Methylcyclohexane Ignition Delay Times

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METHYLCYCLOHEXANE IGNITION DELAY TIMES

UNDER A WIDE RANGE OF CONDITIONS

Thesis

Submitted to

The School of Engineering of the

UNIVERSITY OF DAYTON

In Partial Fulfillment of the Requirements for

The Degree of

Master of Science in Mechanical Engineering

Aditya Nagulapalli

Dayton, Ohio

May 2015

METHYLCYCLOHEXANE IGNITION DELAY TIMES

UNDER A WIDE RANGE OF CONDITIONS

Name: Nagulapalli, Aditya

APPROVED BY:

______Sukh S. Sidhu, Ph.D. Philip. H. Taylor, Ph.D. Advisory Committee Chairman Committee Member Division Head Group Leader Distinguished Research Engineer Distinguished Research Scientist Energy Technologies & Materials Division Environmental Engineering Group University of Dayton Research Institute University of Dayton Research Institute

______Moshan Kahandawala, Ph.D. Committee Member Group Leader Senior Research Engineer Bioenergy & Carbon Mitigation Group University of Dayton Research Institute

______John G. Weber, Ph.D. Eddy M. Rojas, Ph.D., M.A, P.E Associate Dean Dean, School of Engineering School of Engineering

Aditya Nagulapalli

2015

iii

ABSTRACT

METHYLCYCLOHEXANE IGNITION DELAY TIMES UNDER A WIDE

RANGE OF CONDITIONS

Name: Nagulapalli, Aditya University of Dayton

Advisor: Dr. Sukh. S. Sidhu

During the last century, our dependence on oil has increased rapidly and is projected to increase for several decades. There is a critical need to improve the design of the combustion chamber for different kinds of engines to reduce fuel consumption.

Chemical kinetics of the fuel plays an important role in reducing emissions and improving engine efficiency. Studying single components of a conventional fuel allows a fuller understanding of the physical and chemical behavior of the real fuel. Many studies have been conducted on all classes of hydrocarbons, with the exception of cycloalkanes. Only a few studies exist on cycloalkanes, which is an important class of hydrocarbons.

Methylcyclohexane (MCH), which is widely used as a surrogate to represent the cycloalkane portion of a fuel, was chosen as the subject of this study. The shock tube is an established tool used for measuring the ignition delay, and was used as the experimental apparatus. Ignition delay was measured using the end-plate pressure rise, the OH* and CH* chemiluminescence and white light emission.

In addition, experimental results were compared with kinetic modeling data using detailed

MCH mechanisms developed by Pitz et al. and Orme et al. Different modeling approaches, such as constant volume and internal energy (with and without experimental pressure profiles) and constant pressure, were used to validate the models by comparing against experimental ignition delay data. It was observed that the equivalence ratio affects the ignition delay time. For the lower argon concentration (Ar = 93%) and higher pressure (P

~ 16 atm), ignition delay times were longest for rich conditions. Additionally, they were shorter at lower temperatures (T ≤ 1250 K) for stoichiometric conditions in comparison to lean values, but the opposite trend was observed at the higher temperatures (T > 1250 K).

Ignition delay times of stoichiometric mixtures were longer than lean mixtures across the studied temperature range for low pressure (P = 2 atm) and argon concentration (Ar =

93%), as well as high pressure (P ~ 16 atm) and argon concentration (Ar = 98%). The

Orme et al. model using the approach of constant U,V assumption with experimental pressure profile showed a better agreement with experimental results at low temperatures than the approach without experimental pressure profile. Both models and approaches underestimate the experimental ignition delay times at high temperatures.

DEDICATION

Dedicated to Family and Friends

ACKNOWLEDGMENTS

I would like to express my sincere gratitude to my research advisor, Dr. Sukhjinder

S. Sidhu, for his substantial support and motivation throughout my master’s work done at the Shock Tube Research Laboratory. Besides my advisor, I want to extend my earnest thanks to Dr. Moshan Kahandawala for his guidance, inspiration and efforts throughout my research work.

I am indebted to the University of Dayton Research Institute for providing a stimulating environment, as well as the Air Force Research Laboratory for their generous support. Specifically, I would like to express my appreciation for the contract monitor of this project, Mr. Edwin Corporan.

I consider it an honor to work on this project as a member of the Sustainable

Environmental Technologies Group, and thank them for their continued support. The help of Dr. Saumitra Saxena and Mr. Giacomo Flora in their in-depth guidance and constant availability were of great value during this work. Thesis editing by Dr. Jeremy Cain is also greatly appreciated.

Finally, this effort would have been incomplete without the encouragement and the abundant love of my parents, brother and friends. I thank them for their support and understanding during the long years of my education.

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TABLE OF CONTENTS

ABSTRACT ...... iv

DEDICATION ...... vi

ACKNOWLEDGMENTS ...... vii

TABLE OF CONTENTS ...... viii

LIST OF FIGURES ...... xii

LIST OF TABLES ...... xvii

LIST OF SYMBOLS ...... xviii

LIST OF ABBREVIATIONS ...... xix

CHAPTER 1 ...... 1

INTRODUCTION ...... 1

1.1 Background ...... 1

1.2 Ignition Delay Time ...... 3

1.3 Shock Tube ...... 5

1.4 Methylcyclohexane ...... 7

1.5 Current Study ...... 10

CHAPTER 2 ...... 12

EXPERIMENTAL SETUP AND PROCEDURE ...... 12

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2.1 Shock Tube Components ...... 12

2.2 Operation of Shock Tube ...... 17

CHAPTER 3 ...... 20

CALCULATIONS ...... 20

3.1 End Plate Velocity Calculation ...... 20

3.2 Post-Reflected Temperature and Pressure Calculations ...... 22

3.3 Uncertainties of Post-Reflected Pressures and Temperatures ...... 22

3.4 Calculation of the Uncertainties Using the Perturbation Method ...... 23

3.4.1 Example of Uncertainty Propagation ...... 24

3.5 Fuel Mixture Calculation ...... 24

3.6 Fuel Mixture Preparation ...... 26

CHAPTER 4 ...... 27

RESULTS AND DISCUSSION ...... 27

4.1 Overview of Results ...... 27

4.1.1 Ignition Delay Correlation ...... 32

4.1.2 Uncertainty Analysis ...... 36

4.1.3 Modeling ...... 37

4.1.4 Modeling Approach ...... 38

4.2 Discussion ...... 39

4.2.1 Ignition Delay Trends at Different Conditions ...... 39

4.2.2 Impact of Pressures, Equivalence Ratios and Diluent Ratios on Ignition Delay

Times...... 47

4.2.3 Comparison of MCH with Other HC’s ...... 58

CHAPTER 5 ...... 61

CONCLUSION ...... 61

CHAPTER 6 ...... 62

FUTURE STUDIES...... 62

BIBLIOGRAPHY ...... 63

APPENDIX A ...... 69

IGNITION DELAY TIMES MEASURED FROM END PLATE USING OH*, CH*, WL

AND PRESSURE ...... 69

APPENDIX B ...... 72

UNCERTAINTIES ON POST-REFLECTED PRESSURES AND TEMPERATURES 72

APPENDIX C ...... 77

UNCERTAINTIES ON IGNITION DELAY TIMES ...... 77

APPENDIX D ...... 81

CONDITION FOR UNCERTAINTY ANALYSIS ON P5 AND T5...... 81

APPENDIX E ...... 83

CHEMKIN INPUT FILE ...... 83

APPENDIX F...... 84

SAMPLE FILE FOR FUEL MIXTURE PREPARATION ...... 84

APPENDIX G ...... 86

EXAMPLE OF END PLATE VELOCITY CALCULATIONS ...... 86

APPENDIX H ...... 88

IGNITION DELAY DATA FOR 2-METHYLHEPTANE, N-DODECANE, M-XYLENE

AND M-XYLENE/N-DODECANE (23% / 77 %) BLEND ...... 88

LIST OF FIGURES

Figure 1 – Schematic of the shock tube...... 14

Figure 2 – Detailed view of the shock tube test section...... 15

Figure 3 – Schematic of sample preparation unit...... 16

Figure 4 – Shock tube test section with time and distance measurements from the end plate.

...... 21

Figure 5 – Experimental pressure profiles from oscilloscope showing end plate and

sidewall measurements and corresponding incident times...... 22

Figure 6 – Sample oscilloscope trace showing end plate and sidewall pressure profiles

from the combustion of MCH...... 28

Figure 7 – Sample oscilloscope trace showing end plate pressure profile, OH* and CH*

chemiluminescence and WL emissions from the combustion of MCH...... 28

Figure 8 – Ignition delay measurement using the maximum slope extrapolation method.

...... 29

Figure 9 – End plate pressure profiles from MCH combustion at 93% argon dilution and

16 atm. Profiles are shown for equivalence ratios of (a) 0.5, (b) 1.0 and (c) 3.0. .... 30

xii

Figure 10 – End plate pressure profiles for  = 0.5 and 1 at pressures of 2 and 16 atm with

93% and 98% argon dilution, respectively...... 31

Figure 11 – Normalized ignition delays times for equivalence ratios of (a)  = 3.0, (b)

 = 1.0 and (c)  = 0.5...... 34

Figure 12 – Pressures scaled to 20 atm for low argon concentration at (a) stoichiometric

and (b) fuel lean mixtures...... 35

Figure 13 – Ignition delay for  = 0.5, Ar = 93% and P = 20 atm. Experimental (OH*,

CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme

et al.21) results are shown. A curve fit for modeling with a pressure profile shows its

trend...... 41

Figure 14 – Ignition delay for  = 1.0, Ar = 93% and P = 20 atm. Experimental (OH*,

CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme

et al.21) results are shown. A curve fit for modeling with a pressure profile shows its

trend...... 42

Figure 15 – Ignition delay for  = 3.0, Ar = 93% and P = 20 atm. Experimental (OH*,

CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme

et al.21) results are shown. A curve fit for modeling with a pressure profile shows its

trend. Scaled values assume n = -0.60...... 43

Figure 16 – Ignition delay for  = 0.5, Ar = 93% and P = 2 atm. Experimental (OH*, CH*,

WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme et

xiii

al.21) results are shown. A curve fit for modeling with a pressure profile shows its

trend...... 44

Figure 17 – Ignition delay for  = 1.0, Ar = 93% and P = 2 atm. Experimental (OH*, CH*,

WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme et

al.21) results are shown. A curve fit for modeling with a pressure profile shows its

trend...... 45

Figure 18 – Ignition delay for  = 0.5, Ar = 98% and P = 20 atm. Experimental (OH*,

CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme

et al.21) results are shown. A curve fit for modeling with a pressure profile shows its

trend...... 46

Figure 19 – Ignition delay for  = 1.0, Ar = 98% and P = 20 atm. Experimental (OH*,

CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme

et al.21) results are shown. A curve fit for modeling with a pressure profile shows its

trend...... 47

Figure 20 – Comparison of equivalence ratios of 0.5, 1 and 3 (symbols) with Orme et al.21

modeling (lines) for 93% argon dilution at 20 atm...... 49

Figure 21 – Rate of production analysis for  = 0.5, P = 20 atm, Ar = 93%, T = 1000 K.

...... 50

Figure 22 – Rate of production analysis for  = 1, P = 20 atm, Ar = 93%, T = 1000 K. 51

xiv

Figure 23 – Rate of production analysis for  = 0.5, P = 20 atm, Ar = 93%, T = 1500 K.

...... 52

Figure 24 – Rate of production analysis for  = 1, P = 20 atm, Ar = 93%, T = 1500K. . 52

Figure 25 – Comparison of equivalence ratios of 0.5 and 1 (symbols) with Orme et al.21

model (lines) for 93% argon dilution at 2 atm...... 54

Figure 26 – Comparison of equivalence ratios of 0.5 and 1 (symbols) with Orme et al.21

model (lines) for 98% argon dilution at 20 atm...... 54

Figure 27 – Comparison of argon concentrations of 93% and 98% (symbols) with Orme

et al.21 model (lines) for equivalence ratio of 0.5 at 20 atm...... 55

Figure 28 – Comparison of argon concentrations of 93% and 98% (symbols) with Orme

et al.21 model (lines) for equivalence ratio of 1 at 20 atm...... 56

Figure 29 – Comparison of MCH ignition delays at pressures of 2 and 20 atm (symbols)

with Orme et al.21 model (lines) for equivalence ratio of 1 at 93% argon dilution. .. 57

Figure 30 – Comparison of MCH ignition delays at pressures of 2 and 20 atm (symbols)

with Orme et al.21 model (lines) for equivalence ratio of 0.5 at 93% argon dilution. 58

Figure 31 – Comparison of MCH with other hydrocarbons at lean conditions: 2-

methylheptane,47, 48 n-dodecane,7 m-xylene,8 and n-dodecane/m-xylene blend.7 ...... 59

Figure 32 – Comparison of MCH with other hydrocarbons at stoichiometric conditions: 2-

methylheptane,47, 48 n-dodecane,7 m-xylene,8 and n-dodecane/m-xylene blend.7 ...... 60

Figure 33 – Comparison of MCH with other hydrocarbons at rich conditions: 2-

methylheptane,47 n-dodecane,7 m-xylene,8 and n-dodecane/m-xylene blend.7 ...... 60

Figure 34 – Variation of shock wave velocity with axial distance in shock tube...... 87

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LIST OF TABLES

Table 1 Properties of methylcyclohexane ...... 7

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LIST OF SYMBOLS

τign ignition delay time (ms)

tincident incident shock arrival time (μs)

tdwell dwell time (ms)

-1 U1 incident shock velocity (m s )

R universal gas constant (cal mol-1 K-1) n number of moles

3 Vi volume fraction (m )

MW molecular weight (g mol-1)

 specific gravity (g mL-1)

Xi mole fraction of species

Pi partial pressure of species (Torr)

(O/F)act actual oxygen-to-fuel ratio

(O/F)stoic stoichiometric oxygen-to-fuel ratio

 equivalence ratio

xviii

LIST OF ABBREVIATIONS

AEO annual energy outlook

HCs hydrocarbons

ID inner diameter

JP jet propulsion

MCH methylcyclohexane

MW molecular weight

PMT photo multiplier tube

PT pressure transducer

RCM rapid compression machine

ROP rate of production

RP rocket propulsion

SPU sample preparation unit

UDRI University of Dayton Research Institute

U,V internal energy and volume

WL white light

xix

CHAPTER 1

INTRODUCTION

1.1 Background

During the last century, the dependence on oil has increased rapidly and is projected to increase for the next several decades. As a result, pollutants (e.g., NOx, SOx, PM and

HC’s) are emitted into the atmosphere that cause adverse environmental and health effects, among which is an increase in global temperatures from greenhouse gases.1 According to the Annual Energy Outlook (AEO), the transportation sector is a major consumer of fossil fuels.2 It consumed 71% of the total liquid fuels in 2009, and usage by transportation is expected to increase to 73% by 2035. The sensitive relationship between the increasing domestic crude oil production and rising fuel prices shows the strong demand and potential for an alarming global fossil fuel crisis. Although the AEO also reported that the overall pollution levels will be slightly lower than current values by 2035, the projected values of greenhouse gas emissions (particularly CO2) will still be higher than current acceptable limits.

Efforts to ensure efficient, clean combustion of fuels will positively contribute to the aforementioned issues through reduced fuel consumption and pollutant emissions.

Thus, there is a critical need to improve the combustion chamber design in engines.

Knowledge of the kinetic mechanisms governing the combustion of fuels is crucial to

1 achieving this. Chemical kinetics plays an important role in identifying the key reactions responsible for fuel oxidation and pollutant formation.

The reactions describing the global conversion of reactants to products via many intermediate reactions makeup a chemical kinetics mechanism. Computer software is used to process the mechanism in simulating the fuel’s combustion and, thus, obtain temporal evolution of species concentrations, temperature and pressure. However, before utilizing the mechanism to solve applied problems, it must be validated against relevant experimental data.

Practical fuels such as gasoline, diesel and jet fuels consist of hundreds to thousands of different hydrocarbons, including paraffins (normal, branched and cyclo), olefins and aromatics.3 Combustion simulation of these fuels involve complex mechanisms (large number of reactions and species), and their comprehensive modeling is currently not feasible due to the high computational cost and time.3 One common approach used to reduce the computational efforts is to replace the practical fuel with a surrogate fuel that consists of a mixture of selected representative species. The surrogate formulation is chosen to reproduce the physical and/or chemical properties of the real fuel. For this purpose, three types of surrogate fuels exist: physical surrogates (e.g., boiling point, flash point and molecular weight), chemical surrogates (e.g., chemical composition and sooting tendency) and comprehensive surrogates (both physical and chemical). The importance of fuel surrogate components, their relevance to practical systems, and the degree of understanding of their properties and mechanisms has been previously studied.3 It was explained there that the mechanisms for straight and branched alkanes are well understood,

2 but those for cycloalkanes and single- and multi-ring compounds are least understood, in addition to the properties of cycloalkanes and aromatics.

Various hydrocarbon classes such as normal and branched alkanes4-7 and aromatics8 have been studied extensively, and literature reviews are available.9 Thus, it is necessary to focus on other significant and lesser understood species such as cycloparaffins.10

Cycloalkanes are an important class of hydrocarbons11 that constitute ~ 60% by volume in RP-1,12 ~ 20% by volume in Jet-A/Jet-A1/JP-8, 13 and 30–65% by weight in diesel fuels.14 Methylcyclohexane is widely used to represent the cycloalkane portion in diesel and jet fuels.3, 10, 15 The goal of the present study is to provide experimental ignition delay data to the cycloparaffin database by characterizing the ignition behavior of MCH.

It also seeks to utilize the data to validate existing chemical kinetic mechanisms.

1.2 Ignition Delay Time

Ignition delay time represents a global parameter for the validation of chemical kinetic mechanisms. It also provides useful information, such as the chemical kinetic time scale at any temperature for the design of combustion chambers.16 In general, ignition delay is defined as the time taken for a fuel-oxidizer mixture at an initial temperature and pressure to initiate the ignition process.16

In many chemically reacting systems (e.g., combustion), reaction processes are governed by chain reactions. The main elements in chain reactions are chain carriers because they are directly responsible for the global reaction progress. In combustion, radicals that serve as chain carriers have been identified as transient intermediate species.

Ignition takes place once the amount of radicals (radical pool) becomes large enough to consume the fuel. Ignition is experimentally observed from radical species such as OH and CH when they are in an excited state (OH* and CH*).16 Due to the large amount of heat released during combustion, both temperature and pressure rise during ignition. Large pressure rise are typical of ignition conditions involving high fuel concentration,17 and its delayed response is typical of low fuel concentration. The ignition delay time can be defined either by the maximum rate of change or the time when a specie or pressure or visible light emission reaches its peak value; it can also be derived by extrapolating the maximum slope to zero signal level.17

The ignition delay time depends on various parameters such as pressure, temperature, equivalence ratio and fuel composition. Correlations developed from ignition delay data at different parameter settings help understand the dependency on these parameters, as shown in previous investigations.6, 15 The correlations are useful for modelers as an initial step in understanding the kinetic processes.17 Moreover, they allow comparison of data sets at different conditions. Plotting the natural logarithm of ignition delay time against the inverse of pre-ignition temperature gives the global activation energy for the fuel. Ignition delay can be characterized into physical and chemical ignition delay.

The former depends on parameters such as atomization, vaporization and mixing of fuel and air, while the latter depends on the fuel’s chemical composition. Physical effects can be separated from chemical effects by pre-vaporizing and premixing fuel with air and making a homogeneous gas-phase fuel-air mixture. Previous studies on ignition delay times of methylcyclohexane were performed using rapid compression machines18, 19 and shock tubes.15, 20-23 Comparing the data from different reactors with different reaction

4 conditions is difficult. A better approach to cover a wide range of conditions is to use the same system. The shock tube can help understand the effects on MCH ignition delay by studying the chemical effects without reactor specific physical effects. Data from different reactors helps validate the kinetic mechanism and computational approaches taken to simulate the various reactor environments (e.g., fluid dynamic and thermal processes) with a previously validated model.11 The current study uses a shock tube to obtain the ignition delay time data due to its advantage over other systems, as explained below.

1.3 Shock Tube

The shock tube is a well-established tool for chemical kinetic studies. It allows a gas mixture at an initial pressure and temperature to almost instantaneously reach high temperature and pressure by a reflected shock wave. Furthermore, shock tube experiments have good reproducibility and allow smaller fuel volumes (microliters) to be tested compared to experimental engines (gallons). The design and principles of shock tube operation have been explained elsewhere.24, 25 The shock tube consists of a high pressure

(driver) section and a low pressure (driven) section separated by a diaphragm. A sudden burst in the diaphragm produces a planar shock wave as the high pressure gas flows into the driven section. The shock wave compresses the driven gas as it travels into that section.

An expansion fan (rarefaction wave) is also produced by the diaphragm burst, and it travels into the driver section and reflects back from the driver end plate. A contact surface is formed at the interface between the driver and driven gases; it travels rapidly behind the shock front. The incident shock wave advances quickly into the driven section, impinges upon the driven end plate and is reflected back into the driven section, thus, elevating the

5 temperature and pressure to a maximum in the shock tube driven section. The reflected expansion wave quenches the reactions in the driven section upon coming into contact with the post-reflected shocked gas. The interactions between the reflected shock wave and contact surface are explained by Gaydon and Hurle.25 The region behind the reflected shock wave creates a uniform temperature and pressure region until it is quenched by the rarefaction wave. Thus, the shock tube provides a great environment for chemical kinetic studies.

However, non-ideal effects such as incident shock attenuation and boundary layer development behind the reflected shock can lead to uncertainties in pressures and temperatures. Petersen26 explained the non-ideal effects behind a reflected shock wave and developed a reflected shock gas dynamic model to measure post-reflected pressure and temperature uncertainties, which were in good agreement with his experimental data.

Studies on boundary layer instabilities,27 turbulent boundary layer effects on shock tube test times28 and flow instabilities due to shock wave–boundary layer–contact surface interactions29 have been conducted. It has been shown that boundary layer effects can by minimized by tailoring the shock wave.25 Hong et al.30 developed a theoretical model based on their contact surface tailoring studies to estimate the contact surface tailoring conditions in a convergent shock tube. The ignition delay measured in the shock tube is defined as the time interval between the arrival of the incident shock at the end of the driven section (i.e., test section end plate) and detection of the onset of sustained ignition. Shock tubes have been used to measure ignition delay of different fuels. Comparisons are made with ignition delay from other fuel surrogates at similar conditions,7, 8 as well as other studies on MCH.15, 20, 22, 23

1.4 Methylcyclohexane

Methylcyclohexane (C7H14) is a colorless cycloalkane with a faint benzene-like smell. It is a component of jet fuel, and it is widely used in surrogate fuels to represent the cycloalkane portion of jet fuel. Properties of MCH are given in Table 1.

Table 1 – Properties of methylcyclohexane.19

Property Value Molar mass 98.19 g mol-1

Density 0.77 g cm-3

Melting point -195 °F

Boiling point 214 °F

Flash point 25 °F

Auto ignition temperature 482 °F

Several ignition delay studies have previously been performed on MCH. Pitz et al.10 investigated its ignition behavior over a temperature range of 680–980 K at pressures of 10–20 atm with diluents of argon, nitrogen and 50/50 (weight %) nitrogen/argon at stoichiometric conditions using a rapid compression machine. A negative temperature coefficient (NTC) region was observed in the experimental data. Pitz et al. also developed a new low temperature oxidation mechanism for MCH and combined it with an existing high temperature mechanism from Orme et al.21 Their computational work indicated that using n- and iso-alkane based estimates of RO2 isomerization rate constants does not show the NTC region and estimates much longer ignition delays at lower temperatures. Upon replacing the RO2 isomerization rate constants with experimental values from Gulati and

Walker,31 the computed ignition delay times showed a better agreement at low temperatures, as well as the NTC region with experimental ignition delay times from Pitz et al.10

Tanaka et al.19 studied some pure fuels using a rapid compression machine (RCM) and showed that combustion characteristics are strongly dependent on the fuel structure: either single- or two-stage ignition occurred. A two-stage ignition phenomenon was observed for all saturated compounds (including MCH) and olefins tested, while unsaturated cyclic compounds showed a single-stage ignition. The authors explained that the absence of two-stage ignition is most likely associated with the low heat release during the first stage of combustion. Faster burning rates were noticed in MCH combustion than iso-octane and unbranched cyclic compounds.

The phenomenon of two-stage ignition was explained differently by Mittal et al.18

They used an RCM to investigate the auto-ignition of MCH at  = 0.5–1.5, pressures of

15.1 and 25.5 bar and a temperature range of 680–905 K. Two-stage ignition and a strong

NTC behavior were observed. They explained that the ignition behavior was strongly dependent on the ignition temperature: two-stage ignition occurred at low temperatures and single-stage ignition was observed at high temperatures. A shift in the NTC region to higher temperatures at high pressure and oxygen-rich conditions was also observed.

Hawthorn and Nixon20 measured ignition delay times of MCH behind incident shock waves. Very low concentrations of fuel (5% and 1% fuel-oxygen mixtures) were used with argon as a bath gas. A few experiments were run replacing argon with nitrogen, but no significant effect on ignition delay was observed. The ignition delay of MCH/O2/Ar was recorded for a temperature range of 1200–1480 K, at pressures of 0.61, 1.02 and 1.7

8 atm and  = 0.1–2.1. They observed that the influence of equivalence ratio is qualitatively larger in stoichiometric and rich regions. Although the effect of pressure, reactant concentrations and equivalence ratios were studied, no correlations with these variables were developed.

21 Orme et al. studied the ignition delay times of MCH/O2/Ar behind the reflected shock wave over a temperature range of 1250–2100 K for reflected shock pressures of 1,

2 and 4 atm and equivalence ratios of 0.5, 1.0 and 2.0. The ignition delay times measured ranged from less than 50 s to greater than 1 ms. However, since the measurement uncertainty was very high, the small ignition delays were ignored. Orme et al. replicated the experimental conditions previously studied by Hawthorn and Nixon;20 good agreement between both data sets were observed. A detailed chemical kinetic model was also created by Orme et al. Their model showed a good agreement with their experimental measurements of ignition delay times.

15 Vasu et al. measured the ignition delay times of MCH/O2/Ar and MCH/air mixtures behind the reflected shock wave in two different shock tubes. The experiments were conducted at low and high pressure conditions. At low pressure conditions, the ignition delay was measured over post-reflected temperatures of 1225–1560 K, pressures of 1.3–2.9 atm and equivalence ratios of 0.5–2.0 with argon as the diluent. An ignition delay correlation developed for the low pressure data showed a strong dependency on equivalence ratio and oxygen concentration, and the ignition delay times showed a good agreement with several mechanisms. The high pressure ignition delay time data were for a post-reflected shock temperature range of 795–1098 K, pressures of 17.2–49.2 atm and

 = 1 in air. Vasu et al. also studied the effects of pressure on MCH ignition delay by

9 complementing earlier measurements of MCH made in an RCM by Pitz et al.10 Strong ignition was seen in the high pressure data, with lower pressures having longer ignition delays. The NTC behavior was also observed at 45 atm for T < 880 K.

Another study on MCH using a shock tube was conducted by Vanderover et al.,22 who measured the ignition delay of MCH/air at reflected shock temperatures and pressures of 881–1319 K and 10.8–69.5 atm, respectively, at equivalence ratios of 0.25, 0.5 and 1.0.

The ignition delay was measured using the end plate OH* and sidewall pressure profile.

The effect of equivalence ratios, pressures and temperatures on ignition delay was characterized. Inverse dependencies on pressure and equivalence ratios were observed for stoichiometric and lean conditions with a wide range of pressure scaling parameters. Their experimental data showed the NTC behavior for T < 1000 K, which agrees well with prior work done by Orme et al.,21 Pitz et al.10 and Vasu et al.15

Hong et al.23 measured the ignition delay times for MCH behind reflected shock waves, and compared the ignition delay times with cyclohexane and butylcyclohexane

(BCH) at pressures of 1.5 and 3 atm for  = 0.5 and 1 over a temperature range of 1280–

1480 K. They observed that the ignition delay times measured were longer for MCH than

BCH.

1.5 Current Study

Several studies were conducted on the ignition delay of MCH prior to this work.

The present study focused on the ignition delay time measurements from reflected shock wave combustion of MCH/O2/Ar mixtures with argon dilutions of 93% and 98%, pressures of 2 ± 0.06 and 16 ± 1.5 atm, equivalence ratios of 0.5, 1 and 3, and pre-ignition

10 temperatures of 925–1800 K. The experiments were conducted in a shock tube to study the effects of pressure, diluent concentration, equivalence ratio and temperature on the ignition delay times of MCH.

The experiments included a wide range of conditions and were intended to cover fuel-rich ( = 3) and high pressure (16 atm) conditions using argon as a bath gas, which has not been studied before. Thus, the goal of this investigation was to extend the MCH ignition delay database. All experiments were conducted using tailored conditions.

Experiments were performed for a wide range of conditions over constant dwell times (7.6

± 0.2 ms) and scaled to common pressures (2 and 20 atm). The uniqueness of this study is to develop a correlation for ignition delay that depends on all the parameters (i.e., pressure, argon concentration, equivalence ratio and temperature) for the wide range of data set, where other studies have looked at these effects individually. Ignition delay was also modeled using the mechanisms of Orme et al.21 and Pitz et al.10 under different modeling approaches to validate the models with measurements of this study. The ignition delay of

MCH was plotted against other hydrocarbons to study the behavior of cycloalkanes relative to other classes. The uncertainties on P5, T5, fuel concentration and incident shock velocity were calculated, and the experimental uncertainties of ignition delay measurements were also calculated.

CHAPTER 2

EXPERIMENTAL SETUP AND PROCEDURE

The shock tube used in this study is a single pulse, double diaphragm, non-heated shock tube, and is made from SS 304 with ½’’ thick walls. It is used to study the high pressure, high temperature combustion of various hydrocarbon fuels behind reflected shock waves. The shock tube mainly consists of four sections: a driver section that provides the energy to produce the supersonic shock wave, a driven section that allows a planar shock front to develop, a breaker section connecting the driver and the driven sections that also helps initiate the shock and a test section that contains the test mixture.

The experimental device is located in the Shock Tube Laboratory at the University of

Dayton Research Institute. The shock tube was designed to study post-reflected temperatures of 600–1800 K, post-reflected pressures of 1–100 atmospheres and dwell times up to 12 ms. It is used for the combustion of hydrocarbon fuels in the gas phase (i.e., fuels with relatively high vapor pressure).

2.1 Shock Tube Components

The shock tube is comprised of multiple sections, as shown in Figure 1. The driver section of the shock tube is 274 cm long and has an inner diameter (ID) of 7.62 cm. Its inner surface is finely polished. Although the driver section is a single section, it

12 is divided into two parts (driver and breaker sections) for operational purposes. The driver portion is always maintained at a higher pressure than the other sections so that the pressure differential between the chambers will create a shock wave. The gases to be filled in the driver section are chosen with great care so that they do not react with the test gas. It is also important to ensure that the molecular weight is low because the speed of the sound increases with a decrease in molecular weight. Helium is chosen for the driver section, and a predetermined percentage of argon is added to the helium to obtain the desired velocities.

Argon addition also helps match the acoustic impedance of the gases to obtain uniform post-reflected shock pressures of a perfectly tailored shock wave, which is achieved by the tailored interface technique.32

The breaker section attached to the driver section plays an important role in initiating the shock wave. This section is 20.32 cm long and has an ID of 5.08 cm. It is located between the driver and the driven sections, and has Mylar® diaphragms on either side. The diaphragm thickness varies with the differential pressure; a thicker diaphragm is used when higher pressures are maintained in the driver section. A pneumatic valve connects the breaker section to the breaker vacuum chamber that is initially maintained under vacuum.

The driven section is 274 cm long and has an ID of 5.08 cm. Its inner surface is finely polished. The driven section contains ports for filling this portion with test gases or to obtain shock wave pressure-time histories. A dump tank (ID = 30.48 cm, length = 101.6 cm) is also connected to the driven section; this assures only a single reflected pulse and prevents repetitive heating of the test gas by the shock wave.

Dump Tank Isolation Valve Vacuum Pump Test Section with Access Ports Isolation Valve

Breaker Section Driven Section Optical Diagnostic Setup Driver Section Breaker Vacuum Section

Figure 1 – Schematic of the shock tube.

The test section is an important component of the shock tube because the ignition and combustion of flammable reactant mixtures occur there. The test section is 91.44 cm long and 5.08 cm in ID. It also has a finely polished inner surface similar to the driven section. Figure 2 shows the schematic of the test section. It has six access ports: two are used for purging with helium, one is used for introducing the test gases into the test section from the sample preparation unit (SPU) and three are used for measuring pressure. There are four piezoelectric pressure transducers (PCB Piezotronics, model 113A24) total: one at the end plate and three on the sidewall of the test section. All pressure and optical events are monitored using two four-channel digital oscilloscopes (Tektronix, models TDS3014B and TDS3014). A pressure gauge and capacitance manometer are also connected to monitor the pressure inside the test section.

Figure 2 – Detailed view of the shock tube test section.

The SPU is attached to the test section of the shock tube, as shown in Figure 3.

This setup is used to vaporize the liquid fuel (e.g., methylcyclohexane), dilute it with bath gas and introduce it into the test section. The SPU is attached to the test section through

15 the injection port. The SPU consists of a glass bulb for introducing the fuel into a 14.5 L chemically inert air sampling canister (Restek, SilcoCan®) that holds the fuel mixture, a capacitance manometer for pressure measurement, a stainless steel manifold for gas delivery/transport and a vacuum pump.

Figure 3 – Schematic of sample preparation unit.

The experiments were conducted with the diagnostic setup positioned at the end plate of the shock tube, as shown in Figure 2. A quartz rod is mounted flush at the end plate and acts as a window for optical diagnostic setup to measure OH* and CH* chemiluminescence and white light (WL). All measurements were relative to the pressure signal generated by the pressure transducer located at the end plate. A photomultiplier tube

(PMT), fitted with a 20 nm band pass interference filter centered at  = 430 nm, was used to detect CH A-X chemiluminescence. A second PMT, fitted with a 20 nm band pass interference filter centered at  = 307 nm, was used to detect OH A-X chemiluminescence.

Both PMTs (Hamamatsu Corporation, model H5783-04) included the high voltage power supply. Light traveling through the quartz rod is passed through a beam splitter to divert

16 it towards these PMTs. Unfiltered visible light passes through the end of the quartz rod to a PMT for white light emission. The rise time of PMT signals was approximately 2 s.

The shock tube contains two pneumatic valves, one in the breaker section and another in the test section. The former separates the pressurized breaker section and the adjoining vacuum section. Upon opening this valve, a negative pressure will be exerted on the diaphragms, causing them to rupture and create a shock wave. The pneumatic ball valve that separates the test section from the driven section instantaneously opens for 0.5 s and subsequently closes by programming command. The system allows the shock wave to enter the test section, ignite the mixture and trap the products for further study. A control panel is utilized to control the pneumatic valves, turbo pump, monitor the pressure and control the flows of different gases into the driver, breaker and driven sections.

2.2 Operation of Shock Tube

Shock tube operation consists of several processes. The shock tube should be cleaned between tests. The cleaning procedure for the test section involves removing diaphragm debris and soot particles (incomplete combustion products). The diaphragm debris is cleaned up using Kimwipes; soot and other products are thoroughly cleaned by wiping the tube inside with hexane-treated Kimwipes until no soot appears on the wipe.

An oxygen shock is carried out (after every three combustion experiments) to prevent buildup of any residual combustion products on the walls after cleaning with the hexane- treated Kimwipes. An oxygen shock is performed by filling the empty test section with oxygen and creating a shock wave to combust any impurities (soot, dust, etc.) present.

After cleaning, the pneumatic ball valve is closed, the pressure gauges are isolated, and the test section is purged at a high pressure with helium for approximately two minutes.

Two Mylar® diaphragms of different thickness are placed in the breaker section, one at each end. The diaphragm thickness depends upon the post-reflected pressure (P5) to be generated.

The driver, driven, breaker assembly and test sections are pumped down to pressures of 10-3 Torr using vane pumps. The test and driven sections are pumped down further to 10-6 Torr using a turbopump. The test section is monitored for leaks before each experiment. The leak rates measured in the test section should be less than 0.01 Torr per minute.

Once the tube is under vacuum, both pneumatic valves are closed using electronic switches on the control panel. Both diaphragms respond to filling helium in the driver and breaker sections. The driver pressure is maintained at a higher value than the breaker pressure; thus, the diaphragms deflect towards the low pressure side.

The test section is filled with the fuel (MCH) and argon from the canister and oxygen and additional argon (makeup argon for required diluent gas partial pressure) directly from the cylinders. The fuel mixture preparation and calculation are explained in

Chapter 3. After filling the test section with the test gas mixture, it is kept undisturbed for

30 minutes for homogenous mixing. Meanwhile, the driver, driven, and breaker sections are filled with appropriate gases.

Once all the sections are filled with the desired gases, the two pneumatic valves are manually put into auto position. They are electronically opened in sequence to initiate the shock. Rupture of the diaphragms causes a shock wave to travel into the test gas,

18 compressing it and elevating its temperature and pressure to high values for the combustion to take place. The control system is set up to trap the products in the test section by immediately closing the pneumatic ball valve within 0.5 s.

The shock wave arrival is detected by the piezoelectric pressure transducers located on the sidewalls and the end plate of the test section and can be monitored using the four channel digital oscilloscope. The diagnostic setup is attached to the shock tube end plate and is capable of capturing simultaneously the WL and chemiluminescence emissions of

CH* and OH* on to another four channel digital oscilloscope. The ignition delay can be measured from the time of the shock front arrival at the end plate to the onset of the WL and emissions of CH* and OH*. A typical trace of both oscilloscopes is explained in

Chapter 4.

CHAPTER 3

CALCULATIONS

3.1 End Plate Velocity Calculation

The velocity of the incident shock wave at the end plate of the test section was computed using a linear extrapolation of the mean velocities between the pressure transducers located along the side wall of the test section in relation to the location of the end plate. Figure 4 shows the test section of the shock tube, which contains three pressure transducers on the sidewall and one at the end plate. From the oscilloscope trace shown in

Figure 5, the three incident times t1, t2 and t3 are measured. The distances d1, d2 and d3 corresponding to the distances between each pressure transducer and the end plate are known from the shock tube’s physical dimensions. Velocities V1, V2 and V3 can be calculated by dividing the corresponding distance by time. Thus, velocities are calculated as follows:

푉푖 = 푑푖⁄푡푖, i = 1–6. (3.1)

The mean velocities V4, V5 and V6 are calculated using distances and times that are given by the following expressions:

푡4 = 푡1 − 푡3, (3.2a)

푡5 = 푡2 − 푡1, (3.2b)

푡6 = 푡2 − 푡3, (3.2c)

푑4 = 푑1 − 푑3, (3.3a)

푑5 = 푑2 − 푑1, (3.3b)

푑6 = 푑2 − 푑3. (3.3c)

The distances from PT1 to the midpoint of two sidewall pressure transducers (PT2 and PT3, PT3 and PT4 and PT2 and PT4) were calculated. They are denoted by 4, 5 and

6, and are given by the following:

∆4 = 푑5⁄2, (3.4)

∆5 = 푑5 + 푑6⁄2, (3.5)

∆6 = 푑6⁄2. (3.6)

The calculated distances 4, 5 and 6 were plotted against the velocities V4, V5 and V6 and extrapolated to the end plate to obtain the velocity there. An example of this calculation is found in Appendix G.

Figure 4 – Shock tube test section with time and distance measurements from the end plate.

Figure 5 – Experimental pressure profiles from oscilloscope showing end plate and sidewall measurements and corresponding incident times.

3.2 Post-Reflected Temperature and Pressure Calculations

The post-reflected temperatures and pressures are calculated using CHEMKIN-

PRO,33 which utilizes iterative methods to solve the 1–D shock equations. CHEMKIN-

PRO takes initial parameters such as temperatures, pressures, velocities and mole fractions as inputs to generate the post-reflected conditions (Appendix E). The calculation of these post-reflected pressures and temperatures are explained in detail in the CHEMKIN manual.

3.3 Uncertainties of Post-Reflected Pressures and Temperatures

Perturbation methods have been used to calculate the uncertainties of post-reflected pressures and temperatures. The upper and lower perturbed values of the post-reflected conditions are calculated from the uncertainties in the initial temperatures, pressures, velocities and test section mixture. The root sum square formula was applied on the averaged values of the upper and lower perturbations to obtain the uncertainties of post- reflected pressure and temperature. An example of the results obtained from a particular

22 condition is shown in Appendix D. The effects from the above parameters on post-incident and post-reflected pressures and temperatures are listed as absolute values and percentages.

It is important to note that the uncertainty of the incident shock velocity contributes more than other uncertainty values in the uncertainty of post-reflected pressure and temperature.

It is also seen that the uncertainty of the initial pressure contributed less than the uncertainty of the initial temperature, and that the uncertainty of post-reflected temperature and pressure were approximately two orders of magnitude greater than those of the initial temperature and pressure.

3.4 Calculation of the Uncertainties Using the Perturbation Method

Let ∂x be the error of quantity x. The upper and lower perturbed values of y are given by:

푦+ = 푅 (푥 + 휕푥), (3.7)

푦− = 푅 (푥 − 휕푥), (3.8) where R is the function of y in terms of x. Changes to y values are given by:

+ + 푑푦 = |푦 − 푦 |, (3.9)

− − 푑푦 = |푦 − 푦 |. (3.10)

The error ∂y can be calculated from the above values through the expression:

+ − 휕푦 = (푑푦 + 푑푦 )⁄ 2. (3.11)

Therefore, the percentage error results are given by:

% 퐸푟푟표푟 = 100 ∙ (휕푦⁄푦). (3.12)

3.4.1 Example of Uncertainty Propagation

The uncertainty of argon mole fraction in the reactant mixture was calculated from the uncertainty in the partial pressures. Let P1 be the sum of partial pressures of fuel, oxygen and argon in the test section:

푃1 = 푃퐴푟 + 푃푂푥 + 푃푓. (3.13)

The argon mole fraction is expressed as

푃퐴푟 푃퐴푟 푋퐴푟 = = . (3.14) 푃1 푃퐴푟+ 푃푂푥+ 푃푓

Differentiating 3.14 with respect to PAr gives

휕푋퐴푟 1 푃퐴푟 푃푂푥+ 푃푓 푃1− 푃퐴푟 = − 2 = 2 = 2 . (3.15) 휕푃퐴푟 푃퐴푟+ 푃푂푥+ 푃푓 (푃퐴푟+ 푃푂푥+ 푃푓) (푃퐴푟+ 푃푂푥+ 푃푓) 푃1

The uncertainty of the argon partial pressure may be determined by using the root sum square formulae:

2 푃1− 푃퐴푟 푢푃퐴푟 = √((휕푋퐴푟⁄휕푃퐴푟) ∙ 휕푃) = 휕푃 ∙ 2 . (3.16) 푃1

3.5 Fuel Mixture Calculation

The MCH/O2/Ar mixture was studied at different equivalence ratios and argon dilutions. Calculations for one of the conditions using 93% argon and  = 3 is presented in this section. The fuel mixture was prepared in the SPU before being introduced into the test section of the shock tube. Preparation of the fuel mixture is explained in the next section. The calculations for the amounts of fuel and argon to be put into the SPU are explained in this section.

The complete combustion of fuel (MCH: C7H14) into carbon dioxide and water vapor is given below in the balanced, stoichiometric global reaction:

C7H14 + 10.5 O2 → 7 CO2 + 7 H2O. (3.17)

The stoichiometric oxygen-to-fuel ratio is readily calculated:

(푂⁄ 퐹 )푠푡표푖푐 = 10.5⁄ 1 = 10.5. (3.18)

The relation between the actual and stoichiometric oxygen-to-fuel (O/F) ratios can be given as:

(푂⁄ 퐹 )푎푐푡푢푎푙 = (푂⁄ 퐹 )푠푡표푖푐⁄. (3.19)

Assuming Ф = 3, the oxygen-to-fuel ratio is

(푂⁄ 퐹 )푎푐푡푢푎푙 = 10.5⁄ 3 = 3.5 . (3.20)

For an argon dilution of 93%, the remaining 7% is the fuel and oxygen mixture:

푋푂2 + 푋푓 = 0.07. (3.21)

The mole fractions of individual components can be calculated using 3.22 and 3.23:

푋푂2 = 3.5 ∙ 푋푓, (3.22)

푋푓 + 3.5 ∙ 푋푓 = 0.07. (3.23)

Solving 3.22 and 3.23 gives Xf = 0.0155, XO2 = 0.0585 and XAr = 0.93. This allows the partial pressures of all species to be obtained:

푃푓 = 푋푓 ∙ 푃, (3.24a)

푃푂2 = 푋푂2 ∙ 푃, (3.24b)

푃퐴푟 = 푋퐴푟 ∙ 푃. (3.24c)

By substituting the density relationship into the ideal gas equation for the canister, the following expression may be generated for the fuel injection volume:

푃푓 ∙ 푉푐푎푛푖푠푡푒푟 푉푖푛푗 = . (3.25) 휌푓 ∙ 푇 ∙(푅푢⁄푀푊푓)

3.6 Fuel Mixture Preparation

The initial step in the fuel mixture preparation is the injection of the fuel into the glass bulb. Equation 3.25 gives the amount of fuel to be injected into the glass bulb. The

SPU is evacuated to ~ 10-5 Torr before injecting the fuel into the glass bulb. At the time of injection, the glass bulb is isolated from the canister. Upon the injection of a known volume of liquid fuel, some of the MCH vaporizes and reaches the saturated pressure, which is read from the digital pressure measurement. After keeping the fuel in the glass bulb for two minutes to allow the pressures to stabilize, the canister is opened and the MCH vapors start to fill the canister. The canister pressure is monitored at regular intervals. Once the canister pressure stabilizes, a predetermined amount of argon is put into the canister. This argon- fuel mixture is utilized in every experiment, with the oxygen being added separately into the test section for each test. An example case of the fuel mixture preparation is given in

Appendix F for reference.

CHAPTER 4

RESULTS AND DISCUSSION

4.1 Overview of Results

Methylcyclohexane ignition delay times were measured behind the reflected shock wave in a single pulse reflected shock tube. Pressures of 2 and 16 atm, equivalence ratios of 0.5, 1 and 3, argon dilutions of 93% and 98% and a temperature range of 925–1800 K were tested. The experimental ignition delay data are presented in Appendix A.

Ignition delay times were measured from the pressure profiles recorded at the end plate of the test section, as well as the chemiluminescence emissions of CH* and OH* and white light (WL) broadband emissions from the same location. Example oscilloscope traces of these signals from the combustion of MCH are given in Figures 6 and 7. In this study, the ignition delay time is defined as the time difference between the arrival of the incident shock wave at the test section end plate and the maximum rate of change of the optical emissions (OH*, CH* and WL) extrapolated to the pre-ignition baseline, as shown in Figure 8. The dwell time, which is the time available for combustion, is defined as the time interval between the arrival of the incident shock wave at the test section end plate and the arrival of the reflected rarefaction wave at the same location. The measurement of the dwell time is also shown in Figure 7.

Figure 6 – Sample oscilloscope trace showing end plate and sidewall pressure profiles from the combustion of MCH.

Figure 7 – Sample oscilloscope trace showing end plate pressure profile, OH* and CH* chemiluminescence and WL emissions from the combustion of MCH.

The arrival and reflection of the incident shock wave at the end plate is observed from the first sudden rise in the pressure profile recorded there. The incident times are measured using the three sidewall and end plate pressure profiles, i.e., measuring the time

28 between the pressure rise due to the arrival of the incident shock wave at the sidewall and end plate. These times are subsequently used to calculate the incident shock velocity at the test section end plate. The procedure used for this computation is given in section 3.1.

Figure 8 – Ignition delay measurement using the maximum slope extrapolation method.

The experimental pressure profiles recorded at the test section end plate are plotted in Figures 9 and 10. They show the post-reflected pressures, dwell times and the rise in pressures due to ignition (in some instances). Strong oscillatory peaks in the pressure profile are observed for almost all conditions having a 93% bath gas (argon) concentration.

This indicates a strong ignition with a progression to a detonation-like phenomenon.34-36

Saxena et al.37 observed a similar effect in the combustion of ethylene for the same diluent gas and concentrations. When a high fuel concentration mixture (93% bath gas dilution) containing a large volume of unreacted gas homogeneously ignites, strong ignition with transition to supersonic combustion phenomena takes place.36 Supersonic combustion can lead to shock waves that cause strong pressure peaks and steep pressure gradients.

However, the detonation process has no effect on the ignition delay since ignition occurs before detonation commences.38 Although strong peaks are seen at the low pre-ignition pressure (~ 2 atm), a sudden rise in pressure does not appear due to the lower concentration of fuel present in the shock tube test section. A mild ignition with no strong rise in the pressure profile due to ignition was noticed at the higher argon dilution (Ar = 98%).

Although it is likely not the case here, it is noted that mild ignition can also occur due to local hot spots (non-homogeneities in temperature) that can lead to one or several flame kernels.36

Figure 9 – End plate pressure profiles from MCH combustion at 93% argon dilution and 16 atm. Profiles are shown for equivalence ratios of (a) 0.5, (b) 1.0 and (c) 3.0.

Figure 10 – End plate pressure profiles for  = 0.5 and 1 at pressures of 2 and 16 atm with 93% and 98% argon dilution, respectively.

A gradual rise in the pre-ignition pressure is observed in the end plate pressure profiles, as shown in Figures 9 and 10. This phenomenon is possibly due to a boundary layer that builds up behind the incident shock wave. The interaction of the reflected shock wave with the boundary layer gives a gradual rise in pressure. Previous studies17, 26 observed that the boundary layer is formed in shock tubes with small internal diameters.

A previous investigation using a ½’’ diameter shock tube observed an attenuation of the incident shock velocity, indicating the presence of a boundary layer with considerable thickness.25 A similar phenomenon is observed for the low fuel concentration at high post- reflected pressure in this study (see Figure 10). Oehlschlaeger et al.39 measured the ignition delay times for the combustion of iso-octane in a shock tube with an internal diameter of 31

14.1 cm. Shen et al.40 later made measurements with a smaller diameter (5.7 cm) shock tube for the same conditions. The data from the two shock tubes were in good agreement.

Thus, the effect of boundary layer in this work (ID = 5.08 cm) is also considered to be minimal. The boundary layer effect is considered to be nominal on short ignition delay times (< 300 s) over dwell times in the range of 7–8 ms.37 Very little change in the post- reflected pressures and temperatures were observed, indicating a very small effect from boundary layer interaction at the low temperature conditions.

The argon-to-helium ratio is an important parameter in shock tube gas dynamics.

Using the correct ratio helps maintain the required dwell time and achieve a perfectly tailored contact surface, leading to a constant post-reflected (pre-ignition) pressure over the reaction time. Although attempts were made to ensure perfectly tailored conditions, imperfections in tailoring were observed for some experiments involving higher temperatures (T > 1500 K) and argon concentrations (98%), as shown in Figure 10. At these conditions, however, ignition occurred before the contact surface interacted with the reflected shock and, thus, had no impact on the pre-ignition temperature and pressure.

Argon-to-helium ratios (driver section) of 15.2–20.2% were needed to achieve a dwell time of 7.6 ± 0.2 ms. In some cases, particularly for lower temperature conditions, dwell times were extended to 9 ms in order to capture longer ignition delay times. However, the dwell times for experiments with 93% argon and  = 3 were maintained at 7.6 ± 0.2 ms because constant reaction times are necessary for combustion product studies. Characterizing the combustion products is also part of a future work.

4.1.1 Ignition Delay Correlation

Ignition delay correlations were developed for the data measured for equivalence ratio of 0.5, 1 and 3. The computed expressions are the following:

 = 0.5; Ar = 93 – 98 %; P5 ~ 2 – 20 atm; T5  950 – 1640 K

14462±348.4 −1.26±0.131 18.7±1.77 −0.602±0.054 2 휏푖푔푛 = 10 푥퐴푟 푃 푒 푇 , R = 0.982 (4.1)

 = 1.0; Ar = 93 – 98 %; P5 2 – 20 atm; T5  925 – 1800 K

12691±426.3 −0.538±0.144 19.3±2.33 −0.644±0.059 2 휏푖푔푛 = 10 푥퐴푟 푃 푒 푇 , R = 0.969 (4.2)

 = 3.0; Ar = 93 %; P5  16 atm; T5:  940 – 1420 K

9352±779.3 −0.417±0.301 2 휏푖푔푛 = 10 푒 푇 , R = 0.906, (4.3)

where pressure is given in atmospheres and Ar is argon mole fraction. Figure 11 shows the experimental ignition delay times scaled according to their corresponding correlation.

A good agreement between each correlation and the experimental data is observed. In the case of fuel rich ignition ( = 3), the ignition delay times were measured only at pre-ignition pressure of 16 atm and argon concentration of 93%; thus, the effects of these two parameters could not be included in the correlation expression. Additionally, the correlations for lean and stoichiometric conditions show similar pressure dependence but different argon concentration exponents. The pressure dependences were used to scale the ignition delay times to a common post-reflected pre-ignition pressure (2 and 20 atm) in order to account for differences in the pre-ignition pressure (typically ± 10% of the calculated pre-ignition pressure). The good agreement in pressure scaling is seen in Figure

12 for fuel lean and stoichiometric mixtures at the low argon concentration.

Figure 11 – Normalized ignition delays times for equivalence ratios of (a)  = 3.0, (b)  = 1.0 and (c)  = 0.5.

Figure 12 – Pressures scaled to 20 atm for low argon concentration at (a) stoichiometric and (b) fuel lean mixtures.

4.1.2 Uncertainty Analysis

As in any experimental system, there is uncertainty associated with the measured and calculated quantities. This analysis evaluates the uncertainties in measurements of initial pressure and temperature, mixture composition and incident times. It also propagates them onto the post-reflected pressures and temperatures, followed by error propagation onto ignition delay times. Uncertainties propagation was carried out using perturbation methods.

To calculate the final uncertainty on the post-reflected pressures (P5) and temperatures (T5), the uncertainties from the initial conditions need to be propagated onto these final conditions. Those associated with initial conditions include initial pressure and temperature, velocity of the incident shock wave and the mixture composition. The uncertainty of initial pressure and temperature are 0.1 Torr and 1 K, respectively. Shock wave velocities can be measured with an accuracy of 2 µs travel time, and mixture formulations are made within 0.1 Torr since fuel and argon are metered together from the canister. Appendix D shows an example of uncertainty propagation from the initial conditions onto the post-reflected pressure and temperature.

Appendix B contains the uncertainties on post-reflected pressures and temperature for all data. It is observed there that the uncertainty of T5 increases with an increase in its value. However, no effect on this value from initial pressure was observed. It is also noted that the uncertainty amount (% value) in post-reflected pressure is larger than that of post- reflected temperature. The propagated uncertainties onto the post-reflected conditions for each error source are combined using the root–square–sum formula. The procedure for using the perturbation method to calculate the uncertainties is given in section 3.4. As

36 shown here, the root–square–sum formula is used to calculate the uncertainty of ignition delay time:

2 2 ∂τ푖푔푛 ∂τ푖푔푛 στ = √(( ) ∙ dT) + (( ) ∙ dP) . (4.4) 푖푔푛 ∂T ∂P

The contribution of pressure on ignition delay uncertainty is negligible when compared to that from pre-ignition temperature. The uncertainty in ignition delay times is in the range of 6–34%. Ignition delay uncertainty and its contributing factors are given in

Appendix C.

4.1.3 Modeling

The Pitz et al.10 and Orme et al.21 mechanisms for MCH oxidation were used to simulate the current experimental data. The latter is based on the reaction scheme

41 developed by Laskin et al. , where the H2/O2 submechanism was taken from Ó Conaire et al.42; the detailed chemistry that describes the oxidation of MCH and other intermediate species larger than 1,3-butadiene was added to it. Rate constants for MCH oxidation were based on the rate rules applied by Curran and coworkers for n-heptane43 and iso-octane44 oxidation. The MCH mechanism of Pitz et al.10 was developed by adding the low and high

44 temperature chemistry of MCH to a previous mechanism for C1-C6 hydrocarbons. Sub- mechanisms for toluene, benzene and cyclopentadiene were also added.45 The high temperature reactions were added from Orme et al.21 The Orme et al. MCH mechanism consists of 190 species and 904 reactions, while the Pitz et al. mechanism consists of 1001 species and 4436 reactions.

4.1.4 Modeling Approach

All ignition delay times from kinetic modeling were generated using CHEMKIN-

PRO. It uses the mechanism and thermodynamic files to create an intermediate file used for modeling. An analysis was done to validate the models developed by Orme et al.21 and

Pitz et al.10 Kinetic modeling was carried out in CHEMKIN-P RO using the homogeneous batch reactor with constant volume and internal energy assumptions. This was done for experiments with 93% argon dilution since a strong detonation phenomenon was observed during combustion at this condition. Simulations were also carried out with the constant pressure assumption for experiments with higher argon dilution (98%) because only mild ignition was observed at these conditions. However, in reality the combustion process in the shock tube at the fuel/argon concentrations used in this study cannot be fully described either by a constant U, V or a constant pressure approach. At conditions where detonation- like phenomenon is observed, a simultaneous expansion process occurs; this negates the constant volume assumption. To overcome this problem, an experimental pressure profile is imported into CHEMKIN-PRO to generate a temperature profile via isentropic relations for kinetic modeling. The temperature profile generated from the model showed a strong rise in temperature at ignition. A temperature rise was seen at low fuel concentrations, where the pressure rise due to ignition is not significant in the experimental pressure profiles. The generated temperature profile showed ignition delay as a temperature inflection point. Ignition delay from the temperature profile was consistent with the value estimated by the OH radical profile measured from the inflection point due to the ignition event. The approach to use the experimental pressure profile in CHEMKIN-PRO was attempted with both Orme et al.21 and Pitz et al.10 models but was not pursued for the latter

38 due to the excessive computational time requirements (in excess of 1 week vs. 4 hours for the Orme et al. model) to simulate the experiments. A comparison of the ignition delay times from kinetic modeling and experiments is given in the following sections.

4.2 Discussion

4.2.1 Ignition Delay Trends at Different Conditions

Figures 13 to 19 show the ignition delay at different experimental conditions. The experimental values are plotted with kinetic modeling results at different pressures, equivalence ratios and argon dilutions. A semi-log plot was used, with the x-axis being

1000/T and the y-axis as the natural logarithm of ignition delay time in µs. The utility of this semi-log plot is that the global activation energies and pre-exponential factors can be determined from the linear fit to the data:

푙푛 (τ푖푔푛) = 푙푛 (퐴) – (퐸푎/푅) ∙ (1/푇). (4.5)

Post-reflected pressures obtained from CHEMKIN were not identical for all experiments. Pressures were in the range of 1.86–2.07 atm at low pressure conditions and

10.99–19.2 atm at high pressure conditions. The post-reflected pressures (P5) for the former were scaled to 2 atm and those for the latter were scaled to 20 atm. The pressure coefficient obtained from regression analysis was used to scale the ignition delay data via a power law dependence:

푛 휏푖푔푛 ∝ 푃 , (4.6) where the coefficient n was -0.602 for  = 0.5 and -0.644 for  = 1. A similar pressure dependence was observed in the study by Hong et al.23

The ignition delay data obtained from OH* and CH* chemiluminescence, WL and pressure at the end plate of the test section were plotted for all the conditions, as shown in

Figures 13–19. The ignition delay for almost all the data fall within ± 20% of the mean measurement value. This uncertainty is consistent with other studies.46

Figure 13 shows the ignition delay at lean conditions ( = 0.5) for low dilution (Ar

= 93%) at high pressure (20 atm) in the temperature range of 950–1520 K. The figure shows that measurements from the four methods are in good agreement and within the 20% uncertainty. Kinetic modeling results from the Pitz et al.10 and Orme et al.21 mechanisms are plotted against the experimental data. Modeling results for both mechanisms using the constant U,V assumption estimate the ignition delay well above 1080 K, but overestimate it below that value. The ignition delay times from the Orme et al. model using the experimental pressure profile also show good agreement with ignition delay measurements above 1080 K and overestimate below it.

Figure 13 – Ignition delay for  = 0.5, Ar = 93% and P = 20 atm. Experimental (OH*, CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme et al.21) results are shown. A curve fit for modeling with a pressure profile shows its trend.

Figure 14 shows experimental ignition delay times plotted with modeling results for stoichiometric conditions. Results are similar to those observed in Figure 13 for lean conditions: the four methods show good agreement with each other and the models overestimate the experimental values at lower temperatures. Additionally, the constant

U,V assumption with experimental pressure profile (Orme et al. mechanism) gave very good agreement with measurements over the entire temperature range studied.

Results for rich ( = 3) combustion are shown in Figure 15. Although no pressure exponent was derived in the regression analysis, a value of -0.60 is assumed in scaling to

20 atm. Similar to the lean and stoichiometric results, ignition delay times from the different methods are within 20% of the mean value and, thus, are considered to be in good 41 agreement. It was observed that the WL ignition delay data is longer than CH* for most of the measurements, and that the ignition delay times of OH* were comparatively shorter than CH* and WL data. A similar trend was observed by Hall et al.46 in the combustion of ethane, where the OH* occasionally deviated from CH* and was much shorter in some cases. The figure also shows that kinetic modeling results agree well with experimental values over most of the temperature range; the models only start to underestimate values above 1330 K. The constant U,V assumption with the experimental pressure profile (Orme et al. mechanism) also agrees well with measurements, and is slightly closer to experimental values than non-pressure profile fed modeling results above 1330 K.

Figure 14 – Ignition delay for  = 1.0, Ar = 93% and P = 20 atm. Experimental (OH*, CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme et al.21) results are shown. A curve fit for modeling with a pressure profile shows its trend.

Figure 15 – Ignition delay for  = 3.0, Ar = 93% and P = 20 atm. Experimental (OH*, CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme et al.21) results are shown. A curve fit for modeling with a pressure profile shows its trend. Scaled values assume n = -0.60.

Experimental and computational results for low dilution and pressure are shown in

Figures 16 and 17 for lean and stoichiometric conditions, respectively. Similar to the high pressure cases of Figures 13–15, Figure 16 shows good agreement between the experimental measurements at  = 0.5. The models start to underestimate ignition delay above 1500 K and overestimate it below 1150 K. Kinetic modeling using the constant U,V assumption with the experimental pressure profile (Orme et al. model) did not show better agreement than the other approach above 1500 K but below 1150 K.

Good agreement among experimental measurements is also seen at the stoichiometric, low pressure case in Figure 17. It is worth noting that the figure shows a curving pattern in the experimental ignition delay time at low temperatures. This rolling- off effect indicates a change of slope and was previously observed by Vanderover et al.22

43 in the combustion of MCH/air at 50 atm for equivalence ratios of 0.25, 0.5 and 1.0. This behavior was also seen by Hawthorn and Nixon20 at different conditions.

Figure 16 – Ignition delay for  = 0.5, Ar = 93% and P = 2 atm. Experimental (OH*, CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme et al.21) results are shown. A curve fit for modeling with a pressure profile shows its trend.

Comparison of kinetic modeling approaches with experimental results shows good agreement with experimental values, as with the lean condition. Kinetic modeling estimates ignition delay well over most of the temperature range. Similar to the lean condition, the Pitz et al. mechanism predicts values better than Orme et al. mechanism at lower temperatures. It is also seen that the Orme et al. model using the experimental pressure profile does not give better results than the constant U,V assumption above 1400

K, but does give results closer to experimental measurements than the other approach below 1400 K.

Figure 17 – Ignition delay for  = 1.0, Ar = 93% and P = 2 atm. Experimental (OH*, CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme et al.21) results are shown. A curve fit for modeling with a pressure profile shows its trend.

MCH experiments conducted at high pressure and argon concentrations are shown in Figures 18 and 19 for lean and stoichiometric conditions, respectively. In addition to the kinetic modeling approaches used in previously discussed cases, constant pressure modeling with the Orme et al. and Pitz et al. mechanisms was done. For lean mixtures (

= 0.5), the Pitz et al. mechanism shows good agreement with experimental ignition delays above 1150 K. The mechanism also follows the roll-off behavior observed with the experimental data. The Orme et al. mechanism estimates are worse than the Pitz et al. model over the entire temperature range. It is also observed that the results for either model are very similar for both assumptions (constant U,V and P,H). The constant U,V

45 assumption with experimental pressure profile (Orme et al. model) gave better agreement than the other method below 1430 K but worse agreement than both models at higher temperature.

Figure 18 – Ignition delay for  = 0.5, Ar = 98% and P = 20 atm. Experimental (OH*, CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme et al.21) results are shown. A curve fit for modeling with a pressure profile shows its trend.

Figure 19 shows that the agreement between experiment and models is slightly different at stoichiometric conditions. Model estimates agree better at low temperatures than at high temperatures. Moreover, modeling results for the constant U,V assumption with experimental pressure profile (Orme et al. mechanism) agree better over the entire range than the other modeling approaches. Both modeling approaches underestimate ignition delay above 1540 K and overestimate it below 1050 K. Results for the two

46 assumptions (constant U,V and P,H) were close for each model, but they were more distinct than at  = 0.5.

Figure 19 – Ignition delay for  = 1.0, Ar = 98% and P = 20 atm. Experimental (OH*, CH*, WL and pressure measured at the end plate) and modeling (Pitz et al.10 and Orme et al.21) results are shown. A curve fit for modeling with a pressure profile shows its trend.

4.2.2 Impact of Pressures, Equivalence Ratios and Diluent Ratios

on Ignition Delay Times

Experiments were performed at different conditions, and ignition delay time measurements are compared for these conditions to determine the effect of equivalence ratios, argon concentrations and pressures on this parameter. Kinetic modeling results of

47 the Orme et al.21 mechanism for the experimental pressure profile with the constant U,V assumption were compared to the experimental values for all these comparisons.

4.2.2.1 Effect of Equivalence Ratios

The effect of equivalence ratio on MCH ignition delay times was examined for lean

( = 0.5), stoichiometric ( = 1), and rich ( = 3) conditions at a pressure of 20 atm and an argon dilution of 93%. Equivalence ratios of 0.5 and 1 at 20 atm and 98% argon dilution were also compared. Figure 20 shows the comparison of ignition delay time at low dilution. It is observed that the ignition delays times of lean and stoichiometric mixtures are similar over the temperature range. Values for stoichiometric mixtures are slightly higher than lean mixtures at higher temperatures (1330–1540 K) but are slightly smaller at lower temperatures (T < 1030). The ignition delay times of rich mixtures are greater than lean and stoichiometric mixture values over the entire measured temperature range. The data for  = 3.0 and leaner mixtures ( = 0.5 and 1) appear to converge at lower temperatures (~ 990 K). Measurements could not be made at temperatures less than 960

K because the dwell time was shorter than the ignition delay. A similar convergence in ignition delay data was observed in a previous study by Vanderover et al.22 The Orme et al.21 mechanism produces results similar to experimental values over most of the temperature range. Above 1110 K, the model shows the rich data to be above the stoichiometric and lean values, with the latter two similar in value over the temperature range. Below 1110 K, modeling results are close for all three equivalence ratios. This behavior is also seen to a less extent in the experimental data. The modeling results for the lean and stoichiometric cases are overestimated above 1080 K, with the agreement being

48 better for rich conditions over the entire temperature range. To explain the observed modeling behavior, a rate of production (ROP) analysis was performed with the Orme et al.21 mechanism using the CHEMKIN-PRO33 with the constant U,V assumption.

Figure 20 – Comparison of equivalence ratios of 0.5, 1 and 3 (symbols) with Orme et al.21 modeling (lines) for 93% argon dilution at 20 atm.

The ROP analysis was performed to identify the mechanism’s reactions that are critical to ignition delay. The OH radical was used as the target species, and the rate of production at half the ignition delay time was calculated. This analysis was done at low

(1000 K) and high temperature (1500 K) for  = 0.5 and 1. The top ten reactions were selected at each condition to study the change in chemistry. Figures 21–24 show the ROP for the conditions mentioned above. Figures 21 and 22 display the analysis at 1000 K.

They show that OH radical formation from hydroperoxide is the dominant reaction. The higher fuel concentration ( = 1.0) has a higher OH radical concentration (3.6 times more)

49 and, hence, a shorter ignition delay. A similar observation was made by Curran et al.44 for iso-octane. They observed that the production of carbonyl-hydroperoxide species, which lead to chain branching, is directly proportional to the fuel concentration at low temperatures.

Figure 21 – Rate of production analysis for  = 0.5, P = 20 atm, Ar = 93%, T = 1000 K.

Figure 22 – Rate of production analysis for  = 1, P = 20 atm, Ar = 93%, T = 1000 K.

At high temperature, the OH radical formation from the reaction of hydrogen and the molecular oxygen is the dominant reaction as seen from Figures 23 and 24. The leaner fuel mixture has a slightly higher OH radical concentration (1.25 times more) and, hence, shorter ignition delay at 1500 K. The variation in OH concentration with temperature explains the ignition delay trend in Figure 20: shorter ignition delay for  = 0.5 and 1.0 at

1500 K and 1000 K, respectively.

Figure 23 – Rate of production analysis for  = 0.5, P = 20 atm, Ar = 93%, T = 1500 K.

Figure 24 – Rate of production analysis for  = 1, P = 20 atm, Ar = 93%, T = 1500K.

Figure 25 depicts the effect of equivalence ratio of  = 0.5 and 1 on the ignition delay times at a pressure of 2 atm and argon diluent concentration of 93%. The ignition delay ranged from 6491 µs at 1088 K to 120 µs at 1490 K. The ignition delays for  = 1 are slightly higher than at  = 0.5. Due to their change in slope, trends from both data sets appear to converge as they move into lower temperatures, as in the higher pressure condition. It is not apparent whether modeling results show this merging. However, the change in OH chemistry towards the lower temperatures as observed in the ROP analysis at the higher pressure (20 atm) experiments could explain the behavior at this lower pressure condition. Kinetic modeling results underestimate ignition delay for both conditions above 1380 K, and the effect of equivalence ratio is captured by the model.

Figure 26 shows the effect of equivalence ratio at high dilution. The experimental ignition delay times for the lean mixture are slightly lower than stoichiometric values over above 1250 K and are similar below 1250 K. Thus, the behavior observed at low dilution is less pronounced at high dilution. Vanderover et al.22 observed the opposite behavior of leaner mixtures having longer ignition delays in the high pressure (50 atm), high dilution

(Ar = 99%) combustion of MCH/air. The model captures the observed trend in experimental data: the ignition delay times of stoichiometric conditions are slightly above those for lean conditions.

Figure 25 – Comparison of equivalence ratios of 0.5 and 1 (symbols) with Orme et al.21 model (lines) for 93% argon dilution at 2 atm.

Figure 26 – Comparison of equivalence ratios of 0.5 and 1 (symbols) with Orme et al.21 model (lines) for 98% argon dilution at 20 atm.

4.2.2.2 Effect of Dilution

Results for the two argon dilutions studied (93% and 98%) were compared to determine the effect of diluent concentration on ignition delay. Comparisons were made at 20 atm for lean (Figure 27) and stoichiometric (Figure 28) conditions. Figure 27 shows that higher ignition delay times were observed for 98% dilution. This can be attributed to the smaller collision frequency of fuel and oxygen molecules at 98% dilution and the larger amount of diluent to heat during combustion. The mechanism accurately estimates the effect of argon dilution across the temperature range, with values appearing to merge at high temperature.

Figure 27 – Comparison of argon concentrations of 93% and 98% (symbols) with Orme et al.21 model (lines) for equivalence ratio of 0.5 at 20 atm.

The effect of dilution at stoichiometric conditions (Figure 28) shows the same effect of argon concentration as observed for lean mixtures: higher ignition delay is observed for

55 more dilute mixtures. Kinetic modeling results capture this behavior well. It is also observed that the model captures the apparent merging of ignition delays at approximately

1540 K.

Figure 28 – Comparison of argon concentrations of 93% and 98% (symbols) with Orme et al.21 model (lines) for equivalence ratio of 1 at 20 atm.

4.2.2.3 Effect of Pressure

Figure 29 compares the ignition delay at 2 and 20 atm for low dilution, stoichiometric tests. It is clearly seen that the ignition delay times at 2 atm are longer than those at 20 atm. Kinetic modeling estimates the same effect; estimates are closer to experimental values over a larger temperature range for high pressure. Values are overestimated below 1000 K at 20 atm, and are underestimated above 1330 K at 2 atm.

Figure 30 shows the effect of pressure for lean mixtures. Experimental and kinetic

56 modeling results are similar to those at stoichiometric conditions: ignition delay decreases with an increase in pressure. It is observed in Figure 30 that low pressure values are estimated well over a larger temperature range in comparison to the stoichiometric results

(Figure 29). The model overestimates ignition delay at lean and stoichiometric conditions in the lower temperatures for high pressure combustion.

Figure 29 – Comparison of MCH ignition delays at pressures of 2 and 20 atm (symbols) with Orme et al.21 model (lines) for equivalence ratio of 1 at 93% argon dilution.

Figure 30 – Comparison of MCH ignition delays at pressures of 2 and 20 atm (symbols) with Orme et al.21 model (lines) for equivalence ratio of 0.5 at 93% argon dilution.

4.2.3 Comparison of MCH with Other HC’s

Ignition delay times collected in this investigation of MCH may be compared to ignition delay of other hydrocarbons at similar conditions: Ar = 93%, P = 20 atm and  =

0.5, 1.0 and 3.0. Hydrocarbons of different classes involved in the comparison are n- dodecane7 (alkane), 2-methylheptane47, 48 (branched alkane) and m-xylene8 (aromatic) and their data is given in Appendix H. Figures 31–33 compare ignition delay measurements of those hydrocarbons with MCH at lean (Figure 31), stoichiometric (Figure 32) and rich

(Figure 33) conditions. The ignition delay of MCH is similar to that of n-dodecane, 2- methylheptane and the n-dodecane/m-xylene (77%/23% by volume) blend at the three conditions. Like the other hydrocarbons, MCH ignition delay is smaller than m-xylene ignition delay at  = 0.5 and 1. However, at  = 3.0 the ignition delay of MCH is slightly

58 larger than the other hydrocarbons and becomes similar to m-xylene values at high temperature. A similar comparison for a few hydrocarbons was performed by Vermeer et al.34 at lower argon dilutions (70–80%) and pressures of 1–4 atm. They showed that the ignition delay times for MCH are longer than H2 and shorter than propane over a temperature range of 1000–1250 K. Figures 31–33 show that fuel structure and chemical bonding type alter the time in which fuels can undergo oxidation to form products. The chemical processes involved are highly dependent on fuel structure.

Figure 31 – Comparison of MCH with other hydrocarbons at lean conditions: 2- methylheptane,47, 48 n-dodecane,7 m-xylene,8 and n-dodecane/m-xylene blend.7

Figure 32 – Comparison of MCH with other hydrocarbons at stoichiometric conditions: 2-methylheptane,47, 48 n-dodecane,7 m-xylene,8 and n-dodecane/m-xylene blend.7

Figure 33 – Comparison of MCH with other hydrocarbons at rich conditions: 2- methylheptane,47 n-dodecane,7 m-xylene,8 and n-dodecane/m-xylene blend.7

CHAPTER 5

CONCLUSION

It was observed that the equivalence ratio affects the ignition delay time. For lower argon dilution (Ar = 93%) and higher pressure (P ~ 16 atm), the ignition delay time was longest at rich conditions. Ignition delay of stoichiometric mixtures were shorter than lean mixtures at lower temperatures (T ≤ 1250 K), but the opposite was observed at higher temperatures (T > 1250 K). Ignition delay of stoichiometric mixtures was observed to be longer than lean mixtures for high pressure and argon conditions, as well as low pressure and argon conditions. Pressure was also shown to affect the ignition delay; longer ignition delay times were observed at the low pressure (P = 2 atm). Higher argon dilution (Ar =

98%) was also shown to lengthen the time to ignition.

Ignition delay times were modeled using the detailed chemical kinetic mechanism for MCH combustion developed by Orme et al.21 and Pitz et al.10 Both models were run using constant pressure and constant U, V assumptions. Under both sets of assumptions, the models gave ignition delay times that are shorter than experimental results at high temperatures. However, reasonable agreement between models and experiments was observed at lower temperatures (T < 1350 K). The Orme et al. model using the constant

U, V assumption and pressure profile showed better agreement than the other approach

(both models) at low temperatures.

CHAPTER 6

FUTURE STUDIES

In the present investigation, ignition delay times of MCH were measured under different experimental conditions. Measurements were made for gas phase mixtures, and only chemical effects were taken into consideration. The physical effects should also be taken into consideration. Rich mixtures were not studied at low pressures (P = 2 atm) in this study. The current data set should be expanded by making these measurements. It would also be beneficial to characterize combustion products of MCH ignition under a wide range of experimental conditions.

Further attempts should be made to validate the Pitz et al.10 model with all the experimental data of this study. Changes to the model should be made to increase the agreement with experimental data.

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March 20-23, 2011, 2A13-RK73.

APPENDIX A

IGNITION DELAY TIMES MEASURED FROM END PLATE

USING OH*, CH*, WL AND PRESSURE

Ar P5 T5 tign, WL tign, OH tign, CH tign, P  (%) (atm)1 (K)1 (μs)2 (μs)3 (μs)4 (μs)5 0.5 93 14.466 948.77 7251.3 7269.8 7344.3 4658.3 0.5 93 14.716 994.27 4522.2 4509.0 4540.4 4361.8 0.5 93 14.606 1032.41 3300.4 3294.1 3283.4 2985.8 0.5 93 10.996 1076.24 2241.6 2243.5 2213.4 2153.7 0.5 93 16.746 1174.50 771.9 788.5 785.2 734.7 0.5 93 16.836 1220.20 437.8 421.2 453.5 370.2 0.5 93 16.516 1255.07 360.0 359.4 351.1 288.3 0.5 93 16.526 1336.85 145.3 145.0 144.9 148.8 0.5 93 16.426 1431.01 71.5 68.3 77.1 55.3 0.5 93 15.786 1517.10 28.8 28.8 32.0 36.4 1.0 93 16.786 1131.60 1030.3 1048.3 1023.7 1015.1 1.0 93 16.686 1380.63 130.0 126.0 130.0 144.0 1.0 93 16.456 1238.45 386.3 421.0 379.6 404.6 1.0 93 11.126 1045.79 2452.6 2474.3 2417.2 2503.2 1.0 93 14.126 925.53 5657.4 5658.9 5650.7 5736.5 1.0 93 14.786 1004.48 3132.4 3132.4 3132.4 3132.4 1.0 93 15.906 1394.75 121.7 122.0 108.0 124.9 1.0 93 15.906 1453.84 88.1 88.8 70.8 59.0 1.0 93 16.406 1296.69 239.0 240.2 235.1 236.9 1.0 93 16.576 1179.34 670.7 671.1 654.3 585.0 1.0 93 16.666 1344.16 163.6 157.6 155.2 157.6 1.0 93 15.016 982.35 4074.8 3891.6 3957.6 3934.0 1Adjusted for calibration. 2Ignition delay time measured from white light signal, 3OH 4 5 6 signal, CH signal and pressure transducer. Test for P5 ~ 16 atm.

Ar P5 T5 tign, WL tign, OH tign, CH tign, P  (%) (atm)1 (K)1 (μs)2 (μs)3 (μs)4 (μs)5 3.0 93 17.226 1242.34 812.0 651.1 732.4 555.8 3.0 93 17.346 1292.04 600.8 476.9 548.7 419.1 3.0 93 17.756 1121.39 1848.5 1338.3 1657.0 1103.0 3.0 93 17.936 1191.69 1188.3 787.6 882.7 651.4 3.0 93 19.206 1421.99 438.1 321.9 379.7 281.2 3.0 93 17.116 1198.48 891.3 701.7 830.7 659.7 3.0 93 17.216 1310.77 522.3 410.9 484.9 344.9 3.0 93 17.406 1056.96 3513.0 1705.8 2778.6 1307.7 3.0 93 17.446 1013.08 3883.1 2162.4 3337.7 1740.1 3.0 93 17.946 987.37 5970.8 5781.8 5241.7 1186.5 3.0 93 16.906 941.71 6875.2 6875.2 6875.2 4477.0 3.0 93 17.806 1002.67 6079.6 6700.5 6634.7 1981.0 3.0 93 16.906 1018.54 4743.1 6156.5 5778.2 1537.5 3.0 93 17.526 1086.18 2064.9 2857.2 2251.6 1219.4 3.0 93 17.216 1133.60 1621.2 1655.3 1499.6 757.0 3.0 93 17.116 1146.05 1468.1 1526.6 1300.4 707.4 3.0 93 16.886 1309.57 548.6 721.3 352.7 237.8 0.5 98 14.506 1065.84 5642.5 5733.9 5610.6 --- 0.5 98 12.586 1147.66 3030.3 3029.4 3007.4 --- 0.5 98 17.026 1266.26 922.1 910.1 891.8 --- 0.5 98 16.286 1537.73 69.5 70.5 70.5 --- 0.5 98 16.176 1274.36 611.9 624.6 609.8 --- 0.5 98 14.476 1088.80 4821.2 4808.0 4759.5 --- 0.5 98 16.626 1351.61 283.6 284.7 246.3 --- 0.5 98 15.686 1638.13 38.5 39.3 34.7 --- 0.5 98 14.686 1073.39 5040.0 5040.0 5040.0 --- 0.5 98 14.766 1101.36 4160.0 4160.0 4160.0 --- 0.5 98 14.396 1061.35 5050.1 5014.1 5033.7 --- 0.5 98 15.196 1278.44 712.6 698.1 696.6 --- 0.5 98 16.016 1362.96 313.3 314.8 297.3 --- 0.5 98 16.336 1566.16 63.6 61.9 61.9 --- 0.5 98 17.036 1343.08 274.3 250.6 266.8 --- 0.5 98 16.606 1208.08 1833.5 1618.8 1770.7 --- 0.5 98 14.926 1388.52 213.8 176.1 176.1 --- 1Adjusted for calibration. 2Ignition delay time measured from white light signal, 3 4 5 6 OH signal, CH signal and pressure transducer. Test for P5 ~ 16 atm.

Ar P5 T5 tign, WL tign, OH tign, CH tign, P  (%) (atm)1 (K)1 (μs)2 (μs)3 (μs)4 (μs)5 1.0 98 12.466 1128.35 4241.3 4204.3 4185.7 --- 1.0 98 16.236 1511.59 124.9 136.4 136.4 --- 1.0 98 14.716 1040.57 7537.6 7552.8 7552.8 --- 1.0 98 14.036 1499.82 89.6 98.8 128.5 --- 1.0 98 15.816 1797.19 23.6 23.9 17.1 --- 1.0 98 15.966 1713.11 41.0 41.2 40.5 --- 1.0 98 15.576 1149.47 2070.0 2070.0 2070.0 --- 1.0 98 16.696 1235.55 645.6 643.2 643.0 --- 1.0 98 17.286 1330.14 63.0 57.0 62.5 --- 1.0 98 15.636 1648.18 291.7 282.9 239.5 --- 1.0 98 16.626 1403.97 1082.0 1018.7 1090.2 --- 1.0 98 16.626 1265.09 4241.3 4204.3 4185.7 --- 0.5 93 1.937 1433.33 176.0 228.4 204.1 89.2 0.5 93 2.067 1088.49 6383.1 6685.1 5902.2 1858.8 0.5 93 2.077 1346.13 359.6 344.9 360.4 501.0 0.5 93 2.057 1257.07 725.8 1078.5 1457.0 1427.7 0.5 93 2.027 1536.62 106.5 151.3 126.0 133.0 0.5 93 2.007 1146.81 2353.9 2346.6 2301.8 563.6 0.5 93 2.027 1197.92 1525.7 1542.9 1506.8 1578.9 0.5 93 1.867 1493.76 125.0 125.0 125.0 125.0 1.0 93 1.927 1423.80 310.8 316.9 304.9 253.2 1.0 93 2.047 1206.41 1785.4 1778.5 1668.7 1793.2 1.0 93 1.957 1170.58 1980.3 2006.4 1946.9 1889.8 1.0 93 1.947 1395.03 384.4 380.4 376.9 371.7 1.0 93 1.987 1479.79 228.1 240.7 237.8 185.2 1.0 93 2.007 1296.69 994.2 1025.8 1029.7 793.8 1.0 93 1.977 1252.11 1214.6 1224.0 1218.4 1209.3 1.0 93 2.037 1339.73 522.0 522.0 522.0 522.0 1.0 93 2.027 1232.69 1682.2 1681.1 1643.9 1549.8 1.0 93 2.017 1248.16 1279.8 1273.4 1219.2 1238.0 1Adjusted for calibration. 2Ignition delay time measured from white light signal, 3 4 5 6 7 OH signal, CH signal and pressure transducer. Test for P5 ~ 16 atm. Test for P5 = 2 atm.

APPENDIX B

UNCERTAINTIES ON POST-REFLECTED PRESSURES AND TEMPERATURES

T1 P1 US T5 P5 Us T5, T1 T5, Us T5, mix P5, T1 P5, P1 P5, Us P5, mix T5 P5  1 2 -1 (K) (atm) (cm s ) (K) (atm) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)  295.1 0.955 63464 948.8 14.463 1.46 0.05 2.48 0.01 0.53 0.01 4.61 0.04 2.48 4.64 0.25 295.1 0.889 65269 994.3 14.713 1.48 0.05 2.52 0.01 0.52 0.02 4.61 0.04 2.52 4.64 0.27 295.1 0.824 66747 1032.4 14.603 1.50 0.04 2.56 0.01 0.51 0.02 4.62 0.04 2.56 4.65 0.29 295.1 0.574 68410 1076.2 10.993 1.52 0.04 2.61 0.01 0.51 0.02 4.62 0.06 2.61 4.65 0.42 295.1 0.659 72007 1174.5 16.743 1.57 0.04 2.72 0.01 0.49 0.02 4.65 0.05 2.72 4.67 0.37 295.1 0.593 73624 1220.2 16.833 1.59 0.04 2.76 0.02 0.49 0.02 4.66 0.06 2.76 4.68 0.41 295.1 0.461 74835 1255.1 16.513 1.61 0.04 2.80 0.02 0.48 0.03 4.67 0.07 2.80 4.69 0.52 295.1 0.527 77606 1336.8 16.523 1.64 0.04 2.87 1.00 0.48 0.03 4.69 0.06 2.87 4.71 0.46 295.1 0.705 80685 1431.0 16.423 1.68 0.03 2.97 0.02 0.47 0.02 4.72 0.05 2.97 4.75 0.34 295.1 0.749 83405 1517.1 15.783 1.72 0.03 3.05 0.02 0.46 0.02 4.75 0.05 3.05 4.78 0.32 295.1 0.922 63125 925.5 14.124 1.46 0.05 2.40 0.01 0.52 0.01 4.63 0.04 2.40 4.66 0.28 295.1 0.873 65475 982.3 15.014 1.49 0.05 2.46 0.01 0.51 0.02 4.64 0.04 2.46 4.67 0.30 295.1 0.824 66371 1004.5 14.784 1.50 0.05 2.49 0.01 0.51 0.02 4.65 0.04 2.49 4.67 0.32 295.1 0.574 68014 1045.8 11.124 1.52 0.04 2.54 0.01 0.50 0.02 4.66 0.06 2.54 4.68 0.46 1 2 Uncertainty of T1 is ± 1 K. Uncertainty of P1 is ± 0.1 Torr, and the uncertainty of mixture composition is ± 0.1 Torr for each partial 3 4 pressure. Conditions:  = 0.5, Ar = 93%, P5 ~ 16 atm. Conditions:  = 1.0, Ar = 93%, P5 ~ 16 atm.

T1 P1 US T5 P5 Us T5, T1 T5, Us T5, mix P5, T1 P5, P1 P5, Us P5, mix T5 P5  1 2 -1 (K) (atm) (cm s ) (K) (atm) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)  295.1 0.750 71319 1131.6 16.783 1.56 0.04 2.63 0.01 0.49 0.02 4.68 0.04 2.63 4.70 0.35 295.1 0.687 73098 1179.3 16.573 1.58 0.04 2.68 0.01 0.48 0.02 4.70 0.05 2.68 4.72 0.38 295.1 0.626 75248 1238.4 16.453 1.61 0.04 2.75 0.01 0.47 0.02 4.72 0.05 2.74 4.74 0.42 5 295.1 0.576 77312 1296.7 16.403 1.64 0.04 2.81 0.02 0.47 0.02 4.74 0.06 2.81 4.76 0.46 5 295.1 0.551 78958 1344.2 16.663 1.66 0.04 2.85 0.02 0.46 0.02 4.76 0.06 2.85 4.78 0.48 5 295.1 0.527 80201 1380.6 16.683 1.68 0.04 2.89 0.02 0.46 0.03 4.77 0.06 2.89 4.80 0.50 5 295.1 0.494 80677 1394.7 15.903 1.68 0.03 2.91 0.02 0.46 0.03 4.78 0.07 2.91 4.80 0.53 5 295.1 0.461 82642 1453.8 15.903 1.71 0.03 2.96 0.02 0.45 0.03 4.81 0.07 2.96 4.83 0.57 5 295.1 0.889 65789 941.7 16.904 1.49 0.05 2.31 0.01 0.49 0.02 4.69 0.04 2.31 4.72 0.37 5 295.1 0.856 67846 987.4 17.944 1.52 0.05 2.37 0.01 0.49 0.02 4.71 0.04 2.37 4.73 0.38 5 295.1 0.824 68525 1002.7 17.804 1.53 0.05 2.39 0.01 0.48 0.02 4.72 0.04 2.39 4.74 0.40 5 295.1 0.791 68983 1013.1 17.444 1.53 0.05 2.40 0.01 0.48 0.02 4.72 0.04 2.40 4.74 0.42 5 295.1 0.758 69223 1018.5 16.904 1.53 0.05 2.41 0.01 0.48 0.02 4.72 0.04 2.41 4.75 0.43 5 295.1 0.725 70888 1057.0 17.404 1.56 0.05 2.45 0.01 0.48 0.02 4.74 0.04 2.45 4.76 0.45 5 295.1 0.692 72134 1086.2 17.524 1.57 0.05 2.49 0.01 0.47 0.02 4.76 0.04 2.49 4.78 0.47 5 295.1 0.659 73611 1121.4 17.754 1.59 0.05 2.53 0.01 0.47 0.02 4.77 0.05 2.53 4.80 0.50 5 295.1 0.626 74117 1133.6 17.214 1.60 0.05 2.55 0.01 0.47 0.02 4.78 0.05 2.55 4.80 0.52 5 295.1 0.609 74631 1146.1 17.114 1.60 0.04 2.56 0.01 0.47 0.02 4.79 0.05 2.56 4.81 0.54 1 5 2 Uncertainty of T1 is ± 1 K. Uncertainty of P1 is ± 0.1 Torr, and the uncertainty of mixture composition is ± 0.1 Torr for each partial 5 3 4 pressure. Conditions:  = 1.0, Ar = 93%, P5 ~ 16 atm. Conditions:  = 3.0, Ar = 93%, P5 ~ 16 atm.

T1 P1 US T5 P5 Us T5, T1 T5, Us T5, mix P5, T1 P5, P1 P5, Us P5, mix T5 P5 

(K)1 (atm)2 (cm s-1) (K) (atm) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)  295.1 0.593 76487 1191.7 17.933 1.63 0.04 2.61 0.01 0.46 0.02 4.81 0.05 2.61 4.83 0.55 295.1 0.560 76760 1198.5 17.113 1.63 0.04 2.62 0.01 0.46 0.02 4.82 0.05 2.62 4.84 0.59 295.15 0.527 78503 1242.3 17.223 1.65 0.04 2.67 0.01 0.45 0.03 4.84 0.06 2.67 4.86 0.62 5 295.1 0.494 80438 1292.0 17.343 1.68 0.04 2.73 0.01 0.45 0.03 4.87 0.06 2.73 4.89 0.67 5 295.1 0.469 81111 1309.6 16.883 1.69 0.04 2.75 0.01 0.45 0.03 4.88 0.06 2.75 4.90 0.70 5 295.1 0.477 81157 1310.8 17.213 1.69 0.04 2.75 0.01 0.45 0.03 4.88 0.06 2.75 4.90 0.69 5 295.1 0.461 85314 1422.0 19.203 1.74 0.04 2.87 0.02 0.44 0.03 4.95 0.07 2.87 4.97 0.71 5 295.1 0.105 68868 1088.5 2.064 1.53 0.04 2.62 0.08 0.50 0.13 4.64 0.33 2.62 4.68 2.30 5 295.1 0.093 71011 1146.8 2.004 1.56 0.04 2.68 0.09 0.49 0.14 4.65 0.37 2.68 4.70 2.59 5 295.1 0.087 72840 1197.9 2.024 1.58 0.04 2.74 0.10 0.49 0.15 4.67 0.39 2.74 4.71 2.77 5 295.1 0.081 74904 1257.1 2.054 1.61 0.04 2.80 0.12 0.48 0.16 4.69 0.42 2.80 4.73 2.97 5 295.1 0.073 77915 1346.1 2.074 1.65 0.03 2.89 0.14 0.47 0.18 4.72 0.46 2.89 4.76 3.29 5295. 295.1 0.061 80759 1433.3 1.934 1.68 0.03 2.97 0.17 0.46 0.21 4.75 0.55 2.97 4.81 3.93 4 295.11 0.056 82676 1493.8 1.86 1.71 0.03 3.03 0.20 0.46 0.24 4.77 0.61 3.03 4.84 4.35 295.1 0.058 84010 1536.6 2.024 1.73 0.03 3.07 0.20 0.45 0.23 4.79 0.59 3.07 4.85 4.20 295.1 0.082 72775 1170.6 1.955 1.58 0.04 2.67 0.10 0.48 0.16 4.69 0.40 2.67 4.74 3.21 295.1 0.081 74090 1206.4 2.045 1.60 0.04 2.71 0.10 0.48 0.16 0.71 0.41 2.71 4.75 3.23 295.1 0.077 75042 1232.7 2.025 1.61 0.04 2.74 0.11 0.48 0.17 4.71 0.43 2.74 4.76 3.40 295.1 0.075 75596 1248.2 2.015 1.62 0.04 2.76 0.12 0.47 0.18 4.72 0.44 2.76 4.77 3.49 295.1 0.073 75737 1252.1 1.975 1.62 0.04 2.76 0.12 0.47 0.18 4.72 0.45 2.76 4.77 3.58 295.1 0.070 77312 1296.7 2.005 1.64 0.04 2.81 0.13 0.47 0.19 4.74 0.47 2.81 4.79 3.75 295.1 0.067 78806 1339.7 2.035 1.66 0.04 2.85 0.14 0.46 0.20 4.76 0.49 2.85 4.81 3.90 1 2 Uncertainty of T1 is ± 1 K. Uncertainty of P1 is ± 0.1 Torr, and the uncertainty of mixture composition is ± 0.1 Torr for each partial 5 3 4 5 pressure. Conditions:  = 3.0, Ar = 93%, P5 ~ 16 atm. Conditions:  = 0.5, Ar = 93%, P5 = 2 atm. Conditions:  = 1.0, Ar = 93%, P5 = 2 atm. 74

T1 P1 US T5 P5 Us T5, T1 T5, Us T5, mix P5, T1 P5, P1 P5, Us P5, mix T5 P5 

(K)1 (atm)2 (cm s-1) (K) (atm) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)  295.1 0.060 80686 1395.0 1.943 1.68 0.03 2.91 0.16 0.46 0.22 4.78 0.55 2.91 4.84 4.37 295.1 0.058 81649 1423.8 1.923 1.70 0.03 2.93 0.17 0.46 0.23 4.79 0.57 2.94 4.85 4.57 295.15 0.056 83492 1479.8 1.983 1.72 0.03 2.99 0.18 0.45 0.24 4.82 0.59 2.99 4.88 4.73 5 295.1 0.856 66211 1061.4 14.394 1.50 0.04 2.64 0.01 0.51 0.02 4.59 0.04 2.64 4.62 0.99 5 295.1 0.856 66371 1065.8 14.504 1.50 0.04 2.65 0.01 0.52 0.02 4.59 0.04 2.65 4.62 0.99 5 295.1 0.856 66639 1073.4 14.684 1.50 0.04 2.66 0.01 0.51 0.02 4.59 0.04 2.66 4.62 0.99 5 295.1 0.824 67183 1088.8 14.474 1.51 0.04 2.67 0.01 0.51 0.02 4.59 0.04 2.67 4.62 1.03 5 295.1 0.824 67623 1101.4 14.764 1.51 0.04 2.68 0.01 0.51 0.02 4.60 0.04 2.68 4.62 1.03 5 295.1 0.653 69223 1147.7 12.584 1.53 0.04 2.73 0.02 0.50 0.02 4.60 0.06 2.73 4.63 1.29 5 295.1 0.791 71258 1208.1 16.604 1.56 0.03 2.79 0.01 0.50 0.02 4.61 0.05 2.79 4.64 1.07 5 295.1 0.750 73165 1266.3 17.024 1.59 0.03 2.85 0.02 0.49 0.02 4.62 0.05 2.85 4.65 1.13 5 295.1 0.705 73426 1274.4 16.174 1.59 0.03 2.85 0.02 0.49 0.02 4.62 0.05 2.85 4.65 1.20 5 295.1 0.659 73558 1278.4 15.194 1.59 0.03 2.86 0.02 0.49 0.02 4.62 0.05 2.86 4.65 1.28 295.1 0.682 75611 1343.1 17.034 1.62 0.03 2.92 0.02 0.48 0.02 4.64 0.05 2.92 4.66 1.24 295.1 0.659 75878 1351.6 16.624 1.62 0.03 2.93 0.02 0.48 0.02 4.64 0.05 2.93 4.66 1.28 295.1 0.626 76231 1363.0 16.014 1.62 0.03 2.94 0.02 0.48 0.02 4.64 0.06 2.94 4.67 1.35 295.1 0.566 77022 1388.5 14.924 1.64 0.03 2.96 0.02 0.48 0.02 4.65 0.06 2.96 4.67 1.49 295.1 0.527 81486 1537.7 16.284 1.69 0.03 3.09 0.03 0.46 0.03 4.69 0.07 3.09 4.71 1.60 295.1 0.514 82309 1566.2 16.334 1.70 0.03 3.12 0.03 0.46 0.03 4.70 0.07 3.12 4.72 1.64 295.1 0.461 84358 1638.1 15.684 1.73 0.03 3.18 0.03 0.46 0.03 4.72 0.08 3.18 4.74 1.83 1 2 Uncertainty of T1 is ± 1 K. Uncertainty of P1 is ± 0.1 Torr, and the uncertainty of mixture composition is ± 0.1 Torr for each partial 3 4 pressure. Conditions:  = 1.0, Ar = 93%, P5 = 2 atm. Conditions:  = 0.5, Ar = 98%, P5 ~ 16 atm.

T1 P1 US T5 P5 Us T5, T1 T5, Us T5, mix P5, T1 P5, P1 P5, Us P5, mix T5 P5 

(K)1 (atm)2 (cm s-1) (K) (atm) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)  295.1 0.889 65684 1040.6 14.713 1.49 0.05 2.30 0.01 0.49 0.02 4.69 0.04 2.30 4.71 12.1 295.1 0.653 68810 1128.3 12.463 1.53 0.05 2.39 0.01 0.48 0.02 4.72 0.05 2.39 4.74 16.6 295.15 0.791 69543 1149.5 15.573 1.54 0.05 2.41 0.01 0.48 0.02 4.72 0.04 2.41 4.75 13.60 5 8 295.1 0.750 72453 1235.6 16.693 1.58 0.05 2.49 0.01 0.47 0.02 4.76 0.04 2.49 4.78 14.4 5 4 295.1 0.718 73426 1265.1 16.623 1.59 0.05 2.52 0.01 0.47 0.02 4.77 0.04 2.52 4.79 15.1 5 0 295.1 0.687 75526 1330.1 17.283 1.62 0.04 2.58 0.01 0.46 0.02 4.80 0.04 2.58 4.82 15.7 5 5 295.1 0.606 77842 1404.0 16.623 1.65 0.04 2.64 0.01 0.45 0.02 4.83 0.05 2.64 4.85 17.9 5 4 295.1 0.461 80752 1499.8 14.033 1.68 0.04 2.73 0.02 0.45 0.03 4.87 0.07 2.73 4.90 23.8 5 2 295.1 0.527 81103 1511.6 16.233 1.69 0.04 2.74 0.01 0.45 0.03 4.88 0.06 2.74 4.90 20.7 5 3 295.1 0.444 85064 1648.2 15.633 1.74 0.04 2.86 0.02 0.44 0.03 4.95 0.07 2.85 4.96 24.8 5 1 295.1 0.428 86885 1713.1 15.963 1.76 0.03 2.91 0.02 0.43 0.03 4.98 0.07 2.91 5.00 25.8 5 6 295.1 0.395 89188 1797.2 15.813 1.79 0.03 2.98 0.02 0.43 0.03 5.02 0.08 2.98 5.04 28.1 1 5 2 8 Uncertainty of T1 is ± 1 K. Uncertainty of P1 is ± 0.1 Torr, and the uncertainty of mixture composition is ± 0.1 Torr for each partial 5 3 8 pressure. Conditions:  = 1.0, Ar = 98%, P5 ~ 16 atm.

APPENDIX C

UNCERTAINTIES ON IGNITION DELAY TIMES

Ar T5 P5 ign T5 P5 ign,T5 ign,P5 ign  (%) (K) (atm) (s) (%) (%) (%) (%) (%)

0.5 93 1433.3 1.931 228.4 2.97 4.81 30.01 2.89 30.15 0.5 93 1088.5 2.061 6685.1 2.62 4.68 34.82 2.82 34.94 0.5 93 1346.1 2.071 344.9 2.89 4.76 31.03 2.87 31.16 0.5 93 1257.1 2.051 1078.5 2.80 4.73 32.20 2.85 32.32 0.5 93 1536.6 2.021 151.3 3.07 4.85 28.91 2.92 29.05 0.5 93 1146.8 2.001 2346.6 2.68 4.70 33.84 2.83 33.96 0.5 93 1197.9 2.021 1542.9 2.74 4.71 33.05 2.84 33.17 0.5 93 1493.8 1.861 125 3.03 4.84 29.36 2.91 29.50 1.0 93 1423.8 1.921 316.9 2.94 4.85 26.19 3.13 26.38 1.0 93 1206.4 2.041 1778.5 2.71 4.75 28.54 3.06 28.70 1.0 93 1170.6 1.951 2006.4 2.67 4.74 29.00 3.05 29.16 6 1.0 93 1395.0 1.941 380.4 2.91 4.84 26.47 3.12 26.65 1.0 93 1479.8 1.981 240.7 2.99 4.88 25.68 3.14 25.87 1.0 93 1296.7 2.001 1025.8 2.81 4.79 27.49 3.09 27.66 1.0 93 1252.1 1.971 1224.0 2.76 4.77 27.99 3.07 28.16 1.0 93 1339.7 2.031 522.0 2.85 4.81 27.03 3.10 27.20 1.0 93 1232.7 2.021 1681.1 2.74 4.76 28.22 3.07 28.39 1.0 93 1248.2 2.011 1273.4 2.76 4.77 28.04 3.07 28.20

1 Test for P5 = 2 atm.

Ar T5 P5 ign T5 P5 ign,T5 ign,P5 ign  (%) (K) (atm) (s) (%) (%) (%) (%) (%)

0.5 93 948.8 14.461 7269.8 2.48 4.64 37.82 2.79 37.92 0.5 93 994.3 14.711 4509.0 2.52 4.64 36.67 2.79 36.78 0.5 93 1032.4 14.601 3294.1229 2.56 4.65 35.91 2.80 36.02 127 0.5 93 1076.2 10.991 2243.5 2.61 4.65 35.09 2.80 35.20 759 0.5 93 1174.5 16.741 788.5 2.72 4.67 33.44 2.81 33.56 921 0.5 93 1220.2 16.831 421.2 2.76 4.68 32.75 2.82 32.87 0.5 93 1255.1 16.511 359.4 2.80 4.69 32.25 2.82 32.37 0.5 93 1336.8 16.521 145.0 2.87 4.71 31.05 2.84 31.18 0.5 93 1431.0 16.421 68.3 2.97 4.75 29.99 2.86 30.13 0.5 93 1517.1 15.781 28.8 3.05 4.78 29.05 2.87 29.19 1.0 93 1131.6 16.781 1048.3 2.63 4.70 29.50 3.03 29.66 1.0 93 1380.6 16.681 126.0 2.89 4.80 26.58 3.09 26.75 1.0 93 1238.4 16.451 421.0 2.74 4.74 28.13 3.05 28.29 1.0 93 1045.8 11.121 2474.3 2.54 4.68 30.77 3.02 30.92 1.0 93 925.5 14.121 5658.9 2.40 4.66 32.89 3.00 33.03 1.0 93 1004.5 14.781 3132.4 2.49 4.67 31.44 3.01 31.59 1.0 93 1394.7 15.901 122.0 2.91 4.80 26.43 3.09 26.62 1.0 93 1453.8 15.901 88.8 2.96 4.83 25.87 3.11 26.05 1.0 93 1296.7 16.401 240.2 2.81 4.76 27.46 3.07 27.63 1.0 93 1179.3 16.571 671.1 2.68 4.72 28.86 3.04 29.02 1.0 93 1344.2 16.661 157.6 2.85 4.78 26.95 3.08 27.12 1.0 93 982.3 15.011 3891.6 2.46 4.67 31.83 3.01 31.97 1 Test for P5 ~ 16 atm.

Ar T5 P5 ign T5 P5 ign,T5 ign,P5 ign  (%) (K) (atm) (s) (%) (%) (%) (%) (%) 3.0 93 1242.3 17.221 651.1 2.67 4.86 5.25 -----2 5.25 3.0 93 1292.0 17.341 476.9 2.73 4.89 5.16 -----2 5.16 3.0 93 1121.4 17.751 1338.3 2.53 4.80 5.51 -----2 5.51 3.0 93 1191.7 17.931 787.6 2.61 4.83 5.35 -----2 5.35 3.0 93 1422.0 19.201 321.9 2.87 4.97 4.93 -----2 4.93 3.0 93 1198.5 17.111 701.7 2.62 4.84 5.34 -----2 5.34 3.0 93 1310.8 17.211 410.9 2.75 4.90 5.12 -----2 5.12 3.0 93 1057.0 17.401 1705.8 2.45 4.76 5.67 -----2 5.67 3.0 93 1013.1 17.441 2162.4 2.40 4.74 5.79 -----2 5.79 3.0 93 987.4 17.941 5781.8 2.37 4.73 5.86 -----2 5.86 3.0 93 941.7 16.901 6875.2 2.31 4.72 6.00 -----2 6.00 3.0 93 1002.7 17.801 6700.5 2.39 4.74 5.82 -----2 5.82 3.0 93 1018.5 16.901 6156.5 2.41 4.75 5.77 -----2 5.77 3.0 93 1086.2 17.521 2857.2 2.49 4.78 5.59 -----2 5.59 3.0 93 1133.6 17.211 1655.3 2.55 4.80 5.48 -----2 5.48 3.0 93 1146.1 17.111 1526.6 2.56 4.81 5.45 -----2 5.45 3.0 93 1309.6 16.881 721.3 2.75 4.90 5.12 -----2 5.12 1 2 Test for P5 ~ 16 atm. Not available due to lack of correlation; thus, ignition delay uncertainty only due to temperature.

Ar T5 P5 ign T5 P5 ign,T5 ign,P5 ign  (%) (K) (atm) (s) (%) (%) (%) (%) (%) 0.5 98 1065.8 14.501 5733.9 2.65 4.62 35.92 2.78 36.03 0.5 98 1147.7 12.581 3029.4 2.73 4.63 34.40 2.79 34.52 0.5 98 1266.3 17.021 910.0 2.85 4.65 32.50 2.80 32.62 0.5 98 1537.7 16.281 70.5 3.09 4.71 29.07 2.84 29.21 0.5 98 1274.4 16.171 624.6 2.85 4.65 32.38 2.80 32.50 0.5 98 1088.8 14.471 4808.0 2.67 4.62 35.48 2.78 35.59 0.5 98 1351.6 16.621 284.7 2.93 4.66 31.30 2.81 31.43 0.5 98 1638.1 15.681 39.3 3.18 4.74 28.03 2.85 28.18 0.5 98 1073.4 14.681 5040.0 2.66 4.62 35.78 2.78 35.88 0.5 98 1101.4 14.761 4160.0 2.68 4.62 35.24 2.78 35.35 0.5 98 1061.4 14.391 5014.1 2.64 4.62 36.01 2.78 36.12 0.5 98 1278.4 15.191 698.1 2.86 4.65 32.32 2.80 32.44 0.5 98 1363.0 16.011 314.8 2.94 4.67 31.15 2.81 31.28 0.5 98 1566.2 16.331 61.9 3.12 4.72 28.77 2.84 28.91 0.5 98 1343.1 17.031 250.6 2.92 4.66 31.41 2.81 31.54 0.5 98 1208.1 16.601 1618.8 2.79 4.64 33.39 2.79 33.51 0.5 98 1388.5 14.921 176.1 2.96 4.67 30.82 2.81 30.95 1.0 98 1128.3 12.461 4204.3 2.39 4.74 26.85 3.05 27.02 1.0 98 1511.6 16.231 136.4 2.74 4.90 22.98 3.16 23.20 1.0 98 1040.6 14.711 7552.8 2.30 4.71 28.09 3.04 28.25 1.0 98 1499.8 14.031 98.8 2.73 4.90 23.07 3.15 23.29 1.0 98 1797.2 15.811 23.9 2.98 5.04 21.03 3.24 21.27 1.0 98 1713.1 15.961 41.2 2.91 5.00 21.55 3.22 21.79 1.0 98 1149.5 15.571 2070.0 2.41 4.75 26.58 3.06 26.75 1.0 98 1235.6 16.691 1393.3 2.49 4.78 25.56 3.08 25.74 1.0 98 1330.1 17.281 643.2 2.58 4.82 24.57 3.11 24.77 1.0 98 1648.2 15.631 57.0 2.85 4.96 21.98 3.20 22.21 1.0 98 1404.0 16.621 282.9 2.64 4.85 23.88 3.13 24.08 1.0 98 1265.1 16.621 1018.7 2.52 4.79 25.23 3.09 25.42

1 Test for P5 ~ 16 atm.

APPENDIX D

CONDITION FOR UNCERTAINTY ANALYSIS ON P5 AND T5

Experiment: 12-03-10-3mch1 Input Conditions: Property Value Uncertainty

T1 (K): 2.9515e+02 1.0000e+00 (0.339%)

P1 (atm.): 8.2352e-01 1.3158e-04 (0.016%) Molar Fraction species 1: 9.3000e-01 Molar Fraction species 2: 6.3913e-02 Molar Fraction species 3: 6.0870e-03 PHI: 1.0000e+00 0.319% Intial Conditions: Property Value Uncertainty Us (m/s): 6.6371e+02 1.002e+01 (1.510%) M: 2.1086e+00 Mixture Molecular Weight (kg/kmol): 3.9795e-02 Mixture Specific Heat Ratio: 1.6066e+00 ------Post Incident/Reflected Shock Conditions:

Property Value Total T1 P1 Ui Mixture Uncertainty Effect Effect Effect Effect

T2 (K) 6.2215e+02 11.33 (1.821%) 0.127% 0.000% 1.817% 0.004%

P2 (atm) 4.3691e+00 0.140 (3.199%) 0.348% 0.016% 3.180% 0.023% 81

T5 (K) 1.004.5e+03 24.99 (2.488%) 0.047% 0.000% 2.488% 0.008%

P5 (atm) 1.4777e+01 0.690 (4.673%) 0.510% 0.016% 4.726% 0.041%

APPENDIX E

CHEMKIN INPUT FILE

TITL mch_=.5 -Non-Heated shock tube work

P1A 0.840003947! ATM

T1 295.15! K VSHK 66335.7! CM/SEC INIT mch 0.0155555556! MOLE FRACTION

INIT O2 0.0544444444! MOLE FRACTION INIT Ar 0.93 TSTR 0. TEND 1.00E-5 DT 100.E-7 DIA 5.08 !CM**2 VISC 224.3E-6 RTOL 1.E-4 ATOL 1.E-18 CONC RSHK END

APPENDIX F

SAMPLE FILE FOR FUEL MIXTURE PREPARATION

Fuel mixture on 07/26/11 for MCH at  = 5, Ar = 93%. After evacuating the SPU, the pressure readout showed (without tare) the pressure in the SPU with the canister and entire manifold open was 0.3 Torr. The pressure fell from 42.4 Torr to 41.7 Torr after 2 min of injecting the liquid fuel to the glass sample bulb with the canister isolated. Once the canister is opened, the temporal evolution of pressure as the liquid fuel evaporates into it is shown below.

Time (min) Pressure (Torr) 0 0.5 7 4.4 10 5.8 15 8.2 44 18.2 55 20.7 58 21.3 64 22.4 66 22.8 80 23.6 91 23.6 128 23.5

Thus, the actual pressure of fuel is 23.5 - 0.3 = 23.2 Torr. To make the fuel mixture for 

= 5, Ar = 93%, the actual amount of argon required is 1003.9 Torr. Therefore, we need to add argon till the final read out pressure shows 1003.9 + 0.3 = 1004.2 Torr.

APPENDIX G

EXAMPLE OF END PLATE VELOCITY CALCULATIONS

The end plate velocity calculation from the three incident times for an experiment at P5 = 15.43 atm and T5 = 1061 K is explained. The incident times for this experiment (t1, t2 and t3) were measured with an oscilloscope as 608.94 µs, 1126.84 µs and 97.89 µs, respectively. The corresponding distances d1, d2 and d3 for times t1, t2 and t3 are 45.5 cm,

81 cm and 10 cm, respectively. The velocities V1, V2 and V3 are calculated by dividing

-1 -1 distance by time. This results in values of V1 = 74719.14 cm s , V2 = 71882.43 cm s and

-1 V3 = 102150.6 cm s . The distances d4, d5 and d6 and times t4, t5 and t6 can be calculated

-1 -1 using equations 3.2 and 3.3. The velocities V4 = 69464.51 cm s , V5 = 68546.98 cm s

-1 and V6 = 69002.7 cm s were obtained dividing distance by time for values obtained from equations 3.2 and 3.3.

The distances 4, 5 and 6 were calculated using equation 3.4, 3.5 and 3.6. The distances are shown in the table below. The table shows the distance from the farthest pressure transducer to the mid points of two of the sidewall pressure transducers and the corresponding velocities.

Distance  (cm) Velocity (cm s-1)

4 17.75 69465 5 53.25 68547 6 35.50 69003

The calculated distances 4, 5 and 6 are plotted against velocities V4, V5 and V6, and the linear dependence of velocity on distance was generated. The equation obtained was used to determine an end plate velocity of 68347 cm s-1.

Figure 34 – Variation of shock wave velocity with axial distance in shock tube.

APPENDIX H

IGNITION DELAY DATA FOR 2-METHYLHEPTANE, N-

DODECANE, M-XYLENE AND M-XYLENE/N-DODECANE

(23% / 77 %) BLEND

 T5 (K) tign (µs)  T5 (K) tign (µs) -1 47,48 2-Methylheptane, P5 = 20 atm, Ar = 93% (P pressure scaling applied) 0.5 981.9 4927 3.0 1035.7 2012 0.5 1025.3 3459 3.0 1035.7 1736 0.5 1040.1 2421 3.0 1075.3 1617 0.5 1057.4 2022 3.0 1075.3 1804 0.5 1062.4 1892 3.0 1076.3 1592 0.5 1082.4 1665 3.0 1085.8 1526 0.5 1133.4 800 3.0 1087.8 1574 0.5 1196.1 354 3.0 1087.8 1505 0.5 1238.9 210 3.0 1090.4 1435 0.5 1279.6 218 3.0 1106.6 1432 0.5 1318.3 82 3.0 1108.9 1335 0.5 1354.8 76 3.0 1113.8 1163 0.5 1426.3 56 3.0 1119.6 1117 0.5 1493.9 35 3.0 1129.7 1194 0.5 1739.6 12 3.0 1130.5 1197 1.0 978.1 4733 3.0 1130.5 1225 1.0 1003.7 3017 3.0 1131.5 1136 1.0 1029.6 2596 3.0 1134.3 1045 1.0 1046.3 2076 3.0 1153.9 877 1.0 1101.9 1314 3.0 1154.9 1028 1.0 1176.8 632 3.0 1161.3 865

 T5 (K) tign (µs)  T5 (K) tign (µs) 1.0 1269.8 336 3.0 1186.4 750 1.0 1304.3 234 3.0 1187.3 737 1.0 1363.7 131 3.0 1193.8 715 1.0 1421.9 77 3.0 1221.9 521 1.0 1544.7 37 3.0 1248.3 40 4

3.0 987.8 3846 3.0 1260.8 347

3.0 1003.9 3984 3.0 1286.4 32 4 3.0 1013.5 2360 3.0 1298.5 33 2 3.0 1018.3 2166 3.0 1299.0 29 7 3.0 1019.3 2278 3.0 1311.3 320 3.0 1022.2 1909 3.0 1311.8 260

3.0 1029.2 1921 3.0 1329.0 279

-1 7 n-Dodecane, P5 = 20 atm, Ar = 93% (P pressure scaling applied) 0.5 1010.7 2883 1.0 1184.1 549 0.5 1040.1 2537 1.0 1235.7 319 0.5 1042.5 2493 1.0 1263.2 280 0.5 1067.4 1954 1.0 1313.0 191 0.5 1090.0 1278 1.0 1397.2 61 0.5 1125.6 983 1.0 1476.5 36 0.5 1146.2 658 3.0 953.3 4805 0.5 1174.9 520 3.0 1003.9 3086 0.5 1214.5 308 3.0 1004.4 2776 0.5 1287.6 171 3.0 1009.0 2652 0.5 1354.4 89 3.0 1042.8 2002 0.5 1408.5 41 3.0 1049.3 2043 0.5 1481.4 37 3.0 1082.4 1251 0.5 1599.1 9 3.0 1133.7 814 1.0 974.8 6226 3.0 1189.0 603 1.0 1016.5 3260 3.0 1198.2 506 1.0 1031.6 2483 3.0 1231.7 421 1.0 1038.6 2359 3.0 1268.0 356 1.0 1042.3 2330 3.0 1347.7 224 1.0 1084.1 1332 3.0 1424.0 183 1.0 1104.3 1104 3.0 1527.4 128 1.0 1153.1 713 - - -

 T5 (K) tign (µs)  T5 (K) tign (µs) -0.4 8 m-Xylene, P5 = 20 atm, Ar = 93% (P pressure scaling applied) 0.5 1105.2 4466 1.0 1256.3 1055 0.5 1115.5 3525 1.0 1304.7 702 0.5 1144.0 2922 1.0 1359.7 437 0.5 1157.1 2779 1.0 1424.2 271 0.5 1178.3 1775 1.0 1558.0 67 0.5 1186.2 1906 3.0 1118.5 4889 0.5 1229.2 1119 3.0 1125.4 3962 0.5 1261.8 1005 3.0 1177.1 2410 0.5 1297.8 700 3.0 1193.8 1866 0.5 1334.2 498 3.0 1227.5 1739 0.5 1408.7 295 3.0 1261.7 1303 0.5 1482.3 142 3.0 1316.4 790 0.5 1560.9 77 3.0 1392.9 400 0.5 1622.7 41 3.0 1426.8 283 1.0 1104.2 4059 3.0 1503.7 129 1.0 1159.8 2519 3.0 1574.6 118 1.0 1182.9 2118 - - -

n-Dodecane / m-Xylene (77% / 23%), P5 = 20 atm, Ar = 93% (P-1 pressure scaling applied)7 0.5 1011.66 4283 1.0 1067.2 2080 0.5 1019.05 3637 1.0 1157.4 812 0.5 1028.84 2873 1.0 1182.7 540 0.5 1048.60 2352 1.0 1240.3 356 0.5 1071.03 2171 1.0 1258.0 315 0.5 1093.72 1834 1.0 1301.2 169 0.5 1103.87 1033 1.0 1407.0 73 0.5 1160.56 890 1.0 1514.3 37 0.5 1184.23 617 3.0 967.4 5097 0.5 1216.10 407 3.0 991.7 3686 0.5 1283.83 231 3.0 1027.4 3111 0.5 1308.75 161 3.0 1070.3 1895 0.5 1353.51 89 3.0 1126.3 999 0.5 1410.65 50 3.0 1196.0 724 1.0 1008.9 3672 3.0 1213.4 629 1.0 1038.4 2749 3.0 1258.4 464 1.0 1053.0 2731 3.0 1318.3 349