times as a function of 1000/T. At each ambient pressure, the total induction time increases as temperature decreases, eventually reaching a temperature at which ignition does not occur before the droplet has fully evaporated. In general, the total induction time at any given temperature decreases as pressure increases, up until the critical pressure. Above the critical pressure, the total induction time exhibits no clear trend. These results show qualitative agreement with the previous experiments of Tanabe et al.26–28.

The time from droplet insertion until cool ﬂame appearance was measured as the

ﬁrst induction time. Two competing processes govern the ﬁrst induction time: the low- temperature chemical reactions and physical processes, such as droplet heating and fuel vapor and oxygen diffusion. Increased reactivity and heat transfer should decrease the

ﬁrst induction time, while reduced diffusion should increase it. As a consequence, the

ﬁrst induction time is very temperature-dependent, and is less pressure-sensitive than the total induction time. Figure 4.16 shows ﬁrst induction times as a function of 1000/T Results 50

Temperature (K) 1000 900 800 700 600 500 10000 1 atm 2 atm 3 atm 5 atm 5000 10 atm 15 atm 18 atm 20 atm 25 atm Total induction time (ms) 1000

500 1 1.2 1.4 1.6 1.8 2 1000/T

Figure 4.15. Total induction time, or ignition delay time, as a function of temperature for several pressure cases. D 1.1 1.3 mm. 0 = −

for several pressures. These results are somewhat different from the results of Tanabe et al.26 due to several factors. The current work used larger-diameter droplets as well as a longer droplet insertion times (slower translation into the oven), both of which increase the ignition delay time. Unlike Tanabe et al., the present experiments had a wider field of view of the camera and made detection of cool-flames farther from the droplet possible, showing longer first induction time measurement.

The second induction time, or cool-flame burning time, is shown in Figure 4.17 to be strongly pressure dependent and relatively temperature independent. Due to the improved visibility of the cool flame on the high-speed camera, the propagating wave can be seen from much farther from the droplet than in previous studies. This produces longer induction times than the findings of Tanabe et al.28 that used a smaller field of view. For certain temperatures at low pressures (P 5 atm), the cool flame initiation ≤ Results 51

Temperature (K) 1000 900 800 700 600 500 10000 2 atm 3 atm 5 atm 10 atm 5000 15 atm 18 atm 20 atm 25 atm First induction time (ms) 1000

500 1 1.2 1.4 1.6 1.8 2 1000/T

Figure 4.16. First induction time as a function of temperature shown for all ambient pressures where a cool ﬂame is observed, so the ignition delay can be divided into two stages. D 1.1 1.3 mm. 0 = − Temperature (K) 800 700 600 500 1000

100

2 atm 3 atm 5 atm

Second induction time (ms) 10 atm 15 atm 18 atm 20 atm 25 atm 10 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 1000/T

Figure 4.17. Second induction time as a function of temperature shown for all ambient pressures where a cool ﬂame is observed. D 1.1 0 = − 1.3 mm. Results 52

occurs outside of the ﬁeld of view. In these cases, the second induction time can be longer than what is measured.

4.5.1 Pressure Dependence

While the autoignition timing is dependent on both temperature and pressure, examining the ignition delay times as a function of pressure at a constant temperature clariﬁes the two-stage ignition process near the critical pressure. The ambient temperature for the reported cases is 603 K. The ﬁrst and total induction time both decrease as pressure increases up to the critical point, but at pressures above the critical pressure both the

ﬁrst and total induction time begin to increase. These trends are shown in Figure 4.18.

These observations match the results of Kadota et al.11 who found that the ignition delay

time reached a minimum near the critical pressure.

5000 First induction Total induction

1000

500 Induction time (ms)

100 0 5 10 15 20 25 Pressure (atm)

Figure 4.18. First and total induction times are shown as a function of pressure from 2 – 25 atm. The ignition delay times reach a minimum near the critical pressure. T 603 K, D 1.0 1.1 mm. 0 = 0 = − Results 53

500

100 Second induction time (ms)

0 5 10 15 20 25 Pressure (atm)

Figure 4.19. Second induction time is shown as a function of pressure from 2 – 25 atm. The second induction time decreases as pressure increases, even past the critical point. T 603 K, D 1.0 1.1 mm. 0 = 0 = −

Figure 4.19 shows the effect of pressure on the second induction time, which is dependent on the low-temperature chemistry reaction rates. Increasing pressure increases the rate of chemical kinetics. As such, the second induction time decreases as pressure increases, even past the critical pressure.

4.6 Other Aspects of Droplet Combustion in Normal Gravity

4.6.1 Inﬂuence of Droplet Heating and Insertion Time

Previous studies examined the dependence of ignition delay time10 and second induction time28 on droplet diameter, showing that the total induction time increased as droplet diameter increased, but the second induction time remained constant. The current work supports these ﬁndings by examining two rounds of testing with different droplet travel times and initial diameters. The original round of testing used a droplet Results 54

travel time of 800 ms, and an initial diameter of 1.1–1.3 mm. The revised round of testing used a reduced droplet travel time of 200 ms and an initial diameter of 1.0-1.1 mm.

Figure 4.20 compares total induction time as a function of temperature at two ambient pressures for both test sequences. Hot-ﬂame ignition for the larger droplets occurs at least 500 ms slower at any given temperature, demonstrating the impact of droplet heat-up times on ignition delay. In contrast, second induction times at each pressure fall in the same range regardless of droplet size and travel time, as shown in Figure 4.21.

This shows the relative independence of second induction time on physical processes;

it depends on much more on chemical reaction rates.

4.6.2 Droplet Burning

Droplet burning after ignition is as important as the ignition process for practical appli-

cations. Burning rates can be accurately measured at low ambient pressure, and burn-

ing rates follow the well-established d 2-law. Table 4.2 shows burning rate constants at

selected temperatures for ambient pressures of 1 and 2 atm, and droplet history plots

are available for all tests in Appendix A. Burning rate constants were measured from the

middle 60% of the combustion lifetime.

Table 4.2. Burning rates of selected temperature and pressure cases.

³ mm2 ´ Pressure (atm) Temperature (K) Burning rate constant s 1 944 1.315 1 973 1.305 2 773 1.339 2 798 1.419 2 821 1.479 2 849 1.499 Results 55

Temperature (K) 800 700 600 500 5000

1000

500 Total induction time (ms)

Original 3 atm Revised 3 atm Original 10 atm Revised 10 atm 100 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 1000/T

Figure 4.20. Total induction time for selected pressure cases compared for two rounds of testing.

Temperature (K) 800 700 600 500 1000

100 Second induction time (ms) Original 3 atm Revised 3 atm Original 10 atm Revised 10 atm 10 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 1000/T

Figure 4.21. Second induction time for selected pressure cases compared for two rounds of testing. Results 56

The burning rate generally increases as both pressure and temperature increase. No- table in most test cases is a disturbance at D2 1.2mm2, when the droplet shifts upward ≈ on the fiber due to its reduced mass, and the burning rate increases due to the influence of the heated fiber. As pressure increases, gas dissolved into the droplet plays a larger role in transport56, invalidating the d 2-law. Also, at elevated pressures, soot formation close to the droplet obscures its shape, making measurement of burning history unreli- able.

At supercritical pressures, the droplet shape becomes highly amorphous after ignition, boiling and wrinkling as observed by Mikami et al.42 The loss of surface tension past the critical point that causes the droplet to fall from the ﬁber, coupled with heavy sooting at high pressures, impedes analysis of supercritical droplet burning in normal gravity.

4.6.3 Inﬂuence of Pressure of Background Variation

At high pressure, the density variation of the ambient gas increases dramatically with temperature (see Figure C.3). This leads to a high Grashof number and increased turbulent mixing. These disturbances interfere with the ignition dynamics, because the vapor plume that originates at the droplet becomes turbulent and wavy. Figure 4.22 shows the increased disturbance at elevated pressures. Results 57

(a) 1 atm (b) 10 atm (c) 20 atm

Figure 4.22. Comparison of background density variation at various pressures.

This chapter presented results from normal gravity testing, examining the behavior of droplet autoignition. Of note was the formation of both cool and hot ﬂames prior to the establishment of a diffusion ﬂame around the droplet. The ignition timing also provided insight as to the dynamics of two stage ignition in droplets. Preliminary microgravity testing, discussed in the next chapter, shows key differences in the droplet autoignition process. 58

5 Preliminary Microgravity Results

Testing in the 5.2 s drop tower at NASA Glenn Research Center provides a microgravity environment suitable to investigate two-stage ignition of droplets without the inﬂuence of buoyant convection. Results from preliminary microgravity experiments are described in the following section.

5.1 Experimental Conditions

To date, two tests have been carried out, using the same n-dodecane fuel as in normal gravity. Both had an ambient temperature of 623 K and pressure of 3 atm. The drop

6 tower provides 5.18 s of microgravity, with gravitational acceleration of less than 10− g.

5.2 Experimental Procedure

The experimental procedure has several minor differences conﬁgured for microgravity

testing. The pressure chamber and fuel lines are pressurized before the drop vehicle

containing the experimental apparatus is put in place. Finer pressure adjustments can

be carried out remotely using pressure canisters mounted on the drop vehicle. The test

sequence is carried out autonomously, with the trigger command being transmitted re-

motely from the control room. The electric heaters are turned off 5 s prior to the release Preliminary Microgravity Results 59

of the vehicle, and the droplet movement does not occur until 200 ms after the trigger command is received, to reduce instability in the droplet from the initial acceleration.

Video from the microgravity test is visible in real time due to an infrared transmitter that communicates with the control center. Camera images and numerical data are stored in the on-board data acquisition system and retrieved once the drop is completed.

5.3 Microgravity Experimental Results

The overall two-stage ignition process under microgravity was found to be similar to the normal gravity experiments, with several important differences. Figure 5.1 shows the microgravity two-stage ignition graphically on both the high speed and color cameras.

After the droplet is introduced to the hot environment, fuel vapor diffuses radially outward in all directions. Diffusion is slightly weaker in the direction of the fiber due to its cooling effect. As shown in Figure 5.2a, the cool flame ignition occurs near the droplet and propagates spherically outward, inducing thermal expansion in the droplet as the front passes it. The droplet burns with a cool flame until the hot flame ignites near the droplet, pictured in Figure 5.2b. The hot flame also propagates spherically outward, forming a toroidal shape where it interacts with the cool, rich mixture surrounding the droplet. After autoignition, the droplet burns with a spherical diffusion flame until extinction, as evidenced by a spherical soot pattern. Thermo- and electrophoretic effects draws the soot to the colder droplet suspension system. Preliminary Microgravity Results 60

A. 179 ms before ignition: A cool ﬂame, outlined in the grayscale image and invisible in the color image, has formed below the droplet and has propagated toward it.

B. 4 ms after ignition: A premixed hot ﬂame ignition kernel, clearly visible in both the grayscale and color images, forms in the region of fuel vapor below the droplet. The premixed ﬂame propagates toward and ignites the droplet.

C. 424 ms after ignition: Midway through the burning process, a spherical diffusion ﬂame has formed around the droplet, with soot forming at the ﬂame front. Soot travels toward the droplet suspender due to thermophoresis.

Figure 5.1. Image sequence showing representative case of two-stage ignition in microgravity. Test conditions are 3 atm and 623 K. Initial diameter is 1.07 mm. Preliminary Microgravity Results 61

(a) Cool ﬂame. Images shown 10 ms apart.

(b) Hot ﬂame. Images shown 1 ms apart.

Figure 5.2. Image sequences showing flame kernel initiation and spherical front propagation for both the cool flame and hot flame. Test conditions are 3 atm and 623 K. Preliminary Microgravity Results 62

Figure 5.3 shows the droplet burning history for the described test case. The droplet exhibits the same multi-stage thermal expansion as in normal gravity conditions; it expands when the cool ﬂame reaches it and again after autoignition. The burning rate appears generally constant, and the disturbance mentioned in Section 4.6.2 is not ob-

served, due to the absence of gravitational force on the droplet.

1.6

1.4

1.2

) 1.0 2

(mm 0.8 2 D

0.6

0.4

0.2

0.0

-1500 -1000 -500 0 500 1000 Time relative to hot-flame ignition (ms)

Figure 5.3. Square of droplet diameter shown as a function of time from autoignition. Circular markers denote points measured manually. P = 3 atm, T = 623 K, D 1.07 mm. 0 =

5.4 Comparison with Normal Gravity Results

Table 5.1 shows the difference in ignition results for the same test conditions in microgravity and normal gravity. The difference in droplet diameter was small enough to have a minimal effect on the results.

Apart from the well-known microgravity combustion phenomena, the most noticeable difference in the microgravity results is the behavior of the cool ﬂame front. Figure

5.2a shows that the initial cool ﬂame formed much closer to the droplet, opposite the Preliminary Microgravity Results 63

Table 5.1. Comparison of ignition dynamics between microgravity and normal gravity.

µ g 1 g − − D0 (mm) 1.08 1.10 τ1 (ms) 1643 796 τ2 (ms) 223 924 τ (ms) 1865 1719 xCF (mm) 1.84 6.85 vCF (mm/s) 60.8 10.8 xHF (mm) 0.94 1.77

fiber but not directly below the droplet. Unlike the normal gravity cool flame, which propagated upward along the fuel vapor trail, the microgravity cool flame propagated radially outward in all directions until surrounding the droplet. The cool flame formed

1.84 mm from the droplet, about 5 mm closer than under normal gravity. Its propagation speed was almost ﬁve times faster.

Additionally, the spherical zone of colder fuel vapor surrounding the droplet retards the propagating hot flame. In microgravity this zone is larger in radius, as the dense fuel vapor is not affected by convection. The hot flame ignition also occurs closer to the droplet in microgravity, but the difference is less than for the cool flame ignition.

The total induction time is similar for both cases. As the cool ﬂame forms closer and propagates faster to the droplet, the second induction time is much shorter in microgravity than in normal gravity. As such, the ﬁrst induction time is longer in microgravity than in normal gravity, without convection increasing droplet heating and vapor diffusion. Preliminary Microgravity Results 64

Microgravity testing provided an opportunity to examine the droplet autoignition process without the influence of gravity, and with it buoyant and convective effects. The preliminary results show quantitative differences from normal gravity in the dynamics of two-stage ignition and more clearly express the ignition and propagation of initial premixed cool and hot flames. Future testing under microgravity conditions will allow further clarification of the autoignition process at temperatures and pressures closer to the critical point. 65

6 Conclusions

Autoignition of n-dodecane fuel droplets is investigated as a function of ambient pressure and temperature with temperature varying in the range of 500–1000 K and the pressure in the range of 1–25 atm, encompassing the critical pressure of the fuel. The results of this study are summarized as follows:

The ﬁrst, second, and total induction times are measured for n-dodecane • droplets during two-stage ignition. The ﬁrst induction time is shown to increase

as temperature increases but relatively insensitive to pressure. This process is

driven by physical mechanisms such as droplet heating, fuel evaporation, and

mixing of fuel and oxygen. The second induction time depends more on the

chemical kinetics of low-temperature reactions, and decreases as pressure in-

creases.

Two-stage ignitions are observed to proceed as follows: First, a cool-ﬂame front • originates at some distance from the droplet and propagates toward it, followed

by a hot-ﬂame ignition kernel which again propagates and envelops the droplet

establishing a diffusion ﬂame. The measured initial location of the cool and hot

ﬂame kernels and their propagation speed are presented. Conclusions 66

Contrary to earlier studies, the present results show cool-ﬂame formation prior • to the hot ﬂame even in a pressure and temperature region believed to cause

single-stage ignition. This may be due to the limited ﬁeld of view of the earlier

experiments, that could not observe the presence of a cool ﬂame farther from

the droplet.

Preliminary microgravity results are presented. The general results are similar • to the normal gravity tests, but ﬂames tend to be more spherical due to the

absence of buoyancy. 67

7 Suggested Future Research

Future research, both in normal gravity and microgravity, would provide further insight to the phenomena observed in this work and improve the understanding of droplet ignition as a whole.

Further exploration of the two-stage ignition process in normal gravity, at additional temperatures to those measured in this work, would clarify the trends of ignition dynamics and timing; especially the inﬂuence of pressure on hot ﬂame ignition location.

Refinement of the diagnostic equipment could improve identification of cool flame formation.

Microgravity testing of droplet autoignition would provide the most beneﬁcial future research on this topic. Identifying the differences between two-stage ignition in normal gravity and microgravity would improve the theoretical understanding of the two-stage ignition process in droplets. Additionally, a microgravity environment would allow for observation of droplet burning to completion in transcritical conditions, which is impossible in normal gravity. This is a pressing area of research for the development of internal combustion engines, as compression ratios increase to improve efﬁciency.

Finally, a long-term microgravity environment such as the International Space Station Suggested Future Research 68

could allow for observation of high-pressure two-stage ignition and combustion of free-

ﬂoated droplets without the interference of a support ﬁber, which most closely approximates the droplet autoignition process and is most relevant for real-world combustion applications. Appendix 69

Appendix A Data

Raw data gathered from each normal gravity test is shown in the charts below. Pre- liminary testing was performed with a larger droplet diameter range of 1.1–1.3 mm and a longer travel time of 800 ms in the high-temperature region. Later testing was performed with a smaller droplet diameter range of 1.0–1.1 mm and a shorter travel time of 200 ms in the high-temperature region. Additionally, during later testing an exposed-wire type

K thermocouple measured the air temperature just below the droplet.

Each chart contains the square of droplet diameter, photomultiplier tube output, and temperature measurement, as available. The origin of abscissa is the time at which the control and diagnostic systems receive a trigger signal, which provides a consistent reference point for all measurements. Results are shown in chronological order and summarized in Table A.1.

Table A.1. Test conditions for summary plots of included results.

Test Temperature (K) Pressure (atm) Initial Diameter (mm) 53 973 1 1.19 54 944 1 1.15 55 849 2 1.19 56 821 2 1.22 57 798 2 1.27 58 773 2 1.19 59 745 2 1.14 60 721 2 1.22 61 699 2 1.12 62 673 2 1.16 63 648 2 1.10 64 796 3 1.36 65 773 3 1.14 Continued on next page Appendix 70

Test Temperature Pressure Initial Diameter 66 746 3 1.17 67 723 3 1.13 68 696 3 1.24 69 673 3 1.24 70 647 3 1.14 71 622 3 1.16 72 600 3 1.16 73 771 5 1.14 74 721 5 1.24 75 724 5 1.17 76 699 5 1.14 77 675 5 1.2 78 647 5 1.16 79 696 5 1.07 80 696 5 1.24 81 650 5 1.15 82 623 5 1.18 83 599 5 1.15 84 573 5 1.18 85 699 10 1.24 88 648 10 1.22 89 623 10 1.25 90 600 10 1.3 91 571 10 1.19 92 549 10 1.25 93 525 10 1.15 94 624 15 1.21 95 596 15 1.23 96 573 15 1.18 97 546 15 1.35 98 525 15 1.24 99 574 18 1.22 100 550 18 1.14 101 525 18 1.27 102 572 20 1.26 103 550 20 1.22 104 524 20 1.29 Continued on next page Appendix 71

Test Temperature Pressure Initial Diameter 105 574 25 1.26 106 550 25 1.17 107 525 25 1.25 111 603 2 1.06 112 603 3 1.06 113 603 5 1.09 114 603 10 1.13 115 603 15 1.09 116 603 18 1.07 117 603 20 1.11 118 603 25 1.07 125 602 3 1.07 126 623 3 1.10 127 642 3 1.04 128 663 3 1.12 129 682 3 1.07 130 703 3 1.06 131 722 3 1.06 132 743 3 1.11 133 763 3 1.09 134 783 3 1.11 135 584 3 1.13 136 561 3 1.10 1 atm, 973 K, D0 = 1.19 mm

1.6 4.5

1.4 4.0

1.2 3.5 PMT Output (V) 1.0 ) 2 3.0 0.8 (mm 2

D 2.5 0.6

2.0 0.4

1.5 0.2

0.0 1.0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Time after trigger (s)

1 atm, 944 K, D0 = 1.15 mm

1.4

4 1.2

1.0

3 PMT Output (V) ) 2 0.8 (mm 2

D 0.6 2

0.4 1 0.2

0.0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Time after trigger (s) 2 atm, 849 K, D0 = 1.19 mm

2.0

1.5

3 PMT Output (V) ) 2

1.0 (mm 2

D 2

0.5 1

0.0 0 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Time after trigger (s)

2 atm, 821 K, D0 = 1.22 mm

2.0

1.5

3 PMT Output (V) ) 2

1.0 (mm 2

D 2

0.5 1

0.0 0 1.5 2.0 2.5 3.0 Time after trigger (s) 2 atm, 798 K, D0 = 1.27 mm

2.0 4

1.5 3 PMT Output (V) ) 2 (mm 2

D 1.0 2

0.5 1

0.0 0 1.5 2.0 2.5 3.0 Time after trigger (s)

2 atm, 773 K, D0 = 1.19 mm

4 1.5

3 PMT Output (V) ) 2 1.0 (mm 2

D 2

0.5 1

0.0 0 1.5 2.0 2.5 3.0 Time after trigger (s) 2 atm, 745 K, D0 = 1.14 mm

1.6 4 1.4

1.2

3 PMT Output (V)

) 1.0 2 (mm

2 0.8

D 2

0.6

0.4 1

0.2

0.0 0 1.5 2.0 2.5 3.0 Time after trigger (s)

2 atm, 721 K, D0 = 1.22 mm 2.0

1.5

3 PMT Output (V) ) 2 1.0 (mm 2

D 2

0.5 1

0.0 0 1.5 2.0 2.5 3.0 3.5 Time after trigger (s) 2 atm, 699 K, D0 = 1.12 mm

1.6

1.4 4

1.2

3 PMT Output (V) 1.0 ) 2

0.8 (mm 2

D 2 0.6

0.4 1

0.2

0.0 0 1.5 2.0 2.5 3.0 Time after trigger (s)

2 atm, 673 K, D0 = 1.16 mm

1.4 4 1.2

1.0 3 PMT Output (V) ) 2 0.8 (mm 2

D 2 0.6

0.4 1

0.2

0.0 0 1.5 2.0 2.5 3.0 3.5 Time after trigger (s) 2 atm, 648 K, D0 = 1.10 mm

4 1.2

1.0

3 PMT Output (V)

) 0.8 2 (mm 2 0.6 2 D

0.4 1

0.2

0.0 0 1.5 2.0 2.5 3.0 3.5 4.0 Time after trigger (s)

3 atm, 796 K, D0 = 1.36 mm

2.5 4

2.0 PMT Output (V) 3 ) 2 1.5 mm ( 2 2 D

1.0

1 0.5

0.0 0 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Time after trigger (s) 3 atm, 773 K, D0 = 1.14 mm

2.0 3.0

2.5

1.5

2.0 PMT Output (V) ) 2

(mm 1.0 1.5 2 D

1.0

0.5 0.5

0.0 0.0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Time after trigger (s)

3 atm, 746 K, D0 = 1.17 mm

2.0

1.5 PMT Output (V) ) 2 2 (mm

2 1.0 D

1 0.5

0.0 0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 Time after trigger (s) 3 atm, 723 K, D0 = 1.13 mm 2.0 4

1.5 3 PMT Output (V) ) 2

1.0 (mm

2 2 D

0.5 1

0.0 0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 Time after trigger (s)

3 atm, 696 K, D0 = 1.24 mm 4 2.5

2.0 3 PMT Output (V) ) 2 1.5 2 (mm 2 D 1.0

1 0.5

0.0 0 1.5 2.0 2.5 3.0 Time after trigger (s) 3 atm, 673 K, D0 = 1.24 mm

4 2.5

2.0 3 PMT Output (V) ) 2 1.5

(mm 2 2 D 1.0

1 0.5

0.0 0 1.5 2.0 2.5 3.0 3.5 Time after trigger (s)

3 atm, 647 K, D0 = 1.14 mm

1.5 3 PMT Output (V) ) 2 1.0 (mm

2 2 D

0.5 1

0.0 0 1.5 2.0 2.5 3.0 Time after trigger (s) 3 atm, 622 K, D0 = 1.16 mm

2.0 4

1.5 3 PMT Output (V) ) 2

(mm 1.0 2 2 D

0.5 1

0.0 0 1.5 2.0 2.5 3.0 3.5 Time after trigger (s)

3 atm, 600 K, D0 = 1.16 mm 2.0

1.5

3 PMT Output (V) ) 2 1.0 (mm 2

D 2

0.5 1

0.0 0 1.5 2.0 2.5 3.0 3.5 4.0 Time after trigger (s) 5 atm, 771 K, D0 = 1.14 mm

2.0

1.5

1.5 PMT Output (V) ) 2 1.0 (mm

2 1.0 D

0.5 0.5

0.0 0.0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Time after trigger (s)

5 atm, 721 K, D0 = 1.24 mm

2.5 4

2.0 3 PMT Output (V) )

2 1.5 (mm

2 2 D 1.0

1 0.5

0.0 0 1.4 1.5 1.6 1.7 1.8 1.9 Time after trigger (s) 5 atm, 724 K, D0 = 1.17 mm

2.0

1.5

1.5 PMT Output (V) ) 2 1.0 (mm

2 1.0 D

0.5 0.5

0.0 0.0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Time after trigger (s)

5 atm, 699 K, D0 = 1.14 mm 2.0 2.0

1.5 1.5 PMT Output (V) ) 2 1.0 (mm 1.0 2 D

0.5 0.5

0.0 0.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Time after trigger (s) 5 atm, 675 K, D0 = 1.20 mm

2.0 1.5 PMT Output (V) 1.5 ) 2 1.0 (mm 2 D 1.0

0.5 0.5

0.0 0.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Time after trigger (s)

5 atm, 647 K, D0 = 1.16 mm

2.0 2.0

1.5 1.5 PMT Output (V) ) 2

(mm 1.0 2 1.0 D

0.5 0.5

0.0 0.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Time after trigger (s) 5 atm, 696 K, D0 = 1.07 mm

4 2.0

3 PMT Output (V) 1.5 ) 2 (mm 2

D 2 1.0

0.5 1

0.0 0 1.2 1.4 1.6 1.8 2.0 2.2 Time after trigger (s)

5 atm, 696 K, D0 = 1.24 mm

2.5 4

2.0

3 PMT Output (V) ) 2 1.5 (mm 2

D 2 1.0

1 0.5

0.0 0 1.2 1.4 1.6 1.8 2.0 Time after trigger (s) 5 atm, 650 K, D0 = 1.15 mm

2.0

1.5

1.5 PMT Output (V) ) 2

1.0 (mm 2

D 1.0

0.5 0.5

0.0 0.0 1.5 2.0 2.5 3.0 Time after trigger (s)

5 atm, 623 K, D0 = 1.18 mm

2.5

2.0 1.5

) 1.5 2 1.0 (mm 2 D 1.0

0.5 0.5

0.0 0.0 1.5 2.0 2.5 3.0 3.5 Time after trigger (s) 5 atm, 599 K, D0 = 1.15 mm

2.0 1.5

1.5 PMT Output (V) ) 2 1.0 (mm 2

D 1.0

0.5 0.5

0.0 0.0 1.5 2.0 2.5 3.0 3.5 Time after trigger (s)

5 atm, 573 K, D0 = 1.18 mm

1.5

3 PMT Output (V) ) 2 1.0 (mm 2

D 2

0.5 1

0.0 0 2 3 4 5 6 Time after trigger (s) 10 atm, 699 K, D0 = 1.24 mm

4 2.5

2.0

3 PMT Output (V) ) 2 1.5 (mm 2

D 2

1.0

1 0.5

0.0 0 1.25 1.30 1.35 1.40 1.45 Time after trigger (s)

10 atm, 648 K, D0 = 1.22 mm

3.0

2.5 3

2.0 PMT Output (V) ) 2 2 1.5 (mm 2 D

1.0 1

0.5

0.0 0 1.4 1.6 1.8 2.0 Time after trigger (s) 10 atm, 623 K, D0 = 1.25 mm

2.5

2.0 ) 2 1.5 (mm 2 D

1.0

0.5

0.0 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Time after trigger (s)

10 atm, 600 K, D0 = 1.30 mm

4 3.0

2.5 3

2.0 PMT Output (V) ) 2

2 (mm

2 1.5 D

1.0 1

0.5

0.0 0 1.2 1.4 1.6 1.8 2.0 2.2 Time after trigger (s) 10 atm, 571 K, D0 = 1.19 mm

2.5

3 2.0 PMT Output (V) ) 2 1.5 (mm

2 2 D

1.0

1 0.5

0.0 0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Time after trigger (s)

10 atm, 549 K, D0 = 1.25 mm 2.5

4 2.0

3 PMT Output (V) 1.5 ) 2 (mm 2

D 2 1.0

0.5 1

0.0 0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Time after trigger (s) 10 atm, 525 K, D0 = 1.15 mm

3.0 2.0

2.5 1.5

2.0 PMT Output (V) ) 2

(mm 1.5 1.0 2 D

1.0 0.5

0.5

0.0 0.0 1.5 2.0 2.5 3.0 3.5 4.0 Time after trigger (s)

15 atm, 624 K, D0 = 1.21 mm

2.0 4

1.5 3 PMT Output (V) ) 2 (mm 2

D 1.0 2

0.5 1

0.0 0 1.25 1.30 1.35 1.40 1.45 1.50 Time after trigger (s) 15 atm, 596 K, D0 = 1.23 mm

2.0

3 PMT Output (V) 1.5 ) 2 (mm

2 2 D 1.0

1 0.5

0.0 0 1.4 1.6 1.8 2.0 Time after trigger (s)

15 atm, 573 K, D0 = 1.18 mm

4 2.0

1.5 3 PMT Output (V) ) 2 (mm 2

D 1.0 2

0.5 1

0.0 0 1.4 1.6 1.8 2.0 2.2 Time after trigger (s) 15 atm, 546 K, D0 = 1.35 mm

3.0

4 2.5

2.0 3 PMT Output (V) ) 2

(mm 1.5 2

D 2

1.0

1 0.5

0.0 0 1.5 2.0 2.5 3.0 Time after trigger (s)

15 atm, 525 K, D0 = 1.24 mm

2.5 4

2.0

3 PMT Output (V) ) 2 1.5 (mm 2

D 2 1.0

1 0.5

0.0 0 1.5 2.0 2.5 3.0 3.5 4.0 Time after trigger (s) 18 atm, 574 K, D0 = 1.22 mm

4 2.0

3 PMT Output (V) 1.5 ) 2 (mm 2

D 2 1.0

0.5 1

0.0 0 1.4 1.6 1.8 2.0 Time after trigger (s)

18 atm, 550 K, D0 = 1.14 mm

2.0 4

1.5 3 PMT Output (V) ) 2 (mm 2

D 1.0 2

0.5 1

0.0 0 1.2 1.4 1.6 1.8 2.0 2.2 Time after trigger (s) 18 atm, 525 K, D0 = 1.27 mm 3.0

4 2.5

2.0 3 PMT Output (V) ) 2 1.5 (mm 2

D 2

1.0

1 0.5

0.0 0 1.5 2.0 2.5 3.0 Time after trigger (s)

20 atm, 572 K, D0 = 1.26 mm

2.5 4

2.0 3 PMT Output (V) ) 2 1.5

(mm 2 2 D 1.0

1 0.5

0.0 0 1.3 1.4 1.5 1.6 Time after trigger (s) 20 atm, 550 K, D0 = 1.22 mm

3.0

4 2.5

2.0 3 PMT Output (V) ) 2

1.5 (mm 2

D 2

1.0

1 0.5

0.0 0 1.2 1.4 1.6 1.8 2.0 Time after trigger (s)

20 atm, 524 K, D0 = 1.29 mm

3.0 4

2.5

3 PMT Output (V) 2.0 ) 2

(mm 1.5 2

D 2

1.0

1 0.5

0.0 0 1.5 2.0 2.5 3.0 3.5 4.0 Time after trigger (s) 25 atm, 574 K, D0 = 1.26 mm

2.5 4

2.0

3 PMT Output (V) ) 2 1.5 (mm 2

D 2

1.0

1 0.5

0.0 0 1.2 1.4 1.6 1.8 2.0 Time after trigger (s)

25 atm, 550 K, D0 = 1.17 mm

2.0 4

1.5 3 PMT Output (V) ) 2 (mm 2

D 1.0 2

0.5 1

0.0 0 1.2 1.4 1.6 1.8 2.0 2.2 Time after trigger (s) 25 atm, 525 K, D0 = 1.25 mm 3.0

4 2.5

2.0 3 PMT Output (V) ) 2 1.5 (mm 2

D 2

1.0

1 0.5

0.0 0 1.5 2.0 2.5 3.0 Time after trigger (s) 2 atm, 603 K, D0 = 1.06 mm 1.2 900 4

1.0 800 Temperature near droplet (K) 3

0.8 700 PMT Output (V) ) 2 0.6 600 2 (mm 2 D 0.4 500 1 0.2 400

0.0 300 0 1 2 3 4 Time after trigger (s)

Droplet Temperature PMT Output

3 atm, 603 K, D0 = 1.06 mm 1.6 1000 4

1.4 900 Temperature near droplet (K) 1.2 3 800 PMT Output (V) 1.0 ) 2 700 0.8 2 (mm 2 600 D 0.6 500 0.4 1

0.2 400

0.0 300 0 1.0 1.5 2.0 2.5 3.0 Time after trigger (s)

Droplet Temperature PMT Output 5 atm, 603 K, D0 = 1.09 mm 1000 4

900

1.5 Temperature near droplet (K) 3 800 PMT Output (V) ) 2 1.0 700 2 (mm 2 600 D

0.5 500 1

400

0.0 300 0 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Time after trigger (s)

Droplet Temperature PMT Output

10 atm, 603 K, D0 = 1.13 mm 900 4 2.0

800 Temperature near droplet (K) 3 1.5 700 PMT Output (V) ) 2 600 2

(mm 1.0 2 D 500

0.5 1 400

0.0 300 0 0.8 1.0 1.2 1.4 Time after trigger (s)

Droplet Temperature PMT Output 15 atm, 603 K, D0 = 1.09 mm 1200 5 2.0 Temperature near droplet (K) 1000 4 1.5 PMT Output (V)

) 3 2 800 1.0 (mm 2

D 2 600 0.5 1 400

0.0 0 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Time after trigger (s)

Droplet Temperature PMT Output

18 atm, 603 K, D0 = 1.07 mm 900 4 2.0

800 Temperature near droplet (K) 3 1.5 700 PMT Output (V) ) 2 600 2

(mm 1.0 2 D 500

0.5 1 400

0.0 300 0 0.7 0.8 0.9 1.0 1.1 Time after trigger (s)

Droplet Temperature PMT Output 20 atm, 603 K, D0 = 1.11 mm 900 4

2.0

800 Temperature near droplet (K) 3

1.5 700 PMT Output (V) ) 2 600 2 (mm 2 1.0 D 500 1 0.5 400

0.0 300 0 0.7 0.8 0.9 1.0 1.1 Time after trigger (s)

Droplet Temperature PMT Output

25 atm, 603 K, D0 = 1.07 mm 900 4 1.6

800 Temperature near droplet (K) 1.4 3

1.2 700 PMT Output (V) )

2 1.0 600 2 (mm

2 0.8 D 0.6 500

0.4 1 400 0.2

0.0 300 0 0.7 0.8 0.9 1.0 1.1 1.2 Time after trigger (s)

Droplet Temperature PMT Output 3 atm, 602 K, D0 = 1.00 mm 800

1.4 4 700 Temperature near droplet (K) 1.2 PMT Output (V) 1.0 3

) 600 2 0.8 (mm 2 2 D 0.6 500

0.4 400 1 0.2

0.0 300 0 1.0 1.5 2.0 2.5 3.0 Time after trigger (s)

Droplet Temperature PMT Output

3 atm, 623 K, D0 = 1.02 mm 900 5

1.5 800 Temperature near droplet (K) 4

700 PMT Output (V)

) 3 2 1.0 600 (mm 2

D 2 500 0.5 1 400

0.0 300 0 1.0 1.5 2.0 2.5 3.0 Time after trigger (s) Droplet Temperature PMT Output 3 atm, 642 K, D0 = 0.97 mm 900 1.4 4

800 Temperature near droplet (K) 1.2

1.0 700 3 PMT Output (V) ) 2 0.8 600 (mm 2 2 D 0.6 500 0.4 1 400 0.2

0.0 300 0 1.0 1.5 2.0 2.5 Time after trigger (s)

Droplet Temperature PMT Output

3 atm, 663 K, D0 = 1.05 mm 900

800 Temperature near droplet (K) 1.5

700 3 PMT Output (V) ) 2 1.0 600 (mm 2 2 D 500 0.5 1 400

0.0 300 0 1.0 1.5 2.0 2.5 Time after trigger (s)

Droplet Temperature PMT Output 3 atm, 682 K, D0 = 1.00 mm 900 4

800 Temperature near droplet (K) 1.5

700 3 PMT Output (V) ) 2 1.0 600 (mm

2 2 D 500 0.5 1 400

0.0 300 0 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Time after trigger (s)

Droplet Temperature PMT Output

3 atm, 703 K, D0 = 0.99 mm 900

1.5 4

800 Temperature near droplet (K)

700 3 PMT Output (V) ) 2 1.0 600 (mm 2 2 D 500 0.5 1 400

0.0 300 0 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Time after trigger (s)

Droplet Temperature PMT Output 3 atm, 722 K, D0 = 0.99 mm 900 1.6 4 1.4

800 Temperature near droplet (K)

1.2 700 3 PMT Output (V)

) 1.0 2 600

(mm 0.8 2 2 D 0.6 500

0.4 1 400 0.2

0.0 300 0 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Time after trigger (s)

Droplet Temperature PMT Output

3 atm, 740 K, D0 = 1.03 mm 2.0

1.5 ) 2 1.0 (mm 2 D

0.5

0.0 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 3 atm, 763 K, D0 = 1.10 mm 900 4 2.0

800 Temperature near droplet (K)

1.5 3

700 PMT Output (V) ) 2

1.0 600 2 (mm 2 D 500 0.5 1 400

0.0 300 0 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Time after trigger (s)

Droplet Temperature PMT Output

3 atm, 783 K, D0 = 1.11 mm 5 1.6 1000

1.4 Temperature near droplet (K) 4

1.2 PMT Output (V) 800

) 3 2 1.0 (mm

2 0.8

D 2 600 0.6

0.4 1 0.2 400

0.0 0 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Time after trigger (s)

Droplet Temperature PMT Output 3 atm, 584 K, D0 = 1.13 mm 5

1000 Temperature near droplet (K) 1.5 4 PMT Output (V) 800

) 3 2 1.0 (mm 2

D 2 600

0.5 1 400

0.0 0 1 2 3 4 Time after trigger (s)

Droplet Temperature PMT Output

3 atm, 561 K, D0 = 1.10 mm 900 5 1.2

800 Temperature near droplet (K) 1.0 4

700 PMT Output (V) 0.8

) 3 2 600

(mm 0.6 2

D 2 0.4 500

1 0.2 400

0.0 300 0 1 2 3 4 5 Time after trigger (s)

Droplet Temperature PMT Output Appendix 109

Appendix B Experimental Apparatus

Relevant drawings to the experimental apparatus are included. Engineering draw-

ings for mechanical components and a complete plumbing schematic provide more in-

formation regarding the design of the apparatus. Temperature proﬁles at various am-

bient temperatures and pressure show the temperature observed by the droplet as it is

inserted into the high-temperature region. Also included is a plot of the pulse-width

modulation (PWM) frequency of the droplet translation stepper motor that determines

the velocity at which the droplet is inserted. Appendix 110

Figure B.1. Engineering drawing showing full assembly with both high- temperature and deployment regions. Appendix 111

Figure B.2. Engineering drawing of pressure chamber. Appendix 112

Figure B.3. Engineering drawing of electrically heated oven assembly. Appendix 113 B A C B C B B B A B B D D A

Figure B.4. Engineering drawing showing schematic of gas and liquid plumbing. Appendix 114

Final position

6 575K 675K 775K 875K 975K

2 Vertical position (cm)

0 Hot region entrance

-2

Initial position 300 400 500 600 700 800 900 1000 Temperature (K)

Figure B.5. Temperature proﬁles in the chamber at atmospheric pressure for several temperature cases are compared. The largest increase in temperature per unit distance occures at the entrance to the high- temperature region. Appendix 115

Final position 575K, 1 atm 6 575K, 5 atm 675K, 1 atm 675K, 5 atm 775K, 1 atm 775K, 5 atm

2 Vertical position (cm)

0 Hot region entrance

-2

Initial position 300 400 500 600 700 800 Temperature (K)

Figure B.6. Comparison of the temperature proﬁle in the chamber for several ambient temperatures at 1 and 5 atmospheres of pressure. In- creased convection at higher pressures raises the temperature near the droplet above the setpoint temperature. Appendix 116

Figure B.7. Velocity proﬁle of the droplet translation mechanism. Appendix 117

Appendix C Property values of n-Dodecane

The binary diffusivity of n-dodecane in air was estimated using the Chapman-Enskog

theory57 r ³ ´ 0.0018583 T 3 1 1 MA + MB D (C.1) AB = 2 pσAB ΩD,AB where σAB is the characteristic length (Å) and ΩD,AB is a temperature-dependent dimen- sionless diffusion collision integral. The diffusion coefﬁcient increases approximately as a function of the three-halves power of temperature and has an inverse relationship with pressure.

0.25 1 atm 10 atm 25 atm 0.20 /s 2

0.15

0.10 Mass diffusivity ( m

0.05

0.00 300 350 400 450 500 550 600 650 700 Temperature (K)

Figure C.1. Binary diffusivity of n-dodecane in air as a function of temperature for various pressures.

Other property values for n-dodecane were calculated using the CoolProp ﬂuid property database58. Appendix 118

Table C.1. Table of relevant property values for n-dodecane.

Critical temperature 658.1 K Critical pressure 17.932 atm Critical density 226.545 kg/m3 Molecular weight 170.335 kg/mol Boiling point (1 atm) 489.442 K

700

600 Boiling point (K) Latent heat of vapor- 500 ization (kJ/kg-K) Saturated liquid density (kg/m3) 400

300

200

100

0 0 5 10 15 20 25 Pressure (atm)

Figure C.2. Boiling point temperature, latent heat of vaporization, and liquid density at the boiling point as a function of pressure. Appendix 119

1000 6.0 1 atm 10 atm 25 atm

800 5.5

600 5.0

4.5 400

4.0 200

3.5

Enthalpy (kJ/kg-k) 0

3.0 200 Specific heat capacity Cp (kJ/kg-K) 2.5 400 2.0

800 0.14 700 0.12 600

0.10 ) 3 500

0.08 400

0.06 300 Density (kg/ m

0.04 200 Thermal conductivity (W/m-K)

0.02 100

0.00 0 300 350 400 450 500 550 600 650 700 300 350 400 450 500 550 600 650 700 Temperature (K) Temperature (K)

Figure C.3. Enthalpy, speciﬁc heat, thermal conductivity and density as a function of temperature for several pressure cases. Appendix 120

Appendix D Ignition Flame Propagation Data

The propagation speed of the cool-ﬂame and hot-ﬂame fronts come from linear

least-square ﬁts of the position of the front over time. For both cool- and hot-ﬂame

fronts, this position is measured manually at a constant-intensity point along a line nor-

mal to the front and parallel to the direction of its propagation, as shown in Figure D.1.

Figure D.1. Demonstrative image of the ﬂame front position measurement. The position of the ﬂame front, depicted by the horizontal line, is tracked over time along the vector shown in red. Appendix 121

2 atm 3 atm 7 10 603 K 584 K 6 648 K 8 622 K 5 673 K 623 K 699 K 647 K 4 6 673 K 682 K 3 4

Position (mm) 2 Position (mm) 2 1

0 0 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 Time (s) Time (s)

5 atm 10 atm 6 6 599 K 542 K 5 623 K 5 575 K 650 K 600 K 4 4 603 K

3 3

2 2 Position (mm) Position (mm)

1 1

0 0 0 0.05 0.1 0.15 0.2 0 0.02 0.04 0.06 0.08 0.1 Time (s) Time (s)

15 atm 3 573 K 2.5 603 K

1.5

1 Position (mm)

0.5

0 0 0.02 0.04 0.06 0.08 0.1 Time (s)

Figure D.2. Cool ﬂame position shown as a function of time. Appendix 122

2 atm 3 atm 6 1.2 699 K 622 K 5 721 K 1 647 K 821 K 673 K 4 0.8

3 0.6

Position (mm) Position (mm) 0.4

1 0.2

0 0 0 0.2 0.4 0.6 0.8 1 1.2 0 1 2 3 Time (s) 10-3 Time (s) 10-4

5 atm 10 atm 1 3 599 K 542 K 2.5 0.8 623 K 550 K 650 K 575 K 2 0.6 1.5 0.4 1 Position (mm) Position (mm) 0.2 0.5

0 0 0 1 2 3 0 0.2 0.4 0.6 0.8 1 1.2 Time (s) 10-4 Time (s) 10-3

10 atm 7 546 K 6 573 K 5

Position (mm) 2

0 0 1 2 3 4 5 6 Time (s) 10-3

Figure D.3. Hot ﬂame position shown as a function of time. Bibliography 123

Complete References

[1] J. Foster and R. S. Miller. High Pressure Processes in Chemical Engineering, chapter Fundamentals of High Pressure Combustion, pages 53–75. ProcessEng Engineering GmbH, 1 edition, 2010.

[2] J. Sato, M. Tsue, M. Niwa, and M. Kono. Effects of natural convection on high- pressure droplet combustion. Combustion and ﬂame, 82(2):142–150, 1990.

[3] W. A. Rosser, H. Wise, and B. J. Wood. Combustion of fuel droplets. AIAA Journal, 1(5):1076–1081, 1963.

[4] S. K. Aggarwal. Single droplet ignition: Theoretical analyses and experimental ﬁnd- ings. Progress in Energy and Combustion Science, 45:79–107, dec 2014.

[5] C. K. Law. Theory of thermal ignition in fuel droplet burning. Combustion and Flame, 31:285–296, 1978.

[6] G. M. Faeth and D. R. Olson. The ignition of hydrocarbon fuel droplets in air. In SAE Technical Paper Series. SAE International, feb 1968.

[7] G. A. Long and E. A. Grens. Self-ignition behavior of fuel droplets in hot stagnant gases. Chemical Engineering Science, 25(4):623–631, apr 1970.

[8] T. Kadota, H. Hiroyasu, and H. Oya. Spontaneous ignition delay of a fuel droplet in high pressure and high temperature gaseous environments. Bulletin of JSME, 19(130):437–445, 1976.

[9] C. A. Bergeron and W. L. H. Hallett. Autoignition of single droplets of two- component liquid fuels. Combustion Science and Technology, 65(4-6):181–194, jun 1989.

[10] R. Nakanishi, H. Kobayashi, S. Kato, and T. Niioka. Ignition experiment of a fuel droplet in high-pressure high-temperature ambient. In Symposium (International) on Combustion, volume 25, pages 447–453. Elsevier, 1994.

[11] T. Kadota, K. Satoh, D. Segawa, J. Sato, and Y. Marutani. Autoignition and combustion of a fuel droplet in supercritical gaseous environments under microgravity. Symposium (International) on Combustion, 27(2):2595–2601, jan 1998.

[12] H. Ghassemi, S. W. Baek, and Q. S. Khan. Experimental study on binary droplet evaporation at elevated pressures and temperatures. Combustion Science and Technology, 178(6):1031–1053, jun 2006. Bibliography 124

[13] Q. S. Khan, S. W. Baek, and H. Ghassemi. On the autoignition and combustion characteristics of kerosene droplets at elevated pressure and temperature. Combustion Science and Technology, 179(12):2437–2451, oct 2007.

[14] S. Nakaya, M. Tsue, O. Imamura, S. Nishida, K. Yamashita, D. Segawa, and M. Kono. Effects of fuel vapor in ambience on spontaneous ignition of isolated fuel droplet. Combustion Science and Technology, 181(12):1464–1479, nov 2009.

[15] GS Canada and GM Faeth. Combustion of liquid fuels in a ﬂowing combustion gas environment at high pressures. In Symposium (International) on Combustion, volume 15, pages 419–428. Elsevier, 1975.

[16] J. J. Whang, C. Y. Yukao, J. T. Ho, and S. C. Wong. Experimental study of the ignition of single droplets under forced convection. Combustion and Flame, 110(3):366– 376, aug 1997.

[17] H. Kim, S. W. Baek, and D. Chang. Auto-ignition characteristics of singlen-heptane droplet in a rapid compression machine. Combustion Science and Technology, 186(7):912–927, may 2014.

[18] N. Shaygan and S. Prakash. Droplet ignition and combustion including liquid- phase heating. Combustion and Flame, 102(1-2):1–10, jul 1995.

[19] J. Chen and X. Peng. An approach of droplet ignition delay time. Heat Transfer-Asian Research, 38(2):73–82, mar 2009.

[20] N. Peters. Fifteen lectures on laminar and turbulent combustion, 9 1992.

[21] N. Peters, G. Paczko, R. Seiser, and K. Seshadri. Temperature cross-over and non- thermal runaway at two-stage ignition of n-heptane. Combustion and Flame, 128(1-2):38–59, jan 2002.

[22] S. M. Sarathy, C. K. Westbrook, M. Mehl, W. J. Pitz, C. Togbe, P. Dagaut, H. Wang, M. A. Oehlschlaeger, U. Niemann, K. Seshadri, P. S. Veloo, C. Ji, F. N. Egolfopou- los, and T. Lu. Comprehensive chemical kinetic modeling of the oxidation of 2- methylalkanes from c7 to c20. Combustion and Flame, 158(12):2338–2357, dec 2011.

[23] H. Pearlman. Low-temperature oxidation reactions and cool ﬂames at earth and reduced gravity. Combustion and Flame, 121(1-2):390–393, apr 2000.

[24] R. Fairlie, J. F. Grifﬁths, and H. Pearlman. A numerical study of cool ﬂame development under microgravity. Proceedings of the Combustion Institute, 28(2):1693– 1699, jan 2000. Bibliography 125

[25] P. Zhao, W. Liang, S. Deng, and C. K. Law. Initiation and propagation of laminar premixed cool ﬂames. Fuel, 166:477–487, feb 2016.

[26] M. Tanabe, M. Kono, J. Sato, J. Koenig, C. Eigenbrod, and H. J. Rath. Effects of natural convection on two stage ignition of an n-dodecane droplet. In Symposium (International) on Combustion, volume 25, pages 455–461. Elsevier, 1994.

[27] M. Tanabe, M. Kono, J. Sato, J. Koenig, C. Eigenbrod, F. Dinkelacker, and H. J. Rath. Two stage ignition of n-heptane isolated droplets. Combustion Science and Technology, 108:103–119, 1995.

[28] M. Tanabe, T. Bolik, C. Eigenbrod, H. J. Rath, J. Sato, and M. Kono. Spontaneous ignition of liquid droplets from a view of non-homogeneous mixture formation and transient chemical reactions. In Symposium (International) on Combustion, volume 26, pages 1637–1643. Elsevier, 1996.

[29] C. Eigenbrod, J. König, O. Moriue, S. Schnaubelt, and T. Bolik. Experimental and numerical studies on the autoignition process of fuel droplets. In Joint Meeting of the French, British and German Section of The Combustion Institute, TC Institute, ed. Nancy, pages 1–8, 1999.

[30] S. Schnaubelt, O. Moriue, T. Coordes, C. Eigenbrod, and H. J. Rath. Detailed numerical simulations of the multistage self-ignition process of n-heptane, isolated droplets and their veriﬁcation by comparison with microgravity experiments. Proceedings of the Combustion Institute, 28(1):953–960, 2000.

[31] S. Schnaubelt, M. Tanabe, C. Eigenbrod, and H. J. Rath. Veriﬁcation of detailed simulations for two-stage ignition of single droplets by ignition radius. In Space Forum, volume 6, pages 299–306, 2000.

[32] O. Moriue, C. Eigenbrod, H. J. Rath, M. Tsue, M. Kono, and J. Sato. Spontaneous ignition of n-alkane droplets with various volatility. Transactions of the Japan Society for Aeronautical and Space Sciences, 47(157):189–194, 2004.

[33] S. Schnaubelt, C. Eigenbrod, and H. J. Rath. Numerical analysis of the cool ﬂame behavior of igniting n-heptane droplets. Microgravity Science and Technology, 17(3):5–9, sep 2005.

[34] O. Moriue, S. Schnaubelt, C. Eigenbrod, and H. J. Rath. Numerical simulation of the ignition of a single fuel droplet in an air with ﬁnite volume. In Proceedings of 9th International Conference on Liquid Atomization and Spray Systems, volume 701, 2003. Bibliography 126

[35] O. Moriue, K. Matsuo, E. Murase, S. Schnaubelt, and C. Eigenbrod. Veriﬁcation of a numerical simulation model of fuel droplet ignition through microgravity experiments and its further application. Journal of The Japan Society of Microgravity Application, 24(3):251–254, 2007.

[36] R. Stauch and U. Maas. Different ignition modes of n-heptane droplets in air. In Third European Combustion Meeting (ECM), pages 11–13, 2007.

[37] A. Cuoci, M. Mehl, G. Buzzi-Ferraris, T. Faravelli, D. Manca, and E. Ranzi. Autoigni- tion and burning rates of fuel droplets under microgravity. Combustion and Flame, 143(3):211–226, nov 2005.

[38] A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi. Numerical modeling of autoignition of isolated fuel droplets in microgravity. Proceedings of the Combustion Institute, 35(2):1621–1627, 2015.

[39] G. Xu, M. Ikegami, S. Honma, K. Ikeda, X. Ma, H. Nagaishi, D. L. Dietrich, and P.M. Struk. Inverse inﬂuence of initial diameter on droplet burning rate in cold and hot ambiences: a thermal action of ﬂame in balance with heat loss. International Journal of Heat and Mass Transfer, 46(7):1155–1169, mar 2003.

[40] F.A. Williams. Combustion Theory. CRC Press, 1994.

[41] G. M. Faeth, D. P. Dominicis, J. F. Tulpinsky, and D. R. Olson. Supercritical bipro- pellant droplet combustion. In Symposium (International) on Combustion, volume 12, pages 9–18. Elsevier, 1969.

[42] M. Mikami, M. Kono, J. Sato, D. L. Dietrich, and F.A. Williams. Combustion of misci- ble binary-fuel droplets at high pressure under microgravity. Combustion Science and Technology, 90(1-4):111–123, 1993.

[43] J. H. Bae and C. T. Avedisian. High-pressure combustion of submillimeter-sized nonane droplets in a low convection environment. Combustion and Flame, 145(3):607–620, 2006.

[44] V. Nayagam, J. B. Haggard, R. O. Colantonio, A. J. Marchese, F.L. Dryer, B. L. Zhang, and F. A. Williams. Microgravity n-heptane droplet combustion in oxygen-helium mixtures at atmospheric pressure. AIAA Journal, 36(8):1369–1378, aug 1998.

[45] A. Marchese, F.L. Dryer, and V. Nayagam. Numerical modeling of isolated n-alkane droplet ﬂames: initial comparisons with ground and space-based microgravity experiments. Combustion and Flame, 116(3):432–459, feb 1999. Bibliography 127

[46] V. Nayagam, D. L. Dietrich, P. V. Ferkul, M. C. Hicks, and F. A. Williams. Can cool ﬂames support quasi-steady alkane droplet burning? Combustion and Flame, 159(12):3583–3588, dec 2012.

[47] V. Nayagam, D. L. Dietrich, M. C. Hicks, and F. A. Williams. Cool-ﬂame extinction during n-alkane droplet combustion in microgravity. Combustion and Flame, 162(5):2140–2147, may 2015.

[48] V. Nayagam, D. L. Dietrich, and F. A. Williams. Unsteady droplet combustion with fuel thermal expansion. Combustion and Flame, 195:216–219, sep 2018.

[49] G. S. Settles. Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media. Experimental Fluid Mechanics. Springer Berlin Heidelberg, 2012.

[50] C. A. Schneider, W. S. Rasband, and K. W. Eliceiri. NIH image to ImageJ: 25 years of image analysis. Nature Methods, 9(7):671–675, jul 2012.

[51] J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Harten- stein, K. Eliceiri, P. Tomancak, and A. Cardona. Fiji: an open-source platform for biological-image analysis. Nature Methods, 9(7):676–682, jul 2012.

[52] P. M. Struk, M. Ackerman, V. Nayagam, and D. L. Dietrich. On calculating burning rates during ﬁber supported droplet combustion. Microgravity Science and Technology, 11:144–151, 1998.

[53] D. G. Goodwin, R. L. Speth, H. K. Moffat, and B. W. Weber. Cantera: An object- oriented software toolkit for chemical kinetics, thermodynamics, and transport processes, 2018. Version 2.4.0.

[54] B. Lewis and G. Von Elbe. Combustion, Flames and Explosions of Gases. 1938.

[55] S. R. Turns. An Introduction to Combustion. McGraw-Hill, 1 edition, 1996.

[56] H. Jia and G. Gogos. High pressure droplet vaporization; effects of liquid-phase gas solubility. International Journal of Heat and Mass Transfer, 36(18):4419–4431, dec 1993.

[57] R. B. Bird, W. E. Steward, and E. N. Lightfoot. Transport Phenomena. John Wiley & Sons, Inc., 2 edition, 2002.

[58] I. H. Bell, J. Wronski, S. Quoilin, and V. Lemort. Pure and pseudo-pure ﬂuid thermophysical property evaluation and the open-source thermophysical property library CoolProp. Industrial & Engineering Chemistry Research, 53(6):2498–2508, jan 2014.