Energy Transfer in Non-Equilibrium Reacting Gas Flows: Applications in Plasma Assisted Combustion and Chemical Gas Lasers

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Dissertation

Presented in Partial Fulﬁllment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By Zakari Eckert

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Graduate Program in Mechanical Engineering The Ohio State University 2018

Dissertation Committee: Professor Igor Adamovich, Advisor Professor Joseph Heremans Professor Seung Kim Professor Mohammad Samimy c Zakari Eckert, 2018 Abstract

The first part of the dissertation focuses on kinetic modeling of non-equilibrium reacting gas flows excited by nanosecond pulse discharges used for experimental studies of plasma assisted combustion kinetics. The present work provides detailed quantitative insight into kinetics of plasma assisted fuel oxidation processes, including generation of excited species by electron impact, dissociation of molecules during collisional quenching of excited species, formation of stable fuel oxidation products, and coupling between vibrational energy relaxation and chemical reaction kinetics in hydrogen-air, hydrogen-oxygen-argon, and hydrocarbon-oxygen-argon mixtures excited by nanosecond pulse discharges. The focus of the second half of the dissertation is on feasibility analysis of a new chemical carbon monoxide laser. Detailed insight is obtained into kinetics of state-specific vibrational energy transfer in non-equilibrium mixtures of CO, N2, and

O2, vibrationally excited by an RF discharge and by a chemical reaction between atomic carbon vapor and molecular oxygen, to produce laser gain and laser action in a supersonic ﬂow.

ii Acknowledgements

I would like to acknowledge the many people that made the completion of my Ph.D. possible. First, Igor, without whose guidance and direction, this work would not have been possible. Second, to those whose performed the experimental work that is present in conjunc- tion with my work in this dissertation, which provided both structure and validation, including Caroline, Yvonne, Elijah, Matt, and Kraig. Third, to those who guided me through the life choices that led me to where I am. My parents, who stood behind me through my long educational career, Dave, who nurtured the skills that would lead me to engineering, and Allen, who gave me the platform to allow those skills to develop and for me to learn what my passions were. Finally, I would like to thank all those who supported me and believed in me through the years and shared the journey with me.

iii Vita

May 2008 ...... DeKalb High School, Waterloo, IN May 2012 . . . B.S. in Mechanical Engineering, Rose-Hulman Institute of Technology May 2012 ...... B.S. in Mathematics, Rose-Hulman Institute of Technology May 2015 ...... M.S. in Mechanical Engineering, The Ohio State University

Publications

C. Winters, Z. Eckert, Y. Yin, K. Frederickson, and I. V. Adamovich. “Measurements and kinetic modeling of atomic species in fuel-oxidizer mixtures excited by a repetitive nanosecond pulse discharge”. J. Phys. D: Appl. Phys., volume 51(015202), 2018. C. Winters, Y.-C. Hung, E. Jans, Z. Eckert, K. Frederickson, I. V. Adamovich, and N. Popov. “OH radical kinetics in hydrogen-air mixtures at the conditions of strong vibrational nonequilibrium”. J. Phys. D: Appl. Phys., volume 50(505203), 2017. Z. Yin, Z. Eckert, I. V. Adamovich, and W. R. Lempert. “Time-resolved radical

species and temperature distributions in an Ar − O2 − H2 mixture excited by a nanosecond pulse discharge”. Proceedings of the Combustion Institute, volume 35, pages 3455–3462, 2015.

Fields of Study

iv Major Field: Mechanical Engineering

v Table of Contents

Abstract ...... ii

Acknowledgements ...... iii

Vita ...... iv

Table of Contents ...... vi

List of Figures ...... ix

List of Tables ...... xxvi

1 Introduction ...... 1 1.1 Background: Plasma Assisted Combustion...... 1 1.1.1 Energy Partition in Non-Equilibrium Plasmas...... 3 1.1.2 Nanosecond Pulse Discharges: Generating Plasmas at High Reduced Electric Fields...... 5 1.1.3 Nanosecond Pulse Discharges: Enhancing Stability of Large Volume Plasmas...... 9 1.1.4 Non-equilibrium Plasma Processes Aﬀecting Combustion Kinetics 12 Energy Thermalization and Gas Heating in Non-equilibrium Air and Fuel-Air Plasmas...... 12 Vibrationally Excited Species in Non-equilibrium Air and Fuel- Air Plasmas...... 15 Electronically Excited Species and Radicals in Non-equilibrium Air and Fuel-Air Plasmas...... 17 1.1.5 Challenges in Developing a Predictive Plasma Assisted Combus- tion Model...... 20 1.1.6 Previous Work in Kinetic Modeling of Plasma Assisted Combustion 22 1.2 Background: Chemical Carbon Monoxide Lasers...... 28 1.2.1 Electric Power Generation On Hypersonic Vehicles...... 29 1.2.2 Prior Work in Chemical Carbon Monoxide Lasers...... 35

vi 2 Plasma Assisted Combustion Kinetic Model ...... 42 2.1 Plasma Perfectly Stirred Reactor Model...... 42 2.1.1 Governing Equations...... 42 2.1.2 Correction for Forced Convection...... 47 2.1.3 Correction for Diﬀusion of Species...... 51 2.1.4 Heating on Sub-acoustic Time Scale...... 55 2.2 Electron Impact Rate Coeﬃcients...... 57 2.2.1 Argon Dominated Mixtures...... 59 2.2.2 Air Dominated Mixtures...... 63 2.3 Reactions of Excited Species...... 67 2.3.1 Argon Dominated Mixtures...... 67 2.3.2 Air Dominated Mixtures...... 72 2.4 “Conventional” Chemical Reactions...... 81

3 Kinetic Studies of Low-Temperature Plasma Assisted Combustion ...... 84 3.1 Prediction of Radical Species Generated by a Nanosecond Pulse Discharge 84 3.1.1 Brief Description of Plasma Assisted Reaction Kinetics Experiment 85 Reactor Cell with Liquid Metal Electrodes...... 85 Coated Copper Electrode Reactor Cell...... 86 Plasma Generation...... 87 Plasma Uniformity...... 89 H Atom and O Atom Number Density Measurements...... 92 3.1.2 Results and Discussion...... 92 3.2 Coupling of Nitrogen Vibrational Kinetics and Kinetics of the Hydroxyl Radical...... 112 3.2.1 Brief Description of Nanosecond Pulse Discharge Experiment... 115 Discharge Cell...... 115 Discharge Generation...... 116 CARS Measurements...... 119 OH LIF Measurements...... 120 Diﬀusion Conﬁguration...... 121 3.2.2 Results and Discussion...... 121 3.3 Prediction of Fuel Oxidation Product Composition in Mixtures Excited by Nanosecond Pulse Discharges...... 131 3.3.1 Brief Description of the Experiments...... 132 Plasma Flow Reactor...... 132 Discharge Generation...... 134 Gas Chromatography Measurements of Stable Oxidation Species136 3.3.2 Results and Discussion...... 136

vii 4 Supersonic Flow Carbon Monoxide Laser Model ...... 159 4.1 Quasi-one-dimensional Gas Dynamic Equations...... 159 4.2 Chemical Kinetics...... 168 4.3 Vibrational Kinetics...... 170 4.4 Electric Discharge Model...... 183 4.5 Laser Cavity Equations...... 185

5 Kinetic Modeling of Electric Discharge Excited and Chemical Carbon Monoxide Lasers ...... 193 5.1 Generation of Vibrationally Excited Carbon Monoxide by Chemical Reactions...... 194 5.1.1 Measurements of Strongly Vibrationally Excited CO Produced in Reaction of Carbon Vapor with Oxygen...... 194 5.1.2 Prediction of CO Vibrational Level Populations...... 196 5.2 Kinetic modeling of a Supersonic Flow CO Laser Operating in the Presence of Air Species in the Laser Mixture...... 206 5.2.1 Supersonic Flow Carbon Monoxide Laser Excited by an RF Discharge...... 206 5.2.2 Results and Discussion...... 208 5.3 Kinetic modeling of a Supersonic Flow, Chemical Carbon Monoxide Laser Operating in CO-Air Mixture...... 222 5.3.1 Simulation Conditions...... 222 5.3.2 Laser power predictions...... 223

6 Summary and Future Work ...... 233

References ...... 242

Appendix A Comparison of State-Speciﬁc Vibrational Kinetics Rate Coeﬃcients with Literature Data ...... 263 A.1 CO Vibration-to-Vibration Energy Transfer Rates...... 263 A.2 CO Vibration-to-Translation Energy Transfer Rates...... 270 A.3 N2 Vibration-to-Vibration Energy Transfer Rates...... 272 A.4 N2 Vibration-to-Translation Energy Relaxation Rates...... 274 A.5 O2 Vibration-to-Vibration Energy Transfer Rates...... 277 A.6 O2 Vibration-to-Translation Energy Relaxation Rates...... 278

Appendix B Derivation of Small Signal Gain Equation ...... 281

Appendix C Einstein A Coeﬃcients for CO ...... 288

Appendix D Konnov Combustion Mechanism ...... 291

viii List of Figures

1.1 Energy partition versus reduced electric field in dry air plasmas...... 5 1.2 DC breakdown voltages predicted by the Paschen law for different gases. 6 1.3 Schematic of plasma instability caused by positive feedback loop between ionization and gas heating...... 10 1.4 Comparison of experimental and predicted nitrogen “first level” vibrational temperature and gas temperature (left) and nitrogen vibrational level populations (right) in an air discharge. Excitation is caused by a single pulse nanosecond pulse discharge between two spherical electrodes

in dry air at P = 100 Torr, T0 = 300 K...... 23 1.5 Comparison of experimental and predicted OH radical number density

in H2-air mixtures (top) and C2H4-air mixtures (bottom). P = 100 Torr,

initial temperature T0 = 500 K, after excitation by a 50-pulse burst of nanosecond pulse discharges at pulse repetition rate of 10 kHz...... 24 1.6 Time-resolved gas temperature (experimental and predicted), predicted

‘ﬁrst level’ N2 vibrational temperature, O atom number density, and

total number density of electronically excited states of N2 during and after a nanosecond pulse discharge in air between two spherical copper

electrodes at P = 40 Torr and initial temperature T0 = 300 K...... 26

ix 1.7 Normalized fuel remaining at the end of the ﬂow reactor downstream of a discharge section experiencing nanosecond pulse plasma discharges

repeated at pulse repetition rate of 1 kHz in an argon-0.3% O2 buﬀer.

0.0016 Fuel mole fraction is x where x is the number of carbon atoms in

the fuel molecule. Fuels are CH4 (triangles), C2H6 (squares), C3H8

(right angle triangles), HC4H10 (diamonds), and C7H16 (circles)...... 26 1.8 Comparison of experimental data (hollow circles) and model predictions (solid circles) of stable oxidation products for an ethylene (800 ppm), oxygen (3000 ppm), argon mixture at P = 1 atm, excited by a burst of nanosecond pulse discharges at pulse repetition rate of 1 kHz...... 27

1.9 Energy partition of C + O2 reaction among different energy modes of the CO product, predicted by theoretical quantum chemistry calculations. 36 1.10 Vibrational level populations of carbon monoxide produced during gas phase reactions of carbon ablated from a graphite sample with molecular oxygen, measured in crossed molecular beam experiment...... 36 1.11 CO vibrational level populations inferred from infrared emission spectra of carbon monoxide produced in a chemical reaction of carbon species generated in an arc discharge with molecular oxygen, at argon buffer pressure of 20 Torr...... 37 1.12 Schematic of electric discharge excited, supersonic flow carbon monoxide laser...... 39 1.13 Laser power measured in an electric discharge excited, supersonic flow carbon monoxide laser in a mixture of 97 Torr helium with 3.6 Torr CO, in the presence of air species...... 39

x 1.14 Laser spectrum in an electric discharge excited, supersonic ﬂow carbon monoxide laser, in a mixture of 97 Torr helium, 3.6 Torr CO, and

26.3 Torr N2...... 40

2.1 Timing schematic for a repetitively pulsed discharge burst, indicating individual discharge pulses, discharge bursts, and probe laser pulses.... 47 2.2 Schematic of event timing in a burst of discharge pulses in a flow, ignoring the boundary layer effects: (a) Electrode and flow configuration (b) First discharge pulse in the burst and affected flow volume (c) Last discharge pulse in the burst showing flow volume affected by the first and the last pulses, with overlap representing flow affected by the entire burst (d) Time moment at which the flow begins affecting the measurement results...... 49

3.1 Schematic and photograph of the liquid metal electrode reactor cell, showing ﬂow channel, liquid metal electrode reservoirs, and preheating coils...... 86 3.2 Schematic and photograph of the coated copper electrode reactor cell showing the ﬂow channel, ceramic clamps holding polydimethylsiloxane (PDMS) coated copper electrodes, and preheating coils...... 87 3.3 Voltage and coupled energy waveforms in the liquid metal electrode cell for a single pulse (pulse # 25) at pulse repetition rate of 20 kHz, at

P = 300 Torr, initial temperature of T0 = 500 K in a mixture of 1% H2 in Ar...... 88

xi 3.4 Voltage and coupled energy waveforms in the coated copper electrode cell for a single discharge pulse (pulse # 75), at pulse repetition rate of

20 kHz, P = 300 Torr, initial temperature of T0 = 500 K, in a mixture

of 1% O2 in Ar...... 89

3.5 Left: transverse distributions of Ar(1 s5) number density in a repetitive

nanosecond pulse discharge in a 1% O2-Ar mixture, at P = 300 Torr,

T0 = 500 K, and ν = 10 kHz, 0.23 µs after the last pulse in a 50-pulse burst. Right: ICCD image of the plasma in the discharge cell (end view), showing approximate locations of absorption laser beam...... 90

3.6 ICCD image of the plasma in (left) argon and (right) 150 ppm C3H8 -

1% O2 - Ar mixture in the PDMS gel pad cell. P=300 Torr,T0=500 K,

discharge pulse repetition rate 20 kHz, camera gate 1 µs...... 91

3.7 Time resolved H atom number density in a 1% H2-Ar mixture excited

by 50 discharge pulses at 10 kHz and in a 1% H2-0.15%O2-Ar mixture excited by 25 discharge pulses at 20 kHz, measured in the liquid metal electrode cell. Coupled discharge pulse energy is 2.6 mJ/pulse. Dashed line indicates the approximate time scale when the eﬀect of convection on H atom decay becomes signiﬁcant...... 93

3.8 Predicted H and H2 species number densities at the conditions of

Figure 3.7 in a 1% H2-Ar mixture excited by a nanosecond pulse discharge of 50 pulses at 10 kHz, during the burst (left) and during the

afterglow (right), at P = 300 Torr and T0 = 500 K. Coupled discharge pulse energy is 2.6 mJ/pulse...... 95

xii 3.9 Predicted radical (H, O, HO2) and stable (H2O, H2) species number

densities at the conditions of Figure 3.7, in a 1% H2-0.15%O2-Ar mixture excited by a nanosecond pulse discharge burst of 25 pulses at 20 kHz, during the burst (left) and during the afterglow (right), at P=300 Torr

and T0 = 500 K. Coupled discharge pulse energy is 2.6 mJ/pulse...... 96

3.10 Potential energy curves for O2 (top) and H2 (bottom) showing the ground electronic states and the excited states that populated by

electron impact, resulting in dissociation. H2 potential energy curve adapted from Sharp...... 97

3.11 Time resolved O atom number density in a 1% O2-Ar mixture and in a

0.13% H2-1% O2-Ar mixture excited by 75 discharge pulses at 20 kHz in the gel pad cell. Coupled discharge energy is 4.2 mJ/pulse. Dotted line indicates approximate time at which convection of O atoms by the ﬂow becomes important...... 99

3.12 Predicted O atom and O2 number densities in a 1% O2-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the burst (left) and during the afterglow (right), at P = 300 Torr

and T0 = 500 K. Coupled discharge pulse energy is 4.2 mJ/pulse...... 101

3.13 Predicted radical (O, H, OH, HO2) and stable (H2O) species number

densities in a 1% O2-0.13%H2-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the burst (left) and

during the afterglow (right), at P=300 Torr and T0 = 500 K. Coupled discharge pulse energy is 4.2 mJ/pulse...... 102

xiii 3.14 Time resolved O atom number density in a 1% O2-0.25% CH4-Ar

mixture (4.2 mJ/pulse) and a 1% O2-150 ppm C3H8-Ar mixture (1.4 mJ/pulse), excited by a burst of 75 discharge pulses at 20 kHz in the gel pad cell...... 104

3.15 Predicted radical (O, H, OH, HO2) and stable (CH4, H2O) species

number densities in a 1% O2-0.25% CH4-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the

burst (left) and in the afterglow (right), at P=300 Torr and T0 = 500 K. Coupled discharge pulse energy is 4.2 mJ/pulse...... 105

3.16 Predicted radical (O, H, OH, HO2) and stable (C3H8, H2O) species

number densities in a 1% O2-150ppm C3H8-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the

burst (left) and during the afterglow (right), at P=300 Torr and T0 = 500 K. Coupled discharge pulse energy is 1.4 mJ/pulse...... 106

3.17 Time resolved O atom number density in a C3H8-1% O2-Ar mixture

(1.4 mJ/pulse, left) and a C2H4-1% O2-Ar mixture (1.4 mJ/pulse, right) excited by a burst of 75 discharge pulses at 20 kHz in the gel pad cell.. 107

3.18 Predicted radical (O, H, OH, HO2) and stable (C3H8, H2O) species

number densities in a 1% O2-75ppm C3H8-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the

burst (left) and during the afterglow (right), at P = 300 Torr and T0 = 500 K. Coupled discharge pulse energy is 1.4 mJ/pulse...... 109

xiv 3.19 Predicted radical (O, H, OH, HO2) and stable (C2H4, H2O) species

number densities in a 1% O2-150ppm C2H4-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the

burst (left) and during the afterglow (right), at P = 300 Torr and T0 = 500 K. Coupled discharge pulse energy is 1.4 mJ/pulse...... 109

3.20 Predicted radical (O, H, OH, HO2) and stable (C2H4, H2O) species

number densities in a 1% O2-75ppm C2H4-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the

burst (left) and during the afterglow (right), at P = 300 Torr and T0 = 500 K. Coupled discharge pulse energy is 1.4 mJ/pulse...... 110

3.21 Experimental and predicted O atom number density 90 µs after the burst versus initial mole fraction of propane in the mixture excited by

a nanosecond pulse discharge burst. P = 300 Torr,T0 = 500 K, pulse repetition rate is 20 kHz, discharge coupled energy 1.2 mJ/pulse...... 111

3.22 Experimental and predicted O atom number density 70 µs after the burst versus initial mole fraction of ethylene in the mixture excited by

a nanosecond pulse discharge burst. P = 300 Torr,T0 = 500 K, pulse repitition rate 20 kHz, discharge coupled energy 1.4 mJ/pulse...... 111 3.23 Time resolved measurements of OH number density in mixtures with four diﬀerent fuels, excited by a nanosecond pulse discharge at P = 1 atm, showing non-monotonous decay in the afterglow...... 114 3.24 Schematic (left) and photograph (right) of discharge electrode assembly and optical access for the hollow sphere electrode conﬁguration...... 115

xv 3.25 Voltage, current, and coupled energy for diﬀuse ﬁlament discharge

pulse between copper spherical electrodes in a 3% H2-air mixture at P=100 Torr. Coupled pulse energy 10 mJ. Negative polarity pulse waveforms are very similar...... 117 3.26 Single shot plasma emission images between spherical copper electrodes, showing a diﬀuse ﬁlament discharge, with the grounded electrode on

the left. Camera gate 1 µs. Coupled pulse energy 7.5 mJ...... 118 3.27 Coherent Anti-Stokes Raman Spectroscopy (CARS) energy level diagram. Molecules are coherently excited by pump and Stokes photons, which are separated in energy by the rotational-vibrational transition energy, and then interact with a probe photon (typically from the same beam as the pump photon) which generates the anti-Stokes photon, coherent with the pump, Stokes, and probe photons...... 120

3.28 Comparison of experimental and predicted N2 vibrational temperature (left) and gas temperature (right) versus time delay after the discharge

pulse in air and H2-air mixtures. Coupled pulse energy 7.5 mJ...... 122 3.29 Comparison of experimental and predicted OH number density versus

time delay after the discharge pulse in H2-air mixtures. Coupled pulse energy 7.5 mJ...... 124 3.30 Predicted radical species number densities versus time delay after the

discharge pulse in a 5% H2-air mixture. Coupled pulse energy 7.5 mJ.. 126

3.31 Comparison of experimental and predicted N2 vibrational temperature (left) and gas temperature (right) versus time delay after the discharge

pulse in air and H2-air mixtures. Coupled pulse energy 10.2 mJ...... 127

xvi 3.32 Comparison of experimental and predicted OH number density versus

time delay after the discharge pulse in H2-air mixtures. Coupled pulse energy 10.2 mJ...... 127 3.33 Predicted radical species number densities versus time delay after the

discharge pulse in a 5% H2-air mixture. Dashed line represents OH number density predicted by the quasi-stationary approximation in Equation 3.2. Coupled pulse energy 10.2 mJ...... 128 3.34 Schematic of the flow reactor including copper plate electrodes, quartz flow channel, and Macor ceramic sheath...... 133 3.35 Photograph of the discharge section of the flow reactor...... 134 3.36 Experimental voltage waveform measured across the electrodes, Gaus- sian fit used in the nanosecond pulse breakdown model, predicted field in the plasma (left), predicted power coupled to the plasma...... 135 3.37 Comparison of two chemical reaction mechanism predictions (Blue - Aramco, Red - Konnov) and measurements of hydrogen and oxygen concentrations, plotted at the exit of the reactor versus temperature... 137 3.38 Comparison of stable species concentrations at end of flow reactor, predicted using two different reaction mechanisms with experimental

data, plotted at the furnace exit versus temperature. 1600 ppm CH4 -

3000 ppm O2 - Ar mxiture, P = 1 atm, discharge pulse repetition rate 1 kHz...... 138 3.39 Predicted acetylene mole fraction in the discharge region and downstream of the discharge region at the conditions of Figure 3.38 when T = 1159 K...... 140

xvii 3.40 Comparison of stable species concentrations at the end of the heated region of the flow reactor predicted by using two different combustion chemistry mechanisms with experimental data plotted versus final

temperature. 800 ppm C2H4 - 3000 ppm O2 - Ar mixture, P = 1 atm, discharge pulse repetition rate 1 kHz...... 142 3.41 Comparison of stable species concentrations at the end of the heated region of the flow reactor predicted by using two different combustion chemistry mechanisms with experimental data plotted versus final

temperature. 800 ppm C2H4 - 3000 ppm O2 - Ar mixture, P = 1 atm, discharge pulse repetition rate 1 kHz...... 143

3.42 Concentrations of C2H4 and C2H2 in the discharge region and downstream (top) and between the first and second discharge pulses (bottom), at the conditions of Figure 3.40 when T = 600 K...... 146 3.43 Comparison of stable species concentrations at end of the heated region of the flow reactor predicted using two different combustion chemistry mechanisms with experimental data, plotted versus temperature.

533 ppm C3H8 - 3000 ppm O2 - Ar mixture, P = 1 atm, discharge pulse repetition rate 1 kHz...... 149 3.44 Comparison of stable species concentrations at end of ﬂow reactor predicted using two diﬀerent combustion chemistry mechanisms with exper-

imental data, plotted versus temperature. 533 ppm C3H8 - 3000 ppm

O2 - Ar mixture, P = 1 atm, discharge pulse repetition rate 1 kHz..... 150 3.45 Predicted propane mole fraction in the discharge region and downstream (left) and between the ﬁrst two discharge pulses (right), at the conditions of Figure 3.43 when T = 600 K...... 152

xviii 3.46 Predicted, time-resolved C2H2 mole fraction after 20 discharge pulses (left) and 80 discharge pulses (right), at the conditions of Figure 3.43, when T = 600 K...... 154

3.47 Predicted, time-resolved C2H2 mole fraction in the discharge region and downstrean (left), and between two successive pulses (right), at the conditions of Figure 3.43, when T = 1050 K...... 156

3.48 Predicted, time-resolved CH3HCO mole fraction in the discharge region and downstream (top), after 20 discharge pulses (bottom left), and after 80 discharge pulses (bottom right), at the conditions of Figure 3.44, when T = 600 K...... 157

4.1 CO vibrational distribution function (VDF) produced by two carbon

disulﬁde ﬂame reactions, CS2 + O (closed symbols) and CS + O (open symbols)...... 181

5.1 Schematic (left) and photograph (right) of experimental apparatus used to produce carbon vapor, react with oxygen, and measure CO vibrational non-equilibrium in the products...... 195 5.2 Experimental CO fundamental band emission spectrum, averaged over

the length of the observation cell. Ar buffer flow pressure 19.2 Torr, O2 partial pressure 0.2 Torr, flow rate 12 SLM...... 196

5.3 Energy partition of C + O2 reaction into the diﬀerent energy modes of the product CO predicted by quantum mechanical calculations...... 198 5.4 Signal from diﬀerent vibrational levels of carbon monoxide product of a chemical reaction between vapor-phase carbon and molecular oxygen, measured in the cross molecular beam experiment...... 198

xix 5.5 Nascent vibrational distribution assumed in the present work for the CO product of Reaction R 5.1...... 199 5.6 Comparison between CO vibrational distribution function (VDF) predicted by the model and measured in the low speed ﬂow reactor when all carbon vapor is assumed to produce vibrationally excited CO in Reaction R 5.1, with the nascent distribution shown in Figure 5.5. Flow rate is 12 SLM at initial temperature of 450 K, with partial pressures

of 18 Torr Ar, 2 Torr O2, and 1.6 mTorr C vapor...... 200 5.7 Comparison of predicted CO vibrational distribution functions (VDFs) for three diﬀerent initial C vapor partial pressures, at the conditions of Figure 5.6...... 201 5.8 CO vibrational distribution functions (VDFs) produced by two carbon

disulfide flame reactions, CS2 + O (closed symbols) and CS + O (open symbols)...... 203 5.9 Comparison between CO vibrational distribution function (VDF) predicted by the model and measured in the low speed flow reactor at the

2 conditions of Figure 5.6 when 3 of CO is produced via Reaction R 5.1 1 and 3 of CO is generated via Reaction R 5.3...... 205 5.10 Schematic of a Mach 3 supersonic flow channel with the RF discharge section in the plenum and the transverse laser cavity in supersonic flow. 207 5.11 Comparison of experimental and predicted CO vibrational distribution functions (VDFs) in the observation section, for reduced electric field values providing best match with the data. In addition to the mixture specified in the figure labels, the flow includes a buffer of 97 Torr He in all cases. RF discharge power is 2 kW...... 209

xx 5.12 Reduced electric field values inferred by matching experimental CO vibrational distribution functions (VDFs) measured in the observation section of the supersonic wind tunnel (symbols) and interpolation fits (lines)...... 210 5.13 Predicted axial distributions of flow parameters (flow channel height, Mach number, flow velocity, pressure, and temperature) in a supersonic flow CO laser operating in a 3.6 Torr CO - 97 Torr He - 21 Torr air mixture, at RF discharge power of 2 kW...... 213

5.14 Predicted vibrational distribution functions of CO (solid lines), N2

(dashed lines), and O2 (dotted lines) at the conditions of Figure 5.13, with transverse laser cavity beginning approximately 4.5 cm downstream of the throat and output coupler mirror reﬂectivity of 99.8%...... 214 5.15 Comparison of experimental and predicted laser power versus CO partial pressure in CO-He mixtures. He partial pressure 97 Torr, RF discharge power 2 kW...... 215

5.16 Comparison of experimental and predicted laser power versus N2, O2, and air partial pressure. CO and He partial pressures 3.6 and 97 Torr, respectively, RF discharge power 2 kW...... 217 5.17 Comparison of experimental (top) and predicted (bottom) laser spectra in a 3.5 Torr CO-97 Torr He mixture. RF discharge power 2 kW...... 218 5.18 Comparison of experimental (top) and predicted (bottom) laser spectra

in a 3.5 Torr CO - 97 Torr He - 26.3 Torr N2 mixture. RF discharge power 2 kW...... 220

xxi 5.19 Comparison of experimental (top) and predicted (bottom) laser spectra in a 3.5 Torr CO - 97 Torr He - 32 Torr air mixture. RF discharge power 2 kW...... 221 5.20 Predicted laser power in the supersonic ﬂow CO laser vs. carbon vapor partial pressure in the mixture. Carbon vapor-dry air mixture,

P0 = 100 Torr, T0 = 300 K...... 224

5.21 Vibrational distribution functions of CO (solid line), N2 (dashed line),

and O2 (dotted line) in the air mixture containing 3.1 mTorr of C at the begining and end of the laser cavity. Note that due to eﬀectively frozen vibrational kinetics in the supersonic ﬂow, and low laser power, the lines at the beginning of the cavity are obsured by those at the end.225 5.22 Predicted laser spectrum in the mixture of air with 3.1 mTorr of C vapor.227

5.23 Vibrational distribution functions of CO (solid line), N2 (dashed line),

and O2 (dotted line) predicted in air mixture containing 190 mTorr of C vapor, at the conditions when maximum laser output power is predicted (see Figure 5.20)...... 229 5.24 Predicted laser spectrum at the conditions of peak laser power predicted in Figure 5.20, in the mixture of air with 190 mTorr of C vapor...... 229

5.25 Vibrational distribution functions of CO (solid line), N2 (dashed line),

and O2 (dotted line) predicted in air mixture containing 0.72 Torr of C vapor...... 231 5.26 Predicted laser spectrum in the mixture of air containing 0.72 Torr of C vapor...... 231

xxii A.1 Comparison of the measured endothermic rate coefficients (top) at T = 300 K and exothermic rate coefficient calculations (bottom) for vibrational-to-vibrational energy transfer between CO molecules at T = 200–3000 K...... 264 A.2 Comparison of exothermic state-specific rate coefficients from the rate model (solid lines) for vibrational energy transfer for CO-CO with semiclassical three-dimensional trajectory calculations (symbols)...... 265 A.3 Comparison of exothermic state-specific rate coefficients from the rate model (solid lines) for vibrational energy transfer for CO-CO with semiclassical three-dimensional trajectory calculations (symbols)...... 266 A.4 Comparison of exothermic state-specific rate coefficients from the rate model (solid lines) for vibrational energy transfer for CO-CO with semiclassical three-dimensional trajectory calculations (symbols)...... 267 A.5 Comparison of exothermic state-specific rate coefficients from the rate model (solid lines) for vibrational energy transfer for CO-CO with semiclassical three-dimensional trajectory calculations (symbols)...... 268 A.6 Comparison of temperature dependent rate coefficient predicted by the rate model (solid lines) and predicted by semiclassical three-dimensional trajectory calculations (symbols) for vibrational energy transfer between

CO and N2 (left) and state-specific rate coefficient at T =300 K (right) 269 A.7 Comparison of rate coefficients for vibrational energy transfer between

CO and O2 with experimental data...... 269 A.8 Comparison of temperature dependent rate coeﬃcients for vibrational energy relaxation of CO molecules by helium atoms with semiclassical three-dimensional trajectory calculations and experimental data...... 271

xxiii A.9 Comparison of temperature dependent rate coefficients for vibrational energy relaxation of CO molecules by oxygen atoms with experimental data...... 271 A.10 Comparison of state specific rate coefficients for vibrational energy relaxation between CO molecules with semiclassical three-dimensional trajectory calculations (o) and experimental data (x)...... 272 A.11 Comparison of temperature dependent state specific rate coefficients

for vibrational energy transfer for N2-N2 with semiclassical trajectory calculation and experimental data...... 273 A.12 Comparison of temperature dependent state speciﬁc rate coeﬃcients

for vibrational energy transfer between N2 and O2 molecules with semiclassical trajectory calculations...... 274 A.13 Comparison of state-speciﬁc rate coeﬃcients for vibration-to-translation

(VT) relaxation of N2 by He with experimental data...... 275

A.14 Comparison of temperature dependence of N2 VT relaxation rate coef- ﬁcient by O atoms with experimental data...... 276

A.15 Comparison of state-specific N2 VT relaxation rate coefficients by N2 molecules with semiclassical trajectory calculations and experimental data...... 276 A.16 Comparison of state specific rate coefficients for vibrational energy

transfer between O2 molecules with experimental data and semiclassical trajectory models...... 278 A.17 Comparison of state-speciﬁc rate coeﬃcients for VT energy relaxation

of O2 by helium with experimental data...... 279

xxiv A.18 Comparison of state speciﬁc rate coeﬃcients for VT energy relaxation

of O2 by O atoms with experimental data...... 280

A.19 Comparison of state-speciﬁc rate coeﬃcients for VT relaxation of O2 by

O2 and N2 with semiclassical trajectory calculations and experimental data...... 280

xxv List of Tables

2.1 Electron impact processes included in argon dominated mixtures...... 60 2.2 Electron impact processes included in air dominated mixtures...... 64 2.3 Reactions of excited species included in argon dominated mixtures..... 68 2.4 Reactions of excited species in air and fuel-air plasmas...... 73 2.5 Vibrational energy transfer processes included in air dominated mixtures. 78

4.1 Parameters for calculation of vibration-to-vibration (VV) rate coeﬃcients176 4.2 Parameters for calculation of VT rate coeﬃcients...... 178

C.1 Einstein A coeﬃcients for spontaneous emission for CO calculated using the transition dipole moments of Chackerian et al...... 289

xxvi Chapter 1

Introduction

The focus of this dissertation is on development and validation of kinetic models of non-equilibrium, chemically reacting gas ﬂows, with speciﬁc emphasis on plasma assisted combustion, as well as on electric discharge excited and chemical lasers. The main objective of this work is assessing predictive capability of these models and obtaining quantitative insight into dominant kinetic processes controlling kinetics of low-temperature plasma assisted fuel oxidation and combustion, as well as kinetics of molecular energy transfer in strongly non-equilibrium molecular gas mixtures generated by an electric discharge or by chemical reactions.

1.1 Background: Plasma Assisted Combustion

Over the last 10–15 years, remarkable progress has been made in obtaining quantitative insight into kinetics of plasma assisted fuel oxidation, reformation, and ignition by low-temperature plasmas (e.g. see [1,2] and references therein). Although much is still left to be learned on rate coeﬃcients and product distributions of reactions of hydrogen and hydrocarbon molecules with plasma electrons and excited molecules and atoms, the amount of experimental data accumulated in nanosecond pulse discharges in air, hydrogen-air, and small hydrocarbon-air mixtures, as well as signiﬁcant depth of knowlendge in kinetic modeling of non-equilibrium air plasmas (e.g. see [3]), are

1 making possible development of a kinetic mechanism of low-temperature plasma induced combustion, with reasonable predictive capability. This mechanism needs to be validated using experimental data, such as temperature, vibrational level populations, number densities of excited electronic states of atoms and molecules, radical species number densities, ignition temperature, and ignition delay time taken in fuel-air mixtures excited by non-equilibrium plasmas, at well characterized conditions. The goal of the present work is to continue development of such a mechanism, started in Ref. [4], and incorporate critically important processes of molecular energy transfer, plasma chemical reactions of excited species, and conventional chemical reactions in low-temperature fuel-air plasmas sustained by singly pulsed and repetitively pulsed nanosecond duration discharges, which are widely used for plasma assisted combustion applications. Development of this mechanism has been made possible by

recent measurements of time-resolved temperature, N2 vibrational level populations, absolute number densities of key atomic and radical species, such as H, O, and OH, and ignition temperature in plane-to-plane and point-to-point nanosecond pulse dis-

charges in air, H2-air, and hydrocarbon-air mixtures [5–22]. The kinetic mechanisms developed in Ref. [4] is used as a baseline for its further development and validation, and expanding the range of its applicability, based on additional experimental results that have become available recently [21, 22]. Speciﬁcally, predictive capability of this mechanism is tested based on measurements of number densities of key radical species (H and O atoms and OH molecules), generated by hydrogen and hydrocarbon species dissociation reactions by electron impact and by reactive quenching of excited electronic states of argon, nitrogen, and oxygen. One of the goals of the present work is making the kinetic mechanisms available and straightforward to use, such that it can be exercised by a wide range of researchers in the ﬁeld, without having to develop

2 their own kinetic modeling codes.

1.1.1 Energy Partition in Non-Equilibrium Plasmas

It is well known that energy partition among diﬀerent energy modes (rotational, vibrational, electronic, dissociation, and ionization) in non-equilibrium low-temperature, high-pressure plasmas is controlled primarily by the electron energy distribution function [23]. Over a wide range of conditions, this partition can be characterized in terms

E of the reduced electric ﬁeld, N . Electron density, ne, is the other parameter that controls energy coupling to the plasma, such that speciﬁc power loading is proportional

E to the product of N and ne. Thus, prediction of these two key parameters is critical for insight into kinetics of energy transfer and chemical reactions in these plasmas. In a weakly ionized plasma, free electrons gain energy from the electric ﬁeld between collisions and lose it during collisions (predominantly with neutral species). In quasi-steady-state plasmas, the relationship between average energy gain between collisions and average energy lost in a collision is as follows,

P σi(Te)niεi eE i∈processes eEλ = = P , (1.1) Nσ(Te) σi(Te)ni i∈processes where e is the charge of an electron, E is the electric ﬁeld, λ is the electron mean free

2 path, N is the total number density, Te is the electron temperature, deﬁned as 3 the

average electron energy, σ is the total collision cross section for electrons, σi are the

cross sections for individual electron impact processes, ni are the number densities for

the collision partners involved in these processes, and εi are the amounts of electron energy lost in these processes.

3 The numerator on the right hand side of Equation 1.1 is eﬀectively the energy loss per unit distance travelled by the electron, with terms in the sum representing

losses via diﬀerent collisional processes. The denominator is essentially Nσ(Te). It can be seen from Equation 1.1 that for a given chemical composition of the plasma (and obviously the same set of electron impact cross sections, which are functions of electron temperature) at quasi-steady-state, the electron temperature, and therefore electron energy partition among diﬀerent collisional processes (the numerator on the

E right hand side of Equation 1.1) is a function of reduced electric ﬁeld N . The electron energy partition in a plasma versus reduced electric ﬁeld can be predicted by solving the Boltzmann equation for electrons, using experimental electron impact cross sections as inputs [24]. The electron energy partition in a dry air plasma, predicted using this approach, is shown in Figure 1.1. It can be seen that at low

E −17 2 electric ﬁelds ( N < 10 Td, 1 Td = 1 × 10 V cm ) electrons lose energy primarily

to vibrational excitation of oxygen, rotational excitation of N2 and O2, or elastic

collisions with N2 and O2.

E At moderate reduced electric ﬁeld values (10 Td < N < 100 Td), electron energy loss is dominated by the vibrational excitation of nitrogen (up to 90% of total input power). This occurs because electrons with moderate energies, 2–4 eV, readily attach to nitrogen molecules to form an unstable negative ion,

− − e + N2(v−0) −−→ N2 (w > 0) . (R 1.1)

Due to multiple potential energy surface crossings between vibrational states of the

– N2 ion and the N2 molecule, the electron is rapidly released in autodetachment

4 Figure 1.1: Energy partition versus reduced electric ﬁeld in dry air plasmas.

processes,

− − N2 (v ≥ 0) −−→ e + N2(v > 0) . (R 1.2)

E Finally, at high reduced electric ﬁelds ( N > 100 Td), dominant energy loss mechanisms

include electronic excitation, dissociation, and ionization of N2 and O2 (see Figure 1.1). Discussion of dominant energy transfer processes and plasma chemical reactions in fuel-air plasmas in Section 1.1.4 will demonstrate that operating electric discharges at high reduced electric ﬁeld values would considerably increase the rate of chemically active radical species generation in the plasma.

1.1.2 Nanosecond Pulse Discharges: Generating Plasmas at

High Reduced Electric Fields

Figure 1.2 plots the DC electric breakdown voltage in diﬀerent gases in long tubes versus a product of pressure and the distance between the electrodes, predicted by

5 Figure 1.2: DC breakdown voltages predicted by the Paschen law for diﬀerent gases. [23]

the Paschen law [23],

  B(P d) A Vt = ,C = ln   , (1.2) C + ln(P d) 1 ln γ + 1

where Vt is the breakdown voltage across the gap of width d, P is the pressure, γ is the secondary emission coeﬃcient, i.e. the probability that an electron is ejected from the electron surface when an ion strikes it, and A and B are empirical parameters of the gas describing the Townsend ionization coeﬃcient,

BP α = AP exp − (1.3) E where E is the electric field strength. The Townsend ionization coefficient is the number of ionization events that an electron performs as it travels 1 cm along the electric field [23]. From Figure 1.2 it can be seen that above ≈1 cm Torr the breakdown voltage increases linearly with P d. At constant pressure, this implies that the breakdown electric field is constant. The breakdown voltage rise below ≈1 cm Torr occurs because,

6 for very short discharge gaps or very low pressures, electron avalanche grows too slowly, which requires significantly higher electric fields to acheive discharge self-sustainement. These short gap distances and low pressures are out of scope of the present work. From Figure 1.2, it can be seen that breakdown electric field between two electrodes in air at P = 1 atm is approximately E = 30 kV cm−1, i.e. breakdown reduced electric

E field is approximately N ≈ 110 Td. At these conditions, significant fractions of discharge input energy goes to electronic excitation, dissociation, and ionization of nitrogen and oxygen by electron impact (see Figure 1.1). However, achieving higher reduced electric fields during DC breakdown is possible only for very short gaps (in microplasmas) and at very low pressures, i.e. at the conditions not applicable to plasma assisted combustion applications. Also, after breakdown the electric field in the quasi-steady-state weakly ionized air plasma becomes much lower, since the rates of electron impact ionization, e.g.

− − − + e + N2 −−→ e + e + N2 , (R 1.3)

− − − + e + O2 −−→ e + e + O2 , (R 1.4) and electron-ion recombination (primarily dissociative recombination), e.g.

− + e + N2 −−→ N + N, (R 1.5) and

− + e + O2 −−→ O + O, (R 1.6)

7 as well as electron attachment (both dissociative and three-body attachment to oxygen),

− − e + O2 −−→ O + O, (R 1.7) and

− − e + O2 + M −−→ O2 + M, (R 1.8)

E are balanced at signiﬁcantly lower N values (by up to an order of magnitude compared E to breakdown electric ﬁeld, i.e. N ≈ 10 Td). Additional ionization processes, not directly related to electron impact, such as stepwise ionization of molecules and atoms in excited states,

3 3 3 1 − + − − N2(A Σ, B Π, C Π, a Π,... ) + e −−→ N2 + e + e , (R 1.9)

associative ionization in collisions of excited metastable species,

3 3 3 1 3 3 3 1 + − N2(A Σ, B Π, C Π, a Π,... )+N2(A Σ, B Π, C Π, a Π,... ) −−→ N4 +e , (R 1.10)

and Penning ionization, A + B∗ −−→ A+ + e− + B, (R 1.11)

E further contribute to N reduction, since these species accumulate in the discharge E over time. This same effect, reduction of N in the body of the plasma, occurs in quasi-steady RF and microwave discharges. On the other hand, pulsing the applied voltage makes possible generating significantly higher peak electric fields [25,26], thus increasing discharge energy fraction going to electronic excitation and dissociation of molecules and atoms. In this case, the applied electric field, varying on nanosecond

8 time scales, may increase more rapidly compared to electron impact ionization and electron avalanche development, as well as charge separation in the plasma after it is generated, which shields the applied electric ﬁeld. This is one of the main reasons why nanosecond pulse discharges are widely used for plasma assisted combustion applications.

1.1.3 Nanosecond Pulse Discharges: Enhancing Stability of

Large Volume Plasmas

In addition to maximizing reduced electric field in the electric discharge, it is also desirable to maximize the volume of the plasma, especially at high specific energy loading. Plasma instabilities rapidly develop in high pressure, high specific power electric discharges, resulting in formation of constricted high-temperature filaments [2]. The development of one of these instabilities, the ionization/heating instability, is

illustrated schematically in Figure 1.3, where ne is the electron number density, ~j is the electron current density, e is the electron charge, µ is the ion mobility, E~ is the electric ﬁeld vector, T is the heavy species temperature, P is the gas pressure, and

kion is the rate coefficient for electron impact ionization. From Figure 1.3, it is apparent that a local increase in electron density in the plasma results in the increase of current density and Joule heating, as well as causing a temperature rise. Assuming that the temperature rise occurs relatively slowly, such that the pressure remains constant, this leads to the reduction of the number density and an increase of the reduced electric field. Since the rate of electron impact ionization increases exponentially with the electron temperature, which is approximately proportional to the reduced electric field, this results in further electron

9 (a) ne ↑

~ (f) kion ↑ (b) ~j = eneµE ↑

E (e) N ↑ (c) T ↑

(d) P = const. ⇒ N ↓

Figure 1.3: Schematic of plasma instability caused by positive feedback loop between ionization and gas heating.

10 density rise, creating a positive feedback loop. This process is responsible for instability development, discharge constriction, and arc filament formation. The instability development can be delayed in a number of ways. First, at low pressures, ambipolar diffusion of electrons and ions from the incipient filament, as well as conductive heat transfer, delay the temperature rise caused by Joule heating, such that the plasma remains diffuse. A similar effect can be achieved by sustaining the discharge in a high-speed flow, when incipient arc filaments are dissipated by convective cooling [27]. Ionization in the plasma can also be sustained using an efficient external ionization source which does not use an electric field, such as a high-energy electron beam or a laser which strongly excites molecules, which is followed by their associative ionization [28]. Note that a high-energy electron beam is the most efficient way of producing ionization in gases, with up to 50% of beam electron energy going to generating electron-ion pairs. Finally, plasma stability can be enhanced considerably by using short duration, high amplitude voltage pulses, with the pulse duration short compared to the characteristic time scale of Joule heating, typically on the order of 1–100 ns [29]. Although high energy electron beams have been used extensively to generate large-volume, high electron density plasmas at higher pressures, their use remains impractical due to fragility of the electron gun foil and X-ray generation. On the other hand, high peak voltage, nanosecond pulse discharges have been used extensively for plasma generation in plasma assisted combustion applications, due to both effective generation of electronically excited and atomic species and stability of pulsed plasmas at high pressures.

11 1.1.4 Non-equilibrium Plasma Processes Aﬀecting Combus-

tion Kinetics

The principal mechanisms by which electric discharges affect combustion kinetics are (i) thermal, i.e. gas heating in the discharge, due to relaxation of excited species generated in the plasma, and (ii) non-thermal, i.e. plasma chemical reactions among the vibrationally excited species, electronically excited species, and chemically reactive radicals, which may occur at low temperatures. While the thermal effect simply increases the rates of “conventional” chemical reactions in the fuel-oxidizer mixture, it is the non-thermal effect of non-equilibrium plasmas that has attracted the most attention.

Energy Thermalization and Gas Heating in Non-equilibrium Air and Fuel- Air Plasmas

Electron energy transfer in elastic collisions with heavy species, with its rapid subsequent thermalization in translation-translation and rotation-translation energy transfer collisions among heavy species,

e− + M −−→ e− + M + heat, (R 1.12)

is extremely ineﬃcient due to the large disparity in mass. Average electron energy loss per elastic collision is on the order of

∆ε 2m ≈ , (1.4) ε M

12 where ε is the collision energy (dominated by the electron kinetic energy), ∆ε is the kinetic energy transferred from the high energy electron to the heavy collision partner, m is the electron mass, and M is the mass of the collision partner. For example, for

1 H atoms, the energy lost in a collision is only ≈ 2000 of the electron energy, and it is an order of magnitude lower for most molecular gases. Since electron temperatures in non-equilibrium plasmas is of the order of an electron-volt (1 eV ≈ 11 600 K), every elastic collision transfers only 0.1–1 meV from the electrons to the gas. The same eﬀect limits electron energy transfer to rotational excitation of molecules. On the other hand, electron impact excitation of vibrational states,

e− + AB(v−0) −−→ e− + AB(v > 0), (R 1.13)

and electronic states of molecules

e− + AB −−→ e− + AB∗, (R 1.14)

can be very eﬃcient, with up to tens of percent of energy coupled to the plasma stored in vibrational and electronic energy modes of heavy species (see Figure 1.1). Char- acteristic times of energy thermalization during collisional relaxation and quenching of the excited states of molecules vary over several orders of magnitude, from ≈1 s

3 for VT relaxation in pure nitrogen to ≈1 ns for quenching of the N2(C Π) excited

electronic state by O2 (both at atmospheric pressure). Detailed kinetics of energy thermalization and heating in plasmas generated by nanosecond pulse discharges in air

and in H2-air mixtures have been studied experimentally and using kinetic modeling calculations in Refs. [16,30]. Brieﬂy, temperature rise in transient air plasmas occurs

13 in two stages, “rapid” heating controlled by collisional quenching of excited electronic

states of N2 by O2 molecules,

3 3 3 1 N2(A Σ, B Π, C Π, a Π,... ) + O2 −−→ N2 + O + O, (R 1.15)

on the time scale of 1–100 ns atm, and “slow” heating controlled by VT relaxation of vibrationally excited N2 by O atoms,

N2(v > 0) + O −−→ N2(v − 1) + O, (R 1.16)

on the time scale of 1–10 µs atm, with O atoms generated during or shortly after the discharge pulse via electron impact or Reaction R 1.15. In the presence of hydrogen or hydrocarbon species, “rapid” heating may become more pronounced due to additional

quenching processes of excited electronic states of N2 by H2 and hydrocarbons,

3 3 3 1 N2(A Σ, B Π, C Π, a Π,... ) + H2 −−→ N2 + H + H, (R 1.17)

3 3 3 1 N2(A Σ, B Π, C Π, a Π,... ) + RH −−→ N2 + R + H, (R 1.18)

3 3 3 1 N2(A Σ, B Π, C Π, a Π,... ) + RH2 −−→ N2 + R + H2, (R 1.19)

etc., where RH and RH2 denote hydrocarbon molecules. Similarly, “slow” heating at

these conditions may be enhanced due to vibrational relaxation of N2 by H atoms,

N2(v > 0) + H −−→ N2(v − 1) + H. (R 1.20)

Comparison of kinetic modeling predictions of temperature rise in the afterglow

14 of nanosecond pulse discharges in air and H2-air mixtures is in very good agreement with time-resolved temperature and N2 vibrational temperature measurements in these plasmas by CARS [11,16]. As discussed above, the dominant effect of energy thermalization in nanosecond pulse discharge plasmas to increase the rate coefficients of “conventional” chemical reactions, which may strongly affect kinetics of fuel oxidation and ignition.

Vibrationally Excited Species in Non-equilibrium Air and Fuel-Air Plas- mas

Vibrationally excited N2 molecules, which play an important role in the energy balance of non-equilibrium fuel-air plasmas (speciﬁcally the kinetics of “slow” heating, see previous subsection), are generated eﬃciently via by electron impact,

− − N2(v = 0) + e −−→ N2(v > 0) + e , (R 1.21)

E primarily at relatively low values of reduced electric ﬁeld, N ≈10–50 Td (see Figure 1.1).

Because of this, N2 vibrational excitation is a dominant energy transfer process in quasi-steady-state discharges (DC, RF, and microwave) in nitrogen, air, and fuel-air mixtures. The role of vibrationally excited nitrogen molecules in the ground electronic

1 state, N2(X Σ, v), in chemical kinetics of reacting non-equilibrium plasmas remains rather poorly understood. It may well be signiﬁcant for two principal reasions,

(i) high input energy fraction into N2 vibrational excitation by electron impact in electric dischares in air and fuel-air mixtures (see Figure 1.1), and (ii) relatively slow

N2 vibrational relaxation rate, even in plasmas with signiﬁcant concentrations of

15 hydrogen, hydrocarbon species, and oxygen atoms. Because of this, a considerable fraction of energy in transient plasmas is stored in the vibrational energy mode of molecular nitrogen, which aﬀects the rate of temperature rise [30,31] and, indirectly,

rate coeﬃcients of chemical reactions. A more direct eﬀect of N2 vibrational excitation

1 on plasma chemistry, either via reactions with N2(X Σ, v) as one of the reactants, or via vibrational energy transfer from nitrogen molecules to other reactive molecular species, has been a matter of some debate. A reaction pathway, hypothesized in Ref. [32], suggests that vibrationally excited nitrogen may delay OH recombination due to near-resonant vibrational energy transfer

to the “unreactive” HO2 radical,

1 1 N2(X Σ, v = 1)+HO2 −−→ N2(X Σ, v = 0)+HO2(ν2 +ν3) −−→ N2 +H+O2. (R 1.22)

It was also suggested that this process may sustain chain propagation and chain branching chemical reactions of H atoms in the low-temperature afterglow in fuel- air mixtures, and thus extend OH radical lifetime. The underlying assumption of

this hypothesis is that dissociation of HO2 by vibrational energy transfer from N2 would mitigate a major chain termination process during low-temperature oxidation of hydrogen,

H + O2 + M −−→ HO2 + M. (R 1.23)

This would generate additional H atoms, driving a well-known chain branching process,

H + O2 −−→ OH + O, (R 1.24)

16 and

O + H2 −−→ OH + O, (R 1.25)

and thus resulting in higher transient OH number density in the afterglow of nanosecond pulse discharges in preheated atmospheric pressure hydrocarbon-air mixtures [33], which demonstrated anomalously long lifetime and non-monotonous decay of the OH radical in the afterglow and seems to support this hypothesis. Kinetic modeling of atmospheric pressure hydrogen-air plasmas with signiﬁcant initial vibrational excitation

of nitrogen, Tv,N2 ≈ 3000 K, incorporating the process of Reaction R 1.22, predict that this eﬀect would result in transient OH number density rise in the afterglow, peaking

on the time scale of ≈300 µs–4 ms at T =600–800 K [32].

Electronically Excited Species and Radicals in Non-equilibrium Air and Fuel-Air Plasmas

O atoms, H atoms, and electronically excited N2 molecules, which are critical for controlling the energy balance in non-equilibrium fuel-air plasmas (in the kinetics of both “slow” and “rapid” heating, see earlier subsection), also initiate a number of well-known plasma chemical reactions. Electronically excited states and atomic species are generated eﬃciently by electron impact, e.g.

− 3 3 3 − N2 + e −−→ N2(A Σ, B Π, C Π,... ) + e , (R 1.26)

− − O2 + e −−→ O + O + e , (R 1.27)

− 1 − O2 + e −−→ O + O( D) + e , (R 1.28)

− − H2 + e −−→ H + H + e , (R 1.29)

17 RH + e− −−→ R + H + e−. (R 1.30)

In fuel-oxidizer mixtures diluted in argon, electron impact excitation of metastable electronic states of argon, Ar + e− −−→ Ar∗ + e−, (R 1.31)

also becomes a critically important process of electron energy loss in inelastic collisions. Electronic excitation and dissociation processes by electron impact become dominant

E at relatively high values of reduced electric ﬁeld, N ≈ 100 Td (see Figure 1.1). In addition to electron impact dissociation, O atoms and H atoms are generated during

rapid collisional quenching of electronically excited N2 molecules, e.g.

3 3 3 N2(A Σ, B Π, C Π,... ) + O2 −−→ N2 + O + O, (R 1.32)

3 3 3 N2(A Σ, B Π, C Π,... ) + H2 −−→ N2 + H + H, (R 1.33)

3 3 3 N2(A Σ, B Π, C Π,... ) + RH −−→ N2 + R + H, (R 1.34) and

∗ Ar + O2 −−→ Ar + O + O, (R 1.35)

∗ Ar + H2 −−→ Ar + H + H, (R 1.36)

Ar∗ + RH −−→ Ar + R + H. (R 1.37)

Note that these processes also control the rate of “rapid” heating in the plasma, as

discussed in earlier subsections, since the excitation energy of N2 and Ar electronic

states is higher compared to the dissociation energy of O2, H2, and RH. Thus, the main eﬀect of excited electronic states of nitrogen and argon, generated by electron

18 impact, is to produce atomic species and radicals, which are highly reactive even at low temperature, unlike oxygen, hydrogen, and hydrocarbon molecules. Also note that some of the O atoms generated by electron impact dissociation of oxygen are produced in an excited electronic state, O(1D), rather than ground state O(3P). Reactions of O(1D) with hydrogen and hydrocarbon molecules are extremely rapid, with rate coefficients comparable with the gas kinetic rate [34,35], which makes them critically important in the kinetics of plasma assisted combustion. At high reduced electric fields typical for nanosecond pulse discharges, significant fractions of discharge input energy goes into population of excited states of molecules (vibrational and electronic), as well as molecular dissociation and ionization by electron impact (see Figure 1.1). Collisional quenching of the excited states (including reactive quenching) and reactions of radical species generated in the discharge considerably expand the variety of chemical reactions in low-temperature fuel-air mixtures, resulting in fuel oxidation, temperature rise, and, eventually, ignition [2]. From a fundamental kinetics perspective, however, the dominant energy transfer and chemical reaction processes in these plasmas remain not fully understood. In particular, direct quantitative measurements of efficiency of primary radical species generation (such as H and O atoms) in well-characterized nanosecond pulse discharge plasmas are limited. In addition, net rates of primary radical consumption in low-temperature fuel-oxidizer plasmas, which provide insight into the dominant radical reaction pathways, are rather uncertain. Without such understanding, predictive kinetic modeling and analysis of plasma assisted combustion phenomena remains challenging. Most previous measurements of O atoms [5, 20, 36, 37], OH radicals [9, 10, 15, 18, 33, 38], and H atoms [15,20] in plasmas sustained by nanosecond pulse discharges have been done at the conditions when specific energy loading in the plasma and/or its spatial

19 distribution had signiﬁcant uncertainty, such that accurate quantitiative analysis of the dominant kinetic processes involved was challenging. One of the objectives of the present work is to compare predictions of a kinetic model of plasma assisted combustion with measurements of absolute, time-resolved number densities of key radical species generated in repetitive nanosecond pulse discharges in lean fuel/oxidizer mixtures (H and O atoms), at the conditions when discharge pulse energy coupled to the plasma was measured directly. This will provide quantitative insight into rates and product distributions of reactions of fuel species with plasma electrons and excited molecules and atoms, as well as into plasma-generated radical species reactions at low temperatures (below ignition temperature) and high pressures (approaching 1 atm).

1.1.5 Challenges in Developing a Predictive Plasma Assisted

Combustion Model

Kinetic processes discussed in previous sections, which are essential for understanding energy transfer mechanisms in non-equilibrium plasma assisted combustion environments, remain not fully understood. In particular, the efficiency at which combustion radicals (specifically H and O atoms) are produced in nanosecond pulse plasma discharges has not been studied in sufficient detail, which is required for development of a predictive kinetic model. In addition to significant electronic excitation produced at high reduced electric fields (see Figure 1.1), at moderate electric fields a large fraction of the discharge energy is stored in vibrationally excited nitrogen molecules in the

20 ground electronic state,

− − N2(v−0) + e + N2(v > 0) + e . (R 1.38)

Energy coupled to the vibrational mode of nitrogen remains there for time scales longer than most combustion reactions and is thermalized primarily via VT relaxation by O atoms, fuel species, and combustion products. This relatively slow relaxation can delay temperature rise from the discharge, thus delaying some fuel oxidation reactions. Direct coupling between the vibrational mode of nitrogen and combustion kinetics is still not fully understood. One of the diﬃculties of kinetic model development is the fact that plasma chemistry has been studied mainly at low pressures and near room temperature [14, 15, 37]. Additionally, the temperature dependence and product distribution for many reactions of electronically excited states are not known [16,39–41]. Summarizing, quantitative predictions of reaction kinetics in low-temperature plasmas requires knowledge of rates of molecular energy transfer processes, such as electron impact excitation and dissociation of air and fuel species, vibrational relaxation, rates and products of reactive quenching of excited electronic states, as well as a mechanisms of fuel oxidation via “conventional” chemical reactions at low temperatures. Kinetic mechanisms of “conventional” combustion [42, 43] have been developed and validated for high temperature conditions and may well be inapplicable at low temperatures typical for many plasma assisted combustion environments. An illustration of this is found in a recent study [4], which compared absolute time-resolved OH number density and temperature measurements by laser

induced ﬂuorescence (LIF) in lean H2-air and hydrocarbon-air mixtures excited by

21 a burst of nanosecond discharge pulses with kinetic modeling calculations, using conventional hydrocarbon-air combustion mechanisms. Although modeling predictions

for H2-air, CH4-air, and C2H4 –air agree with the data fairly well [4], the agreement

between the model and the data in C3H8-air is quite poor. This demonstrates the need for development of an accurate, predictive plasma assisted combustion chemistry mechanism. Predictive capability of a plasma chemistry model involving such a large number of energy transfer processes and reactions would beneﬁt from a built- in kinetic sensitivity analysis to identify the dominant processes. Identifying the reduced reaction mechanisms is extremely critical, especially for hydrocarbons, since kinetic modeling of coupled nanosecond pulse discharge dynamics, energy transfer in the plasma, and plasma assisted combustion requires incorporating a wide range of time scales, 1 × 10−12–1 × 10−2 s, and is very computationaly intensive even in one-dimensional geometries [25].

1.1.6 Previous Work in Kinetic Modeling of Plasma Assisted

Combustion

While Section 1.1.5 discusses the difficulties in developing a predictive kinetic model for plasma assisted combustion applications, a significant amount of work in this field has been done. The model discussed in detail in Chapter 2 and used for kinetic modeling calculations in Chapter 3 has been used previously to study kinetics of fuel oxidation and vibrational energy transfer in air, hydrogen-air, and hydrocarbon-air mixtures excited by nanosecond pulse discharges [4]. The present work builds on these earlier studies, including kinetics of rapid gas heating caused by the quenching of electronically excited nitrogen [4,40], which is discussed in detail in Section 2.1.4.

22 Figure 1.4: Comparison of experimental and predicted nitrogen “ﬁrst level” vibrational temperature and gas temperature (left) and nitrogen vibrational level populations (right) in an air discharge. Excitation is caused by a single pulse nanosecond pulse discharge between two spherical electrodes in dry air at P = 100 Torr, T0 = 300 K [4,11]

Among several kinetic modeling studies in the field, several significant advances can be mentioned specifically. A quasi-zero-dimental model developed in Ref. [25] demonstrated good agreement with measurements of time-resolved temperature and

N2 vibrational level populations in non-equilibrium plasmas generated by nanosecond pulse discharges in air, as shown in Figure 1.4[4]. Since rate coeﬃcients of many combustion reactions are sensitive to temperature, accurate prediction of energy storage in the vibrational energy mode of nitrogen and its subsequent relaxation, which causes a transient rise in gas temperature at these conditions, is critical. The same model was also used to predict OH radical number density in lean preheated fuel-air mixtures excited by a nanosecond pulse discharge, showing good agreement with absolute, time-resolved measurements in H2-air, CH4-air, and C2H4-air mixtures

(see Figure 1.5[4]), although the modeling predictions in C3H8-air mixtures were not as accurate.

23 Figure 1.5: Comparison of experimental and predicted OH radical number density in H2-air mixtures (top) and C2H4-air mixtures (bottom). P = 100 Torr, initial temperature T0 = 500 K, after excitation by a 50-pulse burst of nanosecond pulse discharges at pulse repetition rate of 10 kHz. [4]

24 In another recent study, a quasi-one-dimensional model of a nanosecond pulse discharge in air was used to predict time-resolved number densities of N, O, and NO [14] and in hydrogen-air [17], providing insight into the mechanism of NO formation in low- temperature transient plasmas. The same kinetic model was used to elucidate detailed kinetic mechanisms of energy thermalization in nanosecond pulse discharge plasmas in air and hydrogen-air mixtures, including two-stage “rapid” heating and “slow” heating [16]. Speciﬁcally, “rapid” heating (on 100–1000 ns time scales) is produced during collisional quenching of electronically excited nitrogen molecules by oxygen, Reaction R 1.32,

3 3 3 1 N2(A Σ, B Π, C Π, a Π,... ) + O2 −−→ N2 + O + O, which is also one of the dominant sources of O atoms in the plasma. “Slow” heating

(on 100–1000 µs time scale) is produced during vibrational relaxation of nitrogen by O atoms [4]. The time scales for changes in temperature, gas temperature, electronically

excited N2 number density, and O atom number density are evident in Figure 1.6. Other experimental and kineic modeling studies directly relevant to the present work are an extensive set of measurements in a plasma ﬂow reactor performed by Tsolas et al.[44–46]. In their work, stable products of plasma assisted fuel oxidation in

preheated Ar-O2-fuel mixtures excited by nanosecond pulse discharges were measured by gas chromatography, over a wide range of temperatures. Mole fractions of fuel oxidized at these conditions are plotted in Figure 1.7, and some of the stable product species are shown in Figure 1.8[44,46]. In addition to the measurements, the authors have also analyzed kinetics of plasma assisted fuel oxidation at these conditions, with some of the modeling predictions

25 Figure 1.6: Time-resolved gas temperature (experimental and predicted), predicted ‘ﬁrst level’ N2 vibrational temperature, O atom number density, and total number density of electronically excited states of N2 during and after a nanosecond pulse discharge in air between two spherical copper electrodes at P = 40 Torr and initial temperature T0 = 300 K. [16]

Figure 1.7: Normalized fuel remaining at the end of the ﬂow reactor downstream of a discharge section experiencing nanosecond pulse plasma discharges repeated at pulse 0.0016 repetition rate of 1 kHz in an argon-0.3% O2 buﬀer. Fuel mole fraction is x where x is the number of carbon atoms in the fuel molecule. Fuels are CH4 (triangles), C2H6 (squares), C3H8 (right angle triangles), HC4H10 (diamonds), and C7H16 (circles). [44]

26 Figure 1.8: Comparison of experimental data (hollow circles) and model predictions (solid circles) of stable oxidation products for an ethylene (800 ppm), oxygen (3000 ppm), argon mixture at P = 1 atm, excited by a burst of nanosecond pulse discharges at pulse repetition rate of 1 kHz. [46]

compared to the experimental data in an ethylene-O2-Ar mixture in Figure 1.8[46]. One of the signiﬁcant results of this work is the inference of product branching ratios during quenching of metastable argon by ethylene [46],

∗ 52 % Ar + C2H4 −−→ Ar + C2H2 + H + H, (R 1.39)

∗ 28 % Ar + C2H4 −−→ Ar + C2H2 + H2, (R 1.40)

∗ 10 % Ar + C2H4 −−→ Ar + C2H3 + H, (R 1.41)

∗ 10 % Ar + C2H4 −−→ Ar + CH2 + CH2. (R 1.42)

In the present work, kinetic analysis by Tsolas et al. is improved, by using a

27 kinetic model without some of the simplifying assumptions used in the previous work, extending the modeling predictions to other fuel mixtures (methane and propane), and analyzing the sensitivity of the modeling predictions to the choice of “conventional” chemistry mechanism, as discussed in detail in Section 3.3. The present kinetic model is based on a comprehensive review of air plasma kinetics by Kossyi et al.[3], including electron impact ionization and associative ionization processes, electron-ion recombination, electron attachment, chemical reactions of nitrogen and oxygen species in the ground electronic state, reactions of electronically excited molecules and atoms, and ion chemistry [3]. Some of these processes are discussed in Section 2.3.1 and Section 2.3.2. While this discussion is mainly focused on processes directly relevant to the present work, detailed and extensive reviews of plasma assisted combustion kinetics can be found in Refs. [1,2].

1.2 Background: Chemical Carbon Monoxide Lasers

Exothermic chemical reactions are commonly used for extraction of energy, where reactants are converted to lower energy products and the excess chemical energy is converted to work. Chemical lasers utilize these types of chemical reactions, where chemical energy is stored in internal modes of the products and is then extracted through the stimulated emission process generating laser power. Recent theoretical and experimental studies of the exothermic reaction of atomic carbon and molecular oxygen have suggested that a signiﬁcant fraction of the excess chemical energy (up to ≈30%) may be stored in the vibrational mode of the carbon monoxide product. These results suggest a potential development of a chemical carbon monoxide laser based on this reaction.

28 Electric discharge excited CO lasers emitting in the mid-infrared have demonstrated high power and high eﬃciency, up to 200 kW [47] and 50% [48]. The reported optimal performance was achieved using electric discharges operated at cryogenic temperatures. In these systems, laser gain is established on ro-vibrational transitions within the ground electronic state of the CO molecule, by rapid VV energy exchange among molecules in vibrationally excited levels initially populated by electron impact in the discharge. This VV exchange process was ﬁrst described by Treanor et al.[49] which results in a highly non-Boltzmann vibrational distribution among vibrational levels of molecules in low-temperature environments. It was shown by Rich [50] to cause partial population inversions between ro-vibrational levels and laser gain along P-branch lines in a high power CO laser.

1.2.1 Electric Power Generation On Hypersonic Vehicles

One of the possible applications of a new chemical CO laser, based on the reaction of carbon vapor with molecular oxygen, is electric power generation on board of a hypersonic vehicle. At these conditions, carbon vapor can be generated by carbon surface ablation by a high-speed flow or by an auxiliary discharge [51], and can be subsequently mixed with air to produced vibrationally excited CO in a chemical reaction with oxygen. Laser power would be generated in a supersonic flow laser cavity and converted to electrical power using photovoltaic cells. Thus, the laser would have to operate in a gas mixture with a significant fraction of air. Additionally, the flow temperature in the laser cavity may be fairly high, due to an oblique shock system slowing the flow upstream of the cavity. However, CO laser operation at elevated temperatures has been demonstrated previously. An optically pumped CO

29 laser operating in a CO-Ar mixture, at temperatures up to T = 450 K, pressure of P = 10 Torr, and CO partial pressure of 0.2–0.3 Torr was demonstrated by Ivanov et al.[52]. A chemical CO laser in a CS2-O2-He-Ar mixture was demonstrated at temperatures up to T = 500 ± 200 K by Boedeker et al.[53]. Adding nitrogen and oxygen to the laser mixture may signiﬁcantly aﬀect the CO vibrational distribution function, both due to VV energy transfer to N2 and O2 and due to VT relaxation by O atoms. Previous measurements of vibrational populations

of CO, N2, and O2 in optically pumped CO-N2, CO-O2, CO-air mixtures by Lee et al.[54] produced quantitiative insight into the eﬀect of air species on the vibrational energy distribution of CO. In these experiments, low vibrational states of CO were excited by resonant absorption of CO pump laser radiation, followed by VV energy

exchange among CO, N2, and O2 molecules. The results show that presence of nitrogen has a weak eﬀect on the CO vibrational distribution function, due to the fact that nitrogen has a larger energy spacing between vibrational levels, compared to that of

carbon monoxide, such that the rate of VV energy transfer from CO to N2 is lower compared to the rate of the reverse process. Because of this, most of the vibrational energy available in the mixture remained in the CO vibrational energy mode, with

relatively little vibrational excitation of N2 [54]. Adding oxygen to the mixture, on the other hand, considerably reduced energy stored in the carbon monoxide vibrational energy mode, such that the oxygen vibrational populations exceeded those of CO [54].

This occurs since O2 has a smaller vibrational energy spacing compared to that of

CO, such that vibrational energy is preferentially transferred from CO to O2 by VV exchange processes. These results demonstrate the negative impact that oxygen has on vibrational excitation of carbon monoxide, which is critical for laser operation in mixtures containing considerable amounts of air. In addition to this, O atoms

30 generated in CO-air mixtures that are reacting or excited by an electric discharge may further reduce vibrational nonequilibrium, due to rapid vibrational relaxation of CO

by O atoms and by CO2. In the present work, kinetic modeling of a supersonic flow, chemical carbon monoxide laser that could be used for conversion of chemical energy to laser power and subsequently to electrical power onboard a hypersonic vehicle is performed. Use of long range aircraft capable of high altitude hypersonic flight will be the next step in expanding the US Air Force global reach and space access [55]. Development of this technology would improve capabilities of both reconnaissance and orbital vehicles [55]. A well known problem in sustained hypersonic flight is lack of auxilary electrical power generation, on the order of 10–100 kW depending on the application [56, 57]. Hypersonic flight (M > 5) requires propulsion using rocket, ramjet, or scramjet engines, in all of which electrical power generation by coupling out some of the propulsion power from a primary engine is extremely challenging. Therefore sustained hypersonic flight requires development of new technologies for auxilary power generation. Designs exist which use the same power generation systems commonly used in current turbofan technologies to work with ramjet propulsion [58]. This approach is not feasible in scramjet engines where the flow remains supersonic throughout the engine flow channel, and therefore this solution limits the flight Mach numbers to the lower range of hypersonic flight. Battery technology lacks energy density when compared to chemical storage methods. Liquid hydrocarbon fuels have energy densities of 40–60 MJ kg−1 while the best rechargable batteries (Li-ion) have energy densities slightly below 1 MJ kg−1. Using non-rechargable lithium batteries only doubles the energy density of lithium-ion batteries, still lagging far behind hydrocarbon fuels, by over an order of magnitude. Therefore chemical energy storage remains the most

31 efficient approach for onboard auxilary power generation during sustained flight, but only if ambient air is used as an oxidizer. The most critical issue is generating electrical power without using mechanical energy conversion, which can be done only at relatively low flight Mach numbers. For this, energy conversion using a chemical laser and a photovoltaic cell is very attractive. This approach allows power extraction from the entire volume of the reacting flow, on time scales much shorter compared to flow residence time, such that it can be used even at high flight Mach numbers, without significantly affecting the flow. In fact, extracting laser power from a non-equilibrium hypersonic expansion flow would help increase the laser efficiency, due to significant temperature reduction during the expansion. Chemical carbon monoxide lasers, based on the reaction of carbon disulfide and molecular oxygen, present similar characteristics to the electric discharge pumped

lasers. The dominant CO product of CS2 + O and CS + O reactions contain several vibrational quanta, with peak population in v = 12 [59]. A major benefit of this system is the formation of total population inversion among the lower vibrational levels, resulting in higher gain on more ro-vibrational transitions, including R-branch lines. This approach has been used in high power chemical CO lasers [53, 59, 60]. Carbon disulfide, however, is a highly toxic compound and more costly than the common allotropes of carbon, making it a less desireable precursor. A novel chemical carbon monoxide laser based on the gas-phase reaction between atomic carbon vapor and molecular oxygen would exhibit numerous advantages over the current chemical or electric discharge carbon monoxide lasers. Higher gain associated with the total population inversion could be produced, and high power and efficiency could be achieved, due to the relatively slow VT and vibration-to-rotation (VR) relaxation

32 processes of CO. Finally, complications of using CS2 would be removed by replacing it with graphite or amorphous carbon as the carbon source in the reaction. Quantum chemical simulations have predicted that one of the dominant products of the reaction between carbon vapor and molecular oxygen would be vibrationally excited CO in the ground electronic state [61]. The heat of reaction

3 3 − 1 + 3 C( P) + O2( Σg ) −−→ CO(X Σ , v) = O( P), (R 1.43)

∆H = −132.6 kcal mol−1 (5.75 eV), is sufficiently large to populate a number of excited vibrational levels (CO vibrational quantum is approximately 0.26 eV). Subsequent crossed molecular beam experiments confirmed that the CO product is vibrationally excited [62]. These results also demonstrate total population inversion over the first five vibrational levels. Higher vibrational levels could not be observed due to spectral bandwidth limitation of the laser probe. Finally, recent work [51] demonstrated formation of highly vibrationally excited CO, up to at least v = 14, with absolute population inversions at v =4–7, in a chemical reaction between carbon vapor and molecular oxygen in a collision-dominated environment (P =15–20 Torr) and at low rotational-translational temperatures (T =400–450 K). This indicates feasibility of development of a new CO chemical laser using carbon vapor and oxygen as the reactants. A high fraction of reaction enthalpy stored in the CO vibrational mode (at least 10–20%) inferred from the data of Ref. [51] suggests that this laser may operate at high efficiency. More detailed discussion of the results of the work in Refs. [51,61,62] can be found in Section 1.2.2. This makes a chemical CO laser excited by a chemical reaction of carbon vapor and oxygen from the airflow a more attractive option for onboard laser power generation.

33 While the main focus of the present work is on kinetic modeling of a chemical carbon monoxide laser, its application for electrical power generation critically depends on the feasibility of use of photovoltaic cells for conversion of laser power to electrical power. Most currently available photovoltaic materials are based on silicon, which has a bandgap in the range of 1.1 eV, corresponding to light at a wavelength of

approximately 1.4 µm. In comparison, carbon monoxide lasers operating on CO fundamental transitions generate power in the range of 4.5–5 µm, which makes most photovoltaic materials ill-suited for this application. Recent work suggests that other photovoltaic materials, such as indium phosphide arsenide antimonide, may have

bandgap as low as 0.3 eV and spectral response up to 4.3 µm [63]. These materials could be used with CO lasers operating on ﬁrst overtone transitions, at wavelengths

in the range of 2–2.5 µm, which have significantly lower efficiency compared to CO fundamental lasers. Additional advances in development of photovoltaic cell materials with smaller bandgap and longer wavelength spectral response are necessary to make conversion of fundamental CO laser power to electrical power. The objectives of the present work are as follows: (i) to predict performance parameters of a new chemical CO laser excited by a chemical reaction between carbon vapor and oxygen, and (ii) to determine how adding significant amounts of nitrogen, oxygen, or air to the laser mixture affects CO laser power and spectrum. For this, kinetic modeling is performed of chemical reactions and vibrational energy transfer in non-equilibrium mixture of CO, helium, nitrogen, and oxygen, excited either by a chemical reaction between carbon vapor and oxygen or by an electric discharge, using the kinetic model described in Chapter 4 with results discussed in Chapter 5. In the modeling calculations, supersonic expansion is used to reduce the temperature of the laser mixture and to study laser operation in a high speed flow, such as would occur

34 in hypersonic ﬂight. Comparison of kinetic modeling predictions with the experiments using an electric discharge excited, supersonic ﬂow CO laser, is used to validate the model and to predict electrically excited and chemical laser performance parameters at the conditions where experimental data are not available.

1.2.2 Prior Work in Chemical Carbon Monoxide Lasers

Recent quantum chemistry simulations of the reaction between C atoms and O2 molecules predicted that at high collision energies (>1 eV), nearly 30% of the reaction enthalpy is stored in the vibrational mode of the CO product, as showin in Figure 1.9[61]. Indeed, subsequent crossed molecular beam experiments demonstrated that this reaction produces a total population inversion among several vibrational levels of CO at high collision energies, as seen in Figure 1.10[62]. In this experiment, carbon atoms and radicals were generated by laser ablation of a graphite sample. These results, however, are obtained at very low densities, such that they characterize a “nascent” vibrational distribution function of CO produced by the chemical reaction, before it is affected by molecular collisions. For operation of a chemical CO laser based on this approach, the CO product vibrational distribution needs to remain strongly non-equilibrium in collision-dominated environments, at pressures of at least several Torr. This was demonstrated in a recent experiment, where carbon vapor generated in an arc discharge in argon with graphite electrodes reacted with molecular oxygen in a flow reactor at pressures of 15–20 Torr and temperatures of T =400–500 K. In this experiment, the flow residence time in the reactor was much longer compared to the characteristic time of chemical reactions, such that the flow of reaction products

35 Figure 1.9: Energy partition of C + O2 reaction among diﬀerent energy modes of the CO product, predicted by theoretical quantum chemistry calculations. [61]

Figure 1.10: Vibrational level populations of carbon monoxide produced during gas phase reactions of carbon ablated from a graphite sample with molecular oxygen, measured in crossed molecular beam experiment. [62]

36 Figure 1.11: CO vibrational level populations inferred from infrared emission spectra of carbon monoxide produced in a chemical reaction of carbon species generated in an arc discharge with molecular oxygen, at argon buffer pressure of 20 Torr. [51] was in the collision dominated regime. Infrared emission spectra of CO product indicated its strong vibrational non-equilibrium, producing total population inversion at some conditions [51]. The CO VDF plotted in Figure 1.11 exhibits total population inversion on vibrational levels 4–7. At these conditions, up to 20% of the reaction enthalpy is stored in the vibrational energy of CO product. This result provides direct experimental verification of theoretical predictions of Schatz [61] and low density molecular beam experiments of Minton [62]. This also confirms the basic premise used in chemical CO laser kinetic modeling work in the present dissertation, that the reaction between carbon atoms and molecular oxygen produces carbon monoxide with sufficient vibrational excitation to produce gain and lasing on CO fundamental transitions.

37 The use of a CO chemical laser for electric power generation onboard a hypersonic vehicle imposes constraints on the properties of the laser medium, in particular its chemical composition, as well as pressure and temperature. Specifically, since the oxygen in chemical reaction with carbon vapor has to come from the airflow, the laser has to operate in a mixture dominated by nitrogen and oxygen, which is the second basic premise of the present work. This was demonstrated recently using an electric discharge excited, supersonic flow CO laser, shown schematically in Figure 1.12[64]. The main objective of these experiments was to study the effect of adding air species

(N2 and O2) to the baseline CO-He laser mixture on laser power and spectra. In the experiment, the laser was excited by a 1–2 kW RF electric discharge operated in the plenum of a Mach 3 supersonic ﬂow channel, generating strong vibrational

excitation of molecular species present in the mixture (CO, N2, and O2), and laser power was coupled out in a transverse laser cavity in the supersonic flow. A typical laser spectrum, as well as laser power measured in different mixtures, are shown in Figure 1.13 and Figure 1.14[64]. The fraction of air added to the flow in these experiments was limited by the capability to sustain the RF discharge in the plenum of the supersonic flow channel. In the present work, these experimental results, as well as the results shown in Figure 1.11, are used for validation of the kinetic model of a chemical supersonic flow CO laser. Note that, in addition to operating in a mixture dominated by air species, the new chemical CO laser may also need to operate at non-cryogenic temperatures, since decelerating the free stream hypersonic airflow to the conditions of the hypersonic laser cavity, as well as the reaction between carbon vapor and oxygen reaction may increase the flow temperature significantly. Previous experimental studies have demonstrated

that chemical CO lasers based on reactions of CS2 and O2 operate in high temperature

38 Figure 1.12: Schematic of electric discharge excited, supersonic ﬂow carbon monoxide laser. [64]

Figure 1.13: Laser power measured in an electric discharge excited, supersonic ﬂow carbon monoxide laser in a mixture of 97 Torr helium with 3.6 Torr CO, in the presence of air species. [64]

39 Figure 1.14: Laser spectrum in an electric discharge excited, supersonic ﬂow carbon monoxide laser, in a mixture of 97 Torr helium, 3.6 Torr CO, and 26.3 Torr N2.[64]

carbon disulfide flames, at temperatures upwards of T = 1000 K [60]. Similarly, an optically pumped CO laser was shown to operate at temperatures up to 450 K [52,53], with laser gain of up to 0.145 %/cm and efficiency for converting input pump laser power to output laser power predicted as high as 28% [52]. While the aforementioned experimental studies work to show feasibility of a new chemical CO laser based on the chemical reaction of carbon vapor and molecular oxygen, operated in a laser mixture dominated by air species, quantitative analysis of energy transfer processes and chemical reactions and prediction of laser performance parameters requires kinetic modeling. The kinetic model needs to incorporate vibrational energy transfer and relaxation processes among the species of interest

(primarily CO, N2, O2, and O atoms), as well as a state speciﬁc chemical reaction

between C atoms and O2 molecules. State speciﬁc sets of VV energy transfer among

the dominant molecular species (CO, N2, and O2) are based on experimental data and semiclassical trajectory calculations for CO-CO [65, 66]; experimental data [67–71]

and semiclassical trajectory calculations for N2-N2 and O2-O2 [72–75]; semiclassical

trajectory calculations for CO-N2 [76–78], CO-O2 [79], and N2-O2 [80,81].

40 In addition to VV processes, the model includes VT relaxation of CO by He [82,83], and by diatomic molecules (CO, N2, and O2)[66, 83], as well as N2 and O2 self relaxation [69, 72–74], relaxation between N2 and O2 [80, 83], N2 and O2 relaxation by He [71,84], and relaxation of O2 [85,86], N2 [41,87] and CO [88,89] by O atoms. State-specific rate coefficients of VV and VT processes are discussed in detail in Section 4.3, and detailed comparison of the rates used in the present work with the literature data is made in Appendix A. The structure of this disseration is as follows. Chapter 2 describes a kinetic model used for analysis of plasma assisted combustion experiments. Chapter 3 present results and discussion of kinetic modeling of several plasma assisted combustion experiments. Chapter 4 describes a kinetic model used for performance analysis of chemical and electric discharge excited CO lasers. Chapter 5 presents results and discussion of kinetic modeling of chemical and electric discharge excited CO lasers, as well as comparison with experimental results. Finally, Chapter 6 provides a summary of the results, presents conclusions, and outlines future work in this field.

41 Chapter 2

Plasma Assisted Combustion Kinetic Model

2.1 Plasma Perfectly Stirred Reactor Model

Chemkin-Pro Plasma Perfectly Stirred Reactor (PPSR) model was used as the basis for the present quasi-zero-dimensional plasma chemistry model. The governing equations are described in Section 2.1.1. Transport processes such as diﬀusion and forced convection are incorporated as quasi-zero-dimensional corrections, as discussed in Sections 2.1.2 and 2.1.3. Additionally, relaxation of excited species generated in the plasma may occur on time scales shorter than the acoustic time scale, which creates a transient pressure overshoot resulting in compression wave formation. The method to account for the pressure overshoot and temperature reduction behind the compression wave front is discussed in Section 2.1.4.

2.1.1 Governing Equations

The Chemkin-Pro PPSR is a modiﬁcation of a well known isotropic perfectly stirred reactor (PSR). The ﬁrst governing equation is the equation of state of a perfect gas,

R P = ρ 0 T, (2.1) µ

42 where P is the pressure, ρ is the mass density, R0 is the universal gas constant, T is the absolute temperature, and µ is the molecular weight of the mixture, deﬁned as

X µ = WkXk, (2.2) k∈species

with Wk being the molecular weight of species k, and Xk is its mole fraction. The Chemkin-Pro PPSR model also accounts for different temperatures for different species, which makes possible predicting electron temperature at the conditions when it is different from the heavy species temperature. In the configuration of the model used for the simulations discussed in Chapter 3, the pressure is specified as an input parameter (assumed to be constant unless the rapid heating correction, discussed in Section 2.1.4, is included). The gas temperature is predicted by the heavy species energy equation, Equation 2.9, such that Equation 2.1 yields the mass density of the mixture. The PPSR model considers an open system, therefore the global mass balance equation is solved as well. The model configuration used for the simulations in Chapter 3 is for a single inlet, single outlet flow reactor, for which the global mass balance is specified as dρ V– =m ˙ − m˙ , (2.3) dt in out where V– is the reactor volume, and m˙ in and m˙ out are the inlet and outlet mass flow rates, respectively. As stated above, the mass density (and thereby the time derivative of the mass density) is obtained from Equation 2.1, therefore Equation 2.3 is used to predict the outlet mass flow rate. The inlet mass flow rate is implicitly specified

43 through the reactor residence time, τres,

ρ V– m˙ in = . (2.4) τres

The choice of the residence time value is discussed in detail in Subsections 2.1.2 and 2.1.3, and the actual values used for modeling of diﬀerent experiments are discussed in Chapter 3. In addition to the global conservation equations, Equation 2.1 and Equation 2.3, ordinary diﬀerential equations (ODEs) for the mass fraction of each species in the mixture, dY ρ V– k =m ˙ (Y − Y ) − m˙ Y + W ω˙ V– , (2.5) dt in k,in k out k k k

th are also solved. In Equation 2.5, Yk is the mass fraction of the k species, and ω˙ k is the molar rate of production of species k by gas phase reactions. The first term on the right hand side of Equation 2.5 represents inlet flow of the kth species into the reactor, the second term represents the outflow of the same species, while the final term accounts for the net rate of production or consumption of the species,

! X Y 0 Y 00 00 0 νmi νmi ω˙ j = νji − νji kfi [Xm] − kri [Xm] . (2.6) i∈reactions m∈species m∈species

0 00 In Equation 2.6, νji and νji are the stoichiometric coeﬃcients for species j in the

reactants and products of chemical reaction i, respectively, kfi and kri are the forward

and reverse rate coeﬃcients of this reaction, respectively, and [Xm] is the molar concentration of species m. The quantity in the ﬁrst set of parentheses in Equation 2.6 is the number of particles of species j produced in each reaction act, and the quantity in the second set of parentheses is the net rate of reaction i per unit stoichiometric

44 coeﬃcient. The expression for the rate coeﬃcients kfi and kri are discussed in greater detail in Sections 2.2–2.4. The energy equation is shown below in the general form,

X dTk X dP ρ V– Y c = − V– h ω˙ W + V– + k p,k dt k k k dt k∈species k∈species X X ˙ m˙ in Yk,inhk,in +m ˙ out Ykhk + Qsource. (2.7) k∈species k∈species

In Equation 2.7, Tk is the temperature of species k, cp,k is the specific heat of species k at temperature Tk, and hk is the specific enthalpy of species k at temperature Tk. Equation 2.7 accounts for different temperatures of the species. The left hand side and first term on the right hand side of Equation 2.7 represent the change in thermal and chemical energy stored in the system, respectively, the second term on the right hand is the work by the system, the third and fourth terms on the right hand side are the enthalpy carried into and out of the system, respectively, by the inlet and outlet mass flows, and the fifth term on the right hand side is energy added from external sources to the system. In the present work, it is assumed that all heavy species are at a single temperature,

T , while electrons are at a diﬀerent (typically much higher) temperature Te. This assumption accounts for electrons in the plasma gaining energy from the externally applied electric ﬁeld and losing it in electron-heavy particle collisions. Therefore

45 Equation 2.7 is split into two separate equations, the electron energy equation,

dTe R dYe ρ V– Yecv,e − Te =m ˙ inYe,incp,e (Te,in − Te) − m˙ outYecp,eTe+ dt We dt ˙ inel ˙ ω˙ e V– cp,eWe(T − Te) − Qloss + Qsource, (2.8) and the heavy species energy equation,

dT R d(YeTe) X dP ρ V– c¯p(1 − Ye) + = − V– hkω˙ kWk + V– + dt We dt dt k6=e X X ˙ inel m˙ in Yk,inhk,in +m ˙ out Ykhk + Qloss. (2.9) k6=e k6=e

In Equation 2.8, c and c are the speciﬁc heats of electrons, equal to 3 R0 and v,e p,e 2 We 5 R0 respectively, Q˙ inel is the electron energy loss in inelastic collisions, and Q˙ , 2 We loss source the same as in Equation 2.7, is the discharge input power. Electron energy loss in elastic collisions with heavy species are neglected, due to the very small electron energy fraction lost in elastic collisions stemming from the large disparity in mass, as discussed in Section 1.1.4 and shown in Equation 1.4. The third term on the right hand side of Equation 2.8 accounts for the implicit assumption that new electrons produced by ionization are created at low temperature (equal to the heavy species temperature), which reduces the ensemble-averaged electron temperature. The heavy species energy equation, Equation 2.9, is obtained by subtracting Equation 2.8 from Equation 2.7, assuming that all heavy species have the same temperature. Equation 2.9 closes the system of governing equations. In the present model, the ion temperature is assumed to be the same as the neutral species temperature. This assumption is known to be inaccurate in low-

46 pressure plasmas [90,91] and in cathode layers [92], where the ion temperature may be significantly higher than the heavy species temperature, due to either low collision frequency (in low-pressure plasmas) or very high electric field (in the cathode layer). However, since the focus of the present work is on analysis of chemical kinetics of high-pressure reacting plasmas, outside of near-electrode layers and sheaths, i.e. at high ion-neutral collision frequencies and relatively low peak electric fields, applied for very short periods of time (a few ns), this assumption is justified.

2.1.2 Correction for Forced Convection

In some of the reacting plasma ﬂows modeled in Chapter 3, dominant chemical kinetic processes occur on the time scale comparable with the residence time in the reactor. For each set of conditions in Chapter 3, comparison of the ﬂow time scale with the characteristic time scale of the measurements is made, as discussed below. The experimental apparatus for which a convection correction may be required is a plane-to-plane, nanosecond pulse, dielectric barrier discharge (DBD) in a rectangular cross section channel. The discharge is operated in a repetitive burst mode, as shown schematically in Figure 2.1.

Discharge Pulses Discharge Burst Probe Laser Pulses

τ τ

Time 10 Hz

Figure 2.1: Timing schematic for a repetitively pulsed discharge burst, indicating individual discharge pulses, discharge bursts, and probe laser pulses.

47 The duration of individual discharge pulses is on the order of 10 ns. However, the burst duration (i.e. the time interval between the first and the last pulses in the burst) can be up to several ms, comparable to the flow residence time between the discharge electrodes. Also, the delay between the discharge burst and the laser pulse can be longer than the flow residence time. An example illustrating the calculation of the flow residence time (convection time) is shown in Figure 2.2. Panel (a) of Figure 2.2 shows the discharge schematic. The gas mixture flows through a rectangular cross section quartz channel from left to right. On the top and bottom walls of the quartz channel are two parallel plate electrodes connected to a nanosecond pulse duration high voltage generator. The volume from which a fluorescence or scattering signal from the probe laser beam is collected is shown in red. Panel (b) of Figure 2.2 shows the flow volume affected by the first discharge pulse. Between the first and the last pulses in the discharge burst, the gas volume affected by the first discharge pulse is convected downstream by the flow, as shown in panel (c) of Figure 2.2. While in the analysis below and in the calculations used in Chapter 3, a fully developed channel flow is assumed, a plug flow is shown in Figure 2.2 for simplicity. Panel (d) shows the flow at the time moment when the measurement volume begins to be affected by a flow volume which has not experienced the entire burst of discharge pulses. This time delay is chosen as the characteristic convection time. In the experiments discussed in Chapter 3, the channel width is greater than the channel height, and the channel length upstream of the electrodes is much greater compared to the height, such that the flow is assumed to be quasi-two-dimensional, fully

developed, and laminar (Reynolds number based on the channel height is Reh ≈ 100).

Therefore the centerline velocity, um, is a factor of 1.5 higher than the cross-section

48 HV HV

Measurement Location

Flow Flow

(a) (b) HV HV

Flow Flow

Figure 2.2: Schematic of event timing in a burst of discharge pulses in a flow, ignoring the boundary layer effects: (a) Electrode and flow configuration (b) First discharge pulse in the burst and affected flow volume (c) Last discharge pulse in the burst showing flow volume affected by the first and the last pulses, with overlap representing flow affected by the entire burst (d) Time moment at which the flow begins affecting the measurement results.

49 averaged velocity,u ¯,

 !2 y u(y) = um 1 − h  , (2.10) 2 3 u = u(y = 0) = u.¯ (2.11) m 2

The average velocity is calculated from the known mass ﬂow rate, temperature, pressure, and channel dimensions,

m˙ = ρuA¯ = ρuhw.¯ (2.12)

In Equation 2.12, m˙ is the mass ﬂow rate measured in the experiments by ﬂow controllers, ρ is the density calculated using Equation 2.1 using the known pressure, initial mixture composition, and temperature, A is the cross sectional area of the channel, with h and w being the height and width, respectively. The characteristic convection time is calculated from the centerline velocity and the distance from the upstream edge of the electrodes to the measurement volume (approximately equal to half the length of the electrodes, L),

L τconv ≈ . (2.13) 2um

Since the discharge burst can heat the ﬂow, the temperature predicted at the end of the discharge burst (without the convection correction) is used to calculate the characteristic convection time, as a lower bound estimate. Once the characteristic convection time is calculated, it is compared to the characteristic time scale of the dominant chemical reactions. If the time scales are of the

50 same order, then the characteristic convection time is used in Equation 2.4 as the reactor residence time, τres. If the characteristic convection time is signﬁcantly longer than the time scale for the chemical kinetics, then the reactor residence time is set to a very large value.

2.1.3 Correction for Diﬀusion of Species

In addition to convection due to the flow through the reactor, discussed in Section 2.1.2, diffusion of reactive species, in particular low atomic or molecular weight species, can occur on time scales comparable to that of chemical kinetics. A diffusion correction to the quasi-zero-dimensional model is included in two different geometries, first in the channel flow shown in Figure 2.2, and second in a diffuse filament discharge between two spherical electrodes, discussed in Section 3.2 The diffusion flux is proportional to the gradient of species number density,

~ji = −Di∇ni. (2.14)

Equation 2.14 is Fick’s first law of diffusion, where ~ji is the flux of species i, Di is its diffusion coefficient, which is dependent on both temperature and gas mixture, and ni is the number density of the species. From the diffusion equation,

dn i = −∇ · j~ = D ∇2n , (2.15) dt i i i

51 it can be shown that the characteristic time for the equilibration of species number density with its number density in the initial mixture composition is

2 lc τdiff = , (2.16) Di

where lc is the characteristic length for diffusion that depends on the geometry. Two different diffusion fluxes occur, unreacted species into the discharge volume and trace product species out of the discharge volume. If either of these processes occurs with

the same diffusion coefficient, Di, and therefore the same characteristic time as self diffusion of the primary constituent species in the gas mixture, the residence time

for the reactor, τres in Equation 2.4, is set equal to τdiff . On the other hand, if the diffusion of a species occurs at a different rate than the bulk mixture (for example H atoms in air), then the diffusion process is included as a zeroth order “diffusion” reaction in the chemical reaction mechanism,

A −−→ Adiﬀ , (R 2.1)

where Adiff represents a non-reactive species with the same thermodynamic properties as species A, acting as an effective “sink” of the diffusing species. Approximating diffusion in this way is appropriate only if the concentration of the diffusing species in the initial reactant mixture is much lower than its concentration in the reacting mixture, and if the effect of diffusion of this species has negligible effect on heat

transfer. For Reaction R 2.1, the rate of reaction, kdiﬀ , is taken as the inverse of the characteristic diﬀusion time,

Di kdiﬀ = 2 . (2.17) lc

52 The characteristic length of diﬀusion is calculated by solving the diﬀusion equation, Equation 2.15, with Dirichlet boundary conditions,

∂n = D∇2n s ∈ [s , s ], (2.18) ∂t min max

n (smin) = 0, n (smax) = 0, (2.19) where s is the spatial coordinate of interest. In the plane-to-plane geometry, shown in Figure 2.2, s is equivalent to the coordinate along the (shorter) vertical dimension of

h h the channel, with smin = − 2 and smax = 2 . In the sphere-to-sphere diﬀuse ﬁlament discharge geometry discussed in Section 3.2, s is the radial coordinate from the

ﬁlament centerline, with smin = 0 and smax set at the radius where the extrapolated concentration of species created in the discharge approaches zero, a multiple of the half width at half maximum (HWHM) of the discharge ﬁlament. Separating variables such that n(t, s) = T (t) · S(s), and analyzing the time varying portion of the solution,

dT = −Dλ2T, (2.20) dt where λ are the eigenvalues of Equation 2.15, gives the characteristic time for diﬀusion,

1 τ = . (2.21) diﬀ Dλ2

Comparing Equation 2.21 with Equation 2.16 shows that

1 l = . (2.22) c λ

Solving for the eigenvalues of the spatial portion of the diﬀusion equation provides

53 the characteristic diﬀusion length scale, lc. In rectangular coordinates for the plane- to-plane geometry, the eigenvalues are solutions of the equation

h cos (λy) = 0, y = ± , (2.23) 2

giving h l = (2.24) c π

as the characteristic diffusion length scale. For polar coordinates in the sphere-to-sphere diffuse filament discharge, the eigenvalues are solutions of the equation

J0(λsmax) = 0, (2.25)

where J0 is the Bessel function of the first kind, with first zero at λsmax = 2.4048 ... such that the characteristic diffusion length scale is

s l ≈ max . (2.26) c 2.4

The diffusion coefficient, D, depends on the mean free path for the diffusing species in the bath gas, as well as the average thermal velocity, i.e. on temperature and pressure. Specifically, the diffusion coefficient scales with temperature and pressure as follows, T 1.5 D ∝ (2.27) P

For stable species, experimental values for the diffusion coefficient are used when available. Whenever experimental data are not available, the diffusion coefficient is

54 calculated using the fit suggested by Fuller et al.[93,94]. The functional form used to calculate the diffusion coefficients, from Tang et al.[95], is

1.0868T (K)1.75 D(A, B)(cm2 s−1) = √ √ , (2.28) p −1 3 3 2 P (Torr) m(A, B)(g mol ) VA + VB where D(A, B) is the diﬀusion coeﬃcient of species A in a bath of species B, m(A, B) is the reduced molecular weight,

2 m(A, B) = , (2.29) 1 + 1 mA mB

and VA is the dimensionless diﬀusion volume of species A. The factor of 1.0868 in Equation 2.28 is from an empirical ﬁt by Fuller et al.[93] that matches an extensive

set of experimental data. In Equation 2.29, mA is the molecular weight of species A in g mol−1. The diﬀusion volumes necessary for the calculation in Equation 2.28 are taken from Tang et al.[95].

2.1.4 Heating on Sub-acoustic Time Scale

In all reactive ﬂows modeled in Chapter 3, ignition does not occur. Therefore, heat release caused by exothermic chemical reactions occurs on the time scale slower than the acoustic time scale, l τ = a , (2.30) acoust a where la is the characteristic length scale over which expansion occurs (e.g. the radius of the discharge ﬁlament or the length of the reaction region) and a is the speed of sound.

55 The acoustic time scale is the time scale for compression wave propagation and pressure equilibration. Basically, on time scales shorter than the acoustic time scale a gas mixture behaves as a constant volume system, and on time scales longer than the acoustic time it behaves as a constant pressure system (assuming that it has suﬃcient space to expand into). The approximate acoustic timescale can be calculated using Equation 2.30. Chemical reactions are not the only processes generating heat release in these reacting mixtures. In particular, heating generated during quenching of excited species generated in the plasma causes signiﬁcant temperature rise on time scales shorter than the acoustic time scale [40]. This results in a transient pressure overshoot, such that the constant pressure assumption used in the Chemkin-Pro PPSR model is no longer valid. In the present work, the transient pressure overshoot caused by heating on the sub-acoustic time scale is calculated as follows,

! t 2 P (t) = P0 + ρ0R (T (t) − T0) exp − . (2.31) τacoust

Equation 2.31 is in good agreement with the solution of 1D reacting compressible ﬂow Navier-Stokes equations [4], which predict compression wave formation and propagation.

In Equation 2.31, the subscript 0 indicates the initial values of parameters. Basically,

Equation 2.31 assumes pressure rise in a constant-volume system at t τacoust (i.e. before the compression wave has time to travel and reduce the pressure behind

the wave front), and gradual pressure equilibration to the initial value, P0, behind the

compression wave front, at t ' τacoust.

56 Since the Chemkin-Pro PPSR model does not have the capability to solve Equa- tion 2.31 coupled with the rest of the simulation, the time-dependent pressure is used as one of the input parameters. The initial approximation for the time-dependent temperature used in the right hand side of Equation 2.31 is obtained assuming constant pressure. Both time-dependent temperature and pressure predicted using this approach are converged after only 3–5 iterations, with accuracy better than 1%.

2.2 Electron Impact Rate Coeﬃcients

Electron impact is the mechanism by which energy added by the externally applied electric field to charged particles is transferred to heavy species, generating excited and reactive species, which broadens considerably the range of energy transfer processes and chemical reactions in the reacting mixture. Similar to “conventional” chemical kinetic processes, the rates of electron impact processes depend strongly on the collision energy, specifically the electron energy. Since in non-equilibrium plasmas, electron temperature is typically much higher than the heavy species temperature (due to electron heating by the applied electric field, and inefficient electron energy loss in elastic electron-neutral colissions), the rates of electron impact processes depend primarily on the electron temperature. The electron energy distribution function (EEDF) and electron swarm parameters, including electron temperature, mobility, diffusion coefficient, and rate coefficients of electron impact processes, can be measured directly [96] or predicted by solving the Boltzmann equation for electrons in the plasma at specific operating conditions determined by the applied electric field waveform, temperature, pressure, and chemical composition of the gas mixture [24, 97]. In most non-equilibrium plasma modeling

57 studies, the Boltzmann equation is solved in the so-called two-term approximation, predicting the isotropic part of the EEDF, yielding the electron temperature as well as the first expansion term of the anisotropic part of the EEDF, yielding electron mobility and drift velocity. This approximation is valid only if the electron drift velocity is much smaller compared to the thermal velocity, and if the characteristic time for EEDF relaxation is much shorter compared to the time scale of the applied electric field waveform. The quasi-steady-state EEDF predicted for the instantaneous value of the reduced electric field (ratio of the electric field to the total number density) can be used to predict electron swarm parameters. At a given reduced electric field, solving the two-term expansion Boltzmann equation allows calculation of both the electron temperature and rate coefficients for electron impact processes, accounting for the non-Maxwellian shape of the EEDF.

The electron swarm parameters can be expressed in terms of F0, the exponential part of the isotropic term of the EEDF, normalized such that

∞ Z 1 ε 2 F0dε = 1, (2.32) 0

where ε is the energy of electrons in electronvolts, and F1, the ﬁrst anisotropic term,

E 1 ∂F0 F1 = , (2.33) N σ˜m ∂ε

E where N is the reduced electric ﬁeld and σ˜m is the total momentum transfer cross section for electrons. In particular, the electron temperature is deﬁned as the average

58 value of the electron energy,

∞ 3 Z 3 kbTe = ε 2 F0dε, (2.34) 2 0 and rate coeﬃcients for electron impact processes are calculated as follows,

1 2e 2 Z ∞ ki = εσiF0dε, (2.35) m 0

where e is the elementary (or electron) charge, m is the electron mass, and σi is the energy dependent cross section. In the present work, Bolsig+, a freeware two-term Boltzmann equation solver [24], was solved for the mixture of interest over a wide range of reduced electric ﬁelds, and the output data, such as electron impact rate coeﬃcients, were interpolated as

functions of the electron temperature, Te,

b c1 c2 c3 c4 k(Te) = ATe exp + 2 + 3 + 4 , (2.36) Te Te Te Te

where A, b, and ci are the ﬁtting parameters. The electron temperature used in Equation 2.36 was predicted by the electron energy equation, Equation 2.8.

2.2.1 Argon Dominated Mixtures

Table 2.1 contains electron impact processes taken into account for kinetic modeling of argon dominated mixtures. The Process column shows the process equation, while the Product column shows the product species assumed in the simulation. This was

59 used to account for predissociated electronic states and electronic states with similar energies, which were grouped into a single state. All cross section are taken from the LXCat database [98]. Whenever the cross section database contains multiple cross sections for a particular process (e.g. involving different excited states of product species), the rate coefficient used is a sum of the rate coefficients based on individual cross sections. For all processes listed in Table 2.1 the reverse superelastic processes are not included in the chemical reaction model. These reactions would represent energy transfer from excited states back into the electron swarm, elevating the electron temperature after a discharge pulse [99]. While this is important for the modeling of electron dynamics, due to the low ionization fraction in the systems studied in Chapter 3, these processes have negligible effect on the reacting mixture chemistry in the afterglow.

Table 2.1: Electron impact processes included in argon dominated mixtures.

# Process Product

(R 2.2)1 e– + Ar −−→ e– + Ar*(11.55 eV) Ar*

(R 2.3) e– + Ar −−→ e– + e– + Ar+ Ar+

2 – – (R 2.4) e + O2 −−→ e + O2(v–1) O2

2 – – (R 2.5) e + O2 −−→ e + O2(v–2) O2

2 – – (R 2.6) e + O2 −−→ e + O2(v–3) O2

2 – – (R 2.7) e + O2 −−→ e + O2(v–4) O2

– – 1 (R 2.8) e + O2 −−→ e + O2(a ∆g ) O2(a) Continued on next page

60 # Process Product

– – 1 + (R 2.9) e + O2 −−→ e + O2(b Σg ) O2(b)

3 – – (R 2.10) e + O2 −−→ e + O2*(4.5 eV) O + O

3 – – 1 (R 2.11) e + O2 −−→ e + O2*(6.0 eV) O + O( D)

3 – – 1 1 (R 2.12) e + O2 −−→ e + O2*(8.4 eV) O( D) + O( D)

3 – – 1 (R 2.13) e + O2 −−→ e + O2*(9.97 eV) O + O( S)

– – – + + (R 2.14) e + O2 −−→ e + e + O2 O2 (R 2.15) e– + O −−→ e– + O(1D) O(1D)

(R 2.16) e– + O −−→ e– + O(1S) O(1S)

3 – – (R 2.17) e + CH4 −−→ e + CH4*(8.8 eV) CH3 + H

3 – – (R 2.18) e + CH4 −−→ e + CH4*(9.4 eV) CH2 + H2

3 – – (R 2.19) e + CH4 −−→ e + CH4*(12.5 eV) CH3 + H

3 – – (R 2.20) e + C2H4 −−→ e + C2H4*(5.8 eV) C2H2 + H2

3 – – (R 2.21) e + C2H4 −−→ e + C2H4*(6.5 eV) C2H2 + H + H

3 – – (R 2.22) e + C2H4 −−→ e + C2H4*(6.9 eV) C2H3 + H

3 – – (R 2.23) e + C2H4 −−→ e + C2H4*(8.4 eV) C2H + H2 + H

3 – – (R 2.24) e + C2H2 −−→ e + C2H2*(7.5 eV) C2H + H

3 – – (R 2.25) e + C2H2 −−→ e + C2H2*(8.7 eV) C2 + H2

3 – – (R 2.26) e + C2H2 −−→ e + C2H2*(9.8 eV) C + CH2

3 – – (R 2.27) e + C2H2 −−→ e + C2H2*(10.6 eV) CH + CH

3 – – (R 2.28) e + H2 −−→ e + H2*(8.9 eV) H + H

3 – – (R 2.29) e + H2 −−→ e + H2*(11.3 eV) H + H

3 – – (R 2.30) e + H2 −−→ e + H2*(11.75 eV) H + H Continued on next page

61 # Process Product

3 – – (R 2.31) e + H2 −−→ e + H2*(11.8 eV) H + H

3 – – (R 2.32) e + H2 −−→ e + H2*(12.4 eV) H + H

3 – – (R 2.33) e + H2 −−→ e + H2*(13.89 eV) H + H

3 – – (R 2.34) e + H2 −−→ e + H2*(14.0 eV) H + H

3 – – (R 2.35) e + H2 −−→ e + H2*(15.0 eV) H + H

3 – – (R 2.36) e + H2 −−→ e + H2*(15.2 eV) H + H

3 – – (R 2.37) e + H2 −−→ e + H2*(16.6 eV) H + H

– – + + (R 2.38) e + H2 −−→ e + H2 H2

1Reaction R 2.2 represents the entire electronic excitation cross section of Ar( 3 p5 4 s), which represents several closely spaced electronic states, 1s5, 1s4, 1s3, and 1s2, combined into a lumped state Ar*, referred to as “metastable argon” throughout this work. Reaction R 2.2 summarizes electron impact excitation of all four states.

2Reactions R 2.4 to R 2.7 are vibrational excitation of oxygen by electron impact. These processes are important for the electron energy balance, accounting for up to several percent of the discharge input energy partition. However, the vibrationally excited oxygen is not very reactive and represents a relatively small fraction of the mixture enthalpy. Therefore the energy going to vibrational excitation of oxygen is assumed to thermalize.

3Many of the processes in Table 2.1 list dissociation products in the Product column for electronic excitations (in particular Reactions R 2.10–R 2.13 for oxygen, Reactions R 2.17–R 2.19 for methane,

Reactions R 2.20–R 2.23 for ethylene, Reactions R 2.24–R 2.27 for C2H2, and Reactions R 2.28–R 2.37

62 for hydrogen). The dissociation products listed in Table 2.1 were chosen based on change in

enthalpy for various dissociation products and the excitation energy. It was found that the results in

Chapter 3 are not very sensitive to the dissociation product distribution, but sensitive to the fact

that radicals in some form were produced in the plasma. Additionally, in argon-dominated mixtures,

the dissociation of fuel, in particular, occurs primarily by collisional quenching of metastable argon

for which dissociation pathways are better understood, particularly for CH4 and C2H4, rather than

electron impact.

2.2.2 Air Dominated Mixtures

Table 2.2 contains electron impact processes taken into account in kinetic modeling of air and fuel-air plasmas. The Process column shows the excited state, while the Product column shows the product which was assumed in the simulation. This was used to account for predissociated electronic states and electronic states that were grouped into a single state. All cross section from the LXCat database [98]. Whenever the cross section database contains multiple cross sections for a particular process (e.g. involving different excited states of the product species), the rate coefficient used is a sum of the rate coefficients based on individual cross sections. For all the processes listed in Table 2.2, the reverse superelastic processes are not included in the chemical reaction model. These reactions represent energy transfer from excited states back to the electrons, elevating the electron temperature after a discharge pulse [99]. While this is important for the modeling of electron dynamics, due to the low ionization fraction in the systems studied in Chapter 3, these processes have negligible effect on the reacting mixture chemistry in the afterglow.

63 Table 2.2: Electron impact processes included in air dominated mixtures.

# Process Product

– – (R 2.39) e + N2 −−→ e + N2(v–1) N2(v–1)

– – (R 2.40) e + N2 −−→ e + N2(v–2) N2(v–2)

– – (R 2.41) e + N2 −−→ e + N2(v–3) N2(v–3)

– – (R 2.42) e + N2 −−→ e + N2(v–4) N2(v–4)

– – (R 2.43) e + N2 −−→ e + N2(v–5) N2(v–5)

– – (R 2.44) e + N2 −−→ e + N2(v–6) N2(v–6)

– – (R 2.45) e + N2 −−→ e + N2(v–7) N2(v–7)

– – (R 2.46) e + N2 −−→ e + N2(v–8) N2(v–8)

1 – – 3 + 3 (R 2.47) e + N2 −−→ e + N2(A Σu , v–0-4) N2(A Σ)

1 – – 3 + 3 (R 2.48) e + N2 −−→ e + N2(A Σu , v–5-9) N2(A Σ)

1 – – 3 + 3 (R 2.49) e + N2 −−→ e + N2(A Σu , v> 10) N2(A Σ)

2a – – 3 3 (R 2.50) e + N2 −−→ e + N2(B Πg ) N2(B Π)

2a – – 3 3 (R 2.51) e + N2 −−→ e + N2(W ∆u ) N2(W ∆)

2a – – 03 – 03 (R 2.52) e + N2 −−→ e + N2(B Σu ) N2(B Σ)

2b – – 01 – 01 (R 2.53) e + N2 −−→ e + N2(a Σu ) N2(a Σ)

2b – – 1 1 (R 2.54) e + N2 −−→ e + N2(a Πg ) N2(a Π)

2b – – 1 1 (R 2.55) e + N2 −−→ e + N2(w ∆u ) N2(w ∆)

2c – – 3 3 (R 2.56) e + N2 −−→ e + N2(C Πu ) N2(C Π)

2c – – 3 + 3 (R 2.57) e + N2 −−→ e + N2(E Σg ) N2(E Σ)

– – 001 + 001 (R 2.58) e + N2 −−→ e + N2(a Σg ) N2(a Σ) Continued on next page

64 # Process Product

– – (R 2.59) e + N2 −−→ e + N2(sum of singlets) N + N

– – – + + (R 2.60) e + N2 −−→ e + e + N2 N2

3 – – (R 2.61) e + O2 −−→ e + O2(v–1) O2

3 – – (R 2.62) e + O2 −−→ e + O2(v–2) O2

3 – – (R 2.63) e + O2 −−→ e + O2(v–3) O2

3 – – (R 2.64) e + O2 −−→ e + O2(v–4) O2

– – 1 (R 2.65) e + O2 −−→ e + O2(a ∆g ) O2(a)

– – 1 + (R 2.66) e + O2 −−→ e + O2(b Σg ) O2(b)

4 – – (R 2.67) e + O2 −−→ e + O2*(4.5 eV) O + O

4 – – 1 (R 2.68) e + O2 −−→ e + O2*(6.0 eV) O + O( D)

4 – – 1 1 (R 2.69) e + O2 −−→ e + O2*(8.4 eV) O( D) + O( D)

4 – – 1 (R 2.70) e + O2 −−→ e + O2*(9.97 eV) O + O( S)

– – – + + (R 2.71) e + O2 −−→ e + e + O2 O2 (R 2.72) e– + O −−→ e– + O(1D) O(1D)

(R 2.73) e– + O −−→ e– + O(1S) O(1S)

– – (R 2.74) e + H2 −−→ e + H2(v–1) H2(v–1)

– – (R 2.75) e + H2 −−→ e + H2(v–2) H2(v–2)

– – (R 2.76) e + H2 −−→ e + H2(v–3) H2(v–3)

4 – – (R 2.77) e + H2 −−→ e + H2*(8.9 eV) H + H

4 – – (R 2.78) e + H2 −−→ e + H2*(11.3 eV) H + H

4 – – (R 2.79) e + H2 −−→ e + H2*(11.75 eV) H + H

4 – – (R 2.80) e + H2 −−→ e + H2*(11.8 eV) H + H Continued on next page

65 # Process Product

4 – – (R 2.81) e + H2 −−→ e + H2*(12.4 eV) H + H

4 – – (R 2.82) e + H2 −−→ e + H2*(13.89 eV) H + H

4 – – (R 2.83) e + H2 −−→ e + H2*(14.0 eV) H + H

4 – – (R 2.84) e + H2 −−→ e + H2*(15.0 eV) H + H

4 – – (R 2.85) e + H2 −−→ e + H2*(15.2 eV) H + H

4 – – (R 2.86) e + H2 −−→ e + H2*(16.6 eV) H + H

– – + + (R 2.87) e + H2 −−→ e + H2 H2

1 3 The reactivity of N2(A Σ) is assumed to be dominated by the energy of the electronic excitation, therefore the vibrational portion of the excitation is assumed to thermalize.

2While electron impact excitation cross sections for each of these electronic states are known, reaction rate data for some of them are not available. It is therefore assumed that electronic states with close energies react with heavy species at the same rate. Three such groupings are denoted with

2a 2b 2c , and , often refered to in the literature as N2(B), N2(a), and N2(C), respectively.

3Reactions R 2.61 to R 2.64 are vibrational excitation of oxygen by electron impact. These processes are important for the electron energy balance, accounting for up to several percent of the energy discharge power partition. However, vibrationally excited oxygen is not very reactive and represents a relatively small fraction of the mixture enthalpy. Therefore the energy going to vibrational excitation of oxygen is assumed to thermalize.

4Many of the processes in Table 2.2 list dissociated products in the Product column for electronic excitations (in particular, Reactions R 2.59 for nitrogen, Reactions R 2.67–R 2.70 for oxygen, and

66 Reaction R 2.77–R 2.86 for hydrogen). Since excitation energy for these states exceed the dissociation

energy, these states are assumed to be predissociated.

2.3 Reactions of Excited Species

2.3.1 Argon Dominated Mixtures

Table 2.3 contains reactions of excited species in argon dominated mixtures. For all the processes listed in Table 2.3, the reverse processes are not included in the chemical reaction model. These reactions would represent energy transfer primarily from ground product state species into excited state reactant species. Since the temperatures in the plasmas studied in the present work, 300–1300 K (0.02–0.11 eV), are signiﬁcantly lower than the excitation energies of the electronic states, 1–12 eV, the rate coeﬃcients of the reverse processes are very slow.

67 Table 2.3: Reactions of excited species included in argon dominated mixtures.

3 # Process k (cm /s), T , Te (K) Ref (R 2.88) Ar* + Ar −−→ Ar + Ar 2.2 · 10−15 [100]

(R 2.89) Ar* + Ar + Ar −−→ Ar + Ar + Ar 1.4 · 10−32 [100]

−10 (R 2.90) Ar* + O2 −−→ Ar + O + O 2.1 · 10 [101]

−11 (R 2.91) Ar* + N2 −−→ Ar + N + N 3.6 · 10 [102]

−11 (R 2.92) Ar* + H2 −−→ Ar + H + H 6.6 · 10 [102] (R 2.93) Ar* + CH −−→ Ar + C + H 5.0 · 10−10 [103]

−10 (R 2.94) Ar* + CH4 −−→ Ar + CH2 + H + H 2.2 · 10 [101, 104]

−10 (R 2.95) Ar* + CH4 −−→ Ar + CH2 + H2 1.1 · 10 [101, 104]

−11 (R 2.96) Ar* + CH4 −−→ Ar + CH + H2 + H 3.0 · 10 [105]

1 −10 (R 2.97) Ar* + C2H4 −−→ Ar + C2H2 + H + H 2.81 · 10 [46, 102]

1 −10 (R 2.98) Ar* + C2H4 −−→ Ar + C2H2 + H2 1.51 · 10 [46, 102]

1 −10 (R 2.99) Ar* + C2H4 −−→ Ar + C2H3 + H 0.54 · 10 [46, 102]

1 −10 (R 2.100) Ar* + C2H4 −−→ Ar + CH2 + CH2 0.54 · 10 [46, 102]

−10 (R 2.101) Ar* + C2H2 −−→ Ar + C2H + H 5.6 · 10 [101]

−10 (R 2.102) Ar* + C2H6 −−→ Ar + C2H5 + H 5.6 · 10 [105, 106]

−12 (R 2.103) Ar* + C2H6 −−→ Ar + CH + CH3 + H2 1.5 · 10 [105, 106]

−12 (R 2.104) Ar* + C2H6 −−→ Ar + CH + CH4 + H 1.5 · 10 [105, 106]

2 −10 (R 2.105) Ar* + C3H8 −−→ Ar + C3H6 + H + H 3.8 · 10 [46, 102]

2 −10 (R 2.106) Ar* + C3H8 −−→ Ar + C3H6 + H2 2.04 · 10 [46, 102]

2 −10 (R 2.107) Ar* + C3H8 −−→ Ar + C3H7 + H 0.73 · 10 [46, 102] Continued on next page

68 3 # Process k (cm /s), T , Te (K) Ref

2 −10 (R 2.108) Ar* + C3H8 −−→ Ar + C2H6 + CH2 0.73 · 10 [46, 102]

+ + −31 (R 2.109) Ar + Ar + Ar −−→ Ar2 + Ar 1.3 · 10 [107]

+ – −7 (R 2.110) Ar2 + e −−→ Ar + Ar 8.0 · 10 [107]

+ – −4 −1 (R 2.111) O2 + e −−→ O + O 6.0 · 10 Te (R 2.112) Ar+ + e– + e– −−→ Ar + e– 1.0 · 10−34 [108]

+ + −9 (R 2.113) CH4 + Ar −−→ CH2 + H2 + Ar 1.0 · 10 [106, 109]

+ + −9 (R 2.114) Ar + H2 −−→ Ar + H2 1.0 · 10 [110]

+ + −10 (R 2.115) Ar + H2 −−→ Ar + H2 1.461 · 10 [111]

1 −13 −1564 (R 2.116) O2(a ∆) + O3 −−→ O2 + O2 + O 9.7 · 10 exp T [3] 1 −20 (R 2.117) O2(a ∆) + O2 −−→ O2 + O2 2.3 · 10 [3]

1 −16 (R 2.118) O2(a ∆) + O −−→ O2 + O 7.0 · 10 [3]

1 −16 (R 2.119) O2(a ∆) + Ar −−→ O2 + Ar 6.0 · 10 [3]

1 −11 (R 2.120) O2(b Σ) + O3 −−→ O2 + O2 + O 1.8 · 10 [3]

1 1 −22 2.4 −241 (R 2.121) O2(b Σ) + O2 −−→ O2(a ∆) + O2 4.3 · 10 T exp T [3] 1 1 −14 (R 2.122) O2(b Σ) + O −−→ O2(a ∆) + O 8.0 · 10 [3]

1 1 −11 −0.1 −4201 (R 2.123) O2(b Σ) + O −−→ O2 + O( D) 6.0 · 10 T exp T [3] 1 −16 (R 2.124) O2(b Σ) + Ar −−→ O2 + Ar 1.0 · 10 [3]

1 1 −11 67 (R 2.125) O( D) + O2 −−→ O + O2(b Σ) 2.56 · 10 exp T [3] 1 −12 67 (R 2.126) O( D) + O2 −−→ O + O2 6.4 · 10 exp T [3] 1 −10 (R 2.127) O( D) + O3 −−→ O + O + O2 2.3 · 10

1 −10 (R 2.128) O( D) + O3 −−→ O2 + O2 1.2 · 10 [3] (R 2.129) O(1D) + Ar −−→ O + Ar 5.0 · 10−12

Continued on next page

69 3 # Process k (cm /s), T , Te (K) Ref

1 1 −12 850 (R 2.130) O( S) + O2 −−→ O( D) + O2 1.333 · 10 exp T [3] 1 1 −10 (R 2.131) O( S) + O3 −−→ O( D) + O + O2 2.9 · 10 [3]

1 −10 (R 2.132) O( S) + O3 −−→ O2 + O2 2.9 · 10 [3]

1 1 1 1 −11 (R 2.133) O( S) + O2(a ∆) −−→ O( D) + O2(b Σ) 3.6 · 10 [3]

1 1 −11 (R 2.134) O( S) + O2(a ∆) −−→ O + O + O 3.4 · 10 [3]

1 1 1 −10 (R 2.135) O( S) + O2(a ∆) −−→ O + O2(a ∆) 1.3 · 10 [3]

1 1 −11 −301 (R 2.136) O( S) + O −−→ O( D) + O 5 · 10 exp T [3] 1 −9 −17906 (R 2.137) O2(a ∆) + H2 −−→ OH + OH 2.8 · 10 exp T [112] 1 −19 0.5 (R 2.138) O2(a ∆) + H2 −−→ O2 + H2 2.6 · 10 T

1 −11 −2530 (R 2.139) O2(a ∆) + H −−→ O + OH 1.3 · 10 exp T [112] 1 −11 −2530 (R 2.140) O2(a ∆) + H −−→ O2 + H 5.2 · 10 exp T [112] 1 −11 (R 2.141) O2(a ∆) + HO2 −−→ O2 + HO2 2.0 · 10 [112]

1 −12 (R 2.142) O2(b Σ) + H2 −−→ O2 + H2 1.0 · 10 [112]

1 −10 (R 2.143) O( D) + H2 −−→ H + OH 1.1 · 10 [34]

1 −16 (R 2.144) O( S) + H2 −−→ O + H2 2.6 · 10 [34]

1 −10 (R 2.145) O( D) + CH4 −−→ CH3 + OH 1.89 · 10 [35]

1 −10 (R 2.146) O( D) + CH4 −−→ CH3O + H 0.31 · 10 [35]

1 −14 (R 2.147) O( S) + CH4 −−→ O + CH4 2.7 · 10 [34]

1 −10 (R 2.148) O( D) + C2H4 −−→ C2H3 + OH 4.0 · 10 [34]

1 −9 (R 2.149) O( S) + C2H4 −−→ C2H4 + O 1.0 · 10 [34]

1 −10 (R 2.150) O( D) + C2H2 −−→ C2H + OH 3.0 · 10

1 −10 (R 2.151) O( S) + C2H2 −−→ C2H2 + O 9.0 · 10 [34] Continued on next page

70 3 # Process k (cm /s), T , Te (K) Ref

3 1 −10 (R 2.152) O( D) + C3H8 −−→ N–C3H7 + OH 3.95 · 10 [35]

3 1 −10 (R 2.153) O( D) + C3H8 −−→ I–C3H7 + OH 3.95 · 10 [35]

1 −9 (R 2.154) O( D) + C3H6 −−→ C3H5 + OH 1.0 · 10 [34]

1 −10 (R 2.155) O( S) + C3H6 −−→ C3H6 + O 8.0 · 10 [34]

1 −10 (R 2.156) O( D) + C2H6 −−→ C2H5 + OH 6.3 · 10 [35]

1 −12 (R 2.157) O( S) + C2H6 −−→ C2H6 + O 1.0 · 10 [34]

71 1The total quenching rate of metastable argon by ethylene was taken from Velazco et al.[102] while the product branching ratio is taken from Tsolas et al.[46].

2The total quenching rate of metastable argon by propane was taken from Velazco et al.[102] while the product branching ratio is assumed to be the same as for ethylene, which was inferred

from experimental results by Tsolas et al.[46].

3Assumed equal distribution of product channels.

2.3.2 Air Dominated Mixtures

Table 2.4 contains reactions of excited species in air and fuel-air mixtures. For all the processes listed in Table 2.4, the reverse processes are not included in the chemical reaction model. These reactions would represent energy transfer primarily from ground product state species into excited state reactant species. Since the temperatures in the plasmas studied in the present work, 300–1300 K (0.02–0.11 eV), are signiﬁcantly lower than the excitation energies of the electronic states, 1–12 eV, the rate coeﬃcients of the reverse processes are very slow.

72 Table 2.4: Reactions of excited species in air and fuel-air plasmas.

3 # Process k (cm /s), T , Te (K) Ref

3 −12 (R 2.158) N2(A Σ) + O2 −−→ N2 + O + O 2.54 · 10 [3]

3 −16 0.55 (R 2.159) N2(A Σ) + O2 −−→ N2O + O 8.68 · 10 T

3 2 −12 (R 2.160) N2(A Σ) + O −−→ NO + N( D) 7 · 10 [3]

3 −11 (R 2.161) N2(A Σ) + N2O −−→ N2 + N + NO 1 · 10 [3]

3 3 3 −4 −2.64 (R 2.162) N2(A Σ) + N2(A Σ) −−→ N2(C Π) + N2 5.54 · 10 T [3]

3 −18 (R 2.163) N2(A Σ) + N2 −−→ N2 + N2 3 · 10 [3]

3 −15 0.55 (R 2.164) N2(A Σ) + O2 −−→ N2 + O2(a) 8.68 · 10 T

3 −15 0.55 (R 2.165) N2(A Σ) + O2 −−→ N2 + O2(b) 8.68 · 10 T

3 2 −19 −0.67 (R 2.166) N2(A Σ) + N −−→ N2 + N( P) 1.79 · 10 T

3 1 −11 (R 2.167) N2(A Σ) + O −−→ N2 + O( S) 2.1 · 10 [3]

3 −11 (R 2.168) N2(A Σ) + NO −−→ N2 + NO 7 · 10 [3]

3 3 −11 (R 2.169) N2(B Π) + N2 −−→ N2(A Σ) + N2 5 · 10

3 3 5 (R 2.170) N2(B Π) −−→ N2(A Σ) 1.5 · 10 [3]

3 3 −10 (R 2.171) N2(B Π) + NO −−→ N2(A Σ) + NO 2.4 · 10 [3]

1a 3 −10 (R 2.172) N2(B Π) + O2 −−→ N2 + O + O 3 · 10 [3]

1a 3 −10 (R 2.173) N2(W ∆) + O2 −−→ N2 + O + O 3 · 10 [3]

1a 03 −10 (R 2.174) N2(B Σ) + O2 −−→ N2 + O + O 3 · 10 [3]

1b,2 01 −10 (R 2.175) N2(a Σ) + O2 −−→ N2 + O + O 3 · 10

1b,2 1 −10 (R 2.176) N2(a Π) + O2 −−→ N2 + O + O 3 · 10

1b,2 1 −10 (R 2.177) N2(w ∆) + O2 −−→ N2 + O + O 3 · 10 Continued on next page

73 3 # Process k (cm /s), T , Te (K) Ref

1b,2 001 −10 (R 2.178) N2(a Σ) + O2 −−→ N2 + O + O 3 · 10

1a 3 2 −10 (R 2.179) N2(B Π) + O −−→ NO + N( D) 3 · 10

1a 3 2 −10 (R 2.180) N2(W ∆) + O −−→ NO + N( D) 3 · 10

1a 03 2 −10 (R 2.181) N2(B Σ) + O −−→ NO + N( D) 3 · 10

1c,2 3 2 −10 (R 2.182) N2(C Π) + O −−→ NO + N( D) 3 · 10

1c,2 3 2 −10 (R 2.183) N2(E Σ) + O −−→ NO + N( D) 3 · 10

1b,2 01 2 −10 (R 2.184) N2(a Σ) + O −−→ NO + N( D) 3 · 10

1b,2 1 2 −10 (R 2.185) N2(a Π) + O −−→ NO + N( D) 3 · 10

1b,2 1 2 −10 (R 2.186) N2(w ∆) + O −−→ NO + N( D) 3 · 10

1b,2 001 2 −10 (R 2.187) N2(a Σ) + O −−→ NO + N( D) 3 · 10

1 3 −13 (R 2.188) N2(a Π) + N2 −−→ N2(B Π) + N2 2 · 10 [3]

1 −10 (R 2.189) N2(a Π) + NO −−→ N2 + N + O 3.6 · 10 [3]

3 3 7 (R 2.190) N2(C Π) −−→ N2(B Π) 3 · 10 [3]

3 1 −11 (R 2.191) N2(C Π) + N2 −−→ N2(a Π) + N2 1 · 10 [3]

3 1 −10 (R 2.192) N2(C Π) + O2 −−→ N2 + O + O( S) 3 · 10 [3]

3 1 −10 (R 2.193) N2(E Σ) + O2 −−→ N2 + O + O( S) 3 · 10 [3]

1 −13 −1564 (R 2.194) O2(a ∆) + O3 −−→ O2 + O2 + O 9.7 · 10 exp T [3] 1 −14 −600 (R 2.195) O2(a ∆) + N −−→ NO + O 2 · 10 exp T [3] 1 −21 (R 2.196) O2(a ∆) + N2 −−→ O2 + N2 3 · 10 [3]

1 −20 0.8 (R 2.197) O2(a ∆) + O2 −−→ O2 + O2 2.3 · 10 T [3]

1 −16 (R 2.198) O2(a ∆) + O −−→ O2 + O 7 · 10 [3]

1 −11 (R 2.199) O2(a ∆) + NO −−→ O2 + NO 2.5 · 10 [3] Continued on next page

74 3 # Process k (cm /s), T , Te (K) Ref

1 −11 (R 2.200) O2(b Σ) + O3 −−→ O2 + O2 + O 1.8 · 10 [3]

1 1 −15 −253 (R 2.201) O2(b Σ) + N2 −−→ O2(a ∆) + N2 4.9 · 10 exp T [3] 1 1 −22 2.4 −241 (R 2.202) O2(b Σ) + O2 −−→ O2(a ∆) + O2 4.3 · 10 T exp T [3] 1 1 −14 (R 2.203) O2(b Σ) + O −−→ O2(a ∆) + O 8 · 10 [3]

1 1 −11 −0.1 −4201 (R 2.204) O2(b Σ) + O −−→ O2 + O( D) 6 · 10 T exp T [3] 1 1 −14 (R 2.205) O2(b Σ) + NO −−→ O2(a ∆) + NO 4 · 10 [3]

2 −14 0.5 (R 2.206) N( D) + O2 −−→ NO + O 8.66 · 10 T [3]

2 1 −13 0.5 (R 2.207) N( D) + O2 −−→ NO + O( D) 3.46 · 10 T [3]

2 −11 (R 2.208) N( D) + NO −−→ N2O 6 · 10 [3]

2 −12 (R 2.209) N( D) + N2O −−→ NO + N2 3 · 10 [3]

2 −14 (R 2.210) N( D) + N2 −−→ N + N2 2 · 10

2 −12 (R 2.211) N( P) + O2 −−→ NO + O 2.6 · 10 [3]

2 3 −11 (R 2.212) N( P) + NO −−→ N2(A Σ) + O 3.4 · 10 [3]

2 2 −18 (R 2.213) N( P) + N2 −−→ N( D) + N2 2 · 10 [3] (R 2.214) N(2P) + N −−→ N(2D) + N 1.8 · 10−12 [3]

1 −11 107 (R 2.215) O( D) + N2 −−→ O + N2 1.8 · 10 exp T [3] 1 1 −11 67 (R 2.216) O( D) + O2 −−→ O + O2(b Σ) 2.56 · 10 exp T [3] 1 −12 67 (R 2.217) O( D) + O2 −−→ O + O2 6.4 · 10 exp T [3] 1 −10 (R 2.218) O( D) + O3 −−→ O + O + O2 2.3 · 10

1 −10 (R 2.219) O( D) + O3 −−→ O2 + O2 1.2 · 10 [3]

1 −10 (R 2.220) O( D) + NO −−→ N + O2 1.7 · 10 [3]

1 −11 (R 2.221) O( D) + N2O −−→ NO + NO 7.2 · 10 [3] Continued on next page

75 3 # Process k (cm /s), T , Te (K) Ref

1 −11 (R 2.222) O( D) + N2O −−→ N2 + O2 4.4 · 10 [3]

3 1 −17 (R 2.223) O( S) + N2 −−→ N + NO 5 · 10 [3]

1 1 −12 −850 (R 2.224) O( S) + O2 −−→ O( D) + O2 1.333 · 10 exp T [3] 1 1 −10 (R 2.225) O( S) + O3 −−→ O( D) + O + O2 2.9 · 10 [3]

1 −10 (R 2.226) O( S) + O3 −−→ O2 + O2 2.9 · 10 [3] (R 2.227) O(1S) + NO −−→ O + NO 2.9 · 10−10

(R 2.228) O(1S) + NO −−→ O(1D) + NO 5.1 · 10−10

1 −12 (R 2.229) O( S) + N2O −−→ O + N2O 6.3 · 10 [3]

1 1 −12 (R 2.230) O( S) + N2O −−→ O( D) + N2O 3.1 · 10 [3]

1 1 1 1 −11 (R 2.231) O( S) + O2(a ∆) −−→ O( D) + O2(b Σ) 3.6 · 10 [3]

1 1 −11 (R 2.232) O( S) + O2(a ∆) −−→ O + O + O 3.4 · 10 [3]

1 1 1 −10 (R 2.233) O( S) + O2(a ∆) −−→ O + O2(a ∆) 1.3 · 10 [3]

1 1 −11 −301 (R 2.234) O( S) + O −−→ O( D) + O 5.0 · 10 exp T [3] 3 −10 −3500 (R 2.235) N2(A Σ) + H2 −−→ N2 + H + H 4.4 · 10 exp T [39] 1a 3 3 −11 (R 2.236) N2(B Π) + H2 −−→ N2(A Σ) + H2 2.5 · 10 [39]

1a 3 3 −11 (R 2.237) N2(W ∆) + H2 −−→ N2(A Σ) + H2 2.5 · 10 [39]

1a 03 3 −11 (R 2.238) N2(B Σ) + H2 −−→ N2(A Σ) + H2 2.5 · 10 [39]

1b 01 −11 (R 2.239) N2(a Σ) + H2 −−→ N2 + H + H 2.6 · 10 [39]

1b 1 −11 (R 2.240) N2(a Π) + H2 −−→ N2 + H + H 2.6 · 10 [39]

1b 1 −11 (R 2.241) N2(w ∆) + H2 −−→ N2 + H + H 2.6 · 10 [39]

1 −9 −17906 (R 2.242) O2(a ∆) + H2 −−→ OH + OH 2.8 · 10 exp T [112] 1 −19 (R 2.243) O2(a ∆) + H2 −−→ O2 + H2 2.6 · 10 Continued on next page

76 3 # Process k (cm /s), T , Te (K) Ref

1 −11 −2530 (R 2.244) O2(a ∆) + H −−→ O + OH 1.3 · 10 exp T [112] 1 −11 −2530 (R 2.245) O2(a ∆) + H −−→ O2 + H 5.2 · 10 exp T [112] 1 −11 (R 2.246) O2(a ∆) + HO2 −−→ O2 + HO2 2.0 · 10 [112]

1 1 −12 (R 2.247) O2(b Σ) + H2 −−→ O2(a ∆) + H2 1.0 · 10 [112]

2 −11 −880 (R 2.248) N( D) + H2 −−→ NH + H 4.6 · 10 exp T [113] 2 −15 (R 2.249) N( P) + H2 −−→ N + H2 2.0 · 10 [113]

1 −10 (R 2.250) O( D) + H2 −−→ H + OH 1.1 · 10 [34]

1 −16 (R 2.251) O( S) + H2 −−→ O + H2 2.6 · 10 [34]

+ – −5 −0.5 (R 2.252) N2 + e −−→ N + N 4.85 · 10 Te

+ – −4 −1.0 (R 2.253) O2 + e −−→ O + O 6.0 · 10 Te

77 1As discussed in Section 2.2.2, rate coeﬃcients of processes involving electronically excited

states of nitrogen are measured only for some of the excited states. The rates for the “lumped”

energy level groups are assumed to apply to all states in the group. Three such groups are

1a 1b 1c denoted with , , and , and are refered to as N2(B), N2(a), and N2(C), respectively, in the

present work.

2 Quenching processes are assumed to occur at the same rate as for the N2(B) state.

3Total reaction rate taken from Ref. [3], product assumed in this work.

Additionally, the model includes state-speciﬁc vibrational energy transfer processes for nitrogen, as shown in Table 2.5

Table 2.5: Vibrational energy transfer processes included in air dominated mixtures.

# Process

(R 2.254) N2(1 < v < 8) + N2(0 < w < 7) ←−→ N2(v-1) + N2(w + 1)

(R 2.255) N2(1 < v < 8) + O ←−→ N2(v-1) + O

The functional form of state-speciﬁc rate coeﬃcients for Reaction R 2.254 and Reaction R 2.255 are the same as in Lanier et al.[16], and are reproduced below.

For Reaction R 2.255, VT relaxation of N2 by O atoms, the rates are as follows,

kv→v−1 = vk1→0 exp (δVT (v − 1)) , (2.37)

78 where 2.87 δVT = 1 , (2.38) T 3

and k T k (T ) = b , (2.39) 1→0 (P τ) where an empirical ﬁt for (P τ) is taken from Candler et al.[114],

− 1 P τ(atm s) = exp 32.2T 3 − 16.35 . (2.40)

For Reaction R 2.254, VV exchange processes for N2-N2, are,

v→v−1 1→0 kw→w+1 = (w + 1)(v)k0→1 exp (δVV |w − (v − 1)|) 3 1 − exp (δ |w − (v − 1)|) , (2.41) 2 2 VV where 6.85 δVV = √ , (2.42) T

1→0 −14 3 −1 and k0→1(300 K) = 1.5 × 10 cm s is taken from Ahn et al.[67], with temperature-dependent scaling as follows [115],

1→0 1.5 k0→1(T ) ∝ T . (2.43)

Both Equation 2.38 and Equation 2.42 are applicable only for calculation of VT

rate coeﬃcients for N2-O and VV rate coeﬃcients for N2-N2, since the constants in Equation 2.38 and Equation 2.42 are dependent on the collision partners.

79 Since Chemkin-Pro does not support the functional form of Equation 2.41 for reaction rate coeﬃcients. Simplifying, Equation 2.41 is reduced to the form

B 3 1 B k = A exp √ − exp √ T 2 2 T 3 B 1 2B = A exp √ + A exp √ , (2.44) 2 T 2 T where

1→0 A = (w + 1)vk0→1, (2.45) and B = 6.85|w − (v − 1)|. (2.46)

Chemkin-Pro does support the Landau-Teller formulation for rate expressions,

BLT CLT k = ALT exp 1 + 2 . (2.47) T 3 T 3

An approximate conversion from the form in Equation 2.44 to Equation 2.47 is as follows, B B exp 1 ≈ exp 1 f(T ) , (2.48) T 2 T 2

if f(T ) ≈ 1 over a wide range of T . Choosing

1 1 T 6 + 300 6 f(T ) = 300 T ≈ 1, (2.49) 2

80 results in an error of a few percent (< 5%) in Equation 2.48 at T =100–2000 K. Then

1 1 !! B B T 6 300 6 exp 1 f(T ) = exp 1 + T 2 T 2 300 T 1 ! B B300 6 = exp 1 1 + 2 , (2.50) 2 · 300 6 T 3 2T 3

such that B BLT = 1 , (2.51) 2 · 300 6

and 1 B300 6 C = , (2.52) LT 2

allows Equation 2.44 to be approximated in the form of Equation 2.47. The errors introduced at T =100–2000 K are signiﬁcantly smaller than the uncertainty in the measured rates, which makes this approximation suitable over the entire range of temperatures of interest in this work.

2.4 “Conventional” Chemical Reactions

In the present work, several “conventional” combustion chemistry mechanisms have been used, depending on which reacting mixture was modeled.

The ﬁrst mechanism used, which is by far the simplest, is a model for H2–O2 combustion in low temperature electric discharges, developed by Popov [39]. It will be referred to as the “Popov mechanism” throughout this work. This mechanism

81 was coupled to the plasma chemistry kinetic model discussed in Section 2.2 and Section 2.3. This mechanism has been validated against measurements of ignition

delay times, H2O, O2, H2, and OH number densities, and gas temperature in both

H2-O2-N2 and H2-O2-Ar mixtures showing good agreement [39]. For simulations other than mixtures with hydrocarbon fuels (in particular the work discussed in Section 3.2), this mechanism was used modeling hydrogen kinetics in discharge- excited mixtures.

The second mechanism, used in the present work for hydrocarbon-O2-Ar simulations, was developed by A. Konnov [43] and will be referred to as the “Konnov mechanism”. It was developed for combustion of small hydrocarbons, up to

C3H8, with speciﬁc emphasis on low temperature kinetics. This makes it applicable plasma assisted combustion (PAC) simulations below ignition temperature, which are dominated by radical reaction kinetics. The mechanism has been reproduced in its original form in Appendix D. The ﬁnal mechanism, referred to as the “Aramco mechanism”, has been developed for combustion applications involving small hydrocarbons including up

to two carbon atoms (up to C2H6)[42]. It has been validated against experimental data in shock tubes, jet-stirred reactors, flow reactors, as well as against flame speed and flame speciation measurements [42]. Depending on the specific fuel, the validation data span a range of temperatures of 300–2500 K, a range of pressures of 0.026–260 atm, and equivalence ratios ranging from 0.05 to 6 [42]. Section 3.3 compares predictions of the Konnov and Aramco mechanisms, also comparing them with measurements of stable species at the exit of a plasma

82 ﬂow reactor. Based on the Konnov mechanism’s applicability to propane and on the results in Section 3.3, only the Konnov mechanism, but not the Aramco mechanism, was used for kinetic modeling in Section 3.1.

83 Chapter 3

Kinetic Studies of Low-Temperature Plasma Assisted Combustion

Nanosecond pulse discharges have been widely used to study kinetics of plasma

E assisted combustion (PAC) due to high peak reduced electric fields, N , that reach several hundred Townsend (1 Td = 1 × 10−17 V cm2)[32]. At these conditions significant fractions of discharge input energy, up to tens of percent, go to electronic excitation of molecular species, as well as their dissociation and ionization, by electron impact [23]. These processes initiate chemical reactions among excited and radical species at low temperatures, which would only occur at high temperatures without plasma excitation. The objective of the work presented in this chapter is to demonstrate how radical species formed in low temperature plasmas affect fuel oxidation kinetics.

3.1 Prediction of Radical Species Generated by

a Nanosecond Pulse Discharge

The main focus of this section is the kinetics of H and O atoms in well-characterized, diﬀuse, “near 0D” nanosecond pulse discharges. Of particular interest are the

84 dominant processes of generation of these species in the discharge and their consumption in the afterglow.

3.1.1 Brief Description of Plasma Assisted Reaction Ki-

netics Experiment

The experiments studied in the present work have been conducted in two diﬀerent plasma ﬂow reactor cells discussed below.

Reactor Cell with Liquid Metal Electrodes

The first cell, referred to as the liquid metal electrode cell, has a rectangular cross section flow channel made of quartz, approximately 20 cm long, 1.5 cm wide, and 0.5 cm high shown in Figure 3.1. Two quartz reservoirs, each 6 cm long and 1.5 cm wide, are fused to the top and bottom of the flow channel, filled with a liquid metal alloy (Ga-In-Sn), and used as electrodes. The entire cell is placed inside a tube furnace, allowing preheating of the premixed reactant flow, using preheating coils visible in Figure 3.1. The experiments have been conducted in fuel-oxygen mixtures diluted in argon, at a pressure of P = 300 Torr and initial temperature of T = 500 K.

85 Figure 3.1: Schematic and photograph of the liquid metal electrode reactor cell, showing ﬂow channel, liquid metal electrode reservoirs, and preheating coils.

Coated Copper Electrode Reactor Cell

The second cell, referred to as the gel pad cell, consists of a rectangular cross section quartz channel approximately 20 cm long, 2.2 cm wide, and 1 cm high, shown in Figure 3.2. Two parallel plate copper electrodes are placed on top and bottom of the channel, as shown in Figure 3.2, and are coated in polydimethylsiloxane (PDMS), a resilient, dielectric material capable of withstanding the elevated temperatures used in the experiments, up to T = 500 K. This was done to remove gaps between the quartz channel and the electrode plates, filled with air. Previous experiments [10] demonstrate that presence of air gaps resulted in corona discharge formation outside the flow channel. This produced significant uncertainty in the discharge energy coupled to the reactant flow, and in some cases triggered discharge filamentation in the channel. The cell was placed into the same tube furnace to preheat the reactant mixture and study kinetics of plasma assisted fuel oxidation

86 Figure 3.2: Schematic and photograph of the coated copper electrode reactor cell showing the ﬂow channel, ceramic clamps holding PDMS coated copper electrodes, and preheating coils. reactions at elevated temperatures.

Plasma Generation

In both reactor cells, encapsulating the electrodes in dielectric (liquid metal electrodes in quartz reservoirs or copper electrodes covered by a layer of PDMS) prevented corona discharge formation, which occurs when high peak voltage pulses are applied to exposed metal electrodes in air heated in the furnace, ensuring that the plasma was produced only in the ﬂow channel and allowing accurate measurements of energy coupled to the plasma. This is the primary advantage of

87 Figure 3.3: Voltage and coupled energy waveforms in the liquid metal electrode cell for a single pulse (pulse # 25) at pulse repetition rate of 20 kHz, at P = 300 Torr, initial temperature of T0 = 500 K in a mixture of 1% H2 in Ar. [22]

these experiments over previous measurements of radical species in plasma assisted combustion (PAC) reactors [10, 18, 19, 44], since coupled energy is no longer an adjustable parameter in the kinetic model. Both cells are powered using a FID GmbH FPG 60-100MC4 pulse generator (peak voltage up to 30 kV, pulse duration of 5 ns, repetition rate up to 100 kHz). The pulser is operated in burst mode, producing bursts of 25-75 pulses at pulse repetition rates of 10–20 kHz and burst repetition rate of 10 Hz. Measurements of voltage and current [8,22] are used to calculate input power waveforms used by the kinetic model. Figure 3.3 shows typical voltage and coupled energy waveforms measured during a burst of pulses in the liquid metal electrode cell, and Figure 3.4 shows the voltage and current waveforms measured in the PDMS gel pad cell.

88 Figure 3.4: Voltage and coupled energy waveforms in the coated copper electrode cell for a single discharge pulse (pulse # 75), at pulse repetition rate of 20 kHz,P = 300 Torr, initial temperature of T0 = 500 K, in a mixture of 1% O2 in Ar. [22]

Plasma Uniformity

Plasma uniformity in the liquid metal electrode cell is quantified using absorption spectroscopy of argon metastable atoms produced in the discharge, showing that their number density in the plasma varies within 20% [22] as shown in Figure 3.5. This justifies the use of a 0D kinetic model for analysis of chemical reaction kinetics in the flow reactor. While the plasma in the liquid metal electrode cell remained relatively uniform over a wide range of operating conditions, see Figure 3.5, the plasma in the PDMS gel pad cell exhibited a more complex structure. In particular, when hydrocarbon fuels were added to the reactant mixture, plasma emission would not fill the entire channel, as illustrated in Figure 3.6. Figure 3.6 shows an ICCD image of the discharge taken through a window at the end of the reactor channel. Since the

89 Figure 3.5: Left: transverse distributions of Ar(1 s5) number density in a repetitive nanosecond pulse discharge in a 1% O2-Ar mixture, at P = 300 Torr, T0 = 500 K, and ν = 10 kHz, 0.23 µs after the last pulse in a 50-pulse burst. Right: ICCD image of the plasma in the discharge cell (end view), showing approximate locations of absorption laser beam. [22]

flow regions near the side walls of the channel appear to be unaffected by the plasma, transverse diffusion of the reactant species, in particular the ones with high diffusion coefficient, such as H atoms or OH, may well become important.

90 Figure 3.6: ICCD image of the plasma in (left) argon and (right) 150 ppm C3H8 - 1% O2 - Ar mixture in the PDMS gel pad cell. P=300 Torr,T0=500 K, discharge pulse repetition rate 20 kHz, camera gate 1 µs.

91 H Atom and O Atom Number Density Measurements

In both ﬂow reactor cells, measurements of H and O atoms were performed using Two-photon Absorption Laser Induced Fluorescence (TALIF). The details of the technique are discussed in Winters et al.[22]. Brieﬂy, in this technique H atoms and O atoms generated in the plasma are excited by absorption of two photons from a pump laser, A + 2 h ν −−→ A∗, (R 3.1)

and fluorescence from the excited state is subsequently measured. The atom number density is put on an absolute scale by measuring fluorescence signal from atomic species of known number density, for which excitation and fluorescence wavelengths are close (Kr for H atoms and Xe for O atoms). Collisional quenching rates, which affect the fluorescence yield, and absorption line shape have been measured in previous studies [20,116].

3.1.2 Results and Discussion

Figure 3.7 compares time-resolved absolute H atom number density measured in

the liquid metal electrode cell, after the discharge burst in 1% H2-Ar and 0.15%

O2-1% H2-Ar mixtures at P = 300 Torr,T0 = 500 K, with the model predictions.

The H2-Ar mixture is excited by a burst of 50 discharge pulses at a pulse repetition

rate of 10 kHz, while the H2-O2-Ar mixture is excited by a burst of 25 pulses at 20 kHz. It can be seen that the model predictions are in good quantitative agreement in both cases, although H atom decay due to recombination is somewhat

92 Figure 3.7: Time resolved H atom number density in a 1% H2-Ar mixture excited by 50 discharge pulses at 10 kHz and in a 1% H2-0.15%O2-Ar mixture excited by 25 discharge pulses at 20 kHz, measured in the liquid metal electrode cell. Coupled discharge pulse energy is 2.6 mJ/pulse. Dashed line indicates the approximate time scale when the eﬀect of convection on H atom decay becomes signiﬁcant.

overpredicted in the H2-Ar case. The dashed line in Figure 3.7 corresponds to the estimated flow residence time between the start of the electrodes and the measurement location, i.e. the time when transport of H atoms by the flow is expected to affect their number density, as discussed in Section 2.1.2.

Figure 3.8 shows the number densities of H and H2 predicted by the model in

the 1% H2-Ar mixture. At these conditions, H atoms are generated rapidly after each discharge pulse, with relatively slow kinetics occuring between the pulses, resulting in a step-wise pattern of H atom number density in the left panel of Figure 3.8. After the discharge burst, H atom decay occurs over a long time period, several ms.

From comparison of the data with the modeling predictions in 1% H2-Ar

93 mixture, it is evident that approximately 30% of the discharge input energy coupled to the plasma (2.6 mJ/pulse) goes to hydrogen dissociation, primarily due to electron impact excitation of argon,

e− + Ar −−→ e− + Ar∗, (R 3.2) followed by dissociative quenching of excited argon atoms by hydrogen molecules,

∗ Ar + H2 −−→ Ar + H + H. (R 3.3)

The energy fraction going to hydrogen dissociation via metastable argon quenching is signiﬁcantly lower compared to that going to argon metastable electronic excitation, ≈ 80%, since its excitation energy, ≈11.6 eV atom−1, is

−1 higher than H2 dissociation energy, ≈4.5 eV molecule . In this strongly diluted mixture, the role of hydrogen dissociation by electron impact is minor, as expected.

In H2-Ar, H atoms decay by three-body recombination with Ar as a third collision partner,

H + H + Ar −−→ H2 + Ar. (R 3.4)

Figure 3.9 plots radical and stable species number densities predicted by the model in the 1% H2-0.15% O2-Ar mixture. Similar to Figure 3.8, the step-wise pattern in both H and O number densities is evident, showing that the atomic species are produced very rapidly after each discharge pulse, on the time scale of ≈10 µs, as Ar* is collisionally quenched by molecular oxygen and hydrogen.

94 Figure 3.8: Predicted H and H2 species number densities at the conditions of Figure 3.7 in a 1% H2-Ar mixture excited by a nanosecond pulse discharge of 50 pulses at 10 kHz, during the burst (left) and during the afterglow (right), at P = 300 Torr and T0 = 500 K. Coupled discharge pulse energy is 2.6 mJ/pulse.

Although O2 number density is a factor of six lower than that of H2, O atoms are produced at nearly the same rate as H atoms, as can be seen by comparing the concentrations of H atoms and O atoms produced in the ﬁrst discharge pulse (see Figure 3.9). It can be seen that most H and O atoms are converted to water vapor by chemical reactions after the burst. When oxygen is added to the mixture, production of O atoms is faster than H

atoms due to faster O2 dissociation by metastable argon,

∗ Ar + O2 −−→ Ar + O + O · (R 3.5)

The rate for Reaction R 3.5 is 2.1 × 10−10 cm3 s−1, compared with the rate for Reaction R 3.3 which is 6.6 × 10−11 cm3 s−1.

Additionally, since the electron energy threshold for O2 dissociation by electron

95 Figure 3.9: Predicted radical (H, O, HO2) and stable (H2O, H2) species number densities at the conditions of Figure 3.7, in a 1% H2-0.15%O2-Ar mixture excited by a nanosecond pulse discharge burst of 25 pulses at 20 kHz, during the burst (left) and during the afterglow (right), at P=300 Torr and T0 = 500 K. Coupled discharge pulse energy is 2.6 mJ/pulse.

impact, 4.5 eV, is lower than that for H2 dissociation by electron impact, 8.9 eV. Figure 3.10, which shows potential energy curves for the ground and predissociated

excited electronic states of O2 and H2, illustrates this, as the electron energy threshold is the energy diﬀerence between the electronically excited state and the ground electronic state at the same internuclear distance.

In O2-H2-Ar mxitures, three-body recombination with O2 molecules,

H + O2 + Ar −−→ HO2 + Ar, (R 3.6)

as well as reaction with HO2,

H + HO2 −−→ OH + OH, (R 3.7)

96 Figure 3.10: Potential energy curves for O2 (top) and H2 (bottom) showing the ground electronic states and the excited states that populated by electron impact, resulting in dissociation. H2 potential energy curve adapted from Sharp [117]

97 also become dominant channels of H atom decay, in addition to Reaction R 3.4. Dur-

12 −3 ing the discharge burst, the HO2 number density remains very low, ≈1 × 10 cm (see Figure 3.9), and nearly constant in time, since Reaction R 3.6 and Reac- tion R 3.7 are in quasi-equilibrium with each other. Comparing the predicted total number density of the primary radicals generated during the discharge burst (H and O atoms), with the number density of the stable

fuel oxidation product, H2O, after the discharge burst, the estimated reaction

[H2O] chain length is [H]+[O] ≈ 1.1, which shows that at the present low-temperature conditions the role of chain branching reactions, such as

H + O2 −−→ OH + O, (R 3.8)

and

O + H2 −−→ OH + H, (R 3.9)

is fairly insigniﬁcant, and the amount of fuel oxidized is controlled by the amount of primary radicals produced by the discharge. Figure 3.11 plots experimental and predicted O atom number densities after

the discharge burst in the gel pad cell with mixtures of 1% O2-Ar and 1% O2-0.13%

H2-Ar at P=300 Torr,T0=500 K, excited by a burst of 75 pulses at 20 kHz, with coupled pulse energy of 4.2 mJ/pulse. It is evident that at these conditions the model reproduces O atom number density at the end of the burst in both mixtures

and reproduces O atom number density during the decay in the H2-O2-Ar mixture.

Figure 3.12 shows O and O2 number densities predicted in the O2-Ar mixture

98 Figure 3.11: Time resolved O atom number density in a 1% O2-Ar mixture and in a 0.13% H2-1% O2-Ar mixture excited by 75 discharge pulses at 20 kHz in the gel pad cell. Coupled discharge energy is 4.2 mJ/pulse. Dotted line indicates approximate time at which convection of O atoms by the ﬂow becomes important.

during and after the burst. Similar to Figure 3.8, it is evident that O atoms are produced rapidly after each discharge pulse, accumulating throughout the burst. Based on the modeling predictions, O atoms at these conditions are produced

mainly by dissociative quenching of electronically excited Ar atoms by O2, in Reaction R 3.5. At these conditions, 67% of the discharge pulse energy coupled to the plasma goes to generating metastable argon atoms by electron impact.

Combining metastable argon atom quenching by O2 and oxygen dissociation via electron impact, a total of 48% of discharge input energy generates oxygen

atoms. Molecular oxygen is readily dissociated via electron impact, due to the O2 dissociation energy, ≈4.5 eV molecule−1, being lower than the excitation energy for metastable argon, 11.5 eV molecule−1. At the end of the discharge burst,

99 approximately half of O2 initially available in the mixture is dissociated via these channels.

From Figure 3.11, it can be seen that in the O2-Ar mixture, the model overpredicts the O atom number density during the decay. At these conditions, O atom kinetics are dominated by three-body recombination, with Ar, O2, and O as a third collision partner,

O + O + M −−→ O2 + M. (R 3.10)

Note that at the present experimental conditions (initial temperature T0 = 500 K), ozone chemistry has a negligible effect on O atom decay kinetics. This leads to a conclusion that O atom decay is dominated by their transport with the axial flow, as well as transverse diffusion to the reactor channel walls, followed by recombination on the walls. The estimated time for transverse diffusion of O

h2 atoms to the channel walls is τdiff ≈ Dπ2 ≈37 ms, where h =1 cm is the channel height and D =2.75 cm2 s−1 is the diﬀusion coeﬃcient for O atoms in argon at the temperature predicted at the end of the discharge burst, T ≈700 K, calculated based on measurements in Ref. [118]. The estimated time for convection out of the

L O atom fluorescence signal collection region is τconv ≈ 2u ≈31 ms, where L ≈ 6 cm is the length of the plasma region and u ≈ 130 cm s−1 is the centerline flow velocity estimated from the mass flow rate of 2 SLM, assuming a fully developed flow in the channel. Both of these time scales are longer compared to the measured O atom

1 e decay time, ≈10 ms (see Figure 3.11). However, the time scale for combined −1 −1 −1 diﬀusion and convection losses, τ = τdiff + τconv ≈10 ms, is comparable with

100 Figure 3.12: Predicted O atom and O2 number densities in a 1% O2-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the burst (left) and during the afterglow (right), at P = 300 Torr and T0 = 500 K. Coupled discharge pulse energy is 4.2 mJ/pulse. the observed recombination decay time. From Figure 3.11 it can be seen that incorporating the eﬀects of diﬀusion and convection into the quasi-zero-dimensional kinetic model makes the agreement between the data and the modeling predictions in the O2-Ar mixture (shown as a dashed line) are noticeably better.

When hydrogen is added to the O2-Ar mixture, 46% of the discharge input power goes to generating O atoms (both by electron impact and via Ar* quenching by O2), and only 1% of input power goes to H atom generation (via Ar* quenching by H2), resulting in a factor of ≈ 50 diﬀerence between O and H number densities predicted early during the burst (see Figure 3.13). The main channel of O atom decay at these conditions is O atom reaction with OH,

O + OH −−→ H + O2. (R 3.11)

101 Figure 3.13: Predicted radical (O, H, OH, HO2) and stable (H2O) species number densities in a 1% O2-0.13%H2-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the burst (left) and during the afterglow (right), at P=300 Torr and T0 = 500 K. Coupled discharge pulse energy is 4.2 mJ/pulse.

In the presence of hydrogen, Reaction R 3.11 and reaction with HO2,

O + HO2 −−→ OH + O2, (R 3.12)

result in signiﬁcant reduction of O atom number density generated by the end of

the discharge burst, compared to the O2-Ar mixture, as well as its more rapid decay after the burst (see Figure 3.11). As discussed above, dominant processes producing

HO2 and OH in the H2-O2-Ar mixture are Reaction R 3.6 and Reaction R 3.7, respectively. Reactions R 3.6, R 3.7, and R 3.11 sum up to the net equivalent O atom decay process, O + H −−→ OH. (R 3.13)

Therefore, the net rate of O atom decay after the discharge burst is controlled

102 almost entirely by the total number density of H atoms generated during the burst, even though it is signiﬁcantly lower compared to that of O atoms (see Figure 3.13). Again, the contribution of chain branching Reaction R 3.9 is minor at this relatively low temperature conditions and accounts for only ≈ 10% of the total O atom decay rate. Comparison of predicted and experimental O atom number densities when methane and propane are added to the mixture are shown in Figure 3.14, which demonstrates very good agreement. Adding methane instead of hydrogen reduces O atom number density at the end of the discharge burst and accelerates its decay even more signiﬁcantly, as illustrated by comparing Figure 3.14 with Figure 3.11. Based on kinetic modeling predictions of the number densities of dominant species

(O, H, OH, HO2, H2O, and CH4) during and after the burst, plotted in Figure 3.15,

this occurs due to much higher OH number density compared to that in the H2-

14 −3 O2-Ar mixture, up to ≈1 × 10 cm , which is only about an order of magnitude below the O atom number density. This accelerates O atom decay considerably, in reaction with OH, Reaction R 3.11. At these conditions, most OH is produced by Reaction R 3.7, as well as by partial oxidation of methane,

O + CH4 −−→ CH3 + OH. (R 3.14)

Again, the net rate of O atom decay is controlled by the number density of H

atoms generated in the discharge, mainly via Ar* quenching by CH4,

∗ Ar + CH4 −−→ Ar + CH2 + H + H, (R 3.15)

103 Figure 3.14: Time resolved O atom number density in a 1% O2-0.25% CH4-Ar mixture (4.2 mJ/pulse) and a 1% O2-150 ppm C3H8-Ar mixture (1.4 mJ/pulse), excited by a burst of 75 discharge pulses at 20 kHz in the gel pad cell.

∗ Ar + CH4 −−→ Ar + CH2 + H2, (R 3.16) and

∗ Ar + CH4 −−→ Ar + CH + H2 + H. (R 3.17)

Note that Reaction R 3.14 accounts only for ≈ 10% of the total O atom decay rate. At these conditions, a single discharge burst oxidized approximately half of the initial amount of fuel available in the mixture (0.25% mole fraction), as shown in the left panel of Figure 3.15. Similar to H2-O2-Ar mxitures, the reaction chain length, estimated as [stable products] ≈ [CH2O]+[CO]+[H2]+[CO2]+[H2O] ≈ 0.6, is [primary radicals] [H]+[O]+[CH3] low, indicating that chain branching reactions remain insigniﬁcant. Figure 3.16 shows detailed modeling predictions for the propane mixture at the conditions of Figure 3.14. An important similarity of Figure 3.16, Figure 3.15, and

104 Figure 3.15: Predicted radical (O, H, OH, HO2) and stable (CH4, H2O) species number densities in a 1% O2-0.25% CH4-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the burst (left) and in the afterglow (right), at P=300 Torr and T0 = 500 K. Coupled discharge pulse energy is 4.2 mJ/pulse.

Figure 3.13 is that both O and H atom number densities increase throughout the discharge burst, a trend which disappears in cases discussed below. In the propane mixture shown in Figure 3.16, the fuel is almost entirely oxidized by the end of the burst with residual mole fraction of only ≈1 ppm. On the other hand, OH and

HO2 number densities during the burst remain low, in quasi-equilbrium with the H and O atom number densities. At these conditions, the rate of O atom decay after the burst is controlled almost entirely by the amount of H atoms produced in the discharge burst, with the average chain length remaining on the order of 1. The left panel of Figure 3.17 plots the results for the propane case from

Figure 3.14 (150 ppm of C3H8 in the mixture), along with another propane mixture with only 75 ppm of C3H8, while the right panel of Figure 3.17 shows comparison of experimental and modeling predictions for two mixtures of ethylene

105 Figure 3.16: Predicted radical (O, H, OH, HO2) and stable (C3H8, H2O) species number densities in a 1% O2-150ppm C3H8-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the burst (left) and during the afterglow (right), at P=300 Torr and T0 = 500 K. Coupled discharge pulse energy is 1.4 mJ/pulse.

(150 ppm and 75 ppm) in 1% O2-Ar. It can be seen that the model predictions for the 150 ppm propane mixture are in good agreement with the data, but in the 75 ppm propane mixture and both ethylene mixtures, O atom decay rate is signiﬁcantly underpredicted, by about a factor of 3. In all cases, the main decay mechanism of O atoms predicted by the model after the burst is the same

as in H2-O2-Ar and CH4-O2-Ar mixtures discussed above, O atom reaction with OH, Reaction R 3.11, which accounts for approximately half of the net O atom decay rate. However, OH production mechanisms in these mixture are diﬀerent. In the 150 ppm propane mixture, OH is produced mainly by the reaction of H

atoms with HO2, Reaction R 3.7, while in the leaner 75 ppm propane mixture and in both ethylene mixtures, it is mostly generated in the reaction of O atoms with HO2, Reaction R 3.12, especially near the end of the discharge burst when

106 Figure 3.17: Time resolved O atom number density in a C3H8-1% O2-Ar mixture (1.4 mJ/pulse, left) and a C2H4-1% O2-Ar mixture (1.4 mJ/pulse, right) excited by a burst of 75 discharge pulses at 20 kHz in the gel pad cell.

the fuel has been nearly completely oxidized. This can be seen in the detailed modeling predictions for the three mixtures, shown in Figure 3.18, Figure 3.19, and Figure 3.20, respectively. As can be seen from the detailed modeling predictions, in all three cases H atom number density during the burst reaches a plateau as the fuel is gradually

depleted, unlike in the CH4-O2-Ar mixture, where H atom number density keeps increasing during the entire burst (see Figure 3.15). The leveling oﬀ of H atom number density occurs in spite of dissociative quenching of Ar* by intermediate hydrocarbon dissociation and oxidation products, as well as by water vapor, which contributes to H atom generation. As a result, OH number density in the afterglow

in all three cases is much lower than that in the CH4-O2-Ar mixture, by over an order of magnitude (compare Figure 3.15 and Figure 3.18). At these conditions,

107 Reaction R 3.12 replaces Reaction R 3.7 in the O atom decay kinetics, such that the net equivalent decay process becomes

O + O −−→ O2, (R 3.18) which is slower and is not affected by the amount of hydrogen atoms generated in the discharge. The fact that the model underpredicts the O atom decay rate in the 75 ppm propane mixture and in both ethylene mixtures suggests that in the experiment, the amount of hydrogen-containing species in the plasma may in fact be higher, either due to ambient air (water vapor) leaking into the reactor or due to the effect of species transport from unreacted flow regions. Since the reactor leak rate is over four orders of magnitude lower compared to the reactant mixture flow rate [22], the upper bound estimate of water vapor impurity in the mixture is ≈1 ppm, much lower than the amount that would significantly affect the modeling predictions (estimated to be ≈ 200 ppm). On the other hand, plasma images taken at these conditions (see Figure 3.6) and additional kinetic modeling analysis suggest that transverse diffusion of H atoms from the peripheral, partially oxidized flow regions near the side walls of the reactor may be the reason for this discrepancy. Basically, this process provides an additional source of H atoms in the reacting mixture, thereby accelerating the rate of O atom decay in the afterglow. At the conditions when the model underpredicts the rate of O atom decay

in the afterglow (75 ppm C3H8 mixture, as well as 75 ppm and 150 ppm C2H4 mixture), it also typically overpredicts the O atom number density at the end

108 Figure 3.18: Predicted radical (O, H, OH, HO2) and stable (C3H8, H2O) species number densities in a 1% O2-75ppm C3H8-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the burst (left) and during the afterglow (right), at P = 300 Torr and T0 = 500 K. Coupled discharge pulse energy is 1.4 mJ/pulse.

Figure 3.19: Predicted radical (O, H, OH, HO2) and stable (C2H4, H2O) species number densities in a 1% O2-150ppm C2H4-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the burst (left) and during the afterglow (right), at P = 300 Torr and T0 = 500 K. Coupled discharge pulse energy is 1.4 mJ/pulse.

109 Figure 3.20: Predicted radical (O, H, OH, HO2) and stable (C2H4, H2O) species number densities in a 1% O2-75ppm C2H4-Ar mixture excited by a nanosecond pulse discharge burst of 75 pulses at 20 kHz, during the burst (left) and during the afterglow (right), at P = 300 Torr and T0 = 500 K. Coupled discharge pulse energy is 1.4 mJ/pulse. of the burst. This is illustrated further in Figure 3.21 and Figure 3.22, which compare O atom number density measured in propane mixtures (90 µs after the discharge burst) and ethylene mixtures (70 µs after the burst) with the modeling calculations at different initial mole fractions of propane and ethylene. Although the modeling predictions reproduce the trend of O atom number density reduction as the fuel mole fraction is increased fairly well, the absolute number density at the conditions when nearly all fuel is oxidized by the end of the burst is consistently overpredicted. Figure 3.21 and Figure 3.22 demonstrate that species measurements at the end of the discharge burst are not sufficient to identify deficiencies in the modeling predictions, and that time-resolved measurements, such as shown in Figure 3.14 and Figure 3.17, are vital for conclusive model validation.

110 Figure 3.21: Experimental and predicted O atom number density 90 µs after the burst versus initial mole fraction of propane in the mixture excited by a nanosecond pulse discharge burst. P = 300 Torr,T0 = 500 K, pulse repetition rate is 20 kHz, discharge coupled energy 1.2 mJ/pulse.

Figure 3.22: Experimental and predicted O atom number density 70 µs after the burst versus initial mole fraction of ethylene in the mixture excited by a nanosecond pulse discharge burst. P = 300 Torr,T0 = 500 K, pulse repitition rate 20 kHz, discharge coupled energy 1.4 mJ/pulse.

111 3.2 Coupling of Nitrogen Vibrational Kinetics

and Kinetics of the Hydroxyl Radical

Section 3.1 discussed generation and decay of radical species in fuel-oxygen mixtures diluted in argon. Comparison of experimental results with kinetic modeling predictions demonstrated that a signiﬁcant fraction of the discharge energy can be coupled to radical generation via electron impact excitation of Ar, followed by dissociative quenching by oxygen and fuel molecules. Since most applications of plasma assisted combustion involve fuel-air mixtures, there is also a need to understand coupling of excited species generated in air plasmas with combustion kinetics. In this section, kinetic modeling is used to study the role of vibrationally excited

1 nitrogen molecules in the ground electronic state, N2(X Σ, v), in chemical kinetics of reacting non-equilibrium plasmas. In these plasmas, the eﬀect of vibrational excitation of nitrogen on chemical reactions may well be signiﬁcant for two principal

reasons, (i) high input energy fraction coupled to N2 vibrational excitation by electron impact in electric discharge air and air-fuel mixtures, and (ii) relatively slow

N2 vibrational relaxation rate, even in plasmas with signiﬁcant concentrations of hydrogen, hydrocarbon species, and oxygen atoms. Because of this, a considerable amount of energy in transient plasmas is stored in the vibrational energy mode of molecular nitrogen, which aﬀects the rate of temperature rise [30,31,40] and,

indirectly, rate coeﬃcients of chemical reactions. A more direct eﬀect of N2

1 vibrational excitation on plasma chemistry, either via reactions with N2(X Σ, v)

112 as one of the reactants, or via vibrational energy transfer from nitrogen molecules to other reactive molecular species, has been a matter of some debate. One such reaction hypothesized by Starikovskiy et al.[119] suggests that vibrationally excited nitrogen may delay OH recombination due to near-resonant vibrational energy transfer to relatively “unreactive” HO2 radical,

1 1 N2(X Σ, v−1) + HO2 −−→ N2(X Σ, v−0) + HO2(v2 + v3) −−→ N2 + H + O2. (R 3.19) It was also suggested that this process may sustain chain propagation and chain branching chemical reactions of H atoms in low-temperature afterglow in fuel-air mixtures, and thus extend OH radical lifetime. The underlying assumption

of this hypothesis is that dissociation of HO2 by vibrational energy transfer from

N2 would mitigate a major chain termination process during low-temperature oxidation of hydrogen,

H + O2 + M −−→ HO2 + M. (R 3.20)

This would generate additional H atoms, driving a well-known chain reaction process,

H + O2 −−→ OH + H, (R 3.21) and

O + H2 −−→ OH + O, (R 3.22)

and thus resulting in higher transient OH number density. Recent time-resolved

113 Figure 3.23: Time resolved measurements of OH number density in mixtures with four diﬀerent fuels, excited by a nanosecond pulse discharge at P = 1 atm, showing non-monotonous decay in the afterglow. [33] measurements of OH number density in nanosecond pulse discharge afterglow in preheated atmospheric pressure hydrocarbon-air mixture [33], which demonstrated anomalously long OH lifetime and its non-monotonous decay in the afterglow, seem to support this hypothesis, as shown in Figure 3.23.

In the present work, comparison of time resolved measurements of N2 vibrational excitation, gas temperature, and OH number density with kinetic modeling predictions are used to analyze the eﬀect of N2 vibrational excitation on OH kinetics in lean H2-air afterglow plasmas sustained by a nanosecond pulse discharge at elevated gas temperatures and high speciﬁc energy loading.

114 Figure 3.24: Schematic (left) and photograph (right) of discharge electrode assembly and optical access for the hollow sphere electrode conﬁguration.

3.2.1 Brief Description of Nanosecond Pulse Discharge

Experiment

Discharge Cell

A schematic of a diﬀuse ﬁlament nanosecond pulse discharge used to generate N2 vibrational excitation and produce OH radicals in H2-air mixtures is shown in Figure 3.24. The discharge is sustained between two spherical electrodes 7 mm in diameter, made of copper, placed 8 mm apart. The electrodes have 1 mm holes drilled through them, aligned axially, to provide optical access to the laser beams

used for temperature, N2 vibrational level population, and OH number density measurements, as shown schematically in Figure 3.24.

The discharge cell was filled with a lean hydrogen-air mixture (1%-5% H2), at a pressure of 100 Torr and initial temperature 300 K. The flow rate through the cell was such that each discharge pulse excited a “fresh” mixture, but sufficiently

115 slow that it did not aﬀect the measurements on the characteristic time scales of vibrational energy transfer and chemical kinetics.

Discharge Generation

The discharge electrodes are connected to a custom-built, externally triggered, high-voltage pulse generator, ﬁrst used by Takashima et al.[120]. The pulser generates an alternating polarity pulse sequence with peak voltage of approximately 10 kV, full width half maximum (FWHM) pulse duration of ≈100 ns at a pulse repetition rate of 10–60 Hz. Positive polarity pulse voltage, current, and coupled energy waveforms are shown in Figure 3.25. Waveforms taken in nitrogen, air,

and H2-air mixture (1-5% H2), as well as coupled pulse energies, are very similar. From Figure 3.25, it can be seen that during breakdown, applied voltage drops by a few hundred volts, while the discharge current begins to rise. Current pulse duration is approximately 50 ns FWHM. As expected, negative polarity pulse waveforms in all gas mixtures are close to the positive polarity waveforms, such as shown in Figure 3.25, since the electrode assembly is symmetric. High-voltage pulses generate a diffuse filament pulsed discharge between the electrodes, approximately 3 mm in diameter, as can be seen in broadband plasma emission images of the discharge, shown in Figure 3.26. In the images, the grounded electrode is on the left. Plasma emission intensity along the filament centerline is somewhat lower, due to the 1 mm laser beam access holes in the electrodes.

116 Figure 3.25: Voltage, current, and coupled energy for diﬀuse ﬁlament discharge pulse between copper spherical electrodes in a 3% H2-air mixture at P=100 Torr. Coupled pulse energy 10 mJ. Negative polarity pulse waveforms are very similar.

117 Figure 3.26: Single shot plasma emission images between spherical copper electrodes, showing a diﬀuse ﬁlament discharge, with the grounded electrode on the left. Camera gate 1 µs. Coupled pulse energy 7.5 mJ

118 CARS Measurements

The experimental setup used for rotational-translational temperature and N2 vibrational level population measurements by CARS is similar to that in Nishihara et al.[121]. The CARS diagnostic is using a combination of two photons (pump and Stokes) to excite a molecules coherently from a lower to a higher vibrational level, as shown in Figure 3.27. The energy diﬀerence between the pump and Stokes photons is equal to the vibrational energy spacing of the molecule. A third “probe” photon (typically another photon from the same laser beam as the pump photon) is scattered, also coherently, from the molecule in the excited state, generating the anti-Stokes photon, as shown in Figure 3.27. The square root of the intensity of the coherent anti-Stokes signal beam is proportional to the diﬀerence between the lower and upper vibrational-rotational state populations. The use of a spectrally broadband Stokes beam provides access to several vibrational-rotational bands, while the use of a spectrally narrowband pump/probe beam provides high spectral resolution of the CARS spectra, making possible rotational temperature inference from the rotational structure of the vibrational bands, as well as measurements of multiple vibrational level populations.

119 Figure 3.27: Coherent Anti-Stokes Raman Spectroscopy (CARS) energy level diagram. Molecules are coherently excited by pump and Stokes photons, which are separated in energy by the rotational-vibrational transition energy, and then interact with a probe photon (typically from the same beam as the pump photon) which generates the anti-Stokes photon, coherent with the pump, Stokes, and probe photons.

OH LIF Measurements

Time-resolved measurements of OH number density were performed by LIF. The details of the technique are discussed in Winters et al.[21,122]. The LIF diagnostic uses a laser beam to excite OH molecules to an excited electronic state (A2Σ+) by resonant absorption of laser photons,

OH(X2Π) + h ν −−→ OH(A2Σ+). (R 3.23)

LIF is the single photon variant of TALIF diagnostics discussed in Section 3.1.1. The excited molecules either decay by ﬂuorescence or by collisional quenching. If the ﬂuorescence lifetime and the quenching rate are known, the relative OH

120 number density can be inferred from the ﬂuorescence signal intensity. The results are put on an absolute scale using calibration by Rayleigh scattering, for which the number density of scattering species and the scattering cross section are known.

Diﬀusion Conﬁguration

In this experiment, radial diffusion from the filament occurs on the time scale comparable to the time scales of vibrational relaxation and OH reaction. In particular, diffusion of light species, such as H, O, and OH, is especially important. Characteristic times for diffusion of both the aforementioned light species out of the discharge filament and the initial mixture into the filament were calculated as discussed in Section 2.1.3 and accounted for in the model.

3.2.2 Results and Discussion

Figure 3.28 plots rotational-translational temperature inferred from the rotational

structure of N2(v–0) band of CARS spectra, as well as the “ﬁrst” level N2 vibrational temperature,

E10 Tv = , (3.1) ln f0 f1

at total coupled energy of 7.5 mJ. In Equation 3.1, E10 =3353 K is the energy

diﬀerence between the ground and ﬁrst excited vibrational levels of N2, and f0 and

f1 are their populations. As can be seen, the agreement between the model and the

data is very good, both for gas temperature and for N2 vibrational temperature.

121 Figure 3.28: Comparison of experimental and predicted N2 vibrational temperature (left) and gas temperature (right) versus time delay after the discharge pulse in air and H2-air mixtures. Coupled pulse energy 7.5 mJ.

From Figure 3.28 it is apparent that the predicted N2 vibrational temperature

increases rapidly during the discharge pulse, up to Tv≈1000 K, while the gas

temperature increases to T = 375 K. At t≈1 µs, the gas temperature decreases slightly, due to gas dynamic cooling, while the pressure overshoot caused by rapid gas heating on sub-acoustic time scales relaxes via an expansion wave and pressure

is reduced to P ≈100 Torr. At 20–40 µs, the “downward” VV exchange,

N2(v−0) + N2(v > 2) −−→ N2(v−1) + N2(v-1), (R 3.24)

increases the “ﬁrst level” N2 vibrational temperature, given by Equation 3.1.

At t = 100–200 µs, N2 vibrational temperature decays primarily due to VT

relaxation of N2 by oxygen atoms produced by the discharge,

N2(v) + O −−→ N2(v − 1) + O, (R 3.25)

122 which results in gradual temperature rise on this time scale (see Figure 3.28).

In H2-air mixtures, the temperature rise is more signiﬁcant, due to additional

energy release during oxidation of hydrogen. Finally, after t = 200 µs, radial

diﬀusion of vibrationally excited nitrogen becomes the dominant process of N2 vibrational temperature decay. Similarly, radial conduction heat transfer results in temperature reduction on the same time scale. Figure 3.29 compares modeling predictions and experimental data for time- resolved, absolute OH number density after the discharge pulse, in three diﬀerent

H2-air mixtures at coupled discharge energy of 7.5 mJ. It can be seen that the model

reproduces peak OH number density in the 5% H2-air mixture, but underpredicts

peak OH number density in both the 1% and 3% H2 mixtures. In all three mixtures, the model fails to reproduce the rise in OH number density detected at

t ≈10–200 µs. This diﬀerence between the experimental data and the modeling predictions is not fully understood, as discussed below. Figure 3.30 plots dominant radical species number densities (ground state

3 O( P) atoms, H atoms, OH, and HO2) versus time delay after the discharge pulse

in a 5% H2-air mixture, at the same discharge coupled energy of 7.5 mJ. Both O and H atoms are generated in the discharge by electron impact dissociation of molecular oxygen,

− − e + O2 −−→ O + O + e , (R 3.26)

− 1 − e + O2 −−→ O + O( D) + e , (R 3.27)

123 Figure 3.29: Comparison of experimental and predicted OH number density versus time delay after the discharge pulse in H2-air mixtures. Coupled pulse energy 7.5 mJ.

and hydrogen,

− e + H2 −−→ H + H, (R 3.28)

as well as by collisional quenching of electronically excited nitrogen molecules,

N2*, by O2,

∗ N2 + O2 −−→ N2 + O + O, (R 3.29)

and H2,

∗ N2 + H2 −−→ N2 + H + H. (R 3.30)

A strong overshoot of OH number density predicted by the model several hundred nanoseconds after the discharge pulse is due to OH formation in a reaction of electronically excited O(1D) atoms with molecular hydrogen,

1 O( D) + H2 −−→ H + OH. (R 3.31)

124 At t≈1 µs, OH decays by reaction with molecular hydrogen,

k1 OH + H2 −−→ H2O + H, (R 3.32) which is also an additional source of H atoms. On longer time scales, t≈3–300 µs, OH is formed by reactions

k2 H + O2 + M −−→ HO2 + M, (R 3.33)

k3 O + HO2 −−→ OH + O2, (R 3.34)

and

k4 H + O2 −−→ OH + O, (R 3.35)

and decays by reaction

k5 OH + O −−→ H + O2, (R 3.36)

as well as by Reaction R 3.32. Figure 3.31, Figure 3.32, and Figure 3.33 compare the modeling predictions with the experimental data at higher coupled discharge pulse energy of 10.2 mJ.

Figure 3.31 and Figure 3.32 also include modeling predictions for a 10% H2-air mixture, for which experimental data are not available. At these conditions, the

model appears to overpredict the discharge energy fraction going to N2 vibrational excitation by electron impact, as well as the peak vibrational temperature (see

Figure 3.31). Both the eﬀect of transient gas temperature reduction at t≈2–10 µs, caused by gas dynamic expansion of the ﬁlament following its heating on a sub-

125 Figure 3.30: Predicted radical species number densities versus time delay after the discharge pulse in a 5% H2-air mixture. Coupled pulse energy 7.5 mJ.

acoustic time scale [4], and the rate of subsequent temperature rise caused by vibrational relaxation (in air and H2-air) and by chemical energy release due to

hydrogen oxidation (in H2-air) are underpredicted. This is most likely due to an inaccurate representation of time-dependent reduced electric ﬁeld in the plasma by the present quasi-zero-dimensional model, which does not take into account kinetic processes in the cathode layer. However, peak temperature predicted by the model,

up to T≈600 K at t≈300 µs, is consistent with the data (see Figure 3.31). As can be seen from Figure 3.31 and Figure 3.32, temperature maxima predicted by

the model in 1-5% H2-air mixtures approximately coincide in time with transient

maxima in OH number density, predicted at t≈300 µs to 1 ms. At the conditions of both Figure 3.30 and Figure 3.33, OH number density at

t>1 µs is controlled by quasi-equilibrium between Reaction R 3.32– R 3.36. Using a quasi-stationary approximation, OH number density on this time scale can be

126 Figure 3.31: Comparison of experimental and predicted N2 vibrational temperature (left) and gas temperature (right) versus time delay after the discharge pulse in air and H2-air mixtures. Coupled pulse energy 10.2 mJ.

Figure 3.32: Comparison of experimental and predicted OH number density versus time delay after the discharge pulse in H2-air mixtures. Coupled pulse energy 10.2 mJ.

127 Figure 3.33: Predicted radical species number densities versus time delay after the discharge pulse in a 5% H2-air mixture. Dashed line represents OH number density predicted by the quasi-stationary approximation in Equation 3.2. Coupled pulse energy 10.2 mJ. described by the following equation,

[H][O ](k M + k ) [OH] ≈ 2 2 4 . (3.2) [O]k5 + [H2]k1

OH number density predicted by Equation 3.2 is plotted by a dashed line in Figure 3.33, showing good agreement with the predictions of the full kinetic model at t > 1 µs. From Equation 3.2, it can be seen that OH number density in the afterglow basically follows the number densities of O and H atoms (the latter is also strongly affected by radial diffusion from the filament at t >100 µs), as well as the gas temperature, which affects the reaction rate coefficients of OH formation and decay (primarily Reaction R 3.35).

Adding hypothetical Reaction R 3.19 (vibrational energy transfer from N2 to

HO2) to the kinetic model demostrats that it does not enhance the rate of OH

128 production. Basically, at the present conditions nearly every HO2 radical formed by a three-body Reaction R 3.33 is rapidly converted to OH by Reaction R 3.34.

Since Reaction R 3.19 competes directly with Reaction R 3.34 for HO2, it results

in a net reduction of OH number density on the time scale of 10–100 µs. Similarly, the modeling predictions show that the gradual temperature rise on 10–500 µs (see Figure 3.28), caused by vibrational relaxation of nitrogen by O atoms and by chemical energy release during hydrogen oxidation, remains a relatively minor factor, weakly affecting chemical kinetics. Although it does increase the rate coefficient of Reaction R 3.35, the effect on OH number density is strongly diminished by H

atom radial diffusion on a shorter time scale, ≈100 µs, which prevents significant OH number density overshoot due to the temperature rise. To estimate the effect of vibrationally excited hydrogen molecules on OH production in the afterglow, and to determine whether a vibrationally stimulated reaction,

k6 H2(v) + O −−→ OH + H, (R 3.37)

may produce a transient rise of OH number density such as observed in the experiments, this reaction was included into the kinetic model. At room temperature,

the ratio of state-speciﬁc rate coeﬃcients of this reaction is k6(v=1) = 2600 [123]. To k6(v=0)

predict H2 vibrational level populations, the revised model also included electron

impact excitation of H2(v–1-3), H2-H2 VV exchange, VV energy transfer from

H2 to H2O which was assumed to relax instantly, and H2 VT relaxation by H2, H,

and O. At the present conditions, the dominant H2 vibrational relaxation channel is VT relaxation by O atoms, which is the most dominant radical species in the

129 plasma (see Figure 3.30). VV and VT rate coefficients were taken from [124]. State specific rates of Reaction R 3.37 were calculated using a model of bimolecular vibrationally enhanced reaction rates [125] and normalized by the thermal reaction rate coefficient from Popov [39]. To evaluate the sensitivity of the modeling

predictions to the uncertainty in the H2-O VT relaxation rate, which has not been measured directly, in the calculations its rate coeﬃcient was varied between values

used in [124] for VT relaxation of H2 by O atoms and by H atoms. The modeling predictions demonstrated that although Reaction R 3.37 occurs on the same time

scale as the OH number density overshoot in the experiments, a few hundred µs, its eﬀect on OH production is fairly insigniﬁcant, mainly due to rapid relaxation

of H2 generated in the discharge by O atoms. The present kinetic modeling predictions (in particular, absence of OH number density overshoot in the afterglow) are consistent with previous modeling calculations [4, 10], which are in very good agreement with the experimental data

taken at similar experimental conditions (lean H2-air mixtures at P=100 Torr and T=500 K)[10]. Thus, the difference between the modeling predictions and the experimental data, indicating significant OH number density overshoot, remains not understood. Since at the present conditions the discharge filament is generated slightly off the symmetry axis, it is possible that the overshoot is caused by rapid diffusion of H atoms from the filament centerline into the line of sight of the LIF

laser beam, on the time scale of several tens of µs, thus accelerating the rate of Reaction R 3.35 and resulting in an overshoot of OH number density. Since vibrational relaxation time scales inversely with pressure, in atmospheric

130 pressure lean H2-air mixtures, at the same speciﬁc energy loading, this eﬀect would cause OH number density overshoot at t≈30–130 µs. This demonstrates that temperature rise caused by vibrational relaxation of nitrogen in the afterglow

of a nanosecond pulse discharge in lean H2-air mixtures at sufficiently high specific energy loading, resulting in strong vibrational non-equilibrium, may become a dominant effect in OH number density overshoot. Increasing specific energy loading, as well as additional energy release during hydrogen oxidation in plasma chemical reactions, would amplify this effect.

3.3 Prediction of Fuel Oxidation Product Com-

position in Mixtures Excited by Nanosecond

Pulse Discharges

In Section 3.1 and Section 3.2, kinetic modeling has been used to analyze production and decay of dominant radical species (H atoms, O atoms, and OH molecules) in diluted fuel-oxygen mixtures and in fuel-air mixtures. Although accurate prediction of reactive radical species number densities is critical for understanding kinetics of fuel oxidation and ignition in reacting mixtures excited by a plasma, prediction of stable oxidation and combustion products provides additional insight into reaction kinetics at these conditions. This is the main objective of the kinetic modeling calculations in this section.

131 The experimental data used for comparison with the present modeling predictions, as well as modeling predictions for hydrogen-air and ethylene-air mixtures, have been obtained by Tsolas et al.[44–46]. The approach used in the present work differes from the previous work by Tsolas et al. in several important ways. First, time-resolved power coupled to the plasma in a repetitive nanosecond pulse discharge is predicted by a nanosecond pulse breakdown model developed previously [25], using experimental pulse voltage waveform as input. The discharge coupled power waveform is used as one of the input parameters in the present model, as discussed in Chapter 2. This approach is more accurate compared to the previous work [46], since it makes possible prediction of kinetic processes during individual discharge pulses, as well as during the intervals between the pulses, instead of assuming “effective” constant values of voltage and electron density in the plasma, averaged over the entire discharge burst, as was done in Ref. [46]. Second, the present model is using the most recent, up-to-date database of electron impact process cross sections [98]. Finally, the present model compares predictions using two different “conventional” reaction mechanisms, both coupled to the plasma chemistry, to identify their differences and assess their predictive capabilities for modeling of plasma assisted combustion.

3.3.1 Brief Description of the Experiments

Plasma Flow Reactor

The plasma ﬂow reactor used in Refs. [44–46] and modeled in the present work is made of a quartz channel, 7 mm by 9 mm rectangular cross section, which was

132 Figure 3.34: Schematic of the ﬂow reactor including copper plate electrodes, quartz ﬂow channel, and Macor ceramic sheath. [44]

placed inside a tube furnace to preheat the flow reactants, as shown in Figure 3.34. The furnace preheated the flow in the reactor to T =300–1300 K. The length of the isothermal flow in the reactor, determined using thermocouple measurements, is 70 cm. Fuel-oxygen mixtures, diluted in argon, are flown through the channel at a constant flow rate of 6 SLM. Diluting the reactant mixture in argon provides thermal inertia, such that exothermal reactions of plasma-assisted fuel oxidation can be studied at nearly isothermal flow conditions, including temperatures above “hot ignition”. Figure 3.34 shows a schematic of the flow reactor while Figure 3.35 shows a photograph of part of the reactor channel and the electric discharge section. Two parallel plate electrodes 50.8 mm long and 12.7 mm wide, made of copper, are placed on the top and bottom walls of the flow channel, as shown schematically in Figure 3.34. The electrodes are separated from the quartz channel by Macor ceramic plates 1 mm thick each, as indicated in Figure 3.34.

133 Figure 3.35: Photograph of the discharge section of the ﬂow reactor. [45]

Discharge Generation

The electrodes shown in Figure 3.34 are powered by a custom-made high-voltage pulse generator, identical to the one described in Section 3.2. The pulser generated alternating polarity voltage pulses with peak voltage of up to 10 kV and FWHM pulse duration of ≈100 ns at a pulse repetition rate of 1 kHz. Figure 3.36 plots a typical applied voltage pulse waveform measured in argon at P = 1 atm, T = 600 K, at pulse repetition rate of 1 kHz. Since in these experiments the discharge current was not measured, the power coupled to the plasma is predicted using a one-dimensional nanosecond pulse breakdown model in a dielectric barrier nanosecond pulse discharge [25] which takes into account sheath formation and plasma self-shielding on nanosecond time scales, and predicts electric field in the plasma, as well as current and coupled power waveforms. The left panel in Figure 3.36 also plots the voltage pulse shape used by the nanosecond pulse breakdown model (a Gaussian fit to the experimental voltage pusle shape, dashed line) as well as the predicted electric field in the plasma. In the model, the

134 Figure 3.36: Experimental voltage waveform measured across the electrodes, Gaussian ﬁt used in the nanosecond pulse breakdown model, predicted ﬁeld in the plasma (left), predicted power coupled to the plasma. [45]

discharge gap is 7 mm, and the thickness of dielectric layers between the plasma

and the electrodes is d = 2.3 mm (d1 = 1.3 mm quartz, ε1 = 3.8 and d2 = 1 mm

Macor ceramic, ε2 = 5.7), as shown in Figure 3.34. The right panel of Figure 3.36 shows time-resolved power coupled to the plasma at these conditions. This power waveform is used as an input in the kinetic model discussed in Chapter 2. Both peak coupled power and coupled pulse energy predicted by the model decrease as the temperature of the flow increased, since breakdown voltage decreases as the number density is reduced. Coupled power waveforms are predicted for 500–1000 K. Since the mass flow rate in the reactor is kept constant, as well as the pulse repetition rate, the number of pulses exciting the flow during the residence time between the electrodes decreases as the temperature in the reactor is increased.

135 Gas Chromatography Measurements of Stable Oxidation Species

Details of these measurements are discussed in Tsolas et al.[45]. The measurement results compared with kinetic modeling predictions in this work are measurements of stable species using a gas chromatograph. For this, the flow of reaction products is sampled into the gas chromatograph at relatively low temperature at the exit of the flow reactor (T ≈ 300 K), to exclude the possibility of reactions downstream of the reaction zone in the furnace. The product mixture composition is determined by measuring the time-dependent flow rate through the chromatograph column. The column, a narrow tube, is filled with structures and compounds which retain different species for different times depending on their chemical and physical properties. By comparing the time-dependent flow rate to calibrated standard mixtures, absolute concentrations of a number of hydrocarbon species can be measured.

3.3.2 Results and Discussion

The modeling predictions are compared with experimental data for four diﬀerent

fuels, H2, CH4, C2H4, C3H8, diluted in argon at atmospheric pressure. The reactant ﬂow temperature was varied from 300 K to 1300 K. In all four cases,

the O2 mole fraction in the argon buﬀer was kept constant at 3000 ppm. Mole

fractions of fuel in the ﬂow were 2000 ppm for H2, 1600 ppm for CH4, 800 ppm for

C2H4, and 533 ppm for C3H8.

Figure 3.37 compares modeling predictions for H2 and O2 at the end of the reactor with the experimental data, using two diﬀerent conventional reaction

136 Figure 3.37: Comparison of two chemical reaction mechanism predictions (Blue - Aramco, Red - Konnov) and measurements of hydrogen and oxygen concentrations, plotted at the exit of the reactor versus temperature. [45]

mechanisms, Aramco [42] and Konnov [43]. It can be seen that the model reproduces both species number densities very well, with slight overprediction of

H2 and O2, at moderate temperatures (T =650–850 K).

Figure 3.38 shows comparison of six stable species mole fractions (CH4, C2H2,

C2H4, C2H6, CO, and CO2) with the data in the CH4-O2-Ar mixture, again using the Aramco and Konnov mechanisms. For both reaction mechanisms, the overall agreement with the data is good over the entire temperature range (T =300– 1300 K) with two notable exceptions.

First, the predicted balance between CO and CO2 near and above the hot ignition threshold is shifted. CO concentration near the hot ignition threshold is overpredicted by both reaction mechanisms, and which also predict signiﬁcantly

higher CO2 mole fraction above the hot ignition point, which corresponds to a lower predicted CO mole fraction. At this rich fuel/oxygen ratio in the diluted

137 Figure 3.38: Comparison of stable species concentrations at end of ﬂow reactor, predicted using two diﬀerent reaction mechanisms with experimental data, plotted at the furnace exit versus temperature. 1600 ppm CH4 - 3000 ppm O2 - Ar mxiture, P = 1 atm, discharge pulse repetition rate 1 kHz. [44] 138 mixture (φ = 1.6), the model predicts complete consumption of oxygen (≈ 1 ppm left at end of reactor), while the experimental data suggest that some oxygen-

containing species other than CO2 may still be present. These could be either O2

or undetected oxygenated species such as CH2O, since approximately 250 ppm of

carbon originally in the fuel is not accounted for in CO and CO2.

Finally, the concentration of C2H2 is signiﬁcantly overpredicted by both reaction mechanisms (see Figure 3.38). Speciﬁcally, modeling calculations using the Aramco mechanism at T = 1159 K (at the conditions when the predicted

C2H2 concentration peaks) predict that only about 7 ppm of acetylene is produced during the discharge burst, with the rest generated downstream of the discharge

burst (see Figure 3.39). According to the modeling predictions, C2H2 is formed by a reaction of vinyl radicals with H atoms,

C2H3 + H −−→ C2H2 + H2, (R 3.38) and decays in reactions of acetylene with O atoms,

80 % C2H2 + O −−→ HCCO + H, (R 3.39) and

20 % C2H2 + O −−→ CH2 + CO. (R 3.40)

139 Figure 3.39: Predicted acetylene mole fraction in the discharge region and downstream of the discharge region at the conditions of Figure 3.38 when T = 1159 K.

The vinyl radical concentration is in quasi-equilibrium between production via reactions of ethylene with OH (60%),

C2H4 + OH −−→ C2H3 + H2O, (R 3.41)

H atoms (25%),

C2H4 + H −−→ C2H3 + H2, (R 3.42) and the methyl radical (15%),

C2H4 + CH3 −−→ C2H3 + CH4, (R 3.43)

and consumption reactions, Reaction R 3.38 along with oxidation by O2,

C2H3 + O2 −−→ CH2O + HCO, (R 3.44)

140 C2H3 + O2 −−→ CH2CHO + O, (R 3.45)

and

C2H3 + O2 −−→ H + CO + CH2O. (R 3.46)

Note that hydrocarbon species are produced and consumed essentially in a

long chain of reactions: CH4 −−→ CH3 −−→ C2H6 −−→ C2H5 −−→ C2H4 −−→

C2H3 −−→ C2H2. Since the concentrations of CH4, C2H6, and C2H4 are all well reproduced by the model (see Figure 3.38), and since every step along this reaction chain depends on the concentrations of the same H, O, and OH radicals,

this suggests that both reaction mechanisms may be missing key steps of C2H2

conversion into oxygenate species, rather than CO and eventually CO2. This is consistent with the model overprediction of CO concentration at this temperature. The analysis of modeling predictions using the Konnov mechanism results in similar conclusions. Figure 3.40 and Figure 3.41 show comparison of ﬁnal species concentrations predicted by the model using two diﬀerent combustion chemistry mechanisms in

the C2H4-O2-Ar mixture. Here the fraction of fuel oxidized at low temperatures, below T ≈800 K, is overpredicted by as much as 30–70%, with the use of the Konnov mechanism resulting in better agreement with the data. Again, the model

reproduces the experimental data for all species besides C2H2 and C3H8 relatively well, especially at high temperatures using the Konnov mechanism. Analyzing the modeling predictions using the Konnov mechanism at T = 600 K,

both C2H4 and C2H2 concentrations after the discharge region remain essentially

141 Figure 3.40: Comparison of stable species concentrations at the end of the heated region of the flow reactor predicted by using two different combustion chemistry mechanisms with experimental data plotted versus final temperature. 800 ppm C2H4 - 3000 ppm O2 - Ar mixture, P = 1 atm, discharge pulse repetition rate 1 kHz. [46]

142 Figure 3.41: Comparison of stable species concentrations at the end of the heated region of the flow reactor predicted by using two different combustion chemistry mechanisms with experimental data plotted versus final temperature. 800 ppm C2H4 - 3000 ppm O2 - Ar mixture, P = 1 atm, discharge pulse repetition rate 1 kHz. [46]

143 constant (see Figure 3.42), since nearly all chemical reactions are driven by radicals

(O, H, and OH) produced in the plasma within ≈30 µs after each discharge pulse. After each pulse, ethylene is consumed via oxidation by O atoms (>60%),

C2H4 + O −−→ CH3 + HCO, (R 3.47)

C2H4 + O −−→ CH2HCO + H, (R 3.48)

C2H4 + O −−→ CH2CO + H2, (R 3.49)

and

C2H4 + O −−→ C2H3 + OH, (R 3.50)

as well as by three-body recombination to form C2H5 (>20%),

C2H4 + H + M −−→ C2H5 + M, (R 3.51)

and oxidation by OH (10%)

C2H4 + OH + M −−→ C2H5O + M, (R 3.52)

and

C2H4 + OH + M −−→ CH2O + CH3. (R 3.53)

144 Oxygen atoms, as discussed in Section 3.1, are produced by quenching of metastable argon atoms by oxygen,

∗ Ar + O2 −−→ Ar + O + O. (R 3.54)

C2H2 is produced by a reaction of C2H3 with molecular oxygen,

C2H3 + O2 −−→ C2H2 + HO2. (R 3.55)

Since C2H3 is produced primarily by oxidation of C2H4, Reaction R 3.50, compar-

ison of C2H4 and C2H2 concentrations predicted by the model with the data in

Figure 3.40 indicates that, while too much C2H4 is consumed, too little C2H3 is

generated. This implies that C2H3 reactions are not represented accurately by either combustion chemistry mechanism. In the Konnov mechanism, only about

3% of C2H3 is converted to C2H2, while the rest recombines back into C2H4 (25%),

C2H3 + H + M −−→ C2H4 + M, (R 3.56)

oxidizes to CH2O and HCO (40%),

C2H3 + O2 −−→ CH2O + HCO, (R 3.57)

and produces larger hydrocarbons (25%). Since C2H3 concentration remains in quasi-equilibrium, if the rates of these reactions are overpredicted, this would

reduce the amount of C2H3 available for production of C2H2 via Reaction R 3.55,

145 Figure 3.42: Concentrations of C2H4 and C2H2 in the discharge region and downstream (top) and between the ﬁrst and second discharge pulses (bottom), at the conditions of Figure 3.40 when T = 600 K.

146 as observed in the modeling predictions. In addition to identifying shortcomings of the mechanisms, comparing the diﬀerences in their predictions can be used to obtain insight into dominant stable

species kinetics. One interesting note is that while C2H3 concentration at T = 600 K is predicted to be in quasi-equilibrium by both reaction mechanisms, the

rates of C2H3 production and consumption between these mechanisms diﬀer by approximately a factor of two, with the one in the Konnov mechanism being higher. Additionally, while the Konnov mechanism predicts that the dominant production

of C2H2 is the reaction of C2H3 with molecular oxygen, Reaction R 3.55, in the

Aramco mechanism the reaction partners of C2H3 are instead H,

C2H3 + H −−→ C2H2 + H2, (R 3.58) and OH,

C2H3 + OH −−→ C2H2 + H2O, (R 3.59)

rather than the reaction with molecular oxygen producing C2H2. This shows that while the two mechanisms predict similar results at the same conditions, the dominant reaction pathways are quite diﬀerent, suggesting that they may not capture detailed kinetics of formation and decay of at least some of the major stable product species. Figure 3.43 and Figure 3.44 compare stable species concentrations predicted by the model with the experimental data, plotted versus the temperature in

the reactor, for the C3H8-O2-Ar mixture. Similar to the ethylene results (see

147 Figure 3.40 and 3.41), the fuel consumption at low temperatures is overpredicted,

this time by almost a factor of two. As in CH4 and C2H4 mixtures, the model strongly overpredicts the acetylene concentration (see Figure 3.38 and 3.40). Somewhat surprisingly, the Aramco mechanism provides better agreement with the data compared with the Konnov mechanism, speciﬁcally for intermediate

species such as C2H4, C2H6, and CH4. However, two of the species for which

the data are available, C4H8 and CH3HCO, are not included in the Aramco mechanism at all (see Figure 3.44). Finally, similar to the methane case, the model overpredicts the fraction of the carbon originally available in the fuel that oxidizes

into CO2 at high temperatures, above the ignition threshold (see Figure 3.43). Again, while there is a number of relatively modest diﬀerences between the two mechanism predictions and the data, the most signiﬁcant are the overprediction of

fuel consumption, C2H2 concentration (both at low temperatures and near ignition

threshold), and CH3HCO concentration. Using the modeling predictions with the Aramco mechanism at T = 600 K as a speciﬁc example, it can be seen that, similar to the ethylene case, at this low temperature the fuel is consumed in step-wise fashion, with rapid consumption during the pulse, slower decay between the pulses, which slows down until the next pulse occurs, and nearly constant concentration downstream of the discharge region (see Figure 3.45). At these conditions, the Aramco mechanism predicts that propane is consumed by extraction of a single hydrogen atom, in reactions with OH (65 %),

C3H8 + OH −−→ C3H7 + H2O, (R 3.60)

148 Figure 3.43: Comparison of stable species concentrations at end of the heated region of the flow reactor predicted using two different combustion chemistry mechanisms with experimental data, plotted versus temperature. 533 ppm C3H8 - 3000 ppm O - Ar mixture, P = 1 atm, discharge pulse repetition rate 1 kHz.[44] 2 149 Figure 3.44: Comparison of stable species concentrations at end of flow reactor predicted using two different combustion chemistry mechanisms with experimental data, plotted versus temperature. 533 ppm C3H8 - 3000 ppm O2 - Ar mixture, P = 1 atm, discharge pulse repetition rate 1 kHz. [44]

150 O (30 %),

C3H8 + O −−→ C3H7 + OH, (R 3.61)

and H (5%),

C3H8 + H −−→ C3H7 + H2. (R 3.62)

As stated in Section 3.1, H and O are produced primarily by collisional quenching of metastable argon,

∗ Ar + O2 −−→ Ar + O + O, (R 3.63)

and

∗ Ar + H2 −−→ Ar + H + H. (R 3.64)

OH is produced by over a dozen diﬀerent reactions with comparable contributions, with the three following reactions being the most important,

HO2 + H −−→ 2 OH, (R 3.65)

HO2 + O −−→ OH + O2, (R 3.66)

and

CH2O + O −−→ HCO + OH. (R 3.67)

While Reaction R 3.65 and Reaction R 3.66 were among dominant processes

of OH formation in Cx Hy -O2-Ar mixtures discussed in Section 3.1, formaldehyde

reactions also became important at these conditions. At these conditions, CH2O is produced primarily through oxidation of larger oxygenated hydrocarbons such

151 Figure 3.45: Predicted propane mole fraction in the discharge region and downstream (left) and between the ﬁrst two discharge pulses (right), at the conditions of Figure 3.43 when T = 600 K.

as C3H7O (32%),

C3H7O −−→ C2H5 + CH2O, (R 3.68)

CH3O (46%),

CH3O + M −−→ CH2O + H + M, (R 3.69)

CH3O + CH3O −−→ CH3OH + CH2O, (R 3.70) as well as

CH3O + O2 −−→ CH2O + HO2, (R 3.71)

and C2H5O (12%),

C2H5O −−→ CH3 + CH2O. (R 3.72)

Referring to the diﬀerence between the Aramco mechanism predictions of C2H2 concentration and the experimental data (see Figure 3.43), two important sets

152 of conditions are analyzed. At a relatively low temperature, T = 600 K, when the model underpredicts the ethylene number density, C2H2 is produced rapidly during each discharge pulse and at short time delays after each pulse (on the order of a few hundred nanoseconds), as shown in Figure 3.46. C2H2 is generated during argon metastable atom quenching by C2H4,

∗ Ar + C2H4 −−→ Ar + C2H2 + H2, (R 3.73) and

∗ Ar + C2H4 −−→ Ar + C2H2 + H + H. (R 3.74)

In the upstream portion of the discharge region, the concentration of C2H2 levels oﬀ until the next pulse (see left panel of Figure 3.46). Downstream, but still in the discharge region, once H atoms are accumulated, C2H2 is consumed by recombination with H atoms,

C2H2 + H + M −−→ C2H3 + M, (R 3.75) approximately 100 µs after each pulse. However, recombination between two successive discharge pulses accounts for only approximately 10-20% of C2H2 production during a single pulse (see right panel of Figure 3.46). As seen from

Figure 3.43, C2H4 concentration at this temperature is reproduced rather accurately, therefore the rate of C2H2 production via quenching of metastable argons in Reaction R 3.73 and R 3.74 is also likely to be predicted accurately. Therefore

153 Figure 3.46: Predicted, time-resolved C2H2 mole fraction after 20 discharge pulses (left) and 80 discharge pulses (right), at the conditions of Figure 3.43, when T = 600 K.

this suggests that both of these mechanisms lack additional low temperature C2H2 production pathways essential for its accurate predictions.

At a high temperature, T = 1050 K, C2H2 concentration is overpredicted (see

Figure 3.43), C2H2 is produced in three stages, as shown in Figure 3.47. First, the

mechanism discussed above produces approximately 25% of C2H2 via metastable argon quenching, Reaction R 3.73 and R 3.74, on ≈100 ns time scale after each

discharge pulse. Then, on the order of 100 µs after the pulse, an additional 25% of

C2H2 is produced by a number of processes. The ﬁrst is unimolecular dissociation

of C3H5,

C3H5 −−→ C2H2 + CH3, (R 3.76)

which is produced in oxidation of C3H6,

C3H6 + OH −−→ C3H5 + HO2, (R 3.77)

154 C3H6 + H −−→ C3H5 + H2, (R 3.78) and

C3H6 + O −−→ C3H5 + OH. (R 3.79)

The second is oxidation of C3H4 by H atoms,

C3H4 + H −−→ C2H2 + CH3, (R 3.80)

which is produced from C3H5, which is itself generated from C3H6, as discussed

above. Finally, collisional dissociation of C2H3, also contributes,

C2H3 + M −−→ C2H2 + H + M. (R 3.81)

The ﬁnal stage of C2H2 production occurs downstream of the discharge, when

approximately 50% of C2H2 is produced via the same reactions as in the second stage, but at a much slower rate (see Figure 3.47). In other words, the peak in

C2H2 concentration predicted by the model at these conditions is directly related

to the predicted peak in C2H6 concentration, which agrees well with the data (see

Figure 3.43). This suggests the existence of a consumption process for C2H2 which is missing from both reaction mechanisms considered in this work.

Finally, using the Konnov mechanism to analyze CH3HCO kinetics at T = 600 K, when the model underpredicts its concentration, the following trend is

identiﬁed. The CH3HCO concentration increases during the ﬁrst half of the discharge region, decays during the second half, and remains nearly constant

155 Figure 3.47: Predicted, time-resolved C2H2 mole fraction in the discharge region and downstrean (left), and between two successive pulses (right), at the conditions of Figure 3.43, when T = 1050 K.

downstream of the discharge section, as shown in Figure 3.48. This occurs because

on a short time scale after each discharge pulse, CH3HCO decays very rapidly, while it is generated much more slowly over the long time period between the pulses. In the discharge region, the rapid decay becomes considerably more dominant, increasing by over an order of magnitude, while the production is reduced by about a factor of two by the end of the discharge region.

The rapid decay is caused by reaction of CH3HCO with O atoms and OH molecules, which are generated in large amounts after each discharge pulse. The slow production includes slow unimolecular decay of large oxygenated species, such as

C3H7O −−→ CH3 + CH3HCO, (R 3.82)

and

O2C3H6OH −−→ CH3HCO + CH2O + OH. (R 3.83)

156 Figure 3.48: Predicted, time-resolved CH3HCO mole fraction in the discharge region and downstream (top), after 20 discharge pulses (bottom left), and after 80 discharge pulses (bottom right), at the conditions of Figure 3.44, when T = 600 K.

157 C3H7O is produced by a reaction of C3H7 with HO2,

C3H7 + HO2 −−→ C3H7O + OH, (R 3.84) which is generated via metastable argon quenching by propane.

O2C3H6OH is produced in two steps, ﬁrst via recombination of OH to C3H6,

C3H6 + OH −−→ C3H6OH, (R 3.85)

then O2,

O2 + C3H6OH −−→ O2C3H6OH. (R 3.86)

Thus, CH3HCO concentration is dominated by low temperature kinetics, and while the Konnov mechanism has a signiﬁcant amount of such reactions included, it appears that signiﬁcant uncertainty remains in prediction of detailed kinetics of relatively complex species.

158 Chapter 4

Supersonic Flow Carbon Monoxide Laser Model

The main objective of this model is to study the effect of adding air species to the laser mixture on the performance of electric discharge excited and chemical carbon monoxide lasers. The present modeling predictions, along with the experimental results obtained in an electrically excited, supersonic flow CO laser are necessary to assess feasibility of operating a chemical, supersonic flow CO laser using air as a major component of the laser mixture.

4.1 Quasi-one-dimensional Gas Dynamic Equa-

tions

The equations for mass conservation, equation of state, momentum conservation, and energy conservation predict velocity, temperature, pressure, and density in an electric discharge excited, non-equilibrium, chemically reacting gas mixture ﬂowing through a high pressure plenum of a supersonic ﬂow channel/laser apparatus, a converging-diverging supersonic nozzle, and a constant cross section supersonic laser cavity.

159 The mass conservation equation for a quasi-one-dimensional compressible ﬂow through a channel of variable area is as follows,

m˙ = ρAu = const., (4.1) where m˙ is the mass flow through the channel, ρ is the gas density, A is the cross sectional area of the channel, and u is the velocity in the x-direction (the direction along the flow channel). Taking the derivative of Equation 4.1 with respect to the axial direction gives the differential form of the mass conservation equation,

dρ du m˙ dA u + ρ = − . (4.2) dx dx A2 dx

Equation 4.2 relates the rate of change of mass flux (flow rate per unit area) to the rate of change in the cross sectional area. Regardless of the flow regime (sub- or supersonic), the mass flux is inversely proportional to the cross sectional area of the channel. Additionally, it is assumed that the flow is a perfect gas, with the equation of state, R P = ρ 0 T, (4.3) µ where P is the gas pressure, R0 is the universal gas constant, T is the gas temperature, µ is the mixture molecular weight defined as

X µ = XiWi, (4.4) i∈species

160 where Xi is the mole fraction of species i and Wi is the molecular weight of that species. Again, taking the derivative of Equation 4.3 over the axial coordinate gives ρ dT dP T dρ d 1 −R + − R = R ρT . (4.5) 0 µ dx dx 0 µ dx 0 dx µ

Analyzing the conservation of momentum in a stationary control volume representing a section of the channel perpendicular to the flow direction, and neglecting the effect of viscosity, relates the nozzle area and the flow velocity to the pressure,

x Z 2 0 = (ρ1u1A1)u1 − (ρ2u2A2)u2 + P1A1 − P2A2 + P sin(θ)dS. (4.6)

θ is the angle between the flow direction and the channel wall, dS is the wall surface area element, and the last term on the right hand side is the net axial force exerted by the channel walls on the flow. For a differential control volume, sin(θ)dS = dA, and the differential form of the conservation of momentum becomes

0 = ρu2A − (ρ + dρ)(u + du)2(A + dA) + PA − (P + dP )(A + dA) + P dA. (4.7)

Neglecting the second order terms in Equation 4.7, and Equation 4.1, d(ρuA) = 0, reduces the momentum conservation equation to Euler’s equation,

dP du + ρu = 0. (4.8) dx dx

161 It can be seen that the negative pressure gradient accelerates the ﬂow along the channel. Finally, the energy equation, which states that in the absence of work interaction, the total ﬂow enthalpy changes via external energy addition or losses,

2 m˙ d(h + u ) 2 = Q − L, (4.9) u dx where h is the thermal and chemical enthalpy of the flow, discussed below, and Q and L are the energy addition and loss terms, respectively. The left hand side of Equation 4.9 represents the change in the energy stored in the flow. Losses represent energy transfer out of the system, primarily by photon emission representing either spontaneous radiative decay of excited species or laser power coupling out of the flow in a laser cavity. Energy addition to the flow is due to the electric discharge power coupled to electrons in the discharge section, which transfer their energy to the neutral species in the mixture. For a reacting flow, the enthalpy, h, is defined as follows,

! X X h = cp,f T + hiYi + ei,v(Yi,v − Yi,v,eq) , (4.10) i∈species v

where cp,f is the frozen specific heat of the mixture at constant pressure, i.e. the specific heat assuming no change in the mixture composition and instantaneous vibrational relaxation as the temperature changes, hi is the specific formation

enthalpy of species i, Yi is the mass fraction of that species, ei,v is the energy

of vibrational state v of that species, Yi,v is the mass fraction of species i in

162 vibrational state v, while Yi,v,eq the mass fraction of species i in vibrational state v at the conditions when i is in equilibrium with the gas temperature, T . Equations 4.2, 4.5, 4.8, and 4.9 comprise a system of coupled linear differential equations for ρ, T , P , and u. Solving the equations requires input parameters such as the nozzle geometry, electric discharge power, losses in the laser cavity, and the rates of change of the mass fractions of chemical species and their vibrational level populations. Variation of the chemical composition of the mixture is discussed in Section 4.2 and Section 4.3, while the electric discharge model is discussed in Section 4.4, and the laser cavity model in Section 4.5. If the flow is not chemically reacting and there is no energy transfer between the flow and the surroundings, the right hand sides of Equations 4.9 and 4.5 are

dA zero. Therefore at the nozzle throat, where dx = 0, the right hand sides of all four governing equations are zero, which implies that derivatives of temperature, velocity, density, and pressure, are zero, suggesting an apparent singularity. This is more evident if energy and momentum balance equations are combined with the algebraic relations for the mass ﬂow rate and equation of state, Equations 4.1 and 4.3, to solve explicitly for the x-derivatives of gas temperature and ﬂow velocity, while also reformulating them in terms of the Mach number, M,

u u M = = q , (4.11) a R0 γ µ T

163 where a is the speed of sound, and γ is the ratio of speciﬁc heats for the gas. This gives 2 1 dA dT u A dx − Φ = 2 (4.12) dx cp,f 1 − M (1 − δM)

for the derivative of T and

du 1 δMM 2 dT dP = c − 1 + (4.13) dx u p,f γM 2 − 1 dx dx

for the derivative of u. In Equation 4.12, Φ is deﬁned as

d 1 γM 2 − 1 dP Φ = µ + . (4.14) dx µ u2 dx

dP dx , appearing in both Equation 4.13 and Equation 4.14, is effectively the net rate of change of the mole-specific flow enthalpy,

! dP Q X dXi X dXi devib,i = − h + (e − e ) + X , (4.15) dx ρu i dx vib,i vib,i,eq dx i dx i∈species i∈species

where Xi is the mole fraction of species i in the mixture, evib,i is the vibrational

energy per mole of species i, and evib,i,eq is the equilibrium vibrational energy per mole of that species at temperature T . The first term represents the specific energy loading by the electric discharge, while the quantity in the parenthesis is the derivative of the chemical enthalpy of the flow, including contribution of vibrational relaxation (compare to right hand side of Equation 4.10). Additionally,

164 δM is defined as 2 γM − 1 X devib,i,eq δM = X , (4.16) c M 2 i dT p,f i∈species which represents the effect of vibrational energy mode excitation on the “frozen” specific heat. Summarizing, there appears to be a singularity in the gas dynamic equations when M ≈ 1. The method used to predict the flow parameters near the throat involves changing the way the derivatives of the four flow parameters are determined near the nozzle throat. First, the flow channel is divided into three separate regions using two Mach number values, one slightly below M = 1, and the other slightly

above M = 1, usually Ml ≈ 0.95 and Mu ≈ 1.1. The three regions are as follows:

(a) the region away from the throat, both at M < Ml and M > Mu, (b) the region

between the lower boundary and the throat, Ml < M < 1, and (c) the region

between the throat and the upper boundary, 1 < M < Mu.

At the point when the ﬂow crosses the Ml boundary, the parameters at the

critical point, i.e. M = 1, Tc, ρc, and ac, are estimated as follows. First, the value

of the critical temperature, Tc, is estimated assuming adiabatic ﬂow with frozen

165 chemical and vibrational kinetics as follows,

u2 u2 h(T ) + = h (T ) + c , 2 f c 2 X X u2 c T + h Y + e (Y − Y ) + = p,f i i i,v i,v i,v,eq 2 i∈species v 2 (4.17) X X a(Tc) c T + h Y + e (Y − Y ) + , p,f c i i i,v i,v i,v,eq 2 i∈species v

R0 u2 γ Tc c T + = c T + µ , p,f 2 p,f c 2 where the left hand side represents the ﬂow conditions at M = Ml, and the right

hand side represents the ﬂow at the critical point. The speed of sound, ac, is then calculated from the critical temperature using in Equation 4.11, which yields the velocity at the throat. The critical density, ρc, is predicted from the isentropic ﬂow relation, γ ρ 2 γ+1 c = . (4.18) ρ0 γ + 1

Since the ﬂow is nearly choked when M = Ml, these values are good initial

estimates of the actual parameters at the throat. Between the location where Ml is reached and the nozzle throat, the ﬂow temperature and velocity are linearly interpolated using the values at the lower threshold and the estimated parameters at the throat,

Tl − Tc T (x) = Tl + · (x − xl), (4.19) xl − xc ul − ac u(x) = ul + · (x − xl). (4.20) xl − xc

166 The density in this region is calculated from the isentropic ﬂow relation as follows,

1 T (x) γ−1 ρ(x) = ρl . (4.21) Tl

The pressure is calculated from the equation of state, Equation 4.3. Note that this approach violates the mass conservation (see Equation 4.1). This problem is resolved by iterating the simulation of the subsonic portion of the nozzle, varying the mass ﬂow rate, and is discussed in more detail below.

Downstream of the throat, the ﬂow parameters are extrapolated until M = Mu. First, the temperature is extrapolated using the isentropic relation,

T (γ + 1) T = c , (4.22) 2 + (γ − 1)M 2 where the Mach number is calculated from the channel area ratio,

γ+1 A 1 2 + (γ + 1)M 2 2(γ−1) = . (4.23) Ac M γ + 1

The flow velocity is calculated as the speed of sound multiplied by the Mach number. The gas density is calculated from the mass flow rate, Equation 4.1, and the pressure is calculated from the equation of state, Equation 4.3. Basically, Equations 4.21, 4.22, and 4.23 assume one-dimensional isentropic flow in the

immediate vicinity of the nozzle throat. Once M = Mu is reached, normal integration of the governing equations is resumed. As discussed above, the mass ﬂow rate through the channel is controlled by

167 the flow conditions at the throat, where the flow is choked. In an equilibrium, non-reacting flow without external energy addition, the conditions at the sonic throat can be calculated exactly from the conditions at the plenum inlet using the one-dimensional isentropic flow relations. With chemical reactions or vibrational relaxation, the values of temperature, velocity, pressure, and speed of sound at the nozzle throat are not known until the simulation reaches that point, and therefore it is impossible to predict whether the flow would reach the sonic conditions at the throat (in fact it is expected that it would not). Therefore, the simulation prior to the nozzle throat is completed, and the mass flow rate required to reach M = 1 is calculated. The bisection method is used to minimize the difference between the mass flow rate calculated at the throat and the initial mass flow rate, requiring several iterations of the subsonic region of the nozzle. Once the bisection method converges, the simulation, including both subsonic and supersonic regions of the nozzle, is completed. This method ensures a mass flow rate in the plenum consistent with the mass flow rate required for the sonic point to be at the nozzle throat.

4.2 Chemical Kinetics

A general chemical reaction equation can be written as

k X 0 −−→f,j X 00 νj,i Ai ←−− νj,i Bi, (R 4.1) kr,j i∈reactantsj i∈productsj

168 0 00 where j is the index for the reaction, νj,i and νj,i are the stoichiometric coeﬃcients

for species i in the reactants and products of reaction j, respectively, Ai and Bi

th are the i reactant and product of reaction j, and kf,j and kr,j are the forward and the reverse rate coeﬃcients for reaction j. Governing equations for the mass fractions of heavy species in the reacting ﬂow are as follows,

  dYi Mi X Y ν0 Y ν00 = (ν00 − ν0 ) k n j,i − k n j,i , (4.24) dx ρu j,i j,i  f,j i,j r,j i,j  j∈reactions i∈reactantsj i∈productsj

where Yi is the mass fractions of species i, Mi is the molar mass of species i, nr,j

are number densitities of reactants for reaction j, and np,j are number densities of products. Rate coeﬃcients of chemical reactions among neutral species, including electronically excited states of molecules and atoms, are given using Arrhenius rate expressions, E k = AT b exp − a , (4.25) f RT where A is the pre-exponential factor, b is the temperature dependence factor,

and Ea is the activation energy. The reverse rate coeﬃcients for the reactions among the ground electronic state species are calculated from detailed balance in equilibrium, when both sides of Equation 4.24 are zero. This yields the relation

169 between the forward and reverse rate coeﬃcients,

ν00 Q j,i ni (0) kf,j i∈productsj P 00 0 ∆G i∈species(νj,i−νj,i) = ν0 = Kc = (R0T ) exp − (4.26) kr,j Q j,i R0T ni i∈reactantsj

(0) where Kc is the equilibrium concentration constant and ∆G is the change in the standard Gibbs free energy for the reaction,

(0) X 00 0 X 0 0 ∆G = νj,igi − νj,igi , (4.27)

i∈productsj i∈reactantsj

0 where gi is the mole-specific standard Gibbs free energy of species i. For reactions of electronically excited species, reverse rate coefficients are not calculated, since they are typically much smaller compared to the forward rate coefficients. Rate coefficients for electron impact reactions are discussed in Section 4.4. Reactions and rate coefficients of vibrational energy transfer among diatomic molecules are discussed in Section 4.3.

4.3 Vibrational Kinetics

State-speciﬁc vibrational energy transfer among major diatomic species, speciﬁcally

CO, N2, and O2, is simulated using a master equation model, which predicts a vibrational distribution function (VDF) for each of these species. The governing

170 equations for vibrational level populations of these species are listed below,

dY M dn dn dn dn i,v = i i,v + i,v + i,v + i,v + dx ρu dt eV dt VV dt VT dt SRD dn dn dn i,v + i,v + i,v . (4.28) dt chem dt abs. dt SE

In Equation 4.28, Yi,v is the mass fraction of species i in the vibrational level v. The terms on the right hand side represent diﬀerent types of energy transfer processes, discussed in greater detail below.

The term marked by a subscript eV denotes energy transfer from electrons to the vibrational energy mode by electron impact processes in an electric discharge,

e− + AB(v−0) −−→ e− + AB(v > 0), (R 4.2) where v is the vibrational quantum number,

vmax dni,0 X = − k n n , (4.29) dt v e i,0 eV v=1

and dni,v = kvneni,0, v > 0. (4.30) dt eV

Rate coeﬃcients of electron impact excitation of vibrational states, kv, are predicted by solving the Boltzmann equation for electrons in the two-term expansion, as discussed in Section 4.4. The discharge adds energy to vibrational modes of all major diatomic species, generating non-equilibrium vibrational level populations.

171 VV energy transfer processes between two diatomic molecules, AB and CD, which conserves the number of vibrational quanta, is listed below,

kf AB(v) + CD(w) ←−−−−→ AB(v − 1) + CD(w + 1). (R 4.3) kr which gives the VV term in Equation 4.28 as

wmax,j dni,v X X = −kf ni,vnj,w + krni,v−1nj,w+1 (4.31) dt VV j∈[N2,O2,CO] w=0

VV processes are critical in vibrational relaxation of diatomic processes at the conditions of strong vibrational disequilibrium, in particular during anharmonic VV pumping [126]. The rates of these processes may be comparable with the gas kinetic rate when the vibrational energy defect is low, such that the process is near resonant. The state-speciﬁc rate coeﬃcients of VV processes depend on the vibrational quantum numbers of both species involved and the gas temperature, as follows [127],

∆E k (v, w → v − 1, w + 1) = Z Sv,v−1 + Lv,v−1 exp − v , (4.32) i,j w,w+1 w,w+1 2T where v and w are the vibrational quantum numbers, as given in Reaction R 4.3, the index i represents the oscillator AB, j the oscillator CD, Z is the gas kinetic rate coeﬃcient, s πk T Z = 4σ2 b , (4.33) 2µ

S and L are the short and long range components of the intermolecular interaction

172 given by Equation 4.36 and Equation 4.39, respectively, and ∆Ev is the vibrational energy defect,

∆Ev = (Ej,v − Ej,v−1) − (Ei,w+1 − Ei,w). (4.34) where the energy of a given vibrational state is calculated using the harmonic and the ﬁrst anharmonic terms in the Dunham expansion,

1 1 E = ω (v + ) 1 − x v + , (4.35) v e 2 e 2

where ωe deﬁnes the energy spacing between the vibrational energy levels for the

species and xe is the ﬁrst anharmonic term, controlling the rate at which the energy spacing decreases as the vibrational quantum number increases.

3 −1 In Equation 4.32, both ki,j and Z have units of cm s , with all other terms representing the energy transfer probability. In Equation 4.33, σ2 is the collision

−8 cross section, σ = 3.75 · 10 cm for CO, N2, and O2. The short-range interaction probability is given as follows [127],

v,v−1 1 ˆ v w + 1 Sw,w+1 = S · T F (λ), (4.36) 2 1 − xe,iv 1 − xe,j(w + 1) where Sˆ is an adjustable parameter dependent on the two species involved, and F (λ) is the vibrational energy defect function,

−2λ −2λ F (λ) = 3 − exp exp , (4.37) 3 3

173 r − 3 c λ = 2 2 |∆E |, (4.38) T v where c is an adjustable parameter for the short range interaction. From Equations 4.36–4.38, it can be seen that the vibrational energy transfer probability (a) increases with vibrational quantum numbers and (b) increases at low vibrational energy defect, i.e. for near-resonant energy transfer processes. The short-range interaction between the molecules is controlled by the short- range repulsive forces (the repulsive part of the Lennard-Jones intermolecular interaction potential), which is approximated by an exponential repulsive potential in simple vibrational energy transfer theories [115, 128]. The near-resonant VV transition probability induced by the short-range interaction is proportional to the squared collision velocity, such that the thermally-averaged probability is proportional to temperature [128]. The strong exponential dependence on the vibrational energy defect results from the fact that for non-resonant processes, the energy needs to be supplied from the translational and rotational modes [128]. This dependence is especially strong at low temperatures (i.e. low translational- rotational energies). Although a simple one-dimensional vibrational energy transfer theory [128] predicts the values of parameters Sˆ and c, in the present work these parameters are evaluated from comparison with experimental data (wherever available) or more advanced semiclassical three-dimensional trajectory calculations using accurate intermolecular potential energy surfaces.

174 The long-range interaction probability is given as follows [127],

ˆ v,v−1 2 w,w+1 2 2 v,v−1 L g g ∆Ev Lw,w+1 = 1,0 1,0 exp − 2 (4.39) T g i g j kb bT where Lˆ is an adjustable parameter dependent on the species involved, gv,v−1 are the matrix elements for vibrational transitions v → v − 1, such that

2 1 1 v,v−1 2 1 + 1 ! v + 2 − 2v + 4 − 2v g xe,i xe,i = xe,i , (4.40) g1,0 1 + 3 − 2v 1 1 i xe,i + 3 − v xe,i xe,i

and b is an adjustable parameter. The long-range interactions between the molecules is controlled by the long-range dipole-dipole (such as for CO-CO) and

dipole-quadrupole (for CO-N2 and CO-O2) attractive electrostatic forces, occuring in collisions among molecules that have a permanent dipole moment (such as CO). The effect of long-range interactions becomes especially strong at low collision energies and long collision durations (i.e. low temperatures) [126]. In particular, the effect of “orbiting” attractive collisions may be very strong at low temperatures [66]. The long-range interaction significantly increases the VV rates, by about 2 orders of magnitude for CO-CO at room temperature, compared to

N2-N2 (see Section A.1 versus Section A.3). The adjustable parameters used in Equation 4.36– 4.40 are determined from comparison of the VV rate coeﬃcients with experimental data [65,67–71] and/or three-dimensional semiclassical trajectory calculatuions for accurate intermolecular interaction potentials [66, 72–81]. The summary of this comparison is given in

175 Table 4.1: Parameters for calculation of VV rate coeﬃcients

Species Sˆ c (K−1) Lˆ b (K) CO–CO 1.64 · 10−6 0.456 1.614 40.9 −7 N2–N2 1.50 · 10 0.360 – – −6 O2–O2 2.00 · 10 0.500 – – −8 CO–N2 7.00 · 10 0.185 0.060 88.7 −8 CO–O2 7.00 · 10 0.185 0.060 88.7 −8 N2–O2 1.50 · 10 0.250 – –

Appendix A. The values of the four ﬁtting parameters, Sˆ, c, Lˆ, and b, are summarized in Table 4.1, based of those given by Lou et al.[127], and modiﬁed to match experimental data and trajectory calculations.

The term in Equation 4.28 denoted by a subscript VT is vibration-to-translation (VT) relaxation, where a molecule in a vibrational level v > 0 collides with another species (molecule or atom) and is de-excited, with the vibrational energy transferred to the kinetic energy of the colliding partners (translational and rotational),

kf AB(v) + M ←−−−−→ AB(v-1) + M, (R 4.4) kr

such that the VT term in Equation 4.28 is

dni,v X = −k n n + k n n . (4.41) dt f i,v j r i,v−1 j VT j∈species

The rate parameterization for VT processes is similar to that for the VV rates and is based on similar theory of vibrational energy transfer induced by short-range repulsing interactions [128]. The role of long-range attractive forces in

176 VT processes is relatively minor, since they are most pronounced for near-resonant processes. State-speciﬁc VT rate coeﬃcients are given as follows,

kbT v ki,j(v → v − 1) = F (λ), (4.42) 1,0 −ωe,i 1 − x v (τi,jP ) F (λ ) 1 − exp T e,i where (τi,jP ) is the characteristic time for vibrational relaxation of species i by collision partner j, multiplied by the pressure, P , which varies with gas temperature as follows, B C (τi,jP ) = exp A + + , (4.43) − 1 − 2 T 3 T 3 where A, B, and C are empirical fitting parameters. Again, although vibrational relaxation time as a function of temperature is predicted by a simple one-dimensional theory of vibrational energy transfer, in the present work, fits to experimental data are used, whenever available. In Equation 4.42, F (λ) is the same vibrational energy defect function as given by Equations 4.37 and 4.38, where now the change in vibrational energy is defined as

∆Ev = Ei,v − Ei,v−1. (4.44)

Note that the values of the adjustable parameter c in the expression for λ for VT and VV processes may be diﬀerent. The values of the adjustable parameters are summarized in Table 4.2.

The term in Equation 4.28 signiﬁed by a subscript SRD is the spontaneous radiative decay term, for the process when a carbon monoxide molecule spontaneously

177 Table 4.2: Parameters for calculation of VT rate coeﬃcients

AB M c A B C CO CO,N2,O2 0.25 -17.65 359.0 -1037.3 CO O 0.18 -7.30 54.0 0.0 CO He 0.567 -15.9249 -209.471 395.339 N2 CO,N2,O2 0.25 -13.63 328.90 -993.3 N2 O 0.18 -2.466 33.11 0.0 N2 He 0.06 -11.71 196.09 -394.0 O2 CO,N2,O2 0.25 -13.5 205.0 -295.0 O2 O 0.18 -3.507 0.0 0.0 O2 He 0.06 -5.98 67.0 0.0

emits an infrared photon and its vibrational energy decreases,

CO(v) −−→ CO(v-∆v) + hν. (R 4.5)

This term is given as,

dni,v X X = − A n + A n . (4.45) dt v,v−∆v CO,v v+∆v,v CO,v+∆v SRD ∆v ∆v where A are the Einstein coefficients for spontaneous emission. In Reaction R 4.5, ∆v = 1 corresponds to the CO fundamental infrared emission, while higher values refer to the overtones (e.g. ∆v = 2 corresponds to the first overtone). In the present model, spontaneous radiative decay processes up to ∆v = 2 are incorporated. The Einstein A coefficients for ∆v = 3 are five orders of magnitude smaller than those for ∆v = 1 at low v’s and are approximately 2 orders of magnitude smaller at v ≈ 30, and therefore are considered negligible. The values for the Einstein A coefficients are computed from transition dipole moments tabulated by Chakerian

178 et al.[129]. The details of these calculations are discussed in Appendix C and the resulting values for the Einstein A coeﬃcients are listed in Table C.1.

The term in Equation 4.28 denoted by a subscript chem. represents productions and consumption of vibrationally excited species via chemical reactions, including reactions which produce non-equilibrium vibrational energy distributions. The rates of all reactions except reaction

k(→ v) C + O2 −−−−→ CO(v) + O (R 4.6)

are assumed to depend only on temperature, rather than vibrational quantum number, and the vibrational distribution of the products of those reactions are discussed below. State-speciﬁc rate coeﬃcients of vibrationally non-equilibrium Reaction R 4.6 are assumed to follow a Gaussian distribution over the vibrational levels of CO,

(v − v∗)2 k(→ v) = k A exp − , (4.46) f πσ

where kf is the total rate coeﬃcient for the process, A is a normalization factor, such that 23 X kf = k(→ v), (4.47) v=0 where the upper limit of the sum, v = 23, is chosen due to the vibrational energy

of CO(v–24) compared to the ground vibrational state is greater than the reaction

179 enthalpy of Reaction R 4.6. Because of this, it is assumed that

k(→ v ≥ 24) = 0. (4.48)

Additionally, in Equation 4.46, v∗ is chosen to be 8, such that the fraction of reaction enthalpy going to CO vibrational mode is equal to that predicted by the quantum chemistry calculations, 30% [61]. The choice of σ is somewhat uncertain. The modeling predictions, discussed in Section 5.1, were found to be nearly independent of the value of σ over a wide range (σ ≈ 1–12), and σ = 5 was chosen based on measurements of state-speciﬁc rate coeﬃcients of a reaction,

CS + O −−→ CO(v) + S, (R 4.7) shown in Figure 4.1. Rate coeﬃcients for reactions which consume CO, e.g.

CO + O2 −−→ CO2 + O, (R 4.8) are assumed not to change the CO vibrational populations, i.e.

nCO,v k(v →) = kf . (4.49) nCO

180 Figure 4.1: CO vibrational distribution function (VDF) produced by two carbon disulﬁde ﬂame reactions, CS2 +O (closed symbols) and CS+O (open symbols). [59]

181 Reactions that produce CO, other than Reaction R 4.6, are assumed to produce a VDF in equilibrium with the temperature,

fv(T ) k(→ v) = kf P , (4.50) fv(T ) v where E1 − E0 Ev − E0 fv(T ) = 2 sinh exp − . (4.51) 2T kbT

The terms signiﬁed by subscripts abs. and SE in Equation 4.28 are the absorption and stimulated emission terms, respectively,

dn dn B F n B F n i,v + i,v = v−1,v v CO,v−1 − v,v+1 v+1 CO,v dt abs. dt SE ∆Ev ∆Ev+1 B F n B F n + v+1,v v+1 CO,v+1 − v,v−1 v CO,v ∆Ev+1 ∆Ev Fv = (Bv−1,vnCO,v−1 − Bv,v−1nCO,v) (4.52) ∆Ev Fv+1 − (Bv,v+1nCO,v − Bv+1,vnCO,v+1) ∆Ev+1 Fv Fv+1 = αv − αv+1 , ∆Ev ∆Ev+1

where Bi,j is the Einstein B coeﬃcient for stimulated emission/absorption transition

from state i to state j, Fv is the laser photon ﬂux at the wavelength resonant with the transition between CO(v) and CO(v-1) vibrational states, ∆Ev is the

energy diﬀerence between these two vibrational states (see Equation 4.44), and αv is the small signal gain for this transition. The terms detailed in Equation 4.52

are coupled with the equations for the photon ﬂuxes, Fv, discussed in Section 4.5.

182 Stimulated emission occurs when a photon ﬂux interacts with vibrationally excited CO molecules, de-exciting them and generating additional photons with the same energy and momentum vector,

CO(v) + h ν ←−−−−→ CO(v-1) + 2 h ν. (R 4.9)

Absorption is the opposite process, when a photon ﬂux is absorbed by CO molecules.

4.4 Electric Discharge Model

The electric discharge model includes the Boltzmann equation for plasma electrons in the two-term approximation, for prediction of electron swarm parameters (drift velocity, energy distribution function, and electron temperature) as well as electron impact rate coeﬃcients for inelastic excitation of heavy species [24]. Electron density in the discharge is calculated as follows,

Q ne = E , (4.53) V– N Nvd where Q is the discharge power, same as in Equation 4.9, V– is the discharge

E volume, N is the reduced electric ﬁeld in the discharge, N is the total number E density, and vd is the drift velocity of electrons (a function of N ). In the present work, the kinetic model is used to predict vibrational energy transfer and lasing in

CO-N2-O2-He mixtures, vibrationally excited by a transverse, capacitively coupled

183 RF discharge sustained in the plenum of a supersonic ﬂow laser. Since the reduced electric ﬁeld in the RF discharge has not been measured, and since the model does not incorporate equations for the electron and ion number densities, or the Poisson

E equation for the electric ﬁeld in the discharge, the N value is used as an adjustable parameter, chosen from the best agreement between CO vibrational distribution function (VDF), measured downstream of the discharge and the model predictions.

E The same value of N , which represents an eﬀective RMS value of the reduced electric ﬁeld in the discharge, was used by the Boltzmann equation solver. The Boltzmann equation solver used in this model is the same as the one discussed in Section 2.2, and its use is summarized here again. The two-term

expansion Boltzmann equation for electrons predicts the ﬁrst (isotropic, F0(ε))

and second (anisotropic, F1(ε)) terms of the electron energy distribution function (EEDF). From the anisotropic term the drift velocity can be calculated [24],

∞ 1r2e Z v = εF dε, (4.54) d 3 m 1 0 where e is the elementary charge and m is the mass of an electron, the value of which can then be used in Equation 4.53. The rate coeﬃcients for electron impact processes can be calculated from the isotropic portion of the EEDF, given by Equation 2.35 and reproduced here,

1 2e 2 Z ∞ ki = εσiF0dε. m 0

184 The rate coeﬃcients for electron impact processes,

e− + A −−→ e− + A∗, (R 4.10)

and electron density are used to model an electron impact process. For excitation of vibrationl states, the predicted rate coefficients are used in Equation 4.29 and Equation 4.30 which capture the electron impact effects in the master equation, Equation 4.28. For excitation of electronic states, Reaction R 4.10 is treated as a standard chemical reaction involving species A and A* in Equation 4.24, using the Boltzmann equation to predict the rate coefficient rather than Equation 4.25.

4.5 Laser Cavity Equations

Finally, the master equation for vibrational populations of carbon monoxide is coupled to the laser cavity model. A carbon monoxide laser generates lasing on multiple ro-vibrational transitions which have sufficient gain to overcome the losses in the optical cavity. Laser gain is the amplification factor representing the stimulated emission process that occurs within a gain medium (such as vibrationally excited CO flow). A photon with a specific energy can interact with the CO molecules in the gain region. It can be absorbed by a CO molecule in the lower vibrational energy state, exciting it to the higher vibrational energy state, or it can cause stimulated emission from a CO molecule in the higher vibrational energy state, such that it becomes de-excited and a second photon is produced,

185 with the same propagation direction, polarization, phase, and wavelength as the incident photon. These processes are shown in Reaction R 4.9. Lasing occurs when the rate of stimulated emission exceeds that of absorption which occurs when the population of the higher energy state exceeds that of the lower energy state. This is referred to as a population inversion. The expression for gain between the high energy state, 2, and low energy state, 1, is given below,

2 c g2 α = A21 2 g(ν) n2 − n1 (4.55) 8πν g1

In Equation 4.55, A21 is the Einstein coeﬃcient for spontaneous emission, c is the speed of light, ν is the frequency, g(ν) is the absorption/emission lineshape

function accounting for Doppler, natural, and collisional (pressure) broadening, ni

is the number density of state i, and gi is the degeneracy of state i. The Doppler lineshape accounts for the ﬁnite temperature of the CO molecules, and is represented by a Gaussian lineshape,

s 2 2 2 MCOc MCOc (ν − ν0) gD(ν) = 2 exp − 2 , (4.56) 2πkbT ν0 2kbT ν0

where ν0 is the frequency of photon that is energy resonant with the transition (i.e. the frequency on the line center). Natural and collisional broadening both cause Lorentzian lineshapes,

γ gL(ν) = 2 2 . (4.57) π ((ν − ν0) + γ )

186 where γ is the half width at half maximum (HWHM) of the profile. For natural broadening, caused by the finite lifetime of the excited state, the broadening parameter is 1 X γ = A , (4.58) 4π u,l l where Au,l is the Einstein coefficient for spontaneous radiative decay of the excited

state, u, to a lower state, l.

For collisional broadening, γ depends on collision frequency, νcol, of a particle in the excited state, ν γ = col . (4.59) 2π

In the case of both natural and collisional broadening, the broadening parameter value is simply the sum of those given in Equations 4.58 and 4.59. When all three broadening mechanisms occur, the resulting lineshape is a Voigt lineshape, which is the convolution of the Doppler and Lorentzian lineshapes,

∞ Z 0 0 gV (ν) = gD(ν)gL(ν − ν )dν . (4.60) −∞

g2 It can be seen from Equation 4.55 that when n2 > n1, the rate of stimulated g1 emission exceeds that of absorption, and the ﬂux of photons of frequency ν is

g2 ampliﬁed, leading to lasing, while if n2 < n1, the ﬂux of photons decreases. g1 Carbon monoxide is capable of lasing on allowed ro-vibrational transitions, (v, J) → (v − k, J ± 1), where v is the vibrational quantum number, J is the rotational quantum number, and k is the number of CO vibrational quanta lost/gained

187 in the stimulated emission/absorption processes. In most CO lasers, k = 1 (representing lasing on fundamental transitions). However, when the population inversion is suﬃciently strong, lasing may also occur on lines corresponding to higher values of k (e.g. ﬁrst overtone lasing [130]). The J → J + 1 transitions belong to the P-branch (smaller energy spacing between the higher and the lower states), while J → J −1 transitions belong to the R-branch (larger energy spacing). Equation 4.55 can also be written in terms of CO vibrational and rotational level populations,

2 c g2 αv,J = A21 2 g(ν)nCO fvfJ − fv−1fJ±1 , (4.61) 8πν g1

where fv is the relative populations of vibrational level v, and fJ is the relative population of rotational level J. In relatively high pressure gas mixtures, the molecular collision frequency is suﬃciently high that the rotational modes of molecules can be assumed to be in equilibrium with the translational energy mode, such that Bv BvJ(J + 1) fJ = (2J + 1) exp − , (4.62) kbT kbT where Bv is the rotational constant for the CO molecule in vibrational level v. Basically, due to a small energy spacing among CO rotational levels, ≈ 2BJ ≈0.5 meV ≈6 K, rotational-translation relaxation occurs over several collisions. A complete derivation of Equation 4.55 for a molecule lasing on ro-vibrational transitions can be found in Appendix B.

188 Due to the much larger energy spacing of CO vibrational levels (≈0.25 eV), relaxation of energy from the CO vibrational mode to the rotational and translational modes, as well as vibrational energy re-distribution within the CO vibrational mode, are much slower. CO vibrational level populations are predicted by the master equation model discussed in Section 4.3.

A “total” population inversion occurs when fv > fv−1. A “partial” population inversion may occur even when fv < fv−1, if fJ > fJ−1. In the case of partial inversion, lasing occurs only on P-branch transitions, and only when fvfJ > g2 fv−1fJ+1, i.e. when the rotational level population ratio overcomes the ratio g1 in vibrational level populations and the degeneracy. This typically occurs at low temperatures, since the rotational level population depends on temperature exponentially (see Equation 4.62). At the conditions of total population inversion, the P-branch transitions always have positive gain, and lasing will occur if the gain is suﬃcient to overcome losses in the cavity. In this case, lasing may also occur on R-branch transitions, if the ratio of vibrational level populations is suﬃcient to overcome the ratio of rotational level populations and losses in the cavity. Incorporating lasing on multiple ro-vibrational transitions into the model would require incorporating rotational relaxation processes, which occur on the same time scale as stimulated emission and absorption, and control the distribution of CO molecules over rotational levels, which is essential for predicting gain and laser power on individual ro-vibrational transitions. As such, the present model assumes that lasing in each vibrational band occurs on only one ro-vibrational transition

189 with highest gain, such that it predicts laser power for diﬀerent vibrational bands.

The photon ﬂux in the cavity on each vibrational band, Fv, is controlled by the rates of stimulated emission and absorption on that band, as follows,

dFv = c max (αv,J ) − Lcav Fv, (4.63) dt J

where Fv is the laser ﬂux on a given vibrational band, and Lcav are the losses in the cavity, including laser power coupled out of the cavity through the output coupler mirror, 1 L = ln (R R ) , (4.64) cav 2l 1 2 where l is the length of the laser cavity (i.e. the width of the supersonic ﬂow

channel), and R1 and R2 are the reflectivities of the two laser cavity mirrors. Equation 4.63 assumes that photons propagate perpendicular to the flow direction in the cavity, such that the photon flux at a particular axial location is controlled by the CO VDF at that location. Since stimulated emission and absorption processes are extremely fast, this results in strong oscillations of the photon flux and laser output power predicted by the model. This model also does not take into account the effect of the mirror curvature and the fact that the photon flux also includes photons propagating over a range of angles to the flow, such that the photons generated near the down-stream edge of the cavity can propagate to the region near the up-stream edge of the cavity before interacting with CO molecules, thereby invalidating the quasi-one-dimensional formulation used for the governing equations of the present model.

190 To account for this, the present model is using a quasi-steady state laser approximation. This assumes that the intra-cavity laser ﬂux on each vibrational band is constant in the entire cavity, corresponding to conditions where the laser is operated as a continuous wave laser. To obtain the quasi-steady intra-cavity laser ﬂux, the quasi-one-dimensional equations discussed previously in this chapter are solved along the laser cavity,

from the start, xcav,i, to the end, xcav,f , several times. During the first such iteration, Equation 4.63 is solved for the unsteady intra-cavity laser flux. This first iteration predicts the gain switching oscillations discussed above, and provides an initial estimate for the laser power and intra-cavity flux on each vibrational band for subsequent iterations. For subsequent iterations, Equation 4.63 is solved in the integral form,

xcav,f Z c 0 = max (αv,J ) − Lcav Fvdx, (4.65) u J xcav,i

or xcav,f xcav,f Z c Z c LcavFvdx = max (αv,J ) Fvdx. (4.66) u u J xcav,i xcav,i Note that the ﬂow velocity, u, is nearly independent of vibrational excitation

in the supersonic region of the nozzle, Lcav is one of the input parameters, and

Fv is by deﬁnition constant due to the quasi-steady laser cavity assumptions. Therefore the only quantity that changes from the start to the end of the cavity in

Equation 4.66 is the gain, αv,J , which is strongly dependent on the CO vibrational

191 level populations and their coupling to the laser fluxes, Fv, (see Equations 4.28 and 4.52). A combination of Newton’s method and the multi-dimensional bisection method are used to find the values of photon fluxes on all lasing fundamental transitions that satisfy Equation 4.66. Knowing the intra-cavity flux, the present

model assumes that losses out of the cavity, Lcav, deﬁned in Equation 4.64, represent power coupled out through the output coupler. Therefore the output laser power on each vibration band is

1 P = c ln (R R ) F . (4.67) out,v 2l 1 2 v

192 Chapter 5

Kinetic Modeling of Electric Discharge Excited and Chemical Carbon Monoxide Lasers

In this chapter, the kinetic model described in Chapter 4 is used to predict and analyze performance parameters of a chemical carbon monoxide laser operated in a supersonic flow. Kinetic modeling of this laser includes the following three case studies. The first case study, discussed in Section 5.1, analyzes kinetics of chemical reactions generating strongly vibrationally non-equilibrium carbon monoxide, which produces a gain medium for the chemical CO laser. Specifically, the model predicts the non-equilibrium distribution of CO reaction product over vibrational levels when carbon vapor reacts with oxygen molecules in a flow reactor, at relatively low flow velocities. In particular, modeling predictions quantify the non- equilibrium produced by this reaction at near room temperature and in collision dominated environments, when redistribution of the nascent CO vibrational populations by vibration-to-translation (VT) and vibration-to-vibration (VV) processes becomes important. The second case study, discussed in Section 5.2, examines the effect of adding

air species (N2 and O2) to the baseline CO-He mixture on the performance of an

193 electric discharge excited, supersonic flow carbon monoxide laser. The main goal of this study is to demonstrate feasibility of CO laser operation in a mixture with a significant fraction of air. The final case study, discussed in Section 5.3, analyzes performance characteristics of a supersonic flow CO laser such as discussed in Section 5.2, but driven by a chemical reaction between carbon vapor and molecular oxygen, instead of an electric discharge.

5.1 Generation of Vibrationally Excited Carbon

Monoxide by Chemical Reactions

5.1.1 Measurements of Strongly Vibrationally Excited CO

Produced in Reaction of Carbon Vapor with Oxygen

The ﬁrst case study analyzes the vibrational population distribution of CO produced in the reaction of carbon vapor with molecular oxygen,

C + O2 −−→ CO(v) + O, (R 5.1)

by comparing the modeling predictions with CO vibrational populations measured a relatively low ﬂow of carbon vapor produced by an arc discharge with graphite electrodes and oxygen, in an argon buﬀer [51]. This section describes the important

194 Figure 5.1: Schematic (left) and photograph (right) of experimental apparatus used to produce carbon vapor, react with oxygen, and measure CO vibrational non-equilibrium in the products. [51]

characteristics of these experiments, and a full description can be found in Jans et al.[51]. Figure 5.1 shows a schematic (left) and photograph (right) of the experimental apparatus used for these measurements [51]. Carbon vapor was produced in an arc discharge sustained in a cell ﬁlled with argon, at P =15–20 Torr, between a

1 cylindrical grounded graphite electrode, 1–2 mm in diameter, and a 4 ” diameter cylindrical powered tungsten electrode. High temperatures produced in the discharge evaporated the graphite electrode to generate carbon vapor. The mixture of argon buﬀer and carbon vapor ﬂowed into an observation cell, where

it was mixed with a secondary flow of Ar-O2 mixture and reacted with oxygen, producing CO. The argon buffer flow rate was 5–20 SLM, and the mole fraction of oxygen in the mixture was 1-10%. Spontaneous infrared emission from vibrationally excited CO on fundamental and first overtone vibrational-rotational transitions was detected by a Bruker

195 Figure 5.2: Experimental CO fundamental band emission spectrum, averaged over the length of the observation cell. Ar buffer flow pressure 19.2 Torr, O2 partial pressure 0.2 Torr, flow rate 12 SLM. [51]

IFS/66s Fourier transform infrared spectrometer (FTIR), used to take CO emission spectra. As shown in Figure 5.1, emission spectra were collected along the length of the observation cell, eﬀectively line-of-sight averaging the emission along the length of the cell (30 cm), from the mixing region to the cell exhaust. Typical CO emission spectra taken at these conditions, used for comparison with the modeling predictions in the present work, are shown in Figure 5.2.

5.1.2 Prediction of CO Vibrational Level Populations

To predict CO VDF in the ﬂow reactor discussed above, the model described in Chapter 4 is exercised in a constant cross section ﬂow of reactants. The simulation begins at the mixing point, where it is assumed that carbon vapor is mixed

instantly with the Ar-O2 ﬂow. The initial mixture composition was the same as

at the experimental conditions, 90% Ar, and 10% O2 at 20 Torr. The amount of

196 carbon vapor in the mixture was assumed to be an adjustable parameter, since the yield of carbon product could not be measured in the experiment. Based on recent measurements of mass distributions of carbon species generated in the arc discharge, using a Residual Gas Analyzer (RGA)[131], C atoms dominate larger

carbon clusters (e.g. C2 yield is about an order of magnitude lower compared to that of C atoms). Therefore the model assumed C vapor atoms to be the only carbon reactant species present in the ﬂow. Kinetics of chemical reactions and vibrational energy transfer in the ﬂow in the observation cell was predicted by the master equation model including 40 vibrational levels of CO. In the model, the nascent vibrational populations of CO produced by Reaction R 5.1 were assumed to be Gaussian, with the peak at v = 8, which matches 30% of reaction enthalpy going into the vibrational mode of CO, predicted by the quantum chemistry calculations by Schatz [61] and shown in Figure 1.9, which was reproduced as Figure 5.3. The width of the Gaussian distribution was chosen such that the ratio of populations of adjacent vibrational states qualitatively matched the results of Minton [62], shown in Figure 1.10 and reproduced as Figure 5.4. It was found that the modeling predictions are not very sensitive to the width of the nascent vibrational distribution, which is discussed in detail below. The nascent distribution used in the present work is as follows,

! 1 (v − 8)2 fv = √ exp − , (5.1) 5π 5

and plotted in Figure 5.5. The modeling predictions are compared with experimental data in Figure 5.6.

197 Figure 5.3: Energy partition of C + O2 reaction into the diﬀerent energy modes of the product CO predicted by quantum mechanical calculations. [61]

Figure 5.4: Signal from diﬀerent vibrational levels of carbon monoxide product of a chemical reaction between vapor-phase carbon and molecular oxygen, measured in the cross molecular beam experiment [62]

198 Figure 5.5: Nascent vibrational distribution assumed in the present work for the CO product of Reaction R 5.1.

In the calculations, the flow rate through the observation cell is 12 SLM, T0 = 450 K, matching experimental flow rate and temperature inferred from the rotational structure of experimental CO emission spectra, and initial partial pressure of C vapor in the mixture, which was an adjustable parameter, is 1.6 mTorr. The order of magnitude of initial C vapor reactant mole fraction in the flow is consistent with the upper bound CO product mole fraction estimated from CO absorption spectra in the observation cell. As can be seen, while the model reproduces the CO VDF at v > 8, the agreement below v = 8 is poor. In particular, the vibrational level where the vibrational populations peak is underpredicted by the model (v = 4 vs. v = 8), leading to overprediction of the VDF from v = 2 to v = 8. The “near-Boltzmann” segment of the experimental VDF that is apparent at v ≤ 2 is also completely missing from the modeling predictions.

199 Figure 5.6: Comparison between CO vibrational distribution function (VDF) predicted by the model and measured in the low speed ﬂow reactor when all carbon vapor is assumed to produce vibrationally excited CO in Reaction R 5.1, with the nascent distribution shown in Figure 5.5. Flow rate is 12 SLM at initial temperature of 450 K, with partial pressures of 18 Torr Ar, 2 Torr O2, and 1.6 mTorr C vapor. [51]

As stated above, it was found that the results in Figure 5.6 are nearly independent of the width of the nascent Gaussian distribution produced by Reaction R 5.1. The width of the CO vibrational distribution predicted in Figure 5.6 is controlled by CO-CO VV processes, with characteristic time scale which scales inversely proportional to CO concentration and therefore inversely proportional to initial C vapor partial pressure. A demonstration of this eﬀect is shown in Figure 5.7. Increasing the C vapor partial pressure from 1.6 mTorr accelerates the VV energy transfer, predicting a wider spread of the VDF in Figure 5.6. At much higher C vapor partial pressures, the predicted VDF is spread even more by VV energy transfer, until at C vapor partial pressure of 16 mTorr it becomes a near-Boltzmann distribution. At these conditions, the tail of the distribution is

200 Figure 5.7: Comparison of predicted CO vibrational distribution functions (VDFs) for three diﬀerent initial C vapor partial pressures, at the conditions of Figure 5.6. strongly aﬀected by VT relaxation of CO by O atoms,

CO(v) + O −−→ CO(v-1) + O, (R 5.2) that are also produced in Reaction R 5.1. However, at intermediate C vapor partial pressures, the “near-Boltzmann” portion of the CO VDF at v ≤ 2 is not predicted. Additionally, at initial C vapor partial pressures well below 1 mTorr, the rate of VV energy transfer becomes very slow, preserving the nascent vibrational distribution produced by Reaction R 5.1 in the entire observation cell, as can be seen in Figure 5.7. At these conditions, the model predicted very low populations of high CO vibrational levels, v > 10, at variance with the experimental data. In Figure 5.6, the initial concentration of C vapor was used as an adjustable parameter to match the tail of the VDF at v > 8. Thus, varying the C vapor initial partial pressure could not reproduce experimental CO VDF at v = 1, 2.

201 In the experiments, the carbon electrode was weighed before and after the run to estimate C vapor mole fraction from the mass difference, runtime, and flow rate of argon buffer through the arc discharge cell. Assuming that all carbon ablated from the electrode was converted into carbon vapor, the partial pressure of C was estimated to be ≈100 mTorr. However, this value is nearly two orders of magnitude above that estimated from the modeling predictions (1.6 mTorr). This suggests that nearly all carbon ablated from the electrode is in solid phase, which can only participate in surface reactions with oxygen. It appears likely that surface reactions of oxygen with solid phase carbon would not produce vibrationally excited CO. Indeed, in the surface reaction the chemical energy released is likely to be partitioned among the chemical bonds of carbon atoms in the cluster, and rapidly thermalized, instead of being stored in the vibrational mode of CO product molecules. To take into account the effect of such a surface reaction, it was added to the kinetic model, assuming that it produces non-vibrationally excited CO,

C(s) + O2 −−→ CO(v−0) + O. (R 5.3)

This assumption is qualitatively consistent with the existence of well known reactions in carbon disulﬁde/oxygen mixtures [59], used to produce gain in chemical CO lasers, shown in Figure 4.1, and reproduced in Figure 5.8. In particular, the reaction,

CS2 + O −−→ CO(v) + S2, (R 5.4)

202 Figure 5.8: CO vibrational distribution functions (VDFs) produced by two carbon disulﬁde ﬂame reactions, CS2 +O (closed symbols) and CS+O (open symbols). [59]

203 produces a near-Boltzmann nascent vibrational distribution of CO, while the reaction, CS + O −−→ CO(v) + S, (R 5.5)

generates carbon monoxide with a strongly non-Boltzmann vibrational distribution, at much higher vibrational levels compared with the ﬁrst reaction, generating a total population inversion, as shown in Figure 5.8.

2 The results of the simulation when 3 of CO is assumed to be produced by 1 Reaction R 5.1, and 3 of CO is assumed to be produced by Reaction R 5.3, in vibrational level v = 0, are shown in Figure 5.9. As can be seen, the agreement becomes significantly better compared with Figure 5.6. This, as well as high C product yield estimated from the rate of electrode ablation in the arc discharge, suggests that CO, at these conditions, is indeed formed in two different reactions, Reaction R 5.1 producing strongly vibrationally excited CO, and surface Reaction R 5.3, which produces non-excited carbon monoxide. At these conditions, the model predicts peak laser gain in the reacting mixture ≈5 mm downstream of the injection/mixing location, with gain of 0.06 %/cm on v = 7,J = 10 → v = 6,J = 11 CO ro-vibrational transition. Transitions on adjacent vibrational bands, e.g. v = 6,J = 10 → v = 5,J = 11, do not reach peak gain until ≈2 cm downstream of the injection location. Note that the length of the observation cell is 30 cm. The peak gain value is approximately equal to lasing threshold for a cavity length of 30 cm and mirror reflectivities of R = 0.98. However, lasing in the observation cell would only be possible if this gain was present at all locations along the length of the cell. Reaching conditions with gain

204 Figure 5.9: Comparison between CO vibrational distribution function (VDF) predicted by the model and measured in the low speed ﬂow reactor at the conditions 2 1 of Figure 5.6 when 3 of CO is produced via Reaction R 5.1 and 3 of CO is generated via Reaction R 5.3.[51]

sufficient for lasing would require significantly higher vibrationally excited CO number density. The low number density of vibrationally excited CO produced in the experiment is most likely due to the low fraction of carbon ablated from the graphite electrode and converted to vapor phase. Clearly, for the new CO chemical laser with vibrationally excited carbon monoxide generated in a chemical reaction of carbon vapor and oxygen to be feasible, the yield of carbon vapor in the arc discharge needs to be increased by at least an order of magnitude. This could be done by sustaining a large-volume, high temperature plasma in a flow of argon buffer with finely dispersed carbon powder. This would greatly increase the total surface area of solid carbon in the plasma, compared to a relatively small volume arc discharge, and potentially increase carbon vapor yield.

205 5.2 Kinetic modeling of a Supersonic Flow CO

Laser Operating in the Presence of Air Species

in the Laser Mixture

The objective of this second case study is prediction of operation parameters of an electric discharge excited CO laser, operating with significant amounts of nitrogen, oxygen, and air in the laser mixture. This capability is essential for insight into vibrational energy transfer among CO, N2, and O2, and for predictive analysis of a supersonic flow, chemical CO laser discussed in the previous section. Since this laser is being designed to operate in a high-speed flow of a mixture of carbon vapor and air, understanding of vibrational energy transfer at these conditions is critical.

5.2.1 Supersonic Flow Carbon Monoxide Laser Excited by

an RF Discharge

A schematic of the laser, which is similar to the electric discharge excited oxygen iodine laser developed by Bruzzese et al. , is shown in Figure 5.10[132]. Briefly, the gas mixture components (carbon monoxide, helium, oxygen, nitrogen, and air) are delivered to the plenum of a supersonic flow channel through a 1 inch diameter, 5 m long delivery line, where they are premixed. After passing through a flow conditioning and expansion section, the flow enters the plenum, which is a rectangular cross section flow channel with a 10 cm width and 2 cm height.

206 Figure 5.10: Schematic of a Mach 3 supersonic ﬂow channel with the RF discharge section in the plenum and the transverse laser cavity in supersonic ﬂow.

The RF discharge section occupies the upstream portion of the plenum. The RF discharge electrodes are made of 10 cm square copper plates and are flush mounted in the top and bottom walls of the discharge section. The electrodes are powered by a 13.56 MHz, 5 kW RF power generator. Downstream of the discharge section, the flow enters an observation section 7.6 cm long, with optical access windows in the center of the top and side walls. This section is in place only for CO infrared emission spectra measurements, and is removed during laser spectra and power measurements, to shorten the distance between the discharge section and the supersonic nozzle. The nozzle, with 0.32 cm by 10 cm throat cross sectional area, has an expansion ratio designed for an exit Mach number of M = 3. Downstream of the nozzle exit, the flow enters the supersonic section with the entrance height of 1 cm. Several 0.5 inch diameter apertures in the side walls of the supersonic section provide optical access to the flow, as shown in Figure 5.10. Cavity mirrors, each with

99.8% reﬂectivity between 4.5 and 5.75 µm, are attached to the side walls 3.2 cm downstream of the nozzle exit, forming a transverse laser cavity, with laser power

207 coupled out on both sides of the cavity. During the experiments, laser spectra and laser power are measured simultaneously. Laser power is measured using the beam on one side of the resonator, by a Scientech AC5000 power meter, and is multiplied by two to account for power coupled out on the other side of the cavity. Laser spectra are measured using the beam on the other side of the resonator, by a Varian Fourier transform infrared spectrometer (FTIR). Downstream of the supersonic section the flow enters a diffuser section before exhausting into a vacuum tank. The steady state supersonic flow run time is approximately 5 s. The kinetic model is using the plenum pressure, the gas mixture composition, the nozzle geometry, the RF discharge power, and the laser mirror reflectivity as inputs. In the quasi-one-dimensional calculations, the expansion angle of the supersonic cavity, which provides boundary layer relief, is not incorporated. The simulation begins at the upstream end of the discharge electrodes and ends at the end of the laser cavity. The only adjustable parameter in the model is the effective reduced electric field value in the RF discharge, the choice of which is discussed below.

5.2.2 Results and Discussion

The comparison between the experimental and the predicted CO vibrational distribution function (VDF) in the observation section for several laser mixtures is shown in Figure 5.11. These measurements have been done for three He-CO

mixtures, two He-CO-O2 mixtures, three He-CO-N2 mixtures, and four He-CO-air mixtures.

208 Figure 5.11: Comparison of experimental and predicted CO vibrational distribution functions (VDFs) in the observation section, for reduced electric field values providing best match with the data. In addition to the mixture specified in the figure labels, the flow includes a buffer of 97 Torr He in all cases. RF discharge power is 2 kW.

The model was exercized for each mixture, and the value of electric field in the discharge was varied until the predicted CO VDF matched the experimental data, as illustrated in Figure 5.11. The resultant “best match” reduced electric field values are plotted in Figure 5.12. After the reduced field values were inferred for every mixture for which CO VDF measurements were available, as shown in Figure 5.12, the effective reduced electric field values in the discharge were interpolated and extrapolated, depending

209 Figure 5.12: Reduced electric ﬁeld values inferred by matching experimental CO vibrational distribution functions (VDFs) measured in the observation section of the supersonic wind tunnel (symbols) and interpolation ﬁts (lines).

210 on mixture composition. In the He-CO mixtures, linear interpolation was used.

For mixtures containing N2 and/or O2, the reduced ﬁeld was interpolated as follows,

E a1Pi + a2 (Pi) = , (5.2) N Pi + a3

E where N is the reduced electric field, Pi is the partial pressure of the species being varied (the x-axis in Figure 5.12), and ai are the fit parameters. Figure 5.12 shows interpolation fits using the values inferred from the experimental VDFs. From Figure 5.11, it can be seen that adding nitrogen to the CO-He mixture results in considerable increase of CO vibrational populations at v > 15. Analysis

of kinetic modeling predictions shows that this occurs due to N2 vibrational excitation by electron impact in the discharge, with subsequent preferential VV

energy transfer from N2 to CO,

N2(v) + CO(w) −−→ N2(v-1) + CO(w + 1), (R 5.6)

due to the smaller vibrational energy spacing in the latter species. Adding oxygen to the CO-He mixture, on the other hand, reduces CO vibrational populations signiﬁcantly (see Figure 5.11). Analysis of the modeling predictions show that at the present conditions, this is due to a combination of two eﬀects, (a) VT relaxation of CO by O atoms,

CO(v) + O −−→ CO(v-1) + O, (R 5.7)

211 generated by O2 electron impact dissocation and (b) higher effective reduced electric field, which reduces the discharge energy fraction going to excitation of the CO vibrational mode by electron impact. In CO-air-He mixtures, the effects

of VV energy transfer from N2 to CO and VT relaxation of CO by O atoms

appear nearly balanced. Note that the predicted O2 dissociation fraction in the RF discharge in CO-air-He mixtures is approximately a factor of two lower compared

to that in CO-O2-He mixtures with the same partial pressure of O2. This is due to lower average electron energy, limited by additional inelastic electron impact

excitation processes of N2. Speciﬁcally, O atom mole fraction predicted in a CO-

air-He mixture with air partial pressure of 21 Torr (4.2 Torr O2 partial pressure), at the end of the discharge, is 1300 ppm, compared with 2700 ppm predicted in a

CO-O2-He mixture with O2 partial pressure of 4.5 Torr. This reduces the eﬀect of CO VT relaxation by O atoms in air-containing mixtures, while also leading to

VV energy transfer from N2 to CO, thereby increasing laser power. Figure 5.13 plots the flow channel height, Mach number, static temperature, static pressure, and flow velocity predicted by the model along the flow channel. The discharge section extends from x = 0 cm to x = 10 cm, the observation section from x = 10 cm to the throat at x = 20.1 cm, and the laser cavity is from x = 24.5 cm to the end of the simulation at x = 27 cm. A linear increase in temperature is predicted in the discharge region, which also causes a slight increase in flow velocity. Between the discharge section and the throat, the temperature continues to rise, albeit at a slower rate, due to relaxation of excited

species generated in the discharge, primarily vibrationally excited CO and N2,

212 Figure 5.13: Predicted axial distributions of flow parameters (flow channel height, Mach number, flow velocity, pressure, and temperature) in a supersonic flow CO laser operating in a 3.6 Torr CO - 97 Torr He - 21 Torr air mixture, at RF discharge power of 2 kW. with electronically excited species being quenched during or very shortly after the discharge section. As the flow passes through the nozzle, the Mach number and the flow velocity increase, while the temperature and the pressure drop significantly. The reduction in pressure and temperature essentially “freeze” most of the collisional processes in the supersonic region, thereby making the predicted laser power and laser spectra nearly independent of the distance between the nozzle exit and the laser cavity. Figure 5.14 plots the predicted vibrational distribution functions of CO (solid

213 Figure 5.14: Predicted vibrational distribution functions of CO (solid lines), N2 (dashed lines), and O2 (dotted lines) at the conditions of Figure 5.13, with transverse laser cavity beginning approximately 4.5 cm downstream of the throat and output coupler mirror reﬂectivity of 99.8%.

lines), N2 (dashed lines), and O2 (dashed lines) at the same conditions as in Figure 5.13. It can be seen that strongly non-equilibrium CO VDF is maintained throughout the nozzle and the laser cavity. At these conditions, vibrational

temperatures of CO and N2 reach quasi-equilibrium via rapid VV exchange,

Reaction R 5.6, with Tv(CO) being signiﬁcantly higher compared to Tv(N2), due to the smaller CO vibrational energy spacing. This eﬀect has been also detected

in previous work by Lee et al.[133]. VV energy transfer from CO to O2,

CO(v) + O2(0) −−→ CO(v-1) + O2(1), (R 5.8)

becomes near energy resonant for v ' 20, and at the present conditions, CO vibrational populations at v ≥ 20 are too low for this energy transfer to be signiﬁcant.

214 Figure 5.15: Comparison of experimental and predicted laser power versus CO partial pressure in CO-He mixtures. He partial pressure 97 Torr, RF discharge power 2 kW.

Figure 5.15 plots laser power output versus CO partial pressure in a CO-He mixture. The results show that laser power peaks at CO partial pressure of ≈3.5– 4.0 Torr. The model reproduces this trend, albeit at a slightly lower CO fraction. The overprediction of laser power (note the two diﬀerent scales in Figure 5.15) over the entire range of CO pressures is expected, since the kinetic model does not account for additional losses in the cavity, other than the power coupled out by lasing.

Figure 5.16 illustrates the eﬀect of adding N2, O2, and air to the baseline CO- He mixture at constant CO partial pressure of 3.6 Torr and RF discharge power of 2 kW. The data show that adding nitrogen to the CO-He mixture results in a

dramatic increase of laser power, from ≈9 W to approximately 30 W, at N2 partial pressures of 10–30 Torr. The modeling predictions reproduce this trend quite well, although again, the laser power is overpredicted by the model by slightly more than

215 a factor of two. This trend is consistent with CO vibrational population increase in the presence of nitrogen (see Figure 5.11), caused by VV energy transfer from

N2 to CO. The laser power is also aﬀected by translational-rotational temperature

reduction in the plenum, as N2 partial pressure is increased, from T = 390 K in the

baseline CO-He mixture down to T = 360 K in the mixture with 20.3 Torr of N2. The temperature reduction is caused by the increase of the fraction of discharge input energy going to vibrational excitation of nitrogen,

− − e + N2(v−0) −−→ e + N2(v > 0), (R 5.9) thereby reducing energy fraction to electronic excitation of CO,

e− + CO −−→ e− + CO(a3Π), (R 5.10) which contributes to the temperature rise during its collisional quenching within the discharge section. Adding oxygen to the baseline CO-He laser mixture dramatically reduces the

laser power, by over an order of magnitude with less than 7 Torr of O2 added. This is consistent with CO vibrational population reduction in the presense of oxygen

(see Figure 5.11) and modest temperature rise as O2 partial pressure increased, from T = 390 K in the baseline CO-He mixture to T = 410 K in the mixture with 8.7 Torr of O2. However, this trend is strongly overpredicted by the kinetic model (see Figure 5.16). The reason for such signiﬁcant diﬀerence is not fully understood, especially since CO VDF in the observation section is predicted fairly

216 Figure 5.16: Comparison of experimental and predicted laser power versus N2, O2, and air partial pressure. CO and He partial pressures 3.6 and 97 Torr, respectively, RF discharge power 2 kW.

accurately at these conditions (see Figure 5.11). Possible reasons for this difference are discussed below. Adding air to the baseline CO-He mixture results in the laser power increasing, by almost a factor of two (see Figure 5.16), before it decreases gradually, suggesting that the effect of nitrogen counteracts that of oxygen. The modeling predictions (solid green line) capture this trend qualitatively, but the predicted power peaks at a much lower air partial pressure and its reduction at high air partial pressures is overpredicted. This trend was found to be sensitive to state-specific rates of VT relaxation of CO by O atoms, Reaction R 5.7. While the relaxation time for this process has been measured [88,89], the scaling of the rates with vibrational quantum number is not known. A semiclassical theory of vibrational energy transfer for a purely repulsive interaction potential [128] predicts VT rates higher

than gas kinetic rate at v ' 30, suggesting that this scaling is overpredicted.

217 Figure 5.17: Comparison of experimental (top) and predicted (bottom) laser spectra in a 3.5 Torr CO-97 Torr He mixture. RF discharge power 2 kW.

Therefore accurate theoretical calculations of VT relaxation rates are critical for the predictive capability of the present model. The dashed green line in Figure 5.16 shows the modeling predictions with VT relaxation of CO by O atoms turned off completely. In this case, the agreement between the modeling predictions and the experiment is significantly better, with the model reproducing the experimental trend. The significant uncertainty in

the rates of this process is a likely reason for the poor agreement in O2-CO-He mixtures. However, it is not sufficient to explain the difference observed. At this time, the origin of this difference remains not fully understood.

218 Figure 5.17, Figure 5.18, and Figure 5.19 plot representative comparisons of predicted and measured laser spectra taken in the baseline CO-He mixture and mixtures with nitrogen and air, respectively. It can be seen that at the baseline conditions, lasing occurs on fundamental vibrational bands ranging from v = 3 → 2 to v = 14 → 13 (see Figure 5.17), and on several rotational transitions in each vibrational band. The laser spectrum exhibits evidence of laser cascade, when lasing on higher vibrational transitions overpopulates lower vibrational levels and triggers lasing on lower transitions. Lasing on relatively low rotational transitions, J 0 = 6–14, is typical for low translational-rotational temperature in the laser cavity, estimated to be T ≈130 K from emission spectra and predicted to be T = 110 K. Adding nitrogen to the ﬂow results in lasing on fundamental bands, ranging from v = 2 → 1 to v = 15 → 14, and signiﬁcantly increases the number of rotational transitions on which lasing occurs in each vibrational band (see Figure 5.18). Finally, adding air produces a spectrum similar to the one observed in the baseline CO-He mixture (see Figure 5.19). In all cases, the modeling predictions reproduce the range and the qualitative trends of vibrational transitions on which lasing

occurs (except for the lowest vibrational transitions in CO-He and CO-N2-He), as well as the rotational quantum numbers on which the laser power in each vibrational band peaks, fairly well.

219 Figure 5.18: Comparison of experimental (top) and predicted (bottom) laser spectra in a 3.5 Torr CO - 97 Torr He - 26.3 Torr N2 mixture. RF discharge power 2 kW.

220 Figure 5.19: Comparison of experimental (top) and predicted (bottom) laser spectra in a 3.5 Torr CO - 97 Torr He - 32 Torr air mixture. RF discharge power 2 kW.

221 5.3 Kinetic modeling of a Supersonic Flow, Chem-

ical Carbon Monoxide Laser Operating in

CO-Air Mixture

This section presents results of kinetic modeling of a chemical CO laser excited by the chemical reaction between carbon vapor and molecular oxygen in a mixture of dry air and carbon vapor. These calculations assume that a plasma ﬂow reactor generating a high yield of carbon vapor has been developed. In a hypersonic ﬂight in the upper atmosphere, carbon vapor is assumed to be produced by ablation of carbon from the surface of the vehicle or by evaporation of carbon powder injected into the high-temperature boundary layer.

5.3.1 Simulation Conditions

The modeling calculations in this section use the same flow geometry as the electric discharge excited laser in Section 5.2, shown schematically in Figure 5.10. This was done for two reasons. First, further experiments with the CO chemical laser will be done using a supersonic flow channel similar to the one used in Ref. [64]. Also, this removes the need for the use of adjustable parameters in the model in the form of flow channel geometry. A mixture of dry air and carbon vapor is assumed to be mixed instantly 2.2 cm upstream of the M = 3 supersonic nozzle throat (a constant cross section plenum section 1 cm long and a converging nozzle profile 1.2 cm long). The length of

222 the subsonic section is chosen to be suﬃciently long to complete the reaction of carbon vapor with oxygen, but short enough to minimize losses due to vibrational relaxation of CO produced by the reaction. The plenum pressure and temperature

are P0 = 100 Torr and T0 = 300 K. The low plenum temperature is consistent with the low temperature at the exit of the arc discharge cell used for carbon vapor generation in Jans et al.[51] (see Section 5.1). The C vapor partial pressure in the mixture is varied from 1 mTorr to 10 Torr. The effect of varying the subsonic section length is discussed below. The flow channel is 10 cm wide, with a throat height of 3.2 mm, same as the flow channel parameters in Ref. [64] and in Section 5.2. The geometry and the location of the laser cavity in the supersonic flow region was again the same as in Section 5.2. The 2.54 cm diameter cavity mirrors begin 3.1 cm downstream of the nozzle throat, where the flow Mach number is M = 3, and both have a reflectivity of 99.8%.

5.3.2 Laser power predictions

The supersonic ﬂow CO chemical laser performance was predicted for carbon vapor partial pressures in the mixture varying from 1 mTorr up to 1 Torr. The modeling predictions include CO VDF, laser power, and laser spectrum. Figure 5.20 plots the predicted laser power. In the range of 1–2 mTorr, the small signal gain crosses the lasing threshold, with laser power increasing very rapidly as carbon vapor is added to the mixture, and lasing occuring on a larger number of fundamental vibrational-rotational transitions. From 5–100 mTorr, laser

223 Figure 5.20: Predicted laser power in the supersonic ﬂow CO laser vs. carbon vapor partial pressure in the mixture. Carbon vapor-dry air mixture, P0 = 100 Torr, T0 = 300 K.

power increases nearly linearly with carbon vapor concentration. Above 100 mTorr CO vapor partial pressure, the laser power begins decreasing due to rapid VT relaxation by O atoms, gas temperature increase due to energy release in the C +

O2 reaction, and shorter time scale for VV energy transfer among CO molecules, which up-pumps CO into high vibrational states that are more rapidly relaxed by collisions with O atoms (Reaction R 5.7).

Figure 5.21 plots the VDFs of CO (solid lines), N2 (dashed lines), and O2 (dotted lines) at the begining of the cavity mirrors (red lines) and at the end of the mirrors (green lines), when 3.1 mTorr of C vapor was added to 100 Torr of air. Note that at this low laser power, the VDFs of all three species are essentially idential at these two locations, such that the lines at the start of the cavity are obscured by those at the end. Due to very low gas temperature in the M = 3 supersonic ﬂow, T ≈110 K, the CO VDF at the beginning of the cavity is almost

224 Figure 5.21: Vibrational distribution functions of CO (solid line), N2 (dashed line), and O2 (dotted line) in the air mixture containing 3.1 mTorr of C at the begining and end of the laser cavity. Note that due to effectively frozen vibrational kinetics in the supersonic flow, and low laser power, the lines at the beginning of the cavity are obsured by those at the end. exactly the same as the VDF at the nozzle throat, since vibrational energy transfer is effectively frozen during rapid supersonic expansion.

As can be seen from Figure 5.21, both N2 and O2 remain vibrationally non- excited, with vibrational temperatures near 300 K. At these low CO partial pressures, VV energy transfer from vibrationally excited CO to N2 and O2 is very slow and occurs on time scales much longer than flow residence time. The VDF of CO, produced by Reaction R 5.1 and controlled by CO-CO VV processes, shows qualitative similarity with that in Figure 5.9. Due to the short flow residence time between the mixing region in the plenum and the nozzle throat, CO-CO VV energy transfer has fairly little effect on the nascent CO VDF.

225 To analyze the laser eﬃciency, we deﬁne the power stored in the CO vibrational mode as follows, X PCO =mY ˙ CO fvev, (5.3) v where PCO is the power stored in the vibrational mode of carbon monoxide, m˙

is the mass ﬂow rate through the channel, YCO is the mass fraction of CO in the

ﬂow, fv is the CO relative population on vibrational level v, and ev is the energy of vibrational level v. At the conditions of Figure 5.21, when the chemical reaction

between C and O2 is completed (after ≈1 µs), PCO = 1.77 W, which is about 30% of the reaction enthalpy, as discussed in Section 5.1. Note that the heat release due to the reaction increases the ﬂow temperature by ≈0.4 K.

By the nozzle throat, PCO decreases to 1.14 W, primarily due to VV transfer

from CO to N2, and remains nearly constant from the throat to the beginning of the cavity mirrors. In Figure 5.21, only a very small diﬀerence between CO VDF at the beginning and at the end of the laser cavity can be seen, showing that a very small fraction of power stored in CO vibrational mode is coupled out at these conditions. The power stored in the vibrational mode of CO decreases by ≈20 mW along the cavity, which matches the laser power at this C partial pressure in Figure 5.20. This represents only about 2% of the energy stored in the CO vibrational mode by Reaction R 5.1, and 0.6% of the total reaction enthalpy, resulting in a very low laser eﬃciency. Figure 5.22 shows the laser spectrum predicted at the conditions of Figure 5.21. Laser power is coupled out only on three vibrational transitions in the region of the CO VDF where the relative population is highest, and the absolute population

226 Figure 5.22: Predicted laser spectrum in the mixture of air with 3.1 mTorr of C vapor.

inversion is strongest, v = 4–6 (see Figure 5.21). Lasing on other vibrational transitions does not occur, since gain on these transitions is too low to overcome the loss through the mirrors.

Figure 5.23 shows the VDFs of CO (solid lines), N2 (dashed lines), and O2 (dotted lines) at the beginning and end of the laser cavity mirrors, predicted when 190 mTorr of C vapor was added to 100 Torr of air, corresponding to the point of

maximum laser power predicted in Figure 5.20. Again, both N2 and O2 remain

vibrationally non-excited, with low vibrational temperatures of Tv,N2 ≈ 640 K and

Tv,O2 ≈ 380 K. At these conditions, VV transfer from CO to N2 and O2 is still relatively slow. The CO VDF predicted at these conditions is similar to that in an electric discharge excited CO laser, with a VV pumped distribution at the beginning of the cavity and no total population inversion. At this high C vapor partial pressure, Reaction R 5.1 stores 107 W in the vibrational mode of CO, representing ≈ 30% of the reaction enthalpy. The

reaction also increases the ﬂow temperature from T0 = 300 K up to 326 K. By the

227 nozzle throat, the power stored in the CO vibrational mode is reduced by almost a factor of three, down to 35 W, with 41 W transfered from CO to the vibrational

mode of N2 by VV energy transfer, 21 W thermalized via VV and VT processes, and ≈1 W lost by spontaneous radiative decay of vibrationally excited CO. At

these conditions, VV energy transfer from CO to O2 remains a minor factor, since

CO-O2 VV rates peak at CO(v ≈ 20), when the energy transfer becomes near resonant. However, the flow residence time remains too short for CO to VV pump up to v ≈ 20. Again, the power stored in the CO vibrational mode remains nearly constant between the nozzle throat and the beginning of the cavity mirrors. By the end of the cavity, 16 W of laser power is coupled out, leaving 19 W stored in the vibrational mode of CO. At these conditions, the laser efficiency is significantly higher, with 15% of total CO vibrational energy and 4.5% of the total reaction enthalpy converted to laser power. Figure 5.24 shows the predicted laser spectrum at the conditions of Figure 5.23, when the predicted laser power is maximum. This spectrum is similar to those measured and predicted in electric discharge excited CO lasers (see Figure 5.18). The laser has significant gain on a wide range of vibrational transitions, ranging from v = 2 → 1 to v = 16 → 15, and shows strong evidence of the laser cascade. Additionally, Figure 5.23 indicates depopulation of higher vibrational states (v > 5) via stimulated emission, by over an order of magnitude, demonstrating that a significant fraction of CO vibrational energy available is coupled out as laser power. The final set of conditions analyzed is at the high pressure end of the curve

228 Figure 5.23: Vibrational distribution functions of CO (solid line), N2 (dashed line), and O2 (dotted line) predicted in air mixture containing 190 mTorr of C vapor, at the conditions when maximum laser output power is predicted (see Figure 5.20).

Figure 5.24: Predicted laser spectrum at the conditions of peak laser power predicted in Figure 5.20, in the mixture of air with 190 mTorr of C vapor.

229 shown in Figure 5.20, at C vapor partial pressure of 720 mTorr. The VDFs for CO

(solid lines), N2 (dashed lines), and O2 (dotted lines) predicted at these conditions are plotted in Figure 5.25, again at the beginning and the end of the cavity mirrors. While the C vapor concentration is now a factor of 200 higher than in Figure 5.21, the laser power predicted at these conditions is similar to that in Figure 5.21 (15 mW vs. 18 mW). The amount of power stored in the vibrational mode of CO by Reaction R 5.1 is over 350 W, while the reaction increases the ﬂow temperature to almost T = 400 K. Between the reaction zone and the nozzle throat, CO loses over 90% of the vibrational energy down to 21 W, half of which (160 W) is transfered by VV

exchange to N2 (Tv,N2 ≈ 900 K), and 166 W is thermalized by VV and VT processes (primarily VT relaxation by O atoms). By the time the non-equilibrium flow reaches the cavity, gain sufficient to overcome the mirror losses exists only on two CO fundamental vibrational transition in the center of the VV pumped plateau, as can be seen in the spectrum in Figure 5.26. With only 18 mW laser power coupled out, the predicted laser efficiency is extremely low, with only 0.005% of the CO vibrational energy and 0.0015% of the reaction ethalpy used to generate laser power. It can be seen that the principal difficulty in scaling the power of a chemical CO laser based on a reaction of carbon vapor and oxygen is controlling the losses of CO vibrational energy between the reaction/mixing zone in the plenum and the laser cavity. These losses require minimizing the channel length and the flow residence time between the injection/mixing region, where chemical reactions

230 Figure 5.25: Vibrational distribution functions of CO (solid line), N2 (dashed line), and O2 (dotted line) predicted in air mixture containing 0.72 Torr of C vapor.

Figure 5.26: Predicted laser spectrum in the mixture of air containing 0.72 Torr of C vapor.

231 occur, and the nozzle throat. This results suggests that carbon vapor should be injected into the airflow in the plenum several mm upstream of the nozzle throat, into a transonic flow with a Mach number of M ≈ 0.5, using a choked flow injector, similar to the one used in an electric discharge excited oxygen-iodine vapor laser [132]. Another possibility is injecting carbon vapor into the supersonic flow, although at these conditions the timescale for mixing between the carbon vapor and the main flow may well become the factor limiting the laser power coupled out in the supersonic cavity.

232 Chapter 6

Summary and Future Work

The first part of the dissertation is focused on kinetic modeling of non-equilibrium reacting plasmas used for experimental studies of plasma assisted combustion kinetics. The present work has provided detailed quantitative insight into kinetics of plasma assisted fuel oxidation processes, including generation of excited species by electron impact, dissociation of molecules during collisional quenching of excited species, formation of stable fuel oxidation products, and coupling between vibrational energy relaxation and chemical reaction kinetics in hydrogen-air, hydrogen-oxygen-argon, and hydrocarbon-oxygen-argon mixtures excited by a nanosecond pulse discharges. A summary of the results and conclusions of each kinetic modeling study is presented below. In fuel-oxygen mixtures diluted in an argon buffer, excited by a burst of nanosecond discharge pulses in a preheated flow reactor, quasi-zero-dimensional kinetic analysis of plasma chemistry showed that significant fractions of discharge pulse input energy, up to 48% in oxygen-argon and 30% in hydrogen-argon mixtures, are used to generate chemically active radicals, in particular H atoms and O atoms. At the conditions where radical species number density in the discharge afterglow is dominated by chemical kinetics, i.e. when the effects of diffusion are insignificant,

233 the model is in very good agreement with measurements of absolute, time-resolved number densities of H atoms and O atoms. Further analysis of the modeling predictions demonstrates that at relatively

low ﬂow temperatures in the reactor (initial temperature of T0 = 500 K), radical chain branching reactions are minor in comparison to chain propagation and chain termination reactions. At these conditions, the average chain length, deﬁned as the ratio of the total number density of stable reaction products to the total number density of primary radicals generated in the discharge, is on the order of 1, for all fuels studied in the experiments (hydrogen, methane, ethylene, and propane). The dominant mechanism of atomic species decay, in particular O atoms, at these low temperature conditions was found to be consistent for all diluted fuel-oxygen mixtures. In particular, O atoms are consumed by reaction with OH,

O + OH −−→ H + O2, (R 6.1)

with OH produced via low temperature HO2 chemistry,

H + HO2 −−→ OH + OH, (R 6.2)

and HO2 produced via three body recombination,

H + O2 + Ar −−→ HO2 + Ar. (R 6.3)

Thus, in the diluted fuel-oxygen mixtures at low temperatures, the decay of

234 oxygen atoms is controlled entirely by the amount of hydrogen atoms generated in the discharge (note that the equivalent process of O atom decay is O + H −−→ OH). After all fuel initially available in the mixture is oxidized, the predicted rate of O atom decay in the afterglow slows down considerably, since in this case Reaction R 6.2 is replaced with a reaction

O + HO2 −−→ OH + O2, (R 6.4)

such that the net equivalent process of O atom decay is no longer controlled by H

atom number density and becomes O + O −−→ O2. In the experiments used for comparison with the modeling predictions, the effect of O atom decay deceleration was not observed, due to diffusion of H atoms into the plasma after nearly all fuel in the mixture was oxidized (this effect was not accounted for in the kinetic model).

Kinetic modeling analysis of oxidation of the same fuels (H2, CH4, C2H4,

and C3H8) over a much wider range of temperatures (T0 =300–1300 K) demonstrates that the model reproduces concentrations of most stable oxidation product

species (CO, CO2, C3H6, C3H8, C2H4, C2H6, and CH4) over this temperature

range fairly accurately. However, modeling predictions of concentrations of C2H2

and CH3CHO concentrations are at variance with the experimental data, for two diﬀerent conventional reaction mechanisms used in the model. Comparison of kinetic modeling calculations using diﬀerent conventional reaction mechanisms indicates that, while the predictions of stable oxidation product species are close to each other, the reactions controlling production and decay of some key species

235 in diﬀerent mechanisms are completely diﬀerent. This suggests that these mechanisms may not provide accurate insight into detailed reaction kinetics, even if their prediction of most steady-state reaction product concentrations is accurate.

In particular, kinetics of acetylene oxidation into CO and CO2 appears to be represented by the conventional reaction mechanisms inaccurately, resulting in significant differences between the experimental concentrations of these species and the modeling predictions, over a wide range of temperatures and for different fuels. Finally, kinetic modeling is used for analysis of OH formation and decay processes in lean hydrogen-air mixtures excited by a single pulse, diffuse filament nanosecond pulse discharge, at the conditions of strong vibrational non-equilibrium of nitrogen. The modeling predictions are in good agreement with time-resolved measurements of gas temperature and nitrogen vibrational temperature, and in fair agreement with time-resolved measurements of OH number density. One of the objectives of this study was to examine possible coupling mechanisms between vibrational relaxation of nitrogen and kinetics of OH reactions, such as near-resonance vibrational energy transfer from N2 to HO2, hypothesized in an earlier work [119]. Analysis of modeling results showed no evidence of direct effect of vibrational energy transfer from nitrogen on OH number density increase in the afterglow of a nanosecond pulse discharge. Also, the effect of vibrational excitation of hydrogen on the rate of reaction

H2(v) + O −−→ OH + H, (R 6.5)

236 is shown to be weak, due to rapid VT relaxation of H2 by O atoms generated in the discharge. On the other hand, it is shown that indirect coupling, via

transient temperature rise caused by vibrational relaxation of N2 by O atoms, on

the timescale of ≈10 µs atm, may have a significant effect on quasi-steady-state concentration of the hydroxyl radical, which is controlled by several well-known reactions of O and H atoms generated by the discharge. Specifically, even modest temperature rise in the afterglow increases the forward rate of reaction of

H + O2 −−→ OH + O, (R 6.6)

resulting in higher OH concentration and accelerating oxidation of hydrogen. This eﬀect becomes more pronounced as the discharge pulse energy and hydrogen mole fraction in the mixture are increased, such that at high pulse energies and equivalence ratios, vibrational relaxation of nitrogen would accelerate ignition of the mixture. The focus of the second half of the dissertation is on feasibility analysis of a new chemical carbon monoxide laser. Detailed insight has been obtained into kinetics of state-speciﬁc vibrational energy transfer in non-equilibrium mixtures

of CO, N2, and O2, vibrationally excited by an RF discharge and by a chemical reaction between carbon atoms and molecular oxygen, to produce laser gain and laser action. Speciﬁcally, comparing kinetic modeling predictions with measurements of vibrational population distribution of carbon monoxide produced by a reaction of carbon species generated in an arc discharge with molecular oxygen, indicated that

237 2 (i) approximately 3 of CO produced is formed in high vibrational levels, centered around v ≈ 8, most likely in the reaction,

C + O2 −−→ CO(v) + O, (R 6.7)

1 and (ii) the remaining 3 of CO product is formed in the ground vibrational level, most likely in the reactions of oxygen with larger carbon clusters generated in the arc discharge or with carbon deposited on the cell walls. This result shows the critical importance of generating atomic carbon vapor for vibrational non- equilibrium and population inversion of CO produced in reactions of carbon species with oxygen. Performance parameters of an electric discharge excited, supersonic ﬂow carbon monoxide laser operated in a Mach 3 laser cavity, predicted by kinetic modeling calculations, is compared with measurements of laser spectra and laser output

power in CO-He, CO-He-N2, CO-He-O2, CO-He-air mixtures. The modeling calculations demonstrate that adding nitrogen to the baseline CO-He mixture results in signiﬁcantlly stronger vibrational excitation of CO, caused by higher

discharge energy fraction going to CO and N2 vibrational excitation (due to higher reduced electric ﬁeld in the discharge) and by VV energy transfer from nitrogen to CO (due to its smaller vibrational energy spacing). This eﬀect also

results in signiﬁcantly higher laser power obtained in CO-He-N2 mixtures (by up to a factor of 3 compared to the baseline CO-He mixture), as well as lasing on a large number of CO fundamental vibrational transitions, consistent with the experimental results.

238 On the other hand, adding oxygen to the baseline CO-He mixture reduces CO vibrational excitation considerably, primarily due to the electric field in the discharge being too high for efficient vibrational excitation of CO. Additionally, it is likely that CO vibrational levels are depopulated via VT relaxation by O atoms, although the kinetic model strongly overpredicts this effect, due to significant uncertainty in scaling of VT rates with vibrational quantum number. Adding oxygen also results in considerable reduction of the laser power predicted by the model. Again, this effect is strongly overpredicted compared to the experimental results, such that lasing is detected at O2 mole fractions up to 6%, while the model predicts that adding only 1.5% of O2 to the baseline CO-He mixture would result in absence of laser action. Although the effect of adding oxygen is not completely understood, it is likely due to overprediction of quantum number scaling of VT rates for CO-O by a simple theory of vibrational energy transfer used by the kinetic model, while experimental data for this process are not available. Adding air to the baseline CO-He mixture results in a higher laser power, similar to adding nitrogen and consistent with the experimental data. Basically, the positive effect of adding nitrogen appears to outweight the negative effect of adding oxygen. Laser action has been detected in the experiment, and predicted by the kinetic model, for CO-He mixtures with up to 30% of air. In the experiment, further increase in the mole fraction of air in the mixture was precluded by the limited range of operation of the RF discharge exciting the laser mixture in the plenum. This result indicates that a chemical CO laser, which is not dependent on the electric discharge for excitation of the laser mixture, is capable of operating

239 in a mixture of carbon vapor and air. Finally, performance parameters of a supersonic flow, chemical laser excited by a reaction of carbon vapor and molecular oxygen, and operating in a mixture of carbon vapor and air have been predicted in a parametric kinetic modeling study. The results show that lasing would be achieved at C vapor mole fraction in air of only 10−5 (1 mTorr partial pressure of carbon vapor in 100 Torr plenum pressure of air), when vibrational non-equilibrium in CO product would be sufficient to overcome mirror losses in the laser cavity. Peak laser power is predicted at CO mole fraction in air of approximately 0.2% (CO partial pressure of 200 mTorr). At higher CO mole fractions, flow temperature rise caused by the exothermic reaction between carbon vapor and oxygen, as well as rapid CO vibrational relaxation, become detrimental and the predicted laser power begins to decrease, such that laser action becomes impossible at CO mole fractions of 1% (CO partial pressure of 1 Torr). The results of modeling calculations also indicate that the length of the subsonic part of the flow channel needs to be shortened, to minimize relaxation losses and increase laser power and efficiency. The kinetic models developed in this dissertation to analyze plasma assisted combustion (PAC) kinetics and chemical CO laser performance have been validated by comparing the modeling predictions with several sets of experimental data, both providing confidence in the models and identifying their shortcomings. However, both models have considerable room for improvement. In the future, expanding the range of applicability of the plasma assisted combustion (PAC) model to other fuels, higher equivalence ratios, and higher pressures, as well as its validation, are

240 essential for its use as a predictive tool for applications using complex hydrocarbon fuels at pressures above atmospheric pressure. Further improvement of the CO laser model includes incorporating more accurate rates for VT relaxation of CO by O atoms, as well as model validation using experimental data obtained in a small-scale chemical CO laser (currently under development). This is essential for the use of the model for design and optimization of future chemical CO lasers operating at higher power.

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262 Appendix A

Comparison of State-Speciﬁc Vibrational Kinetics Rate Coeﬃcients with Literature Data

This appendix contains comparison of the models used in Chapter 4 to calculate state-speciﬁc rate coeﬃcients of VV and VT energy transfer processes with more accurate semiclassical trajectory calculations and experimental data from the literature. Note that kinetic modeling calculations in the present work are performed at temperatures of 100–500 K. Therefore the choice of the adjustable parameters in the rate model discussed in Chapter 4 prioritized accurate prediction of the rates at these lower temperatures.

A.1 CO Vibration-to-Vibration Energy Trans-

fer Rates

Figures A.1–A.5 show state-speciﬁc, temperature dependent rate coeﬃcients for VV transfer for CO-CO. The rate model discussed in Equation 4.32 shows good agreement with three-dimensional semiclassical trajectory calculations and measurements of the rates across the parameter space, except at temperatures above 1000 K (see Figures A.1–A.5).

263 Figure A.1: Comparison of the measured endothermic rate coeﬃcients [65] (top) at T = 300 K and exothermic rate coeﬃcient calculations [66] (bottom) for vibrational- to-vibrational energy transfer between CO molecules at T = 200–3000 K.

264 Figure A.2: Comparison of exothermic state-speciﬁc rate coeﬃcients from the rate model (solid lines) for vibrational energy transfer for CO-CO with semiclassical three-dimensional trajectory calculations (symbols). [66]

265 Figure A.3: Comparison of exothermic state-speciﬁc rate coeﬃcients from the rate model (solid lines) for vibrational energy transfer for CO-CO with semiclassical three-dimensional trajectory calculations (symbols). [66]

266 Figure A.4: Comparison of exothermic state-speciﬁc rate coeﬃcients from the rate model (solid lines) for vibrational energy transfer for CO-CO with semiclassical three-dimensional trajectory calculations (symbols). [66]

Rate coeﬃcients for VV energy transfer between N2 and CO are compared with semiclassical three-dimensional trajectory calculations in Figure A.6. The analytic model used to predict the state-speciﬁc rates is in very good agreement with the trajectory calculations, describing accurately the rate dependence on temperature and vibrational quantum number.

The set of VV rates for CO-O2 is shown in Figure A.7. As can be seen, only

a single experimental measurement of the CO(v–1) + O2(v–0) −−→ CO(v–0) +

O2(v–1) rate coeﬃcient at T = 300 K is available. The rates used in the present work (Equation 4.32) are scaled to reproduce this measurement. The parameters in Equation 4.32 used to predict the rates for higher vibrational quantum numbers

and higher temperatures are the same as those used for CO-N2 VV rates, plotted in Figure A.6.

267 Figure A.5: Comparison of exothermic state-speciﬁc rate coeﬃcients from the rate model (solid lines) for vibrational energy transfer for CO-CO with semiclassical three-dimensional trajectory calculations (symbols). [66]

268 Figure A.6: Comparison of temperature dependent rate coefficient predicted by the rate model (solid lines) and predicted by semiclassical three-dimensional trajectory calculations (symbols) for vibrational energy transfer between CO and N2 (left) and state-specific rate coefficient at T =300 K (right) [76,78]

Figure A.7: Comparison of rate coeﬃcients for vibrational energy transfer between CO and O2 with experimental data. [79]

269 A.2 CO Vibration-to-Translation Energy Trans-

fer Rates

In addition to the VV rates, VT relaxation of CO vibrational energy is also important, primarily in collisions with He (see Figure A.8) and O atoms (see Figure A.9). From Figure A.8, it can be seen that the rates given by Equation 4.42 are in very good agreement with the data [83] and semiclassical trajectory calculations [82]. For CO-O VT rates, Equation 4.42 overpredicts the shock tube data at T =2000– 4000 K. This behavior of the VT rates also suggests that they may be overpredicted by Equation 4.42 at high vibrational quantum number, since reduction of the CO vibrational quantum energy spacing results in the same trend of VT rates increase as increase of temperature. This may well overpredict the VT rates for CO-O in the present model. This will be discussed again in Section A.6, where state-speciﬁc

rates of VT relaxation of O2 by O atoms are compared with experimental data. VT relaxation rates for CO in collision with diatomic molecules are shown in Figure A.10. It can be seen that the parameters used to calculate the rates provide much better agreement at temperatures above 400 K. Note, however, that at T =300 K these rates are 6–7 orders of magnitude below those for CO VT relaxation by O atoms. Since O atoms are generated in signiﬁcant quantities both in the electric discharge used in the supersonic ﬂow laser analyzed in Section 5.2

and in the chemical reaction between C vapor and O2 molecules, as discussed in Section 5.1 and 5.3, CO VT relaxation by diatomic molecules is negligible in

270 Figure A.8: Comparison of temperature dependent rate coeﬃcients for vibrational energy relaxation of CO molecules by helium atoms with semiclassical three- dimensional trajectory calculations [82] and experimental data [83]

Figure A.9: Comparison of temperature dependent rate coeﬃcients for vibrational energy relaxation of CO molecules by oxygen atoms with experimental data. [88,89]

271 Figure A.10: Comparison of state speciﬁc rate coeﬃcients for vibrational energy relaxation between CO molecules with semiclassical three-dimensional trajectory calculations (o) and experimental data (x). [66,83]

comparison.

A.3 N2 Vibration-to-Vibration Energy Transfer

Rates

The rate coeﬃcients for VV processes for N2-N2 are shown in Figure A.11. As can be seen, Equation 4.32 with the parameters listed in Table 4.1 provides very good agreement with both semiclassical trajectory calculations and experimental data over a wide range of vibrational levels and temperatures.

The rates for VV processes between CO and N2 are shown and discussed in Section A.1.

Additionally, the rates for single quantum VV energy transfer from N2 to O2 are shown in Figure A.12. These rates are also reproduced well by Equation 4.32,

272 Figure A.11: Comparison of temperature dependent state speciﬁc rate coeﬃcients for vibrational energy transfer for N2-N2 with semiclassical trajectory calculation and experimental data. [67,73,75]

273 Figure A.12: Comparison of temperature dependent state speciﬁc rate coeﬃcients for vibrational energy transfer between N2 and O2 molecules with semiclassical trajectory calculations. [80]

although they are very slow in comparison to VV rates for CO-CO and N2-N2

due to the large energy diﬀerence between the N2 vibrational quanta and the O2 vibrational quanta.

A.4 N2 Vibration-to-Translation Energy Relax-

ation Rates

The VT processes for N2 are somewhat less important than those for CO, which are discussed in Section A.2, since energy stored in the nitrogen vibrational mode

only has an indirect eﬀect on laser performance via CO–N2 VV processes.

In regards to VT relaxation of N2 by helium, few experimental data points are available in the literature, as shown in Figure A.13. The rates predicted by Equation 4.42 were scaled to match the experimental data point shown in Figure A.13 and extrapolated using the analytic model discussed in Chapter 4.

274 Figure A.13: Comparison of state-speciﬁc rate coeﬃcients for VT relaxation of N2 by He with experimental data. [84]

For N2 VT relaxation by O atoms, a trend similar to the one discussed for CO VT relaxation by O atoms appears (see Section A.2). Again, the analytic model used in Equation 4.42 greatly overpredicts the increase in relaxation rate with temperature (see Figure A.14). Scaling of state speciﬁc rates versus vibrational quantum number and temperature is predicted by Equation 4.42, since no experimental data are available for model validation.

Finally, state-speciﬁc rate coeﬃcients of N2 VT relaxation by diatomic molecules are plotted in Figure A.15. Again, it can be seen that Equation 4.42 overpredicts the rates at low temperatures (T <500 K), although reproducing the scaling with vibrational quantum number. Note, however, that at low temperatures, N2 VT relaxation is dominated by relaxation by O atoms (see Figure A.14), such that

relaxation by N2 and O2 is negligible in comparison.

275 Figure A.14: Comparison of temperature dependence of N2 VT relaxation rate coeﬃcient by O atoms with experimental data. [41,87]

Figure A.15: Comparison of state-speciﬁc N2 VT relaxation rate coeﬃcients by N2 molecules with semiclassical trajectory calculations and experimental data. [73,83]

276 A.5 O2 Vibration-to-Vibration Energy Transfer

Rates

VV rates for O2-CO and O2-N2 are discussed in Sections A.1 and A.3, respectively.

Figure A.16 compares room temperature VV rate coeﬃcients for O2-O2 predicted by Equation 4.32 with experimental data and semiclassical trajectory calculations, illustrating very good agreement with the data and advanced theoretical models.

277 Figure A.16: Comparison of state speciﬁc rate coeﬃcients for vibrational energy transfer between O2 molecules with experimental data and semiclassical trajectory models. [68–72]

A.6 O2 Vibration-to-Translation Energy Relax-

ation Rates

VT relaxation rates for O2-He, plotted versus vibrational quantum number, Fig- ure A.17, show good agreement with experimental data [71,84].

O2-O relaxation rate coeﬃcients plotted versus temperature and vibrational quantum number in Figure A.18 indicate that Equation 4.42 is in poor agreement with experimental data [85,86]. It can be seen that the rate coeﬃcient [85] exhibit very weak dependence on temperature and vibrational quantum number at variance with the predictions of the simple theoretical model of Equation 4.42. This is not at all surprising, since the model of Equation 4.42 has been developed for

collinear collisions of non-reacting partners. For O2-O and CO-O, atom exchange and reactive collisions may well aﬀect vibrational energy transfer. In this case,

278 Figure A.17: Comparison of state-speciﬁc rate coeﬃcients for VT energy relaxation of O2 by helium with experimental data. [71,84]

simple collision models are not applicable, and modeling collision dynamics using accurate potential energy surfaces is critical for accurate predictions of energy transfer rate coeﬃcients and chemical reaction rates. This suggests that the rates for CO relaxation by O atoms may also be signiﬁcantly overpredicted for high vibrational quantum numbers.

Similar to VT relaxation of CO and N2, rate coeﬃcients for VT relaxation

of O2 by diatomic molecules, plotted in Figure A.19, are much slower compared to those by He and O atoms. These rates are well reproduced by Equation 4.42, which is applicable for non-reacting collisions.

279 Figure A.18: Comparison of state speciﬁc rate coeﬃcients for VT energy relaxation of O2 by O atoms with experimental data. [85,86]

Figure A.19: Comparison of state-speciﬁc rate coeﬃcients for VT relaxation of O2 by O2 and N2 with semiclassical trajectory calculations and experimental data. [71,72]

280 Appendix B

Derivation of Small Signal Gain Equation

Consider a particle (molecule or atom) with only two energy levels, separated by energy difference, ∆E, interacting with a flux of photons of a frequency such that ∆E = hν, where h is the Planck constant. The interactions between the particle and the photon flux include absorption, when a particle in the lower energy level absorbs a photon and is excited to the higher energy level, and stimulated emission, when a particle in the higher energy level emits a photon with the same energy and momentum as the incident photons. In addition, spontaneous emission, when a particle in the higher energy level emits a photon, is also possible. In the isotropic environment the balance of photons can be written as

∂n(ν) ∂n(ν) ∂n(ν) ∂n(ν) = + + , (B.1) ∂t ∂t abs. ∂t stim.em. ∂t spont. where n(ν) is the number density of photons at a speciﬁc frequency. In Equa- tion B.1 elastic scattering of photons, as well as inelastic scattering not resulting in absorption or emission, are neglected. The ﬁrst two terms can be expressed as

∂n(ν) = −B12n1I(ν), (B.2) ∂t abs.

281 and ∂n(ν) = B21n2I(ν), (B.3) ∂t stim.em. where ni is the number density of particles in state i, Bij is the Einstein B coeﬃcient for the transition from i to j, representing stimulated emission or absorption, depending on which state has higher energy, and I(ν) is the spectral radiance power per unit solid angle, per unit area, per unit wavelength. Note that

some literature sources deﬁne Bij in terms of spectral power density, which would change the derivation somewhat, although the results would remain the same. The spontaneous radiative decay is written as follows,

∂n(ν) = A21n2, (B.4) ∂t spont.

where Aij is the Einstein A coeﬃcient for spontaneous radiative decay from state i to state j. Now consider an ensemble of particles (molecules or atoms) and photons in equilibrium at temperature T . At these conditions, the net rate of change of the number density of photons is zero,

0 = −B12n1I(ν) + B21n2I(ν) + A21n2. (B.5)

Also, at these conditions, the spectral radiance, I(ν), is given by the Planck distribution, 2hν3 1 I(ν) = B(ν, T ) = , (B.6) 2 c exp hν − 1 kbT where c is the speed of light, and kb is the Boltzmann constant. The ratio of

282 the population of the particles in the two energy levels follows the Boltzmann distribution, n g hν 2 = 2 exp − , (B.7) n1 g1 kbT where gi is the degeneracy of state i, and the energy spacing of the states, ∆E, has been replaced with hν. Plugging in Equations B.6 and B.7 into Equation B.5

divided by n1 gives

g hν 2hν3 1 g hν 0 = 2 exp − B − B + A 2 exp − . 21 12 2 21 g1 kbT c exp hν − 1 g1 kbT kbT (B.8) Equation B.8 must be valid for any temperature value. By inspection, it is apparent that in the high temperature limit hν 1 , this gives kbT

g2 B12 = B21, (B.9) g1 which relates the two Einstein B coeﬃcients, while in the low temperature limit hν 1 , kbT 2hν3 A = B , (B.10) 21 c2 21

relating the Einstein B and Einstein A coeﬃcients. Since Equations B.9 and B.10 are independent of temperature, they are also valid at any temperature value. Indeed, it is easy to see that plugging them back into Equation B.8 satisﬁes it in the entire range of temperatures.

283 Therefore, Equation B.1 becomes

2 ∂n(ν) g2 c = n2 − n1 A21 3 I(ν) + A21n2. (B.11) ∂t g1 2hν

chν Converting the spectral radiance to the photon number density, I(ν) = 4π n(ν), where 4π is the full solid angle, gives

3 ∂n(ν) g2 c = n2 − n1 A21 2 n(ν) + A21n2. (B.12) ∂t g1 8πν

Converting the rate of change of photon number density in time to the rate of change of photon number density in space, along the photon propagation direction, gives 2 ∂n(ν) c g2 = A21 2 g(ν) n2 − n1 n(ν) + A21n2. (B.13) ∂x 8πν g1

The g(ν) line shape factor has been added to Equation B.13 to account for the fact that not all photons have the same frequency. Specifically, collisions among particles interrupts the emission process, which affects the length of the wavepacket emitted, i.e. the range of frequencies present in the wavepacket. In addition, thermal motion of the particles also affects the frequency of the photons emitted, due to the Doppler effect. g(ν) represents the relative fraction of photons at the frequency ν, such that

Z ∞ g(ν)dν = 1. (B.14) 0

Generalizing Equation B.13 for particles with multiple energy levels, we note

284 populations of vibrational-rotational energy levels in diatomic molecules are given as follows,

ni = Nfvi fvi,Ji , (B.15)

where N is the total number density of the species, fv is the relative population

of vibrational level v, and fv,J is the relative population of rotational level J (for molecules in vibrational level v). Since vibrational relaxation of diatomic molecules is relatively slow, vibrational level populations may deviate from the Boltzmann distribution. On the other hand, coupling between the rotational mode and translational motion is very strong, such that the rotational level populations can be assumed to be in equilibrium at the gas temperature. For a given vibrational level, energies of rotational levels can be approximated as

EJ = J(J + 1)Bv, (B.16)

where Bv is the rotational constant dependent on the moment of inertia of the molecule (which is aﬀected by vibrational motion). Additionally, each rotational

level has angular momentum vector direction degeneracy of gJ = 2J + 1. The degeneracy of the vibrational levels is one. Using the Boltzmann distribution for rotational level populations,

Bv(2J + 1) BvJ(J + 1) fv,J = exp − , (B.17) kbT kbT

285 we obtain the expression for the population inversion,

g2 2J2 + 1 n2 − n1 = N fv2 fv2,J2 − fv1 fv1,J1 g1 2J1 + 1 g2 −EJ2 2J2 + 1 g1 −EJ1 = N fv2 exp − fv1 exp Z2 kbT 2J1 + 1 Z1 kbT Bv2 −Bv2 J2(J2 + 1) = N fv2 (2J2 + 1) exp − kbT kbT 2J2 + 1 Bv1 −Bv1 J1(J1 + 1) (2J1 + 1) fv1 exp . (B.18) 2J1 + 1 kbT kbT

Plugging Equation B.18 into Equation B.13 gives

2 ∂n(ν) c Bv2 −Bv2 J2(J2 + 1) = A21 2 g(ν) (2J2 + 1) N fv2 exp − ∂x 8πν kbT kbT Bv1 −Bv1 J1(J1 + 1) fv1 exp n(ν) + A21n2. (B.19) kbT kbT

This equation relates the rate of change of the photon ﬂux with the population inversion in the non-equilibrium medium. At the conditions when the small signal

g2 gain is greater than zero (i.e. positive population inversion, n2 > n1), it typically g1 dominates the spontaneous emission term, which can be neglected.

Note that in Equation B.19, A21 is the Einstein A coefficient for spontaneous emission on a specific ro-vibrational transition, which can be related to the Einstein A coefficient for spontaneous emission for an entire vibrational band as follows,

SJ2 Av2,J2→v1,J1 = Av2→v1 , (B.20) 2J2 + 1

286 where for a transition from J1 to J2, SJ2 = max(J1,J2). Substituting this into Equation B.19 gives

2 ∂n(ν) c Bv2 −Bv2 J2(J2 + 1) = Av2→v1 max(J1,J2) 2 g(ν)N fv2 exp − ∂x 8πν kbT kbT Bv1 −Bv1 J1(J1 + 1) fv1 exp n(ν). (B.21) kbT kbT

The entire factor in front of n(ν) in the ﬁrst term on the right hand side of Equation B.21 is the small signal gain coeﬃcient discussed in Chapter 4,

2 c Bv2 −Bv2 J2(J2 + 1) αv2,J2 = Av2→v1 max(J1,J2) 2 g(ν)N fv2 exp − 8πν kbT kbT Bv1 −Bv1 J1(J1 + 1) fv1 exp (B.22) kbT kbT

287 Appendix C

Einstein A Coeﬃcients for CO

For the calculation of small signal gain and the rate of spontaneous radiative decay of vibrationally excited carbon monoxide, the Einstein A coefficients are required. This section describes the calculations of these values and tabulates them. To calculate Einstein coefficients for spontaneous emission, the transition dipole moments are taken from Chackerian et al.[129], where they were measured for the range vibrational quantum numbers of v =1–36. The transition moments were used to calculate Einstein A coefficients for spontaneous emission using the following relationship,

E − E 64π4 A = µ2 u l , (C.1) ul hc 3h

where Aul is the Einstein A coeﬃcient for the spontaneous radiative transition

2 from state u to state l, µ is the transition dipole moment, Ei is the energy of state i, h is the Planck constant, and c is the speed of light. The Einstein A coeﬃcients are tabulated in Table C.1.

288 Table C.1: Einstein A coeﬃcients for spontaneous emission for CO calculated using the transition dipole moments of Chackerian et al.[129]

Fundamental Bands First Overtone Bands

−1 −1 v Av,v−1(s ) Av,v−2(s ) 1 34.92 0.00

2 67.05 1.08

3 96.54 3.19

4 123.49 6.28

5 148.00 10.27

6 170.18 15.09

7 190.19 20.65

8 208.09 26.86

9 224.01 33.61

10 238.11 40.85

11 250.30 48.49

12 261.01 56.41

13 269.95 64.57

14 277.40 72.90

15 283.47 81.33

16 288.24 89.78

17 291.63 98.22

Continued on next page

289 −1 −1 v Av,v−1(s ) Av,v−2(s ) 18 293.92 106.61

19 295.01 114.92

20 295.01 123.09

21 293.87 131.13

22 291.85 138.88

23 289.07 146.50

24 285.21 153.91

25 280.57 161.16

26 275.25 168.08

27 269.12 174.71

28 262.37 181.15

29 255.00 187.25

30 246.92 193.11

31 238.42 198.11

32 229.40 203.96

33 219.89 208.81

34 210.06 213.40

35 199.80 217.55

36 189.34 221.29

290 Appendix D

Konnov Combustion Mechanism

ELEM E N O H C AR HE END SPECIES !Konnov Mech Defined Species H OH HO2 H2O H2O2 CO CO2 HCO CH3 CH4 C2H6 CH2O C2H5 CH2 CH3O CH2OH CH C2H2 C2H4 C2H3 CH3OH CH3HCO C2H CH2CO HCCO C2H4O ! ethylene oxide SCH2 ! CH2(1) - singlet C2 C2O CH3CO C CH3CO3 ! CH3C(O)OO CH3CO3H ! CH3C(O)OOH CH3O2 CH3O2H C2H5O2H C2H5O2 CH3CO2 CH3CO2H ! CH3C(O)OH acetic acid C2H5OH C2H5O ! CH3-CH2-O(.) SC2H5O ! CH3-CH(.)-OH PC2H5O ! CH2(.)-CH2-OH CH2HCO CN H2CN NH HCN NO HCNO HOCN HNCO NCO N2O NH2 N2O3 HNO NO2 C2N2 NNH NH3 N2H2 HONO NO3 HNO3 N2H3 N2H4 CNN HCNN N2O4 NH2OH HNOH H2NO HNNO HCNH H2CNO ! H2C*N=O CH3NO ! Nitrosomethyl CH2CHOW ! CH2CHO exited C2H3O ! CH2-CH(.) ! |__O__| CH3HCOW ! CH3HCO exited C3H6OH O2C3H6OH C3H5O2 ! CH2=CHCH2OO C3H5O2H ! CH2=CHCH2OOH C3H5O ! CH2=CHCH2O(.) NC3H7O2 ! CH3CH2CH2OO(.) NC3H7O2H ! CH3CH2CH2OOH IC3H7O2 ! CH3CH(OO.)CH3 IC3H7O2H ! CH3CH(OOH)CH3 IC3H7O ! CH3CH(O)CH3 NC3H7O ! CH3CH2CH2O(.) C3H6 C3H8 IC3H7 ! CH3C(.)HCH3 NC3H7 ! CH3CH2C(.)H2 C3H2 C3H3 ! propargyl CH2=C=CH SC3H5 ! 1-propenyl or 2-methylvinyl or H3C-CH=(.)CH PC3H4 ! propyne or methylacetylene CH3CCH TC3H5 ! 2-propenyl (CH2=C)(.)-CH3 or 1-methylvinyl radical C3H6O ! propene oxide C2H5CHO ! propionaldehyde C2H5CO ! propionaldehyde radical C3H5 ! allyl radical CH2CH=CH2 C3H4 ! allene or propadiene CH2=C=CH2 IC4H7 ! CH2=CHCHCH3 C4H2 C4H C4H6 ! 1,3-butadiene CH2=CHCH=CH2 H2C4O

291 C4H4 ! 1-buten-3yne CH#CCH=CH2 IC4H5 ! 1,3-butadien-2-yl (two mesomers) CH2=CHC=CH2 NC4H5 ! 1,3-butadienyl CH2=CHCH=CH C4H8 ! 1-butene CH3CH2CH=CH2 T2C4H8 ! trans-2-butene CH3CH=CHCH3 (E)-2-butene C2C4H8 ! cis-2-butene CH3CH=CHCH3 (Z)-2-butene IC4H3 ! 1-buten-3-yn-2yl (two mesomers) CH2=CC#CH NC4H3 ! 1-buten-3-ynyl CH=CHC#CH C6H6 ! benzene C6H5O ! phenoxy radical C6H5 ! phenyl END

REACTIONS !****************************************************************************** ! A. Konnov’s mechanism, units: cm3/mol/s, cal, K !****************************************************************************** !********************************************************************* ! ! A.KONNOV’s detailed reaction mechanism VER 0.5 CHECKED ! C6H10, C6H9 deleted 3/5/99, C3H4CY deleted 4/5/99 ! NH2OH added 11/11/99 HNOH, H2NO added 12/11/99 ! HNNO added 13/11/99 C2H5CHO added 16/03/00 C2H5CO added 17/03/00 ! HCNH, CH3NO, H2CNO added 20/06/00 !********************************************************************* H+H+M=H2+M 7.000E+17 -1.0 0.0 H2/0.0/ N2/0.0/ H/0.0/ H2O/14.3/ CO/3.0/ CO2/3.0/ H+H+H2=H2+H2 1.000E+17 -0.6 0.0 H+H+N2=H2+N2 5.400E+18 -1.3 0.0 H+H+H=H2+H 3.200E+15 0.0 0.0 O+O+M=O2+M 1.000E+17 -1.0 0.0 O/71.0/ O2/20.0/ NO/5.0/ N2/5.0/ N/5.0/ H2O/5.0/ O+H+M=OH+M 6.200E+16 -0.6 0.0 H2O/5.0/ H2+O2=OH+OH 2.500E+12 0.0 39000.0 O+H2=OH+H 5.060E+04 2.67 6290.0 H+O2=OH+O 9.750E+13 0.0 14850.0 H+O2(+M)=HO2(+M) 1.480E+12 0.6 0.0 LOW /3.50E+16 -0.41 -1116.0/ TROE /0.5 100000 10/ AR/0.0/ H2O/10.6/ H2/1.5/ CO2/2.4/ H+O2(+AR)=HO2(+AR) 1.480E+12 0.6 0.0 LOW /7.00E+17 -0.8 0.0/ TROE /0.45 10 100000/ H+OH+M=H2O+M 2.200E+22 -2.0 0.0 H2O/6.4/ AR/0.38/ CO2/1.9/ H2+OH=H2O+H 1.000E+08 1.6 3300.0 OH+OH=H2O+O 1.500E+09 1.14 100.0 HO2+OH=H2O+O2 2.890E+13 0.0 -500.0 HO2+O=OH+O2 1.630E+13 0.0 -445.0 H+HO2=H2+O2 4.280E+13 0.0 1411.0 H+HO2=OH+OH 1.700E+14 0.0 875.0 H+HO2=H2O+O 3.000E+13 0.0 1720.0 HO2+HO2=H2O2+O2 4.200E+14 0.0 12000.0 DUPLICATE HO2+HO2=H2O2+O2 1.300E+11 0.0 -1640.0 DUPLICATE OH+OH(+M)=H2O2(+M) 7.200E+13 -0.37 0.0 LOW /2.2E+19 -0.76 0.0/ TROE /0.5 100000 10/ H2O/0.0/ OH+OH(+H2O)=H2O2(+H2O) 7.200E+13 -0.37 0.0 LOW /1.45E+18 0.0 0.0/ H2O2+OH=HO2+H2O 1.000E+12 0.0 0.0 DUPLICATE H2O2+OH=HO2+H2O 5.800E+14 0.0 9560.0 DUPLICATE H2O2+H=HO2+H2 1.700E+12 0.0 3755.0 H2O2+H=H2O+OH 1.000E+13 0.0 3575.0 H2O2+O=HO2+OH 2.800E+13 0.0 6400.0 N2+O=NO+N 1.800E+14 0.0 76100.0 N+O2=NO+O 9.000E+09 1.0 6500.0 NO+M=N+O+M 9.640E+14 0.0 148300.0

292 N2 /1.5/ NO /3.0/ CO2/2.5/ NO+NO=N2+O2 3.000E+11 0.0 65000.0 N2O(+M)=N2+O(+M) 1.260E+12 0.0 62620.0 LOW / 4.000E+14 0.0 56640.0/ O2/1.4/ N2/1.7/ H2O/12.0/ NO/3.0/ N2O/3.5/ N2O+O=N2+O2 1.000E+14 0.0 28200.0 N2O+O=NO+NO 6.920E+13 0.0 26630.0 N2O+N=N2+NO 1.000E+13 0.0 20000.0 N2O+NO=N2+NO2 2.750E+14 0.0 50000.0 NO+O(+M)=NO2(+M) 1.300E+15 -0.75 0.0 LOW /4.72E+24 -2.87 1551.0/ TROE /0.962 10.0 7962.0 / AR /0.6/ NO2 /6.2/ NO /1.8/ O2 /0.8/ N2O /4.4/ CO2/0/ H2O /10.0/ NO+O(+CO2)=NO2(+CO2) 1.300E+15 -0.75 0.0 LOW /4.0E+22 -2.16 1051.0/ TROE /0.962 10.0 7962.0 / NO2+O=NO+O2 3.910E+12 0.0 -238.0 NO2+N=N2O+O 8.400E+11 0.0 0.0 NO2+N=NO+NO 1.000E+12 0.0 0.0 NO2+NO=N2O+O2 1.000E+12 0.0 60000.0 NO2+NO2=NO+NO+O2 3.950E+12 0.0 27590.0 NO2+NO2=NO3+NO 1.130E+04 2.58 22720.0 NO2+O(+M)=NO3(+M) 1.330E+13 0.0 0.0 LOW / 1.49E+28 -4.08 2467.0 / TROE /0.86 10.0 2800.0 / H2O/10.0/ O2/0.8/ H2/2.0/ CO2 /0/ NO2+O(+CO2)=NO3(+CO2) 1.330E+13 0.0 0.0 LOW / 1.34E+28 -3.94 2277.0 / TROE /0.86 10.0 2800.0 / NO3=NO+O2 2.500E+06 0.0 12120.0 NO3+NO2=NO+NO2+O2 1.200E+11 0.0 3200.0 NO3+O=NO2+O2 1.020E+13 0.0 0.0 NO3+NO3=NO2+NO2+O2 5.120E+11 0.0 4870.0 N2O4(+M)=NO2+NO2(+M) 4.050E+18 -1.1 12840.0 LOW /1.96E+28 -3.8 12840./ AR/0.8/ N2O4/2.0/ NO2/2.0/ N2O4+O=N2O3+O2 1.210E+12 0.0 0.0 NO2+NO(+M)=N2O3(+M) 1.600E+09 1.4 0.0 LOW /1.0E+33 -7.7 0.0/ N2/1.36/ N2O3+O=NO2+NO2 2.710E+11 0.0 0.0 N2+M=N+N+M 1.000E+28 -3.33 225000.0 N/5/ O/2.2/ NH+M=N+H+M 2.650E+14 0.0 75500.0 NH+H=N+H2 3.200E+13 0.0 325.0 NH+N=N2+H 9.000E+11 0.5 0.0 NH+NH=NNH+H 5.100E+13 0.0 0.0 NH+NH=NH2+N 5.950E+02 2.89 -2030.0 NH+NH=N2+H2 1.000E+08 1.0 0.0 NH2+M=NH+H+M 3.160E+23 -2.0 91400.0 NH+H2=NH2+H 1.000E+14 0.0 20070.0 NH2+N=N2+H+H 6.900E+13 0.0 0.0 NH2+NH=N2H2+H 1.500E+15 -0.5 0.0 NH2+NH=NH3+N 1.000E+13 0.0 2000.0 NH3+NH=NH2+NH2 3.160E+14 0.0 26770.0 NH2+NH2=N2H2+H2 1.000E+13 0.0 1500.0 N2H3+H=NH2+NH2 5.000E+13 0.0 2000.0 NH3+M=NH2+H+M 2.200E+16 0.0 93470.0 NH3+M=NH+H2+M 6.300E+14 0.0 93390.0 NH3+H=NH2+H2 5.420E+05 2.4 9920.0 NH3+NH2=N2H3+H2 1.000E+11 0.5 21600.0 NNH=N2+H 3.000E+08 0.0 0.0 NNH+M=N2+H+M 1.000E+13 0.5 3060.0 NNH+H=N2+H2 1.000E+14 0.0 0.0 NNH+N=NH+N2 3.000E+13 0.0 2000.0 NNH+NH=N2+NH2 2.000E+11 0.5 2000.0 NNH+NH2=N2+NH3 1.000E+13 0.0 0.0 NNH+NNH=N2H2+N2 1.000E+13 0.0 4000.0 N2H2+M=NNH+H+M 5.000E+16 0.0 50000.0 H2O/15.0/ O2/2.0/ N2/2.0/ H2/2.0/ N2H2+M=NH+NH+M 3.160E+16 0.0 99400.0 H2O/15.0/ O2/2.0/ N2/2.0/ H2/2.0/ N2H2+H=NNH+H2 8.500E+04 2.63 -230.0 N2H2+N=NNH+NH 1.000E+06 2.0 0.0 N2H2+NH=NNH+NH2 1.000E+13 0.0 6000.0 N2H2+NH2=NH3+NNH 8.800E-02 4.05 -1610.0 N2H3+NH=N2H2+NH2 2.000E+13 0.0 0.0 N2H3+NNH=N2H2+N2H2 1.000E+13 0.0 4000.0 N2H3+M=NH2+NH+M 5.000E+16 0.0 60000.0

293 N2H3+M=N2H2+H+M 1.000E+16 0.0 37000.0 N2H3+H=N2H2+H2 1.000E+13 0.0 0.0 N2H3+H=NH+NH3 1.000E+11 0.0 0.0 N2H3+N=N2H2+NH 1.000E+06 2.0 0.0 N2H3+NH2=NH3+N2H2 1.000E+11 0.5 0.0 N2H3+N2H2=N2H4+NNH 1.000E+13 0.0 6000.0 N2H3+N2H3=NH3+NH3+N2 3.000E+12 0.0 0.0 N2H3+N2H3=N2H4+N2H2 1.200E+13 0.0 0.0 N2H4(+M)=NH2+NH2(+M) 5.000E+14 0.0 60000.0 LOW/1.50E+15 0.0 39000.0 / N2/2.4/ NH3/3.0/ N2H4/4.0/ N2H4+M=N2H3+H+M 1.000E+15 0.0 63600.0 N2/2.4/ NH3/3.0/ N2H4/4.0/ N2H4+H=N2H3+H2 7.000E+12 0.0 2500.0 N2H4+H=NH2+NH3 2.400E+09 0.0 3100.0 N2H4+N=N2H3+NH 1.000E+10 1.0 2000.0 N2H4+NH=NH2+N2H3 1.000E+09 1.5 2000.0 N2H4+NH2=N2H3+NH3 1.800E+06 1.71 -1380.0 N+OH=NO+H 2.800E+13 0.0 0.0 N2O+H=N2+OH 2.200E+14 0.0 16750.0 N2O+H=NH+NO 6.700E+22 -2.16 37155.0 N2O+H=NNH+O 5.500E+18 -1.06 47290.0 N2O+H=HNNO 8.000E+24 -4.39 10530.0 N2O+OH=N2+HO2 1.000E+14 0.0 30000.0 HNO+NO=N2O+OH 8.500E+12 0.0 29580.0 HNO+NO+NO=HNNO+NO2 1.600E+11 0.0 2090.0 NH+NO+M=HNNO+M 1.630E+23 -2.6 1820.0 HNNO+H=N2O+H2 2.000E+13 0.0 0.0 HNNO+H=NH2+NO 1.000E+12 0.0 0.0 HNNO+O=N2O+OH 2.000E+13 0.0 0.0 HNNO+OH=H2O+N2O 2.000E+13 0.0 0.0 HNNO+OH=HNOH+NO 1.000E+12 0.0 0.0 HNNO+NO=N2+HONO 2.600E+11 0.0 1610.0 HNNO+NO=NNH+NO2 3.200E+12 0.0 540.0 HNNO+NO=N2O+HNO 1.000E+12 0.0 0.0 HNNO+NO2=N2O+HONO 1.000E+12 0.0 0.0 HNNO+NO2=NNH+NO3 1.000E+13 0.0 17000.0 NO2+H=NO+OH 1.320E+14 0.0 362.0 NO2+OH=HO2+NO 1.810E+13 0.0 6676.0 NO2+HO2=HONO+O2 4.640E+11 0.0 -479.0 NO2+H2=HONO+H 7.330E+11 0.0 28800.0 NO2+NH=N2O+OH 8.650E+10 0.0 -2270.0 NO2+NH=NO+HNO 1.245E+11 0.0 -2270.0 NO3+H=NO2+OH 6.620E+13 0.0 0.0 NO3+OH=NO2+HO2 1.210E+13 0.0 0.0 NO3+HO2=HNO3+O2 5.550E+11 0.0 0.0 NO3+HO2=NO2+OH+O2 1.510E+12 0.0 0.0 N2O4+H2O=HONO+HNO3 2.520E+14 0.0 11590.0 N2O3+H2O=HONO+HONO 3.790E+13 0.0 8880.0 H+NO(+M)=HNO(+M) 1.520E+15 -0.41 0.0 LOW /4.00E+20 -1.75 0.0 / H2O/10.0/ O2/1.5/ AR/0.75/ H2/2.0/ CO2/3.0/ HNO+H=NO+H2 4.460E+11 0.72 655.0 HNO+OH=NO+H2O 1.300E+07 1.88 -956.0 HNO+O=OH+NO 5.000E+11 0.5 2000.0 HNO+O=NO2+H 5.000E+10 0.0 2000.0 HNO+O2=NO+HO2 2.200E+10 0.0 9140.0 HNO+N=NO+NH 1.000E+11 0.5 2000.0 HNO+N=H+N2O 5.000E+10 0.5 3000.0 HNO+NH=NH2+NO 5.000E+11 0.5 0.0 HNO+NH2=NH3+NO 2.000E+13 0.0 1000.0 HNO+HNO=N2O+H2O 3.630E-03 3.98 1190.0 HNO+HNO=HNOH+NO 2.000E+08 0.0 4170.0 HNO+NO2=HONO+NO 6.020E+11 0.0 2000.0 NO+OH(+M)=HONO(+M) 2.000E+12 -0.05 -721.0 LOW / 5.08E+23 -2.51 -67.6 / TROE /0.62 10.0 100000.0 / H2O/10.0/ O2/2.0/ AR/0.75/ H2/2.0/ CO2/0.0/ NO+OH(+CO2)=HONO(+CO2) 2.000E+12 -0.05 -721.0 LOW / 1.70E+23 -2.3 -246.0 / TROE /0.62 10.0 100000.0 / NO2+H+M=HONO+M 1.400E+18 -1.5 900.0 HONO+H=HNO+OH 5.640E+10 0.86 4970.0 HONO+H=NO+H2O 8.120E+06 1.89 3840.0 HONO+O=OH+NO2 1.200E+13 0.0 5960.0 HONO+OH=H2O+NO2 1.690E+12 0.0 -517.0 HONO+NH=NH2+NO2 1.000E+13 0.0 0.0 HONO+HONO=H2O+NO2+NO 1.000E+13 0.0 8540.0 HONO+NH2=NO2+NH3 5.000E+12 0.0 0.0 NO2+OH(+M)=HNO3(+M) 2.410E+13 0.0 0.0 LOW / 6.42E+32 -5.49 2350.0 /

294 TROE /1.0 10.0 1168.0 / H2O/10.0/ O2/2.0/ AR/0.75/ H2/2.0/ CO2/0.0/ NO2+OH(+CO2)=HNO3(+CO2) 2.410E+13 0.0 0.0 LOW / 5.80E+32 -5.4 2186.0 / TROE /1.0 10.0 1168.0 / NO+HO2+M=HNO3+M 1.500E+24 -3.5 2200.0 HNO3+H=H2+NO3 5.560E+08 1.53 16400.0 HNO3+H=H2O+NO2 6.080E+01 3.29 6290.0 HNO3+H=OH+HONO 3.820E+05 2.3 6980.0 HNO3+OH=NO3+H2O 1.030E+10 0.0 -1240.0 NH3+O=NH2+OH 1.100E+06 2.1 5210.0 NH3+OH=NH2+H2O 5.000E+07 1.6 950.0 NH3+HO2=NH2+H2O2 3.000E+11 0.0 22000.0 NH2+HO2=NH3+O2 1.650E+04 1.55 2027.0 NH2+O=H2+NO 5.000E+12 0.0 0.0 NH2+O=HNO+H 4.500E+13 0.0 0.0 NH2+O=NH+OH 7.000E+12 0.0 0.0 NH2+OH=NH+H2O 9.000E+07 1.5 -460.0 NH2+OH=NH2OH 1.790E+13 0.2 0.0 NH2+HO2=HNO+H2O 5.680E+15 -1.12 707.0 NH2+HO2=H2NO+OH 2.910E+17 -1.32 1248.0 NH2+O2=HNO+OH 1.000E+13 0.0 26290.0 NH2+O2=H2NO+O 6.000E+13 0.0 29880.0 NH2+NO=NNH+OH 2.290E+10 0.425 -814.0 NH2+NO=N2+H2O 2.770E+20 -2.65 1258.0 NH2+NO=H2+N2O 1.000E+13 0.0 33700.0 NH2+NO2=N2O+H2O 1.620E+16 -1.44 270.0 NH2+NO2=H2NO+NO 6.480E+16 -1.44 270.0 NH+O=NO+H 7.000E+13 0.0 0.0 NH+O=N+OH 7.000E+12 0.0 0.0 NH+OH=HNO+H 2.000E+13 0.0 0.0 NH+OH=N+H2O 2.000E+09 1.2 0.0 NH+OH=NO+H2 2.000E+13 0.0 0.0 NH+HO2=HNO+OH 1.000E+13 0.0 2000.0 NH+O2=HNO+O 4.000E+13 0.0 17880.0 NH+O2=NO+OH 4.500E+08 0.79 1190.0 NH+H2O=HNO+H2 2.000E+13 0.0 13850.0 NH+N2O=N2+HNO 2.000E+12 0.0 6000.0 NNH+O=NH+NO 2.000E+14 0.0 4000.0 NH+NO=N2+OH 6.100E+13 -0.50 120.0 N2H4+O=N2H2+H2O 8.500E+13 0.0 1200.0 N2H4+O=N2H3+OH 2.500E+12 0.0 1200.0 N2H4+OH=N2H3+H2O 3.000E+10 0.68 1290.0 N2H4+OH=NH3+H2NO 3.670E+13 0.0 0.0 N2H4+HO2=N2H3+H2O2 4.000E+13 0.0 2000.0 N2H3+O=N2H2+OH 2.000E+13 0.0 1000.0 N2H3+O=NNH+H2O 3.160E+11 0.5 0.0 N2H3+O=NH2+HNO 1.000E+13 0.0 0.0 N2H3+OH=N2H2+H2O 3.000E+10 0.68 1290.0 N2H3+OH=NH3+HNO 1.000E+12 0.0 15000.0 N2H3+O2=N2H2+HO2 3.000E+12 0.0 0.0 N2H3+HO2=N2H2+H2O2 1.000E+13 0.0 2000.0 N2H3+HO2=N2H4+O2 8.000E+12 0.0 0.0 N2H3+NO=HNO+N2H2 1.000E+12 0.0 0.0 N2H2+O=NH2+NO 1.000E+13 0.0 0.0 N2H2+O=NNH+OH 2.000E+13 0.0 1000.0 N2H2+OH=NNH+H2O 5.920E+01 3.4 -1360.0 N2H2+HO2=NNH+H2O2 1.000E+13 0.0 2000.0 N2H2+NO=N2O+NH2 3.000E+10 0.0 0.0 NNH+O=N2+OH 1.700E+16 -1.23 500.0 NNH+OH=N2+H2O 2.400E+22 -2.88 2444.0 NNH+O2=N2+HO2 1.200E+12 -0.34 150.0 NNH+O2=N2O+OH 2.900E+11 -0.34 150.0 NNH+HO2=N2+H2O2 1.000E+13 0.0 2000.0 NNH+NO=N2+HNO 5.000E+13 0.0 0.0 NH2OH+OH=HNOH+H2O 2.500E+13 0.0 4250.0 H2NO+M=H2+NO+M 7.830E+27 -4.29 60300.0 H2O/10.0/ H2NO+M=HNO+H+M 2.800E+24 -2.83 64915.0 H2O/10.0/ H2NO+M=HNOH+M 1.100E+29 -3.99 43980.0 H2O/10.0/ H2NO+H=HNO+H2 3.000E+07 2.0 2000.0 H2NO+H=NH2+OH 5.000E+13 0.0 0.0 H2NO+O=HNO+OH 3.000E+07 2.0 2000.0 H2NO+OH=HNO+H2O 2.000E+07 2.0 1000.0 H2NO+HO2=HNO+H2O2 2.900E+04 2.69 -1600.0 H2NO+NH2=HNO+NH3 3.000E+12 0.0 1000.0 H2NO+O2=HNO+HO2 3.000E+12 0.0 25000.0 H2NO+NO=HNO+HNO 2.000E+07 2.0 13000.0 H2NO+NO2=HONO+HNO 6.000E+11 0.0 2000.0 HNOH+M=HNO+H+M 2.000E+24 -2.84 58935.0

295 H2O/10.0/ HNOH+H=HNO+H2 4.800E+08 1.5 380.0 HNOH+H=NH2+OH 4.000E+13 0.0 0.0 HNOH+O=HNO+OH 7.000E+13 0.0 0.0 DUPLICATE HNOH+O=HNO+OH 3.300E+08 1.5 -360.0 DUPLICATE HNOH+OH=HNO+H2O 2.400E+06 2.0 -1190.0 HNOH+HO2=HNO+H2O2 2.900E+04 2.69 -1600.0 HNOH+NH2=HNO+NH3 1.800E+06 1.94 -1150.0 HNOH+NO2=HONO+HNO 6.000E+11 0.0 2000.0 HNOH+O2=HNO+HO2 3.000E+12 0.0 25000.0 HNOH+HNO=NH2OH+NO 1.000E+12 0.0 3000.0 !END CO+HO2=CO2+OH 1.500E+14 0.0 23650.0 CO+OH=CO2+H 1.170E+07 1.354 -725.0 CO+O+M=CO2+M 6.160E+14 0.0 3000.0 H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/0.88/ CH4/3.2/ CH3OH/7.5/ CO+O2=CO2+O 2.500E+12 0.0 47800.0 HCO+M=H+CO+M 1.560E+14 0.0 15760.0 H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/1.0/ CH4/3.2/ CH3OH/7.5/ HCO+OH=CO+H2O 1.000E+14 0.0 0.0 HCO+O=CO+OH 3.000E+13 0.0 0.0 HCO+O=CO2+H 3.000E+13 0.0 0.0 HCO+H=CO+H2 9.000E+13 0.0 0.0 HCO+O2=CO+HO2 2.700E+13 0.0 1190.0 HCO+CH3=CO+CH4 1.200E+14 0.0 0.0 HCO+HO2=CO2+OH+H 3.000E+13 0.0 0.0 HCO+HCO=CH2O+CO 3.000E+13 0.0 0.0 HCO+HCO=H2+CO+CO 2.200E+13 0.0 0.0 CH4(+M)=CH3+H(+M) 2.400E+16 0.0 104913.0 LOW /4.5E+17 0.0 90800/ TROE /1.0 10.0 1350.0 7830.0/ CH4/0.0/ H2/2.0/ CO/2.0/ CO2/3.0/ H2O/5.0/ CH4(+CH4)=CH3+H(+CH4) 2.400E+16 0.0 104913.0 LOW /8.4E+18 0.0 90800/ TROE /0.31 2210.0 90/ CH4+HO2=CH3+H2O2 9.000E+12 0.0 24641.0 CH4+OH=CH3+H2O 1.548E+07 1.83 2774.0 CH4+O=CH3+OH 7.200E+08 1.56 8485.0 CH4+H=CH3+H2 1.300E+04 3.0 8050.0 CH4+CH2=CH3+CH3 4.300E+12 0.0 10038.0 CH4+O2=CH3+HO2 4.000E+13 0.0 56900.0 CH3+M=CH2+H+M 2.720E+36 -5.31 117100.0 H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/1.0/ CH4/3.2/ CH3OH/7.5/ CH3+M=CH+H2+M 1.000E+16 0.0 85240.0 H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/0.88/ CH4/3.2/ CH3OH/7.5/ CH3+HO2=CH3O+OH 1.800E+13 0.0 0.0 CH3+OH=CH2OH+H 2.640E+19 -1.8 8068.0 CH3+OH=CH3O+H 5.740E+12 -0.23 13931.0 CH3+OH=CH2+H2O 8.900E+18 -1.8 8067.0 CH3+OH=CH2O+H2 3.190E+12 -0.53 10810.0 CH3+O=H+CH2O 8.430E+13 0.0 0.0 CH3+O2=CH2O+OH 3.400E+11 0.0 8940.0 CH3+O2=CH3O+O 1.320E+14 0.0 31400.0 CH3+CH3=C2H5+H 5.000E+12 0.099 10600.0 CH3+CH3(+M)=C2H6(+M) 9.210E+16 -1.174 636.0 LOW /1.13E+36 -5.246 1705/ TROE /0.405 1120.0 69.6/ H2/2.0/ CO/2.0/ CO2/3.0/ H2O/5.0/ CH3+CH3O=CH4+CH2O 2.409E+13 0.0 0.0 CH3+CH2OH=CH4+CH2O 8.500E+13 0.0 0.0 CH3+H=SCH2+H2 6.000E+13 0.0 15100.0 CH3+O2(+M)=CH3O2(+M) 7.800E+08 1.2 0.0 LOW/5.8E+25 -3.30 0.0/ TROE /0.495 2325.5 10/ CH3+CH3=C2H4+H2 1.000E+14 0.0 32000.0 CH3+OH=SCH2+H2O 7.200E+13 0.0 2780.0 CH2+OH=CH2O+H 2.500E+13 0.0 0.0 CH2+O=CO+H2 4.800E+13 0.0 0.0 CH2+O=CO+H+H 7.200E+13 0.0 0.0 CH2+O=CH+OH 3.000E+14 0.0 11920.0 CH2+O=HCO+H 3.000E+13 0.0 0.0 CH2+H=CH+H2 3.120E+13 0.0 -1340.0 CH2+O2=HCO+OH 4.300E+10 0.0 -500.0 CH2+O2=CO2+H2 6.900E+11 0.0 500.0 CH2+O2=CO2+H+H 1.600E+12 0.0 1000.0

296 CH2+O2=CO+H2O 1.900E+10 0.0 -1000.0 CH2+O2=CO+OH+H 8.600E+10 0.0 -500.0 CH2+O2=CH2O+O 5.000E+13 0.0 9000.0 CH2+CO2=CH2O+CO 1.100E+11 0.0 1000.0 CH2+CH2=C2H2+H2 1.580E+15 0.0 11950.0 CH2+CH2=C2H2+H+H 2.000E+14 0.0 11000.0 CH2+CH2=CH3+CH 2.400E+14 0.0 9940.0 CH2+CH2=C2H3+H 2.000E+13 0.0 0.0 CH2+CH3=C2H4+H 4.200E+13 0.0 0.0 CH2+CH=C2H2+H 4.000E+13 0.0 0.0 CH2+C=CH+CH 1.620E+12 0.67 46800.0 CH2+M=C+H2+M 1.600E+14 0.0 64000.0 CH2+M=CH+H+M 5.600E+15 0.0 89600.0 SCH2+M=CH2+M 6.000E+12 0.0 0.0 H2/2.5/ H2O/5.0/ CO/1.875/ CO2/3.75/ AR/0.6/ CH4/1.2/ C2H2/8.0/ C2H4/4.0/ C2H6/3.6/ H/33.3/ SCH2+O2=CO+OH+H 3.000E+13 0.0 0.0 SCH2+H=CH+H2 3.000E+13 0.0 0.0 SCH2+O=CO+H+H 1.500E+13 0.0 0.0 SCH2+O=CO+H2 1.500E+13 0.0 0.0 SCH2+OH=CH2O+H 3.000E+13 0.0 0.0 SCH2+HO2=CH2O+OH 3.000E+13 0.0 0.0 SCH2+H2O2=CH3O+OH 3.000E+13 0.0 0.0 SCH2+H2O=>CH3OH 1.800E+13 0.0 0.0 SCH2+CH2O=CH3+HCO 1.200E+12 0.0 0.0 SCH2+HCO=CH3+CO 1.800E+13 0.0 0.0 SCH2+CH3=C2H4+H 1.800E+13 0.0 0.0 SCH2+CH4=CH3+CH3 4.000E+13 0.0 0.0 SCH2+C2H6=CH3+C2H5 1.200E+14 0.0 0.0 SCH2+CO2=CH2O+CO 3.000E+12 0.0 0.0 SCH2+CH2CO=C2H4+CO 1.600E+14 0.0 0.0 CH+OH=HCO+H 3.000E+13 0.0 0.0 CH+O=CO+H 4.000E+13 0.0 0.0 CH+O=C+OH 1.520E+13 0.0 4730.0 H2O+C=CH+OH 7.800E+11 0.67 39300.0 CH+O2=HCO+O 4.900E+13 0.0 0.0 CH+O2=CO+OH 4.900E+13 0.0 0.0 CH+CO2=HCO+CO 3.220E-02 4.44 -3530.0 CH+CH4=C2H4+H 3.900E+14 -0.4 0.0 CH+CH3=C2H3+H 3.000E+13 0.0 0.0 CH2+OH=CH+H2O 1.130E+07 2.0 3000.0 CH+H=C+H2 7.900E+13 0.0 160.0 CH+H2O=CH2O+H 1.170E+15 -0.75 0.0 CH+H2O=CH2OH 5.700E+12 0.0 -760.0 CH+CH2O=CH2CO+H 1.000E+14 0.0 -515.0 CH3O+M=CH2O+H+M 5.400E+13 0.0 13500.0 H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/0.88/ CH4/3.2/ CH3OH/7.5/ CH3O+HO2=CH2O+H2O2 3.000E+11 0.0 0.0 CH3O+OH=CH2O+H2O 1.800E+13 0.0 0.0 CH3O+O=CH2O+OH 1.800E+12 0.0 0.0 CH3O+H=CH2O+H2 1.800E+13 0.0 0.0 CH3O+O2=CH2O+HO2 2.200E+10 0.0 1750.0 CH3O+CH2O=CH3OH+HCO 1.000E+11 0.0 2980.0 CH3O+CO=CH3+CO2 6.810E-18 9.2 -2850.0 CH3O+HCO=CH3OH+CO 9.000E+13 0.0 0.0 CH3O+C2H5=CH2O+C2H6 2.410E+13 0.0 0.0 CH3O+C2H3=CH2O+C2H4 2.410E+13 0.0 0.0 CH3O+C2H4=CH2O+C2H5 1.200E+11 0.0 6750.0 CH3O+H=CH2OH+H 3.400E+06 1.6 0.0 CH3O+H=SCH2+H2O 1.000E+12 0.0 0.0 CH2O+M=HCO+H+M 5.000E+35 -5.54 96680.0 H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/1.0/ CH4/3.2/ CH3OH/7.5/ CH2O+M=CO+H2+M 1.100E+36 -5.54 96680.0 H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/1.0/ CH4/3.2/ CH3OH/7.5/ CH2O+HO2=HCO+H2O2 4.110E+04 2.5 10210.0 CH2O+OH=HCO+H2O 3.433E+09 1.18 -447.0 CH2O+O=HCO+OH 4.100E+11 0.57 2760.0 CH2O+H=HCO+H2 1.260E+08 1.62 2166.0 CH2O+O2=HCO+HO2 6.000E+13 0.0 40650.0 CH2O+CH3=HCO+CH4 7.800E-08 6.1 1970.0 C2H6(+M)=C2H5+H(+M) 8.850E+20 -1.228 102210.0 LOW /6.90E+42 -6.431 107175.0/ SRI /47.61 16182.0 3371.0/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ C2H6+HO2=C2H5+H2O2 1.330E+13 0.0 20535.0 C2H6+OH=C2H5+H2O 7.200E+06 2.0 870.0 C2H6+O=C2H5+OH 1.000E+09 1.5 5800.0 C2H6+H=C2H5+H2 1.400E+09 1.5 7400.0 C2H6+H=CH3+CH4 5.400E+04 0.0 11630.0

297 C2H6+O2=C2H5+HO2 6.000E+13 0.0 52000.0 C2H6+CH3=C2H5+CH4 1.470E-07 6.0 6060.0 C2H6+CH2=CH3+C2H5 6.500E+12 0.0 7911.0 C2H6+C2H3=C2H4+C2H5 8.566E-02 4.14 2543.0 C2H6+HCO=CH2O+C2H5 4.700E+04 2.72 18235.0 C2H5(+M)=C2H4+H(+M) 1.110E+10 1.037 36767.0 LOW /4.0E+33 -4.99 40000.0/ TROE /0.832 10 1203.0/ H2/2.0/ CO/2.0/ CO2/3.0/ H2O/5.0/ CH4/2.0/ C2H6/0.0/ AR/0.7/ C2H5(+C2H6)=C2H4+H(+C2H6) 8.200E+13 0.0 39880.0 LOW /1.0E+18 0.0 33380.0/ TROE /0.75 97.0 1379.0/ C2H5+HO2=C2H4+H2O2 1.800E+12 0.0 0.0 C2H5+OH=C2H4+H2O 2.409E+13 0.0 0.0 C2H5+OH=>CH3+CH2O+H 2.409E+13 0.0 0.0 C2H5+O=CH2O+CH3 4.240E+13 0.0 0.0 C2H5+O=CH3HCO+H 5.300E+13 0.0 0.0 C2H5+O=C2H4+OH 3.460E+13 0.0 0.0 C2H5+H=C2H4+H2 1.700E+12 0.0 0.0 C2H5+O2=C2H4+HO2 2.560E+19 -2.77 1980.0 C2H5+CH3=C2H4+CH4 1.100E+12 0.0 0.0 C2H5+C2H5=C2H4+C2H6 1.400E+12 0.0 0.0 C2H5+HO2=C2H5O+OH 3.000E+13 0.0 0.0 C2H4+M=C2H2+H2+M 3.500E+16 0.0 71530.0 H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/1.0/ CH4/3.2/ CH3OH/7.5/ C2H4+M=C2H3+H+M 2.600E+17 0.0 96570.0 H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/1.0/ CH4/3.2/ CH3OH/7.5/ C2H4+OH=C2H3+H2O 5.530E+05 2.31 2900.0 C2H4+O=CH3+HCO 8.100E+06 1.88 180.0 C2H4+H=C2H3+H2 4.490E+07 2.12 13366.0 C2H4+O2=C2H3+HO2 4.000E+13 0.0 61500.0 C2H4+C2H4=C2H5+C2H3 1.860E+14 0.0 64200.0 C2H4+CH3=C2H3+CH4 4.200E+12 0.0 11100.0 C2H4+O=CH2HCO+H 4.700E+06 1.88 180.0 C2H4+O=CH2O+CH2 3.000E+04 1.88 180.0 C2H4+O=CH2CO+H2 6.700E+05 1.88 180.0 C2H4+O=C2H3+OH 1.510E+07 1.91 3790.0 C2H4+OH=CH2O+CH3 2.000E+12 0.0 960.0 C2H4+OH(+M)=PC2H5O(+M) 5.420E+12 0.0 0.0 LOW /1.19E+27 -3.1 0.0/ C2H4+HO2=C2H3+H2O2 1.120E+13 0.0 30400.0 C2H4+CH3O=C2H3+CH3OH 1.000E+11 0.0 10000.0 C2H3(+M)=C2H2+H(+M) 2.100E+14 0.0 39740.0 LOW /4.15E+41 -7.5 45500.0/ TROE /0.65 100000 10/ H2/2.0/ CO/2.0/ CO2/3.0/ H2O/5.0/ CH4/2.0/ C2H6/3.0/ AR/0.7/ C2H3+HO2=>CH3+CO+OH 3.000E+13 0.0 0.0 C2H3+OH=C2H2+H2O 3.000E+13 0.0 0.0 C2H3+H=C2H2+H2 1.200E+13 0.0 0.0 C2H3+O=CH3+CO 1.000E+13 0.0 0.0 C2H3+O2=CH2O+HCO 1.700E+29 -5.312 6500.0 C2H3+CH=CH2+C2H2 5.000E+13 0.0 0.0 C2H3+CH3=C2H2+CH4 2.050E+13 0.0 0.0 C2H3+C2H=C2H2+C2H2 3.000E+13 0.0 0.0 C2H3+HCO=C2H4+CO 9.034E+13 0.0 0.0 C2H3+CH2O=C2H4+HCO 5.420E+03 2.81 5862.0 C2H3+C2H3=C2H2+C2H4 1.450E+13 0.0 0.0 C2H3+O=C2H2+OH 1.000E+13 0.0 0.0 C2H3+O=CH2+HCO 1.000E+13 0.0 0.0 C2H3+O=CH2CO+H 1.000E+13 0.0 0.0 C2H3+OH=CH3HCO 3.000E+13 0.0 0.0 C2H3+O2=C2H2+HO2 5.190E+15 -1.26 3310.0 DUPLICATE C2H3+O2=C2H2+HO2 2.120E-06 6.0 9484.0 DUPLICATE C2H3+O2=CH2HCO+O 3.500E+14 -0.61 5260.0 C2H3+CH2=C2H2+CH3 3.000E+13 0.0 0.0 C2H2=C2H+H 2.373E+32 -5.28 130688.0 C2H2+O2=HCCO+OH 2.000E+08 1.5 30100.0 C2H2+O2=C2H+HO2 1.200E+13 0.0 74520.0 C2H2+OH=C2H+H2O 3.385E+07 2.0 14000.0 C2H2+OH=CH2CO+H 1.100E+13 0.0 7170.0 C2H2+O=CH2+CO 1.200E+06 2.1 1570.0 C2H2+O=HCCO+H 5.000E+06 2.1 1570.0 C2H2+CH3=C2H+CH4 1.800E+11 0.0 17290.0 C2H2+O=C2H+OH 3.000E+14 0.0 25000.0 C2H2+OH=CH3+CO 4.830E-04 4.0 -2000.0 C2H2+HO2=CH2CO+OH 6.100E+09 0.0 7950.0 C2H2+O2=HCO+HCO 4.000E+12 0.0 28000.0 C2H+OH=HCCO+H 2.000E+13 0.0 0.0

298 C2H+OH=C2+H2O 4.000E+07 2.0 8000.0 C2H+O=CO+CH 1.450E+13 0.0 460.0 C2H+O2=HCO+CO 9.000E+12 0.0 0.0 C2H+H2=C2H2+H 7.880E+05 2.39 346.0 C2H+O2=CO+CO+H 9.000E+12 0.0 0.0 C2H+O2=HCCO+O 6.000E+11 0.0 0.0 CH2CO(+M)=CH2+CO(+M) 3.000E+14 0.0 71000.0 LOW /2.300E+15 0.0 57600.0/ H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/1.0/ CH4/3.2/ CH3OH/7.5/ CH2CO+O2=CH2O+CO2 2.000E+13 0.0 61500.0 CH2CO+HO2=>CH2O+CO+OH 6.000E+11 0.0 12738.0 CH2CO+O=HCCO+OH 1.000E+13 0.0 8000.0 CH2CO+OH=CH2OH+CO 1.000E+13 0.0 0.0 CH2CO+H=CH3+CO 3.280E+10 0.851 2840.0 CH2CO+CH3=C2H5+CO 2.400E+12 0.0 8000.0 CH2CO+CH2=C2H4+CO 2.900E+12 0.0 3800.0 CH2CO+CH2=HCCO+CH3 3.600E+13 0.0 11000.0 CH2CO+CH3=HCCO+CH4 7.500E+12 0.0 13000.0 CH2CO+OH=CH2O+HCO 2.800E+13 0.0 0.0 CH2CO+H=HCCO+H2 1.800E+14 0.0 8600.0 CH2CO+O=HCO+HCO 7.500E+11 0.0 1350.0 CH2CO+O=HCO+CO+H 7.500E+11 0.0 1350.0 CH2CO+O=CH2O+CO 7.500E+11 0.0 1350.0 CH2CO+OH=HCCO+H2O 7.500E+12 0.0 2000.0 HCCO+M=CH+CO+M 6.000E+15 0.0 58821.0 H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/0.88/ CH4/3.2/ CH3OH/7.5/ HCCO+OH=HCO+CO+H 1.000E+13 0.0 0.0 HCCO+OH=C2O+H2O 3.000E+13 0.0 0.0 HCCO+O=CO+CO+H 1.000E+14 0.0 0.0 HCCO+O=CH+CO2 2.950E+13 0.0 1110.0 HCCO+H=CH2+CO 1.500E+14 0.0 0.0 HCCO+O2=CO2+CO+H 5.400E+11 0.0 850.0 HCCO+CH2=C2H+CH2O 1.000E+13 0.0 2000.0 HCCO+CH2=C2H3+CO 3.000E+13 0.0 0.0 HCCO+CH3=C2H4+CO 2.000E+12 0.0 0.0 HCCO+CH=CO+C2H2 5.000E+13 0.0 0.0 HCCO+HCCO=CO+C2H2+CO 1.000E+13 0.0 0.0 HCCO+OH=HCO+HCO 1.000E+13 0.0 0.0 HCCO+O2=CO+CO+OH 5.400E+11 0.0 850.0 HCCO+O2=CO2+HCO 5.400E+11 0.0 850.0 CH3OH(+M)=CH3+OH(+M) 1.700E+16 0.0 90885.0 LOW /6.60E+16 0.0 65730.0/ TROE /0.82 200.0 1438.0/ CH3OH+HO2=CH2OH+H2O2 9.640E+10 0.0 12580.0 CH3OH+OH=CH2OH+H2O 1.440E+06 2.0 -840.0 CH3OH+OH=CH3O+H2O 1.000E+13 0.0 1700.0 CH3OH+O=CH2OH+OH 1.630E+13 0.0 5030.0 CH3OH+H=CH2OH+H2 1.640E+07 2.0 4520.0 CH3OH+CH3=CH2OH+CH4 3.190E+01 3.17 7172.0 CH3OH+CH3=CH3O+CH4 1.450E+01 3.1 6935.0 CH3OH+C2H5=C2H6+CH3O 1.440E+01 3.1 8942.0 CH3OH+H=CH3+H2O 2.000E+14 0.0 5300.0 CH3OH+O=CH3O+OH 1.000E+13 0.0 4680.0 CH3OH+CH3=C2H6+OH 2.000E+12 0.0 15000.0 CH3OH+CH3O=CH2OH+CH3OH 3.000E+11 0.0 4070.0 CH3OH(+M)=CH2OH+H(+M) 1.380E+16 0.0 95950.0 LOW /5.35E+16 0.0 70800.0/ TROE /0.82 200.0 1438.0/ CH3OH+H=H2+CH3O 4.000E+13 0.0 6095.0 CH3OH+O2=CH2OH+HO2 2.050E+13 0.0 44900.0 CH3OH+C2H5=C2H6+CH2OH 3.190E+01 3.2 9161.0 CH2OH+M=CH2O+H+M 1.140E+43 -8.0 43000.0 H2O/16.0/ CH4/3.0/ CO2/3.75/ CO/1.875/ H2/2.5/ CH3OH/6.0/ CH2OH+H=CH2O+H2 1.000E+13 0.0 0.0 CH2OH+O2=CH2O+HO2 1.500E+15 -1.0 0.0 duplicate CH2OH+O2=CH2O+HO2 7.200E+13 0.0 3570.0 duplicate H+CH2OH=SCH2+H2O 1.000E+12 0.0 0.0 CH2OH+O=CH2O+OH 9.000E+13 0.0 0.0 CH2OH+OH=CH2O+H2O 1.000E+13 0.0 0.0 CH2OH+HO2=CH2O+H2O2 1.210E+13 0.0 0.0 CH2OH+CH2OH=CH3OH+CH2O 4.820E+12 0.0 0.0 CH2OH+CH2OH=CH2O+CH2O+H2 1.000E+15 -0.7 0.0 CH2OH+HCO=CH3OH+CO 1.210E+14 0.0 0.0 CH2OH+CH2O=CH3OH+HCO 5.490E+03 2.8 5900.0 CH2OH+CH3O=CH3OH+CH2O 2.400E+13 0.0 0.0 CH3O+CH3O=CH3OH+CH2O 2.320E+13 0.0 0.0 CH3HCO=CH3+HCO 7.100E+15 0.0 81790.0 CH3HCO+HO2=CH3CO+H2O2 3.000E+12 0.0 12000.0

299 CH3HCO+OH=CH3CO+H2O 2.300E+10 0.73 -1100.0 CH3HCO+O=CH3CO+OH 5.800E+12 0.0 1800.0 CH3HCO+H=CH3CO+H2 4.100E+09 1.16 2400.0 CH3HCO+O2=CH3CO+HO2 3.000E+13 0.0 39200.0 CH3HCO+CH3=CH3CO+CH4 7.600E+00 3.4 3740.0 CH3HCO+H=CH2HCO+H2 7.000E+08 1.5 7400.0 CH3HCO+O=CH2HCO+OH 5.000E+08 1.5 5800.0 CH3HCO+OH=CH2HCO+H2O 2.000E+14 0.0 6000.0 CH3HCO+HO2=CH2HCO+H2O2 3.000E+13 0.0 15000.0 CH3HCO+CH2=CH3CO+CH3 1.660E+12 0.0 3510.0 CH3HCO+CH3=CH2HCO+CH4 1.580E+00 4.0 7720.0 CH3HCO+CH3O=CH3CO+CH3OH 5.000E+12 0.0 0.0 CH3HCO+C2H5=CH3CO+C2H6 1.260E+12 0.0 8500.0 CH3HCO+C2H3=CH3CO+C2H4 8.130E+10 0.0 3680.0 CH2HCO=CH3CO 1.600E+11 0.0 21600.0 CH3HCO+CH2HCO=CH3CO+CH3HCO 3.000E+12 0.0 11200.0 CH3CO(+M)=CH3+CO(+M) 2.800E+13 0.0 17150.0 LOW /6.0E+15 0.0 14070.0/ TROE /0.5 100000 10/ H2/2.5/ H2O/6.2/ CO/1.875/ CO2/3.75/ AR/0.88/ CH4/3.2/ CH3OH/7.5/ CH3CO+H=CH2CO+H2 1.150E+13 0.0 0.0 CH3CO+H=CH3+HCO 2.150E+13 0.0 0.0 CH3CO+O=CH2CO+OH 4.000E+13 0.0 0.0 CH3CO+O=CH3+CO2 1.500E+14 0.0 0.0 CH3CO+CH3=C2H6+CO 3.300E+13 0.0 0.0 CH3CO+CH3=CH4+CH2CO 6.100E+12 0.0 0.0 CH2HCO+H=CH2CO+H2 2.000E+13 0.0 0.0 CH2HCO+O2=CH2O+OH+CO 1.800E+10 0.0 0.0 CH2HCO+O2=CH2CO+HO2 1.500E+11 0.0 0.0 CH2HCO=CH2CO+H 1.580E+13 0.0 35200.0 C2H5O=CH3+CH2O 1.000E+15 0.0 21600.0 C2H5O+O2=CH3HCO+HO2 3.600E+10 0.0 1090.0 C2H5O=CH3HCO+H 2.000E+14 0.0 23300.0 C2H5O+OH=CH3HCO+H2O 1.000E+14 0.0 0.0 C2H5O+H=CH3HCO+H2 1.000E+14 0.0 0.0 C2H5O+O=CH3HCO+OH 1.210E+14 0.0 0.0 C2H5O+HO2=CH3HCO+H2O2 1.000E+14 0.0 0.0 C2H5O+C2H5O=C2H5OH+CH3HCO 5.000E+13 0.0 0.0 C2H5O+PC2H5O=C2H5OH+CH3HCO 5.000E+13 0.0 0.0 C2H5O+SC2H5O=C2H5OH+CH3HCO 5.000E+13 0.0 0.0 SC2H5O+M=CH3HCO+H+M 5.000E+13 0.0 21860.0 SC2H5O+H=CH3HCO+H2 2.000E+13 0.0 0.0 SC2H5O+OH=CH3HCO+H2O 1.500E+13 0.0 0.0 SC2H5O+O=CH3HCO+OH 9.040E+13 0.0 0.0 SC2H5O+O2=CH3HCO+HO2 8.400E+15 -1.20 0.0 duplicate SC2H5O+O2=CH3HCO+HO2 4.800E+14 0.0 5000.0 duplicate SC2H5O+HO2=CH3HCO+H2O2 1.000E+13 0.0 0.0 SC2H5O+SC2H5O=C2H5OH+CH3HCO 3.500E+13 0.0 0.0 SC2H5O+PC2H5O=C2H5OH+CH3HCO 5.000E+13 0.0 0.0 PC2H5O=SC2H5O 1.000E+11 0.0 27000.0 PC2H5O+PC2H5O=C2H5OH+CH3HCO 3.400E+13 0.0 0.0 C2H5OH=CH2OH+CH3 3.100E+15 0.0 80600.0 C2H5OH+OH=SC2H5O+H2O 3.000E+13 0.0 5960.0 C2H5OH+OH=C2H5O+H2O 1.138E+06 2.0 914.0 C2H5OH+OH=PC2H5O+H2O 2.563E+06 2.06 860.0 C2H5OH+O=SC2H5O+OH 6.000E+05 2.46 1850.0 C2H5OH+O=C2H5O+OH 4.820E+13 0.0 6856.0 C2H5OH+O=PC2H5O+OH 5.000E+12 0.0 4411.0 C2H5OH+H=C2H5+H2O 5.900E+11 0.0 3450.0 C2H5OH+H=SC2H5O+H2 4.400E+12 0.0 4570.0 C2H5OH+HO2=SC2H5O+H2O2 2.000E+13 0.0 17000.0 C2H5OH+CH3=SC2H5O+CH4 4.000E+11 0.0 9700.0 C2H5OH+CH3=PC2H5O+CH4 3.000E+00 4.0 10480.0 C2H5OH+CH3=C2H5O+CH4 8.000E+10 0.0 9400.0 C2H5OH+CH3O=SC2H5O+CH3OH 2.000E+11 0.0 7000.0 C2H5OH+CH2O=C2H5O+CH3O 1.500E+12 0.0 79500.0 C2H5OH+C2H5O=C2H5OH+SC2H5O 2.000E+11 0.0 7000.0 C2H5OH=C2H5+OH 5.000E+16 0.0 91212.0 C2H5OH=C2H4+H2O 1.000E+14 0.0 76706.0 C2H5OH+O2=PC2H5O+HO2 4.000E+13 0.0 50900.0 C2H5OH+O2=SC2H5O+HO2 4.000E+13 0.0 51200.0 C2H5OH+O2=C2H5O+HO2 2.000E+13 0.0 56000.0 C2H5OH+H=PC2H5O+H2 2.000E+12 0.0 9500.0 C2H5OH+H=C2H5O+H2 1.760E+12 0.0 4570.0 C2H5OH+HO2=H2O2+C2H5O 1.000E+11 0.0 15500.0 C2H5OH+HO2=H2O2+PC2H5O 1.000E+11 0.0 12500.0 C2H5OH+C2H5=PC2H5O+C2H6 1.500E+12 0.0 11700.0 C2H5OH+C2H5=SC2H5O+C2H6 4.000E+13 0.0 10000.0 C2H5OH+CH2OH=SC2H5O+CH3OH 4.000E+11 0.0 9700.0

300 C+OH=CO+H 5.000E+13 0.0 0.0 C+O2=CO+O 1.200E+14 0.0 4000.0 C+CH3=C2H2+H 5.000E+13 0.0 0.0 C+CH2=C2H+H 5.000E+13 0.0 0.0 CH2O+CH3O2=HCO+CH3O2H 2.000E+12 0.0 11660.0 CH3O2+H=CH3O+OH 9.600E+13 0.0 0.0 CH3O2+OH=CH3OH+O2 6.000E+13 0.0 0.0 CH3O2+CH3=CH3O+CH3O 2.400E+13 0.0 0.0 CH3O2+CH3O2=>CH2O+CH3OH+O2 2.700E+10 0.0 -780.0 CH3O2+CH3O2=>CH3O+CH3O+O2 2.800E+10 0.0 -780.0 CH3O2+H2O2=CH3O2H+HO2 2.400E+12 0.0 10000.0 CH3O2H=CH3O+OH 6.000E+14 0.0 42300.0 CH3O2+HO2=CH3O2H+O2 2.290E+11 0.0 -1550.0 CH3O2H+OH=CH3O2+H2O 1.150E+12 0.0 -380.0 CH4+CH3O2=CH3+CH3O2H 1.810E+11 0.0 18600.0 C2H6+CH3O2=C2H5+CH3O2H 2.950E+11 0.0 14940.0 CH3OH+CH3O2=CH2OH+CH3O2H 1.810E+12 0.0 13800.0 CH3O2H+O=OH+CH3O2 2.000E+13 0.0 4750.0 CH3CO+O2=CH3CO3 1.000E+10 0.0 -2700.0 CH3HCO+CH3CO3=CH3CO+CH3CO3H 1.200E+11 0.0 4900.0 CH3HCO+C2H5O2=CH3CO+C2H5O2H 1.150E+11 0.0 10000.0 C2H5+O2(+M)=C2H5O2(+M) 2.200E+10 0.772 -570.0 LOW /7.10E+42 -8.24 4270.0 / C2H5O2=C2H4+HO2 5.620E+11 0.0 28900.0 C2H5O2+HO2=C2H5O2H+O2 3.400E+11 0.0 -1300.0 C2H5O2H=C2H5O+OH 4.000E+15 0.0 43000.0 C2H5O2H+O=OH+C2H5O2 2.000E+13 0.0 4750.0 C2H5O2H+OH=C2H5O2+H2O 2.000E+12 0.0 -370.0 CH4+C2H5O2=CH3+C2H5O2H 1.140E+13 0.0 20460.0 CH4+CH3CO3=CH3+CH3CO3H 1.140E+13 0.0 20460.0 C2H4+C2H5O2=C2H3+C2H5O2H 1.000E+12 0.0 25000.0 C2H4+CH3CO3=C2H3+CH3CO3H 3.000E+12 0.0 29000.0 CH3CO3+HO2=CH3CO3H+O2 1.000E+12 0.0 0.0 CH3CO3H=>CH3CO2+OH 1.150E+13 0.0 32550.0 CH3CO3H=>CH3+CO2+OH 2.000E+14 0.0 40150.0 CH3CO3+CH3O2=>CH3CO2+CH3O+O2 1.080E+15 0.0 3600.0 CH3CO3+CH3O2=>CH3CO2H+CH2O+O2 2.470E+09 0.0 -4200.0 CH3CO3+HO2=>CH3CO2+OH+O2 2.590E+11 0.0 -2080.0 CH3CO3+CH3CO3=>CH3CO2+CH3CO2+O2 1.690E+12 0.0 -1060.0 CH3CO2+M=>CH3+CO2+M 8.700E+15 0.0 14400.0 CH3CO2H=CH4+CO2 7.080E+13 0.0 74600.0 CH3CO2H=CH2CO+H2O 4.470E+14 0.0 79800.0 CH3CO2H+OH=CH3CO2+H2O 2.400E+11 0.0 -400.0 CH3OH+C2H5O2=CH2OH+C2H5O2H 6.300E+12 0.0 19360.0 CH3OH+CH3CO3=CH2OH+CH3CO3H 6.300E+12 0.0 19360.0 CH2O+C2H5O2=HCO+C2H5O2H 1.300E+11 0.0 9000.0 CH2O+CH3CO3=HCO+CH3CO3H 1.000E+12 0.0 10560.0 C2H4+CH3O2=C2H3+CH3O2H 1.000E+13 0.0 25000.0 CH3HCO+CH3O2=CH3CO+CH3O2H 1.150E+11 0.0 10000.0 C2H5OH+CH3O2=SC2H5O+CH3O2H 1.000E+13 0.0 10000.0 C2H5+CH3O2=C2H5O+CH3O 2.410E+13 0.0 0.0 C2H4+HO2=C2H4O+OH 2.200E+12 0.0 17200.0 C2H4+CH3O=C2H4O+CH3 1.000E+11 0.0 14500.0 C2H4+CH3O2=C2H4O+CH3O 7.000E+11 0.0 14500.0 C2H4O=>CH3HCOW 1.600E+13 0.0 54300.0 CH3HCOW+M=>CH3HCO+M 1.000E+14 0.0 0.0 CH3HCOW=>CH3+HCO 5.000E+08 0.0 0.0 C2H4O+H=H2+C2H3O 8.000E+13 0.0 9740.0 C2H4O+H=H2O+C2H3 5.000E+09 0.0 5030.0 C2H4O+H=C2H4+OH 9.510E+10 0.0 5030.0 C2H4O+CH2HCO=CH3HCO+C2H3O 1.000E+11 0.0 14000.0 C2H4O+CH3=CH4+C2H3O 1.070E+12 0.0 11900.0 C2H4O+O=OH+C2H3O 1.910E+12 0.0 5300.0 C2H4O+OH=H2O+C2H3O 1.780E+13 0.0 3600.0 C2H3O=>CH2CHOW 1.000E+11 0.0 10000.0 C2H3O=>CH3+CO 8.000E+11 0.0 10000.0 C2H3O+H+M=>C2H4O+M 4.000E+15 0.0 0.0 CH2CHOW+M=>CH2HCO+M 1.000E+14 0.0 0.0 CH2CHOW=>CH3+CO 1.000E+08 0.0 0.0 CH2CHOW=>OH+C2H2 1.000E+11 0.0 17000.0 CH2CHOW=>CH2CO+H 1.000E+08 0.0 0.0 C2H4O+O2=HO2+C2H3O 1.000E+14 0.0 52000.0 C2H4O+HO2=H2O2+C2H3O 5.000E+13 0.0 18000.0 CH3HCOW+O2=>HO2+CH3CO 1.000E+14 0.0 0.0 CH2CHOW+O2=>HO2+CH2CO 1.000E+14 0.0 0.0 CH2+C2H2=H+C3H3 1.200E+13 0.0 6620.0 CH2+C2H4=C3H6 3.160E+12 0.0 5280.0 SCH2+C2H4=>C3H6 1.000E+14 0.0 0.0 CH2+C3H8=CH3+IC3H7 1.500E+00 3.46 7470.0 CH2+C3H8=CH3+NC3H7 9.000E-01 3.65 7150.0 SCH2+C2H2=C3H3+H 1.800E+14 0.0 0.0 C2H3+CH2=C3H4+H 3.000E+13 0.0 0.0

301 C2H3+C2H2=C4H4+H 1.930E+12 0.0 6000.0 C2H3+C2H3=C4H6 7.230E+13 0.0 0.0 C2H2+CH3=SC3H5 1.610E+40 -8.58 20331.0 C2H2+CH3=C3H5 2.610E+46 -9.82 36951.0 C2H2+CH3=C3H4+H 6.740E+19 -2.08 31591.0 CH2CO+C2H3=C3H5+CO 1.000E+12 0.0 3000.0 HCCO+C2H2=C3H3+CO 1.000E+11 0.0 3000.0 C3H8(+M)=C2H5+CH3(+M) 1.100E+17 0.0 84400.0 LOW /7.83E+18 0.0 65000.0/ C3H8+O2=NC3H7+HO2 4.000E+13 0.0 50870.0 C3H8+O2=IC3H7+HO2 4.000E+13 0.0 47690.0 C3H8+HO2=NC3H7+H2O2 4.760E+04 2.55 16490.0 C3H8+HO2=IC3H7+H2O2 9.640E+03 2.6 13910.0 C3H8+OH=NC3H7+H2O 3.160E+07 1.80 934.0 C3H8+OH=IC3H7+H2O 7.060E+06 1.90 -159.0 C3H8+O=NC3H7+OH 3.715E+06 2.4 5505.0 C3H8+O=IC3H7+OH 5.495E+05 2.5 3140.0 C3H8+H=NC3H7+H2 1.336E+06 2.54 6756.0 C3H8+H=IC3H7+H2 1.300E+06 2.4 4470.0 C3H8+CH3=NC3H7+CH4 9.000E-01 3.65 7150.0 C3H8+CH3=IC3H7+CH4 1.500E+00 3.46 5480.0 C3H8+C2H5=NC3H7+C2H6 9.000E-01 3.65 9140.0 C3H8+C2H5=IC3H7+C2H6 1.200E+00 3.46 7470.0 C3H8+C2H3=NC3H7+C2H4 6.000E+02 3.3 10502.0 C3H8+C2H3=IC3H7+C2H4 1.000E+03 3.1 8829.0 C3H8+IC3H7=NC3H7+C3H8 8.440E-03 4.2 8720.0 C3H8+C3H5=NC3H7+C3H6 2.350E+02 3.3 19800.0 C3H8+C3H5=IC3H7+C3H6 7.840E+01 3.3 18200.0 C3H8+CH3O=NC3H7+CH3OH 4.340E+11 0.0 6460.0 C3H8+CH3O=IC3H7+CH3OH 1.450E+11 0.0 4570.0 NC3H7=C2H4+CH3 1.260E+13 0.0 30404.0 NC3H7+O2=C3H6+HO2 1.000E+12 0.0 5000.0 IC3H7=C2H4+CH3 1.000E+12 0.0 34500.0 IC3H7+O2=C3H6+HO2 2.754E+10 0.0 -2151.0 C3H6=C3H5+H 4.570E+14 0.0 88900.0 C3H6=SC3H5+H 7.590E+14 0.0 101300.0 C3H6=TC3H5+H 1.450E+15 0.0 98060.0 C3H6=C2H3+CH3 1.100E+21 -1.2 97720.0 C3H6+HO2=C3H6O+OH 1.050E+12 0.0 14210.0 C3H6+HO2=C3H5+H2O2 9.640E+03 2.6 13910.0 C3H6+HO2=SC3H5+H2O2 7.500E+09 0.0 12570.0 C3H6+HO2=TC3H5+H2O2 3.000E+09 0.0 9930.0 C3H6+OH=C3H5+H2O 3.120E+06 2.0 -300.0 C3H6+OH=SC3H5+H2O 2.140E+06 2.0 2780.0 C3H6+OH=TC3H5+H2O 1.110E+06 2.0 1450.0 C3H6+O=C2H5+HCO 6.833E+06 1.57 -628.0 C3H6+O=CH3+CH3CO 9.111E+06 1.57 -628.0 C3H6+O=C2H4+CH2O 4.555E+06 1.57 -628.0 NC3H7=C3H6+H 1.000E+14 0.0 37286.0 C3H6+H=IC3H7 5.704E+09 1.16 874.0 C3H6+H=C3H5+H2 6.457E+12 0.0 4445.0 C3H6+H=SC3H5+H2 7.810E+05 2.5 12280.0 C3H6+O2=SC3H5+HO2 1.950E+12 0.0 39000.0 C3H6+O2=TC3H5+HO2 1.950E+12 0.0 39000.0 C3H6+O2=C3H5+HO2 1.950E+12 0.0 39000.0 C3H6+CH3=C3H5+CH4 2.210E+00 3.5 5680.0 C3H6+CH3=SC3H5+CH4 1.350E+00 3.5 12850.0 C3H6+CH3=TC3H5+CH4 8.400E-01 3.5 11660.0 C3H6+C2H5=C3H5+C2H6 2.230E+00 3.5 6640.0 C3H6O=C2H5+HCO 2.450E+13 0.0 58500.0 C3H6O=C2H5CHO 1.820E+14 0.0 58500.0 C3H6O=CH3+CH3CO 4.540E+13 0.0 59900.0 C3H6O=CH3+CH2HCO 2.450E+13 0.0 58820.0 C3H6O=CH3+C2H3O 8.000E+15 0.0 92010.0 C2H5CHO=C2H5+HCO 2.450E+16 0.0 73000.0 C2H5CHO+O=C2H5CO+OH 5.680E+12 0.0 1540.0 C2H5CHO+OH=C2H5CO+H2O 1.210E+13 0.0 0.0 C2H5CHO+HO2=C2H5CO+H2O2 1.520E+09 0.0 0.0 C2H5CHO+C2H5=C2H5CO+C2H6 5.000E+10 0.0 6290.0 C2H5CO=C2H5+CO 5.890E+12 0.0 14400.0 C3H5+O2=>CH2O+CH2HCO 5.000E+12 0.0 19190.0 C3H5+H=C3H4+H2 1.800E+13 0.0 0.0 C3H5+O=>C2H4+CO+H 1.807E+14 0.0 0.0 C3H5+CH3=C3H4+CH4 3.000E+12 -0.32 -130.0 C3H5+C2H5=C3H4+C2H6 9.640E+11 0.0 -130.0 C3H5+C2H3=C3H4+C2H4 2.400E+12 0.0 0.0 C3H5+C2H3=C3H6+C2H2 4.800E+12 0.0 0.0 SC3H5+O2=CH3HCO+HCO 4.340E+12 0.0 0.0 SC3H5+HO2=>CH2CO+CH3+OH 4.500E+12 0.0 0.0 SC3H5+H=C3H4+H2 3.333E+12 0.0 0.0 SC3H5+O=>CH2CO+CH3 1.807E+14 0.0 0.0 SC3H5+CH3=C3H4+CH4 1.000E+11 0.0 0.0

302 SC3H5+C2H5=C3H4+C2H6 1.000E+11 0.0 0.0 SC3H5+C2H3=C3H4+C2H4 1.000E+11 0.0 0.0 TC3H5+O2=CH3CO+CH2O 4.335E+11 0.0 0.0 TC3H5+HO2=>CH2CO+CH3+OH 4.500E+12 0.0 0.0 TC3H5+H=C3H4+H2 3.333E+12 0.0 0.0 TC3H5+O=>HCCO+CH3+H 1.807E+14 0.0 0.0 TC3H5+CH3=C3H4+CH4 1.000E+11 0.0 0.0 TC3H5+C2H5=C3H4+C2H6 1.000E+11 0.0 0.0 TC3H5+C2H3=C3H4+C2H4 1.000E+11 0.0 0.0 C3H4+M=C3H3+H+M 2.000E+18 0.0 80000.0 H2O/16.0/ CO2/3.75/ CO/1.875/ H2/2.5/ CH4/3.0/ C3H6/16.0/ C2H4/16.0/ C3H8/16.0/ C3H4(+M)=PC3H4(+M) 1.070E+14 0.0 64300.0 LOW /3.48E+17 0.0 48390.0/ C3H4+O2=C3H3+HO2 4.000E+13 0.0 61500.0 C3H4+HO2=>CH2CO+CH2+OH 8.000E+12 0.0 19000.0 C3H4+OH=CH2CO+CH3 3.120E+12 0.0 -397.0 C3H4+OH=C3H3+H2O 2.000E+07 2.0 1000.0 C3H4+O=C2H3+HCO 1.100E-02 4.613 -4243.0 C3H4+H=C3H5 1.200E+11 0.69 3000.0 C3H4+H=TC3H5 8.500E+12 0.0 2000.0 C3H4+H=C3H3+H2 2.000E+07 2.0 5000.0 C3H4+CH3=C3H3+CH4 2.000E+11 0.0 7700.0 PC3H4+M=C3H3+H+M 4.700E+18 0.0 80000.0 H2O/16.0/ CO2/3.75/ CO/1.875/ H2/2.5/ CH4/3.0/ C3H6/16.0/ C2H4/16.0/ C3H8/16.0/ PC3H4+O2=>HCCO+OH+CH2 2.000E+08 1.5 30100.0 PC3H4+O2=C3H3+HO2 5.000E+12 0.0 51000.0 PC3H4+HO2=>C2H4+CO+OH 3.000E+12 0.0 19000.0 PC3H4+OH=C3H3+H2O 2.000E+07 2.0 1000.0 PC3H4+OH=CH2CO+CH3 5.000E-04 4.5 -1000.0 PC3H4+O=CH2CO+CH2 6.400E+12 0.0 2010.0 PC3H4+O=C2H3+HCO 3.200E+12 0.0 2010.0 PC3H4+O=HCCO+CH3 6.300E+12 0.0 2010.0 PC3H4+O=>HCCO+CH2+H 3.200E+11 0.0 2010.0 PC3H4+H=TC3H5 6.500E+12 0.0 2000.0 PC3H4+H=C3H3+H2 2.000E+07 2.0 5000.0 PC3H4+H=C2H2+CH3 1.300E+05 2.5 1000.0 PC3H4+CH3=C3H3+CH4 1.500E+00 3.5 5600.0 PC3H4+C2H3=C3H3+C2H4 1.000E+12 0.0 7700.0 PC3H4+C3H5=C3H3+C3H6 1.000E+12 0.0 7700.0 C3H3+H=C3H2+H2 5.000E+13 0.0 3000.0 C3H3+O=>C2H+HCO+H 7.000E+13 0.0 0.0 C3H3+O=>C2H2+CO+H 7.000E+13 0.0 0.0 C3H3+OH=C3H2+H2O 1.000E+13 0.0 0.0 C3H3+O2=CH2CO+HCO 3.010E+10 0.0 2870.0 C3H3+CH=IC4H3+H 7.000E+13 0.0 0.0 C3H3+CH=NC4H3+H 7.000E+13 0.0 0.0 C3H3+CH2=C4H4+H 4.000E+13 0.0 0.0 C3H3+C3H3=C6H5+H 2.000E+12 0.0 0.0 CH+C2H2=C3H2+H 1.000E+14 0.0 0.0 C3H2+O2=HCCO+CO+H 1.000E+14 0.0 3000.0 C3H2+OH=C2H2+HCO 5.000E+13 0.0 0.0 C3H2+CH2=IC4H3+H 3.000E+13 0.0 0.0 C4H8=IC4H7+H 4.078E+18 -1.0 97350.0 C4H8=C2C4H8 4.000E+11 0.0 60000.0 C4H8=T2C4H8 4.000E+11 0.0 60000.0 C4H8=C3H5+CH3 1.000E+16 0.0 73000.0 C4H8=C2H3+C2H5 1.000E+19 -1.0 96770.0 C4H8+O2=IC4H7+HO2 4.000E+12 0.0 33200.0 C4H8+HO2=IC4H7+H2O2 1.000E+11 0.0 17060.0 C4H8+OH=NC3H7+CH2O 6.500E+12 0.0 0.0 C4H8+OH=CH3HCO+C2H5 1.000E+11 0.0 0.0 C4H8+OH=C2H6+CH3CO 1.000E+10 0.0 0.0 C4H8+OH=IC4H7+H2O 2.250E+13 0.0 2217.0 C4H8+O=C3H6+CH2O 2.505E+12 0.0 0.0 C4H8+O=CH3HCO+C2H4 1.250E+12 0.0 850.0 C4H8+O=C2H5+CH3CO 1.625E+13 0.0 850.0 C4H8+O=IC4H7+OH 9.600E+12 0.0 1970.0 C4H8+O=NC3H7+HCO 1.800E+05 2.5 -1029.0 C4H8+H=IC4H7+H2 5.000E+13 0.0 3900.0 C4H8+CH3=IC4H7+CH4 1.000E+11 0.0 7300.0 C4H8+C2H5=IC4H7+C2H6 1.000E+11 0.0 8000.0 C4H8+C3H5=IC4H7+C3H6 7.900E+10 0.0 12400.0 C4H8+SC3H5=IC4H7+C3H6 8.000E+10 0.0 12400.0 C4H8+TC3H5=IC4H7+C3H6 8.000E+10 0.0 12400.0 C2C4H8=T2C4H8 4.000E+13 0.0 62000.0 C2C4H8=C4H6+H2 1.000E+13 0.0 65500.0 C2C4H8=IC4H7+H 4.074E+18 -1.0 97350.0 C2C4H8=SC3H5+CH3 2.000E+16 0.0 95000.0 C2C4H8+OH=IC4H7+H2O 1.250E+14 0.0 3060.0 C2C4H8+OH=CH3HCO+C2H5 1.400E+13 0.0 0.0 C2C4H8+O=IC3H7+HCO 6.030E+12 0.0 0.0 C2C4H8+O=CH3HCO+C2H4 1.000E+12 0.0 0.0

303 C2C4H8+H=IC4H7+H2 1.000E+13 0.0 3500.0 C2C4H8+CH3=IC4H7+CH4 1.000E+11 0.0 8200.0 T2C4H8=IC4H7+H 4.074E+18 -1.0 97350.0 T2C4H8=SC3H5+CH3 2.000E+16 0.0 96000.0 T2C4H8+OH=IC4H7+H2O 1.000E+14 0.0 3060.0 T2C4H8+OH=CH3HCO+C2H5 1.500E+13 0.0 0.0 T2C4H8+O=IC3H7+HCO 6.030E+12 0.0 0.0 T2C4H8+O=CH3HCO+C2H4 1.000E+12 0.0 0.0 T2C4H8+H=IC4H7+H2 5.000E+12 0.0 3500.0 T2C4H8+CH3=IC4H7+CH4 1.000E+11 0.0 8200.0 IC4H7=C4H6+H 1.200E+14 0.0 49300.0 IC4H7=C2H4+C2H3 1.000E+14 0.0 49000.0 IC4H7+H=C4H6+H2 3.160E+12 0.0 0.0 IC4H7+O2=C4H6+HO2 1.000E+11 0.0 0.0 IC4H7+CH3=C4H6+CH4 1.000E+13 0.0 0.0 IC4H7+C2H3=C4H6+C2H4 4.000E+12 0.0 0.0 IC4H7+C2H5=C4H6+C2H6 4.000E+12 0.0 0.0 IC4H7+C2H5=C4H8+C2H4 5.000E+11 0.0 0.0 IC4H7+C2H5=T2C4H8+C2H4 5.000E+11 0.0 0.0 IC4H7+C2H5=C2C4H8+C2H4 5.000E+11 0.0 0.0 IC4H7+C3H5=C4H6+C3H6 4.000E+13 0.0 0.0 IC4H7+IC4H7=C4H6+C4H8 3.160E+12 0.0 0.0 C2H3+C2H4=C4H6+H 3.000E+12 0.0 1000.0 C4H6+H=NC4H5+H2 3.000E+07 2.0 13000.0 C4H6+H=IC4H5+H2 3.000E+07 2.0 6000.0 C4H6+OH=NC4H5+H2O 2.000E+07 2.0 5000.0 C4H6+OH=IC4H5+H2O 2.000E+07 2.0 2000.0 C4H6+O=C2H4+CH2CO 1.000E+12 0.0 0.0 C4H6+O=PC3H4+CH2O 1.000E+12 0.0 0.0 C2H2+NC4H5=C6H6+H 2.800E+03 2.9 1400.0 NC4H5+OH=C4H4+H2O 2.000E+07 2.0 1000.0 NC4H5+H=C4H4+H2 3.000E+07 2.0 1000.0 NC4H5+H=IC4H5+H 1.000E+14 0.0 0.0 IC4H5=C4H4+H 2.000E+15 0.0 45000.0 NC4H5=C4H4+H 1.600E+14 0.0 41400.0 C4H4+OH=IC4H3+H2O 1.000E+07 2.0 2000.0 C4H4+OH=NC4H3+H2O 7.500E+06 2.0 5000.0 C4H4+H=NC4H3+H2 2.000E+07 2.0 15000.0 NC4H3+H=IC4H3+H 1.000E+14 0.0 0.0 IC4H3+CH2=C3H4+C2H 2.000E+13 0.0 0.0 IC4H3+O2=CH2CO+HCCO 1.000E+12 0.0 0.0 IC4H3+OH=C4H2+H2O 3.000E+13 0.0 0.0 IC4H3+O=CH2CO+C2H 2.000E+13 0.0 0.0 IC4H3+H=C4H2+H2 5.000E+13 0.0 0.0 NC4H3+C2H2=C6H5 2.800E+03 2.9 1400.0 NC4H3+M=C4H2+H+M 1.000E+16 0.0 59700.0 H2O/16.0/ CO2/3.75/ CO/1.875/ H2/2.5/ CH4/3.0/ C3H6/16.0/ C2H4/16.0/ C3H8/16.0/ IC4H3+M=C4H2+H+M 4.460E+15 0.0 46516.0 H2O/16.0/ CO2/3.75/ CO/1.875/ H2/2.5/ CH4/3.0/ C3H6/16.0/ C2H4/16.0/ C3H8/16.0/ IC4H3+O=H2C4O+H 2.000E+13 0.0 0.0 H2C4O+H=C2H2+HCCO 5.000E+13 0.0 3000.0 H2C4O+OH=CH2CO+HCCO 1.000E+07 2.0 2000.0 C4H2+OH=H2C4O+H 6.660E+12 0.0 -410.0 C2H2+C2H2=IC4H3+H 2.200E+12 0.0 64060.0 C2H2+C2H2=NC4H3+H 1.000E+12 0.0 66000.0 C2H2+C2H2=C4H4 5.500E+12 0.0 37000.0 C4H2(+M)=C4H+H(+M) 2.200E+14 0.0 116740.0 LOW /3.50E+17 0.0 80065.0/ H2O /16.0/ H2 /2.5/ CO /1.875/ CO2 /3.75/ CH4 /3.0/ C3H6 /16.0/ C2H4 /16.0/ C3H8 /16.0/ C4H2+O=C3H2+CO 2.700E+13 0.0 1720.0 C2H2+C2H=C4H2+H 1.820E+14 0.0 467.0 C2H2+C2H=NC4H3 1.000E+13 0.0 0.0 C4H+O2=C2H+CO+CO 1.000E+14 0.0 0.0 C2O+H=CH+CO 1.320E+13 0.0 0.0 C2O+O=CO+CO 5.200E+13 0.0 0.0 C2O+OH=CO+CO+H 2.000E+13 0.0 0.0 C2O+O2=CO+CO+O 2.000E+13 0.0 0.0 C2O+O2=CO+CO2 2.000E+13 0.0 0.0 C2+H2=C2H+H 6.600E+13 0.0 7950.0 C2+O=C+CO 3.600E+14 0.0 0.0 C2+O2=CO+CO 9.000E+12 0.0 980.0 C2+OH=C2O+H 5.000E+13 0.0 0.0 C6H5+OH=C6H5O+H 5.000E+13 0.0 0.0 C6H5+O2=C6H5O+O 2.600E+13 0.0 6120.0 C6H5+HO2=C6H5O+OH 5.000E+13 0.0 1000.0 C6H6+H=C6H5+H2 3.000E+12 0.0 8100.0 C6H6+OH=C6H5+H2O 1.680E+08 1.42 1450.0 C6H6+O=C6H5O+H 2.780E+13 0.0 4910.0 C6H6+O2=C6H5O+OH 4.000E+13 0.0 34000.0 H+C6H5=C6H6 7.800E+13 0.0 0.0 C3H3+O=>C2H3+CO 3.800E+13 0.0 0.0

304 C3H3+O=CH2O+C2H 2.000E+13 0.0 0.0 C3H3+O2=>HCCO+CH2O 6.000E+12 0.0 0.0 C3H3+CH3=C2H5+C2H 1.000E+13 0.0 37500.0 C3H3+CH3=C4H6 5.000E+12 0.0 0.0 C3H6+C2H3=C3H5+C2H4 2.210E+00 3.5 4680.0 C3H6+C2H3=SC3H5+C2H4 1.350E+00 3.5 10860.0 C3H6+C2H3=TC3H5+C2H4 8.400E-01 3.5 9670.0 C3H6+CH3O=C3H5+CH3OH 9.000E+01 2.95 12000.0 CH2+C2H2=C3H4 1.200E+13 0.0 6620.0 C3H4+C3H4=C3H5+C3H3 5.000E+14 0.0 64700.0 C3H4+OH=CH2O+C2H3 1.700E+12 0.0 -300.0 C3H4+OH=HCO+C2H4 1.700E+12 0.0 -300.0 C3H4+O=CH2O+C2H2 1.000E+12 0.0 0.0 C3H4+O=>CO+C2H4 7.800E+12 0.0 1600.0 C3H4+C3H5=C3H3+C3H6 2.000E+12 0.0 7700.0 C3H4+C2H=C3H3+C2H2 1.000E+13 0.0 0.0 PC3H4=C2H+CH3 4.200E+16 0.0 100000.0 PC3H4+C2H=C3H3+C2H2 1.000E+13 0.0 0.0 C3H2+O2=HCO+HCCO 1.000E+13 0.0 0.0 C2H2+C2H3=NC4H5 2.510E+05 1.9 2100.0 C2H3+C2H3=IC4H5+H 4.000E+13 0.0 0.0 IC4H5+H=C4H4+H2 3.000E+07 2.0 1000.0 C4H2+H=C4H+H2 1.000E+14 0.0 35000.0 C4H6+OH=C3H5+CH2O 7.230E+12 0.0 -994.0 C4H8+IC4H7=IC4H7+C2C4H8 3.980E+10 0.0 12400.0 C4H8+IC4H7=IC4H7+T2C4H8 3.980E+10 0.0 12400.0 C3H3+C3H3=C6H6 3.000E+11 0.0 0.0 C3H3+C3H4=C6H6+H 1.400E+12 0.0 10000.0 C3H5+C2H5=C3H6+C2H4 2.600E+12 0.0 -130.0 C3H6+OH=C2H5+CH2O 8.000E+12 0.0 0.0 C3H6+OH=CH3+CH3HCO 3.400E+11 0.0 0.0 C3H5+O2=C3H4+HO2 1.200E+12 0.0 13550.0 CH2O+C3H5=HCO+C3H6 8.000E+10 0.0 12400.0 CH3HCO+C3H5=CH3CO+C3H6 3.800E+11 0.0 7200.0 C3H8+CH3O2=NC3H7+CH3O2H 6.030E+12 0.0 19380.0 C3H8+CH3O2=IC3H7+CH3O2H 1.990E+12 0.0 17050.0 C3H8+C2H5O2=NC3H7+C2H5O2H 6.030E+12 0.0 19380.0 C3H8+C2H5O2=IC3H7+C2H5O2H 1.990E+12 0.0 17050.0 C3H8+IC3H7O2=NC3H7+IC3H7O2H 6.030E+12 0.0 19380.0 C3H8+IC3H7O2=IC3H7+IC3H7O2H 1.990E+12 0.0 17050.0 C3H8+NC3H7O2=NC3H7+NC3H7O2H 6.030E+12 0.0 19380.0 C3H8+NC3H7O2=IC3H7+NC3H7O2H 1.990E+12 0.0 17050.0 NC3H7+O2=NC3H7O2 4.820E+12 0.0 0.0 IC3H7+O2=IC3H7O2 6.620E+12 0.0 0.0 NC3H7+HO2=NC3H7O+OH 3.200E+13 0.0 0.0 IC3H7+HO2=IC3H7O+OH 3.200E+13 0.0 0.0 NC3H7+CH3O2=NC3H7O+CH3O 3.800E+12 0.0 -1200.0 IC3H7+CH3O2=IC3H7O+CH3O 3.800E+12 0.0 -1200.0 NC3H7+NC3H7O2=NC3H7O+NC3H7O 3.800E+12 0.0 -1200.0 IC3H7+NC3H7O2=IC3H7O+NC3H7O 3.800E+12 0.0 -1200.0 NC3H7+IC3H7O2=NC3H7O+IC3H7O 3.800E+12 0.0 -1200.0 IC3H7+IC3H7O2=IC3H7O+IC3H7O 3.800E+12 0.0 -1200.0 NC3H7O2+HO2=NC3H7O2H+O2 4.600E+10 0.0 -2600.0 IC3H7O2+HO2=IC3H7O2H+O2 4.600E+10 0.0 -2600.0 CH3+NC3H7O2=CH3O+NC3H7O 3.800E+12 0.0 -1200.0 CH3+IC3H7O2=CH3O+IC3H7O 3.800E+12 0.0 -1200.0 NC3H7O2H=NC3H7O+OH 4.000E+15 0.0 43000.0 IC3H7O2H=IC3H7O+OH 4.000E+15 0.0 43000.0 NC3H7O=C2H5+CH2O 5.000E+13 0.0 15700.0 IC3H7O=CH3+CH3HCO 4.000E+14 0.0 17200.0 C3H6+OH(+M)=C3H6OH(+M) 1.810E+13 0.0 0.0 LOW /1.33E+30 -3.5 0.0/ C3H6OH=>C2H5+CH2O 1.400E+09 0.0 17200.0 C3H6OH=>CH3+CH3HCO 1.000E+09 0.0 17200.0 C3H6OH+O2=O2C3H6OH 1.000E+12 0.0 -1100.0 O2C3H6OH=>CH3HCO+CH2O+OH 1.000E+16 0.0 25000.0 C3H6+CH3O2=C3H5+CH3O2H 2.000E+12 0.0 17000.0 C3H6+CH3O2=C3H6O+CH3O 4.000E+11 0.0 11720.0 C3H6+C2H5O2=C3H5+C2H5O2H 3.200E+11 0.0 14900.0 C3H6+C3H5O2=C3H5+C3H5O2H 3.200E+11 0.0 14900.0 C3H6+C3H5O2=C3H6O+C3H5O 1.050E+11 0.0 14200.0 C3H6+CH3CO3=C3H5+CH3CO3H 3.200E+11 0.0 14900.0 C3H6+NC3H7O2=C3H5+NC3H7O2H 3.200E+11 0.0 14900.0 C3H6+IC3H7O2=C3H5+IC3H7O2H 3.200E+11 0.0 14900.0 C3H6+NC3H7O2=C3H6O+NC3H7O 1.700E+07 0.0 0.0 C3H5+O2=C3H5O2 1.200E+10 0.0 -2300.0 C3H5+HO2=C3H5O+OH 9.000E+12 0.0 0.0 C3H5+CH3O2=C3H5O+CH3O 3.800E+11 0.0 -1200.0 C3H5O2+CH3=C3H5O+CH3O 3.800E+11 0.0 -1200.0 C3H5O2+C3H5=C3H5O+C3H5O 3.800E+11 0.0 -1200.0 C3H5O2+HO2=C3H5O2H+O2 4.600E+10 0.0 -2600.0 C3H5O2+HO2=>C3H5O+OH+O2 1.000E+12 0.0 0.0

305 C3H5O2+CH3O2=>C3H5O+CH3O+O2 1.700E+11 0.0 -1000.0 C3H5O2+C3H5O2=>C3H5O+C3H5O+O2 3.700E+12 0.0 2200.0 C3H5O=CH2O+C2H3 1.000E+14 0.0 21600.0 C3H5O2H=C3H5O+OH 4.000E+15 0.0 43000.0 CH2O+C3H5O2=HCO+C3H5O2H 1.300E+11 0.0 10500.0 CH2O+NC3H7O2=HCO+NC3H7O2H 1.300E+11 0.0 9000.0 CH2O+IC3H7O2=HCO+IC3H7O2H 1.300E+11 0.0 9000.0 C2H4+NC3H7O2=C2H3+NC3H7O2H 7.100E+11 0.0 25000.0 C2H4+IC3H7O2=C2H3+IC3H7O2H 7.100E+11 0.0 25000.0 CH4+C3H5O2=CH3+C3H5O2H 1.140E+13 0.0 20460.0 CH4+NC3H7O2=CH3+NC3H7O2H 1.140E+13 0.0 20460.0 CH4+IC3H7O2=CH3+IC3H7O2H 1.140E+13 0.0 20460.0 CH3OH+NC3H7O2=CH2OH+NC3H7O2H 6.300E+12 0.0 19360.0 CH3OH+IC3H7O2=CH2OH+IC3H7O2H 6.300E+12 0.0 19360.0 CH3HCO+C3H5O2=CH3CO+C3H5O2H 1.150E+11 0.0 10000.0 CH3HCO+NC3H7O2=CH3CO+NC3H7O2H 1.150E+11 0.0 10000.0 CH3HCO+IC3H7O2=CH3CO+IC3H7O2H 1.150E+11 0.0 10000.0 C+N2+M=CNN+M 1.120E+15 0.0 0.0 C2H+NO=HCN+CO 6.000E+13 0.0 570.0 C2H+HCN=CN+C2H2 3.200E+12 0.0 1530.0 CH2+NO=HCN+OH 5.000E+11 0.0 2870.0 HCN+M=H+CN+M 3.570E+26 -2.6 124900.0 C2N2+M=CN+CN+M 3.200E+16 0.0 94400.0 CN+N2O=CNN+NO 6.000E+13 0.0 15360.0 DUPLICATE CN+N2O=CNN+NO 1.800E+10 0.0 1450.0 DUPLICATE CH+N2(+M)=HCNN(+M) 3.100E+12 0.15 0.0 LOW / 1.30E+25 -3.16 740.0 / TROE /0.667 235.0 2117.0 4536.0 / H2O/10.0/ O2/2.0/ AR/0.75/ H2/2.0/ HCNN+H=H2+CNN 5.000E+13 0.0 0.0 HCNN+H=>CH2+N2 2.000E+13 0.0 3000.0 HCNN+O=OH+CNN 2.000E+13 0.0 20000.0 HCNN+O=CO+H+N2 5.000E+13 0.0 15000.0 HCNN+O=HCN+NO 5.000E+13 0.0 15000.0 HCNN+OH=H2O+CNN 1.000E+13 0.0 8000.0 HCNN+OH=H+HCO+N2 1.000E+13 0.0 16000.0 HCNN+O2=HO2+CNN 1.000E+12 0.0 4000.0 HCNN+O2=>H+CO2+N2 4.000E+12 0.0 0.0 HCNN+O2=HCO+N2O 4.000E+12 0.0 0.0 CNN+O=CO+N2 1.000E+13 0.0 0.0 CNN+O=CN+NO 1.000E+14 0.0 20000.0 CNN+OH=H+CO+N2 1.000E+13 0.0 1000.0 CNN+H=NH+CN 5.000E+14 0.0 40000.0 CNN+OH=HCN+NO 1.000E+12 0.0 1000.0 CNN+H=HCN+N 5.000E+13 0.0 25000.0 CNN+O2=NO+NCO 1.000E+13 0.0 5000.0 HNO+CH3=NO+CH4 8.200E+05 1.87 954.0 HONO+CH3=NO2+CH4 8.100E+05 1.87 5504.0 H2NO+CH3=CH3O+NH2 2.000E+13 0.0 0.0 H2NO+CH3=HNO+CH4 1.600E+06 1.87 2960.0 HNOH+CH3=HNO+CH4 1.600E+06 1.87 2096.0 NH2OH+CH3=HNOH+CH4 1.600E+06 1.87 6350.0 NH2OH+CH3=H2NO+CH4 8.200E+05 1.87 5500.0 N2H2+CH3=NNH+CH4 1.600E+06 1.87 2970.0 N2H3+CH3=N2H2+CH4 8.200E+05 1.87 1818.0 N2H4+CH3=N2H3+CH4 3.300E+06 1.87 5325.0 CH4+NH=CH3+NH2 9.000E+13 0.0 20080.0 CH4+NH2=CH3+NH3 1.200E+13 0.0 15150.0 CH3+NH2=CH2+NH3 1.600E+06 1.87 7570.0 C2H6+NH=C2H5+NH2 7.000E+13 0.0 16700.0 C2H6+NH2=C2H5+NH3 9.700E+12 0.0 11470.0 C3H8+NH2=NC3H7+NH3 1.700E+13 0.0 10660.0 C3H8+NH2=IC3H7+NH3 4.500E+11 0.0 6150.0 CH3+NO(+M)=CH3NO(+M) 1.000E+13 0.0 0.0 LOW /1.90E+18 0.0 0.0/ SRI /0.03 -790.0 1.0/ CH3NO+H=H2CNO+H2 4.400E+08 1.5 377.0 CH3NO+H=CH3+HNO 1.800E+13 0.0 2800.0 CH3NO+O=H2CNO+OH 3.300E+08 1.5 3615.0 CH3NO+O=CH3+NO2 1.700E+06 2.08 0.0 CH3NO+OH=H2CNO+H2O 3.600E+06 2.0 -1192.0 CH3NO+OH=CH3+HONO 2.500E+12 0.0 1000.0 CH3NO+CH3=H2CNO+CH4 7.900E+05 1.87 5415.0 CH3NO+NH2=H2CNO+NH3 2.800E+06 1.94 1073.0 H2CNO=HNCO+H 2.300E+42 -9.11 53840.0 H2CNO+O2=CH2O+NO2 2.900E+12 -0.31 17700.0 H2CNO+H=CH3+NO 4.000E+13 0.0 0.0 H2CNO+H=HCNO+H2 4.800E+08 1.5 -894.0 H2CNO+O=HCNO+OH 3.300E+08 1.5 -894.0

306 H2CNO+O=CH2O+NO 7.000E+13 0.0 0.0 H2CNO+OH=CH2OH+NO 4.000E+13 0.0 0.0 H2CNO+OH=HCNO+H2O 2.400E+06 2.0 -1192.0 H2CNO+CH3=C2H5+NO 3.000E+13 0.0 0.0 H2CNO+CH3=HCNO+CH4 1.600E+06 1.87 -1113.0 H2CNO+NH2=HCNO+NH3 1.800E+06 1.94 -1152.0 CH3+NO2=CH3O+NO 1.400E+13 0.0 0.0 CH+NO2=HCO+NO 1.200E+14 0.0 0.0 CH2+NO2=CH2O+NO 4.200E+13 0.0 0.0 CN+NO=N2+CO 1.000E+11 0.0 0.0 HNCO+M=H+NCO+M 5.000E+15 0.0 120000.0 HNCO+N=NH+NCO 4.000E+13 0.0 36000.0 CH3O+HNO=CH3OH+NO 3.160E+13 0.0 0.0 NCO+HO2=HNCO+O2 2.000E+13 0.0 0.0 N2O+CO=CO2+N2 2.510E+14 0.0 46000.0 N2O+CH2=CH2O+N2 1.000E+12 0.0 0.0 N2O+CH3=CH3O+N2 9.000E+09 0.0 0.0 N2O+HCO=CO2+H+N2 1.700E+14 0.0 20000.0 N2O+HCCO=CO+HCO+N2 1.700E+14 0.0 25500.0 N2O+C2H2=HCCO+H+N2 6.590E+16 0.0 61200.0 N2O+C2H3=CH2HCO+N2 1.000E+11 0.0 0.0 HOCN+O=NCO+OH 1.500E+04 2.64 4000.0 HOCN+H=NCO+H2 2.000E+07 2.0 2000.0 HOCN+H=NH2+CO 1.200E+08 0.61 2080.0 HOCN+OH=NCO+H2O 6.380E+05 2.0 2560.0 HOCN+CH3=NCO+CH4 8.200E+05 1.87 6620.0 HOCN+NH2=NCO+NH3 9.200E+05 1.94 3645.0 CN+NO2=CO+N2O 4.930E+14 -0.752 344.0 CN+NO2=CO2+N2 3.700E+14 -0.752 344.0 CN+CO2=NCO+CO 3.670E+06 2.16 26900.0 CN+NH3=HCN+NH2 9.200E+12 0.0 -357.0 HNCO+CN=HCN+NCO 1.500E+13 0.0 0.0 NCO+CN=CNN+CO 1.800E+13 0.0 0.0 HONO+NCO=HNCO+NO2 3.600E+12 0.0 0.0 NCO+CH2O=HNCO+HCO 6.000E+12 0.0 0.0 CH+N2=HCN+N 3.680E+07 1.42 20723.0 NH2+C=CH+NH 5.800E+11 0.67 20900.0 C+N2=CN+N 5.200E+13 0.0 44700.0 CH2+N2=HCN+NH 4.800E+12 0.0 35850.0 C2+N2=CN+CN 1.500E+13 0.0 41700.0 H2CN+N=N2+CH2 6.000E+13 0.0 400.0 H2CN+H=HCN+H2 2.400E+08 1.5 -894.0 H2CN+O=HCN+OH 1.700E+08 1.5 -894.0 H2CN+O=HNCO+H 6.000E+13 0.0 0.0 H2CN+O=HCNO+H 2.000E+13 0.0 0.0 H2CN+M=HCN+H+M 3.000E+14 0.0 22000.0 H2CN+HO2=HCN+H2O2 1.400E+04 2.69 -1610.0 H2CN+O2=CH2O+NO 3.000E+12 0.0 6000.0 H2CN+CH3=HCN+CH4 8.100E+05 1.87 -1113.0 H2CN+OH=HCN+H2O 1.200E+06 2.0 -1192.0 H2CN+NH2=HCN+NH3 9.200E+05 1.94 -1152.0 C+NO=CN+O 2.000E+13 0.0 0.0 CH+NO=HCN+O 8.690E+13 0.0 0.0 CH+NO=CN+OH 1.680E+12 0.0 0.0 CH+NO=CO+NH 9.840E+12 0.0 0.0 CH+NO=NCO+H 1.670E+13 0.0 0.0 CH2+NO=HNCO+H 2.500E+12 0.0 5970.0 CH2+NO=HCNO+H 3.800E+13 -0.36 576.0 CH2+NO=NH2+CO 2.300E+16 -1.43 1331.0 CH2+NO=H2CN+O 8.100E+07 1.42 4110.0 CH3+NO=HCN+H2O 2.400E+12 0.0 15700.0 CH3+NO=H2CN+OH 5.200E+12 0.0 24240.0 HCCO+NO=HCNO+CO 4.640E+13 0.0 700.0 HCCO+NO=HCN+CO2 1.390E+13 0.0 700.0 SCH2+NO=HCN+OH 1.000E+14 0.0 0.0 HCNO=HCN+O 4.200E+31 -6.12 61210.0 HCNO+H=HCN+OH 1.000E+14 0.0 12000.0 HCNO+H=HNCO+H 2.100E+15 -0.69 2850.0 HCNO+H=HOCN+H 1.400E+11 -0.19 2484.0 HCNO+H=NH2+CO 1.700E+14 -0.75 2890.0 HCNO+O=HCO+NO 7.000E+13 0.0 0.0 CH2+N=HCN+H 5.000E+13 0.0 0.0 CH2+N=NH+CH 6.000E+11 0.67 40500.0 CH+N=CN+H 1.670E+14 -0.09 0.0 CH+N=C+NH 4.500E+11 0.65 2400.0 N+CO2=NO+CO 1.900E+11 0.0 3400.0 N+HCCO=HCN+CO 5.000E+13 0.0 0.0 CH3+N=H2CN+H 7.100E+13 0.0 0.0 CH3+N=HCNH+H 1.200E+11 0.52 367.6 HCNH=HCN+H 6.100E+28 -5.69 24270.0 HCNH+H=H2CN+H 2.000E+13 0.0 0.0 HCNH+H=HCN+H2 2.400E+08 1.5 -894.0

307 HCNH+O=HNCO+H 7.000E+13 0.0 0.0 HCNH+O=HCN+OH 1.700E+08 1.5 -894.0 HCNH+OH=HCN+H2O 1.200E+06 2.0 -1192.0 HCNH+CH3=HCN+CH4 8.200E+05 1.87 -1113.0 C2H3+N=HCN+CH2 2.000E+13 0.0 0.0 CN+H2O=HCN+OH 4.000E+12 0.0 7400.0 CN+H2O=HOCN+H 4.000E+12 0.0 7400.0 OH+HCN=HOCN+H 3.200E+04 2.45 12120.0 OH+HCN=HNCO+H 5.600E-06 4.71 -490.0 OH+HCN=NH2+CO 6.440E+10 0.0 11700.0 HOCN+H=HNCO+H 1.000E+13 0.0 0.0 HCN+O=NCO+H 1.380E+04 2.64 4980.0 HCN+O=NH+CO 3.450E+03 2.64 4980.0 HCN+O=CN+OH 2.700E+09 1.58 26600.0 CN+H2=HCN+H 2.000E+04 2.87 1600.0 CN+O=CO+N 1.900E+12 0.46 720.0 CN+O2=NCO+O 7.200E+12 0.0 -400.0 CN+OH=NCO+H 4.000E+13 0.0 0.0 CN+HCN=C2N2+H 1.510E+07 1.71 1530.0 CN+NO2=NCO+NO 5.320E+15 -0.752 344.0 CN+N2O=NCO+N2 6.000E+12 0.0 15360.0 C2N2+O=NCO+CN 4.570E+12 0.0 8880.0 C2N2+OH=HNCO+CN 1.860E+11 0.0 2900.0 C2N2+OH=HOCN+CN 2.000E+12 0.0 19000.0 HNCO+H=H2+NCO 1.760E+05 2.41 12300.0 HNCO+H=NH2+CO 3.600E+04 2.49 2340.0 HNCO+M=NH+CO+M 1.100E+16 0.0 86000.0 N2/1.5/ O2/1.5/ H2O/18.6/ HNCO+O=NCO+OH 2.200E+06 2.11 11430.0 HNCO+O=NH+CO2 9.800E+07 1.41 8530.0 HNCO+O=HNO+CO 1.500E+08 1.57 44012.0 HNCO+OH=NCO+H2O 3.450E+07 1.5 3600.0 HNCO+OH=NH2+CO2 6.300E+10 -0.06 11645.0 HNCO+HO2=NCO+H2O2 3.000E+11 0.0 29000.0 HNCO+O2=HNO+CO2 1.000E+12 0.0 35000.0 HNCO+NH2=NCO+NH3 5.000E+12 0.0 6200.0 HNCO+NH=NCO+NH2 1.040E+15 0.0 39390.0 NCO+H=NH+CO 5.360E+13 0.0 0.0 NCO+O=NO+CO 4.200E+13 0.0 0.0 NCO+O=N+CO2 8.000E+12 0.0 2500.0 NCO+N=N2+CO 2.000E+13 0.0 0.0 NCO+OH=NO+HCO 5.000E+12 0.0 15000.0 NCO+M=N+CO+M 2.200E+14 0.0 54050.0 NCO+NO=N2O+CO 4.600E+18 -2.01 934.0 NCO+NO=N2+CO2 5.800E+18 -2.01 934.0 NCO+O2=NO+CO2 2.000E+12 0.0 20000.0 NCO+HCO=HNCO+CO 3.600E+13 0.0 0.0 NCO+NO2=CO+NO+NO 2.830E+13 -0.646 -326.0 NCO+NO2=CO2+N2O 3.570E+14 -0.646 -326.0 NCO+HNO=HNCO+NO 1.800E+13 0.0 0.0 NCO+NCO=CO+CO+N2 3.000E+12 0.0 0.0 NO+HCO=CO+HNO 7.240E+13 -0.4 0.0 NO2+CO=CO2+NO 9.000E+13 0.0 33800.0 NO2+HCO=H+CO2+NO 8.400E+15 -0.75 1930.0 CH3O+NO2=HONO+CH2O 3.000E+12 0.0 0.0 CH3O+NO=CH2O+HNO 1.300E+14 -0.7 0.0 NO2+CH2O=HONO+HCO 1.000E+10 0.0 15100.0 NO+CH2O=HNO+HCO 1.000E+13 0.0 40820.0 NO2+HCO=HONO+CO 1.000E+13 0.0 0.0 NO2+HCO=OH+NO+CO 1.000E+14 0.0 0.0 NCO+N=NO+CN 2.700E+18 -0.995 17200.0 CN+CH4=HCN+CH3 9.000E+04 2.64 -300.0 C+NO=CO+N 2.800E+13 0.0 0.0 NH+CO2=HNO+CO 1.000E+13 0.0 14350.0 NCO+CH4=HNCO+CH3 1.000E+13 0.0 8130.0 C+N2O=CN+NO 4.800E+12 0.0 0.0 CH+NH2=HCN+H+H 3.000E+13 0.0 0.0 CH+NH=HCN+H 5.000E+13 0.0 0.0 CH2+NH=HCN+H+H 3.000E+13 0.0 0.0 CH3+N=HCN+H+H 2.000E+11 0.0 0.0 CH3+N=HCN+H2 7.100E+12 0.0 0.0 CH4+N=NH+CH3 1.000E+13 0.0 24000.0 C3H3+N=HCN+C2H2 1.000E+13 0.0 0.0 CH+N2O=HCN+NO 1.340E+13 0.0 -510.0 CH+N2O=CO+H+N2 5.200E+12 0.0 -510.0 ! END

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