On the experimental and theoretical investigations of lean ...cj82nd62b/fulltext.pdftemperatures, laminar flames and flame morphology of synthetic gas (syngas) and Gas-to-Liquid (GTL)

On the Experimental and Theoretical Investigations of Lean Partially Premixed

Combustion, Burning Speed, Flame Instability and Plasma Formation of Alternative Fuels

at High Temperatures and Pressures

A Dissertation Presented

By

Omid Askari

to

The Department of Mechanical and Industrial Engineering

In partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

In the field of

Mechanical Engineering

Northeastern University

Boston, Massachusetts

2016

2

© Copyright by

Omid Askari

2016

All Rights Reserved

3

Dedicated to My Daughter:

Hannah Askari

who always has inspired me with her love

4

Ph.D. Committee Members

Dr. Hameed Metghalchi

Professor of Mechanical Engineering


319 Snell Engineering Center

Boston, MA 02115

(617) 373-2937

[email protected]

Principle Advisor

Dr. Yiannis Angelo Levendis

Distinguished Professor of Mechanical Engineering


303 Snell Engineering Center

Boston, MA 02115

(617) 373-3806

[email protected]

Dr. Gian Paolo Beretta

Professor of Fluid and Thermal Sciences

Università di Brescia

Dipartimento di Ingegneria Meccanica e Industriale

via Branze 38, 25123 Brescia, Italy

+390303715568

[email protected]

mailto:[email protected]



5

Table of Contents

Acknowledgments........................................................................................................................... 9

Abstract ......................................................................................................................................... 10

List of Figures ............................................................................................................................... 12

List of Tables ................................................................................................................................ 20

1. Introduction .............................................................................................................................. 22 1.1. Introduction ........................................................................................................................ 23

1.2. Selected Fuels..................................................................................................................... 26

1.2.1. Compressed Natural Gas (CNG) ................................................................................ 26

1.2.2. Hydrofluorocarbons (HFCs) ....................................................................................... 26 1.2.3. Synthetic Gas (syngas) ............................................................................................... 28 1.2.4. Gas-to-Liquid (GTL) .................................................................................................. 29

1.3. Experimental Facilities....................................................................................................... 31

1.3.1. Experimental Setup Configuration ............................................................................. 31 1.3.2. Combustion Spherical Chamber ................................................................................. 32

1.3.3. Combustion Cylindrical Chamber for Laminar Burning Speed Measurement .......... 32 1.3.4. Spray Cylindrical Chamber for High-Pressure Injection............................................ 34 1.3.5. High-Pressure Fuel Delivery System.......................................................................... 34

1.3.6. Electronic Control Unit (ECU) and Data Acquisition System ................................... 35 1.3.7. Z-shaped Schlieren Photography System ................................................................... 35

1.3.8. Gas Supply System ..................................................................................................... 37

1.3.9. Gas Chromatography .................................................................................................. 37

1.4. Dissertation Structure ......................................................................................................... 38

2. Fundamental Study of Spray and Partially Premixed Combustion of Methane/Air Mixture .. 39

2.1. Abstract .............................................................................................................................. 40 2.2. Introduction ........................................................................................................................ 40

2.3. Experimental Facilities....................................................................................................... 42 2.4. Experimental Procedures ................................................................................................... 44 2.5. Results and Discussion ....................................................................................................... 45

2.5.1. Fuel Injection Quantities Investigation ....................................................................... 45 2.5.1.1. Effect of Fuel Pressure on Equivalence Ratio ..................................................... 46

2.5.1.2. Effect of Chamber Pressure on Equivalence Ratio .............................................. 46 2.5.2. Spray Development Process ....................................................................................... 47

2.5.2.1. Injection Pressure Effects .................................................................................... 49 2.5.2.2. Chamber Pressure Effects .................................................................................... 50

2.5.3. Flame Propagation Process ......................................................................................... 51

3. Lean Partially Premixed Combustion Investigation of Methane Direct-Injection under Different

Characteristic Parameters ......................................................................................................... 61 3.1. Abstract .............................................................................................................................. 62 3.2. Introduction ........................................................................................................................ 62

6

3.3. Experimental Setup and Procedures................................................................................... 64 3.4. Results and Discussion ....................................................................................................... 67

3.4.1. Spark Delay Time Effects in Lean Combustion Mode ............................................... 67 3.4.2. Injection Pressure Effects ........................................................................................... 68

3.4.3. Chamber Pressure and Temperature Effects............................................................... 69 3.4.4. Hydrogen Addition Effects ......................................................................................... 72 3.4.5. Diluent Addition Effects ............................................................................................. 75

4. Developing Alternative Approaches to Predicting the Laminar Burning Speed of Refrigerants

Using the Minimum Ignition Energy ....................................................................................... 79

4.1. Abstract .............................................................................................................................. 80 4.2. Introduction ........................................................................................................................ 80 4.3. Flammability Characteristics ............................................................................................. 81

4.3.1. Minimum Ignition Energy .......................................................................................... 82 4.3.2. Minimum Ignition Current ......................................................................................... 82 4.3.3. Maximum Experimental Safe Gap ............................................................................. 82

4.4. Theoretical Correlation and Results ................................................................................... 84 4.5. Single-variable Analysis .................................................................................................... 85

4.6. Multi-variable Analysis ...................................................................................................... 90

5. On the Thermodynamic Properties of Thermal Plasma in the Flame Kernel of Hydrocarbon/Air

Premixed Gases ........................................................................................................................ 96

5.1. Abstract .............................................................................................................................. 97 5.2. Introduction ........................................................................................................................ 97

5.3. Plasma Application in Spark Ignition Process ................................................................. 101 5.4. Method of Calculation...................................................................................................... 103

5.4.1. Dissociation Temperature Range .............................................................................. 104 5.4.2. Ionization Temperature Range ................................................................................. 104

5.4.2.1. Thermodynamic Properties of Individual Monoatomic Species ....................... 104 5.4.2.2. Partition Function .............................................................................................. 106

5.4.2.2.1. Cut-off Criteria ............................................................................................ 107

5.4.2.2.2. Reduced Ionization Potential ...................................................................... 108 5.4.2.3. Complete Equilibrium Solution Based On Gibbs Free Energy Minimization .. 109

5.4.2.3.1. Iterative Solution ......................................................................................... 110 5.4.3. Mixture Thermodynamic Properties ......................................................................... 111

5.4.4. Ideal Gas Model Validation ...................................................................................... 114 5.4.5. Fitting of Thermodynamic Properties ....................................................................... 115

5.5. Results and Discussion ..................................................................................................... 118

6. Laminar Burning Speed Measurement and Flame Instability Study of H2/CO/Air Mixtures at

High Temperatures and Pressures Using a Novel Multi-Shell Model ................................... 129 6.1. Abstract ............................................................................................................................ 130 6.2. Introduction ...................................................................................................................... 130

6.3. Experimental Facilities..................................................................................................... 133 6.4. Multi-Shell Model and Formulation ................................................................................ 134

6.4.1. Governing Equations ................................................................................................ 135

6.5. Results and Discussion ..................................................................................................... 141

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6.5.1. Flame Structure and Instability Study ...................................................................... 141 6.5.2. Stretch Effect Investigation ...................................................................................... 148 6.5.3. Laminar Burning Speed ............................................................................................ 150

7. The Effect of Exhaust Gas Recirculation (EGR) on Flame Structure and Laminar Burning

Speeds of H2/CO/Air Premixed Flame at High Pressures and Temperatures ........................ 155 7.1. Abstract ............................................................................................................................ 156 7.2. Introduction ...................................................................................................................... 156 7.3. Experimental Facilities..................................................................................................... 159 7.4. Flame Morphology Study and Stability Analysis ............................................................ 160

7.5. Burning Speed Measurements ......................................................................................... 167 7.5.1. Burning Model .......................................................................................................... 167 7.5.2. Stretch Effect Investigation ...................................................................................... 171

7.5.3. Laminar Burning Speed ............................................................................................ 172

8. Cell Formation Effect on the Burning Speed and Flame Front Area of Synthetic Gas (Syngas)

at High Pressures and Temperatures ...................................................................................... 179

8.1. Abstract ............................................................................................................................ 180 8.2. Introduction ...................................................................................................................... 180

8.3. Experimental Setup and Procedures................................................................................. 182 8.4. Theoritical Model ............................................................................................................. 184 8.5. Results and Discussion ..................................................................................................... 188

8.5.1. Flame Structure and Instability Study ...................................................................... 188 8.5.2. Cell Formation Analysis ........................................................................................... 190

8.5.2.1. Effect of Temperature ........................................................................................ 193 8.5.2.2. Effect of Pressure ............................................................................................... 195

8.5.2.3. Effect of Equivalence Ratio ............................................................................... 197 8.5.2.4. Effect of Hydrogen Concentration ..................................................................... 198

9. Auto-Ignition Characteristics Study of Gas-to-Liquid (GTL) Fuel at High Pressures and Low

Temperatures .......................................................................................................................... 201 9.1. Abstract ............................................................................................................................ 202

9.2. Introduction ...................................................................................................................... 202 9.3. Experimental Setup .......................................................................................................... 205 9.4. Results and Discussion ..................................................................................................... 207

10. Theoretical Prediction of Laminar Burning Speed and Ignition Delay Time of Gas-to-Liquid

Fuel ......................................................................................................................................... 215 10.1. Abstract ........................................................................................................................ 216

10.2. Introduction .................................................................................................................. 216 10.3. Detailed Kinetics Model............................................................................................... 219 10.4. Results and Discussion ................................................................................................. 221

10.4.1. Chemical Mechanisms Comparison ..................................................................... 221 10.4.2. Ignition Delay Time .............................................................................................. 223

10.4.3. Laminar Burning Speed and Flame Thickness ..................................................... 227

11. Recommendations for Future Work, Summary and Conclusions ....................................... 230

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11.1. Chapter 2 ...................................................................................................................... 231 11.2. Chapter 3 ...................................................................................................................... 232 11.3. Chapter 4 ...................................................................................................................... 233 11.4. Chapter 5 ...................................................................................................................... 233

11.5. Chapter 6 ...................................................................................................................... 234 11.6. Chapter 7 ...................................................................................................................... 235 11.7. Chapter 8 ...................................................................................................................... 235 11.8. Chapter 9 ...................................................................................................................... 236 11.9. Chapter 10 .................................................................................................................... 236

12. References ........................................................................................................................... 238

13. Appendix ............................................................................................................................. 266

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Acknowledgments

It is my extreme pleasure to express my special appreciation and thanks to my advisor Professor

Hameed Metghalchi. Hameed is someone you will instantly love and never forget once you meet him.

He has been supportive and has given me the freedom to pursue various projects in his lab without

objection. I would like to thank you for your guidance, patience, encouragement and continues moral

support during the course of this work. My PhD has been an amazing experience with you and I thank

you wholeheartedly, not only for your tremendous academic support, but also for giving me so many

wonderful opportunities. Your advice on both research as well as on my career have been priceless.

You have been both a great academic mentor and a best friend to me and I feel honored and blessed to

have the opportunity to work with you.

I would like to thank my dissertation committee members: Professor Yiannis Levendis and

Professor Gian Paolo Beretta for their time, interest, brilliant comments, challenging questions and

excellent feedbacks which helped to make this work better, a special thanks to Professor Gian Paolo

Beretta for his great collaboration and excellent comments on plasma study. I would also like to express

my sincere gratitude to all my teachers at Northeastern University: Professor John Cipolla, Professor

Uichiro Narusawa, the late Professor Yaman Yener, Professor Reza Sheikhi and Professor Mohammad

Taslim, thank you all.

The former and current members of the Energy and Combustion Research Laboratory have

contributed immensely to my personal and professional time at Northeastern University. The group

has been a source of friendships as well as good advice and collaboration. Dr. Kian Eisazadeh-Far, my

dear friend who was the source of inspiration and great advices. I am thankful from Dr. Ali Moghaddas,

my dear friend for all his support and assistance, I wish him luck and happiness. Many thanks go to

my colleagues: Mr. Kevin Vein, Mr. Alden Ahlholm, Mr. Ziyu Wang, Dr. Farzan Parsinejad, Dr.

Mimmo Elia, Dr. Mohammad Janbozorgi, Mr. Emad Rokni, Dr. Fatemeh Hadi, Mr. Matthew Ferrari,

Mr. Guangying Yu, Mr. Mohammad Alswat and Mr. Matteo Sirio.

My next thanks go to the Department of Mechanical Engineering for their kindness and helpfulness.

I would especially like to thank Mr. John Doghty and Mr. Kevin Mccue who helped me a lot in

technical issues in our lab. I also extend my thanks to Ms. Joyce Crain and Mr. Noah Japhet with

their assistance in logistical issues.

Finally, a very special thanks go to my family for all their support, encouragement and continuous

emotional support and for their limitless love, and for that I am grateful and indebted.

10

Abstract

This dissertation investigates the combustion and injection fundamental characteristics of

different alternative fuels both experimentally and theoretically. The subjects such as lean partially

premixed combustion of methane/hydrogen/air/diluent, methane high pressure direct-injection,

thermal plasma formation, thermodynamic properties of hydrocarbon/air mixtures at high

temperatures, laminar flames and flame morphology of synthetic gas (syngas) and Gas-to-Liquid

(GTL) fuels were extensively studied in this work. These subjects will be summarized in three

following paragraphs.

The fundamentals of spray and partially premixed combustion characteristics of directly

injected methane in a constant volume combustion chamber have been experimentally studied.

The injected fuel jet generates turbulence in the vessel and forms a turbulent heterogeneous fuel-

air mixture in the vessel, similar to that in a Compressed Natural Gas (CNG) Direct-Injection (DI)

engines. The effect of different characteristics parameters such as spark delay time, stratification

ratio, turbulence intensity, fuel injection pressure, chamber pressure, chamber temperature,

Exhaust Gas recirculation (EGR) addition, hydrogen addition and equivalence ratio on flame

propagation and emission concentrations were analyzed. As a part of this work and for the purpose

of control and calibration of high pressure injector, spray development and characteristics

including spray tip penetration, spray cone angle and overall equivalence ratio were evaluated

under a wide range of fuel injection pressures of 30 to 90 atm and different chamber pressures of

1 to 5 atm.

Thermodynamic properties of hydrocarbon/air plasma mixtures at ultra-high temperatures

must be precisely calculated due to important influence on the flame kernel formation and

propagation in combusting flows and spark discharge applications. A new algorithm based on the

statistical thermodynamics was developed to calculate the ultra-high temperature plasma

composition and thermodynamic properties. The method was applied to compute the

thermodynamic properties of hydrogen/air and methane/air plasma mixtures for a wide range of

temperatures (1,000-100,000 K), pressures (10-6-100 atm) and different equivalence ratios within

flammability limit. In calculating the individual thermodynamic properties of the atomic species,

the Debye-Huckel cutoff criterion has been used for terminating the series expression of the

electronic partition function.

11

A new differential-based multi-shell model was developed in conjunction with Schlieren

photography to measure laminar burning speed and to study the flame instabilities for different

alternative fuels such as syngas and GTL. Flame instabilities such as cracking and wrinkling were

observed during flame propagation and discussed in terms of the hydrodynamic and thermo-

diffusive effects. Laminar burning speeds were measured using pressure rise data during flame

propagation and power law correlations were developed over a wide range of temperatures,

pressures and equivalence ratios. As a part of this work, the effect of EGR addition and substitution

of nitrogen with helium in air on flame morphology and laminar burning speed were extensively

investigated. The effect of cell formation on flame surface area of syngas fuel in terms of a newly

defined parameter called cellularity factor was also evaluated. In addition to that the experimental

onset of auto-ignition and theoretical ignition delay times of premixed GTL/air mixture were

determined at high pressures and low temperatures over a wide range of equivalence ratios.

12

List of Figures

Figure 1.1. Refrigerant safety group classification [36] ............................................................... 27

Figure 1.2. Experimental setup configuration............................................................................... 32

Figure 1.3. Spherical chamber design and placement of the ports ............................................... 33

Figure 1.4. Different views of combustion cylindrical chamber and its components .................. 33

Figure 1.5. Exploded view of spray cylindrical chamber and its components ............................. 34

Figure 1.6. High-pressure fuel delivery system schematic ........................................................... 35

Figure 1.7. Electronic Control Unit (ECU) and Data Acquisition System ................................... 36

Figure 1.8. Z-shaped Schlieren Photography System ................................................................... 36

Figure 1.9. Gas supply system configuration................................................................................ 37

Figure 2.1. Cross sectional view of constant volume combustion chamber ................................. 43

Figure 2.2. Experimental arrangement.......................................................................................... 43

Figure 2.3. Comparison of the overall equivalence ratio for various fuel pressures at chamber

pressure 1 bar as a function of injection duration. ..................................................... 46

Figure 2.4. Comparison of the overall equivalence ratio for various chamber pressures at fuel

pressure of 90 bar as a function of injection duration. .............................................. 47

Figure 2.5. Definitions of spray tip penetration (STP) and spray cone angle (SCA). .................. 48

Figure 2.6. A sequence of Schlieren images of methane spray process. ...................................... 48

Figure 2.7. (a) Spray tip penetration and (b) spray cone angle under different injection pressures

and chamber pressure 1 bar as a function of time. .................................................... 49

Figure 2.8. (a) Spray tip penetration and (b) spray cone angle under different chamber pressures

and injection pressure 90 bar as a function of time. .................................................. 50

Figure 2.9. Snapshots of methane/air combustion for stratification ratio of 100% and overall

equivalence ratio of 0.8 as a function of spark delay timing (Tsd)............................. 52

Figure 2.10. Snapshots of methane/air combustion for spark delay timing of 1 ms and overall

equivalence ratio of 0.8 as a function of stratification ratio (S.R.). ........................... 53

Figure 2.11. (a) Pressure and (b) rate of pressure rise at different spark delay timing and overall

equivalence ratio 0.8. ................................................................................................. 54

13

Figure 2.12. Peak pressure versus stratification ratio at different spark delay timings, (a) Ф=0.6

and (b) Ф=1.0 ............................................................................................................ 55

Figure 2.13. Maximum rate of pressure rise versus stratification ratio at different spark delay

timings, (a) Ф=0.6 and (b) Ф=1.0 .............................................................................. 57

Figure 2.14. Initial combustion duration versus stratification ratio at different spark delay timings,

(a) Ф=0.6 and (b) Ф=1.0 ............................................................................................ 58

Figure 2.15. Main combustion duration versus stratification ratio at different spark delay timings,

(a) Ф=0.6 and (b) Ф=1.0 ............................................................................................ 59

Figure 3.1. Injection duration setting for various (a) hydrogen fractions and (b) diluent fractions as

a function of equivalence ratio .................................................................................. 66

Figure 3.2. Methane distribution around the spark discharge location at two different spark delay

times (a) Tsd = 1 ms and (b) Tsd = 5 ms at equivalence ratio of 0.6 ........................... 67

Figure 3.3. Effect of injection pressure on peak pressure and maximum rate of pressure rise at

chamber pressure of 1 bar, chamber temperature of 298 K and spark delay time of 1

ms for equivalence ratios of 0.6, 0.8 and 1.0 ............................................................. 68

Figure 3.4. Effect of injection pressure on initial combustion duration at different spark delay times

at chamber pressure of 1 bar and chamber temperature of 298 K for equivalence ratios

of 1.0 and 0.6 ............................................................................................................. 69

Figure 3.5. Effect of chamber temperature and chamber pressure on peak pressure at injection

pressure of 90 bar, spark delay time of 1 ms and equivalence ratios of 0.6, 0.8 and 1.0

................................................................................................................................... 70

Figure 3.6. Effect of chamber temperature and chamber pressure on maximum rate of pressure rise

at injection pressure of 90 bar, spark delay time of 1 ms and equivalence ratios of 0.6,

0.8 and 1.0 .................................................................................................................. 71

Figure 3.7. Effect of chamber temperature and chamber pressure on main combustion duration at

injection pressure of 90 bar, spark delay time of 1 ms and equivalence ratios of 0.6,

0.8 and 1.0 .................................................................................................................. 71

Figure 3.8. Effect of hydrogen addition on flame propagating process at four different times after

spark ignition (1.0, 2.4, 3.9 and 5.4 ms), injection pressure of 90 bar, spark delay time

of 1 ms and equivalence ratio of 0.8 .......................................................................... 72

Figure 3.9. Effect of hydrogen addition on peak pressure and maximum rate of pressure rise at

injection pressure of 90 bar, chamber pressure of 1 bar, chamber temperature of 298

K and spark delay time of 1 ms for equivalence ratios of 0.6, 0.8 and 1.0 ............... 73

14

Figure 3.10. Effect of hydrogen addition on main combustion duration and NOx concentration at

injection pressure of 90 bar, chamber pressure of 1 bar, chamber temperature of 298

K and spark delay time of 1 ms for equivalence ratios of 0.6, 0.8 and 1.0 ............... 74

Figure 3.11. Effect of diluent addition on peak pressure at injection pressure of 90 bar, chamber

pressure of 1 bar, chamber temperature of 298 K and equivalence ratios of 0.6, 0.8 and

1.0 for different spark delay times ............................................................................. 75

Figure 3.12. Snapshots of combustion instability as a function of time after spark in diluent fraction

of 25%, spark delay time of 40 ms and equivalence ratio of 1.0 ............................... 76

Figure 3.13. Effect of diluent addition on maximum rate of pressure rise, main combustion duration

and NOx concentration at injection pressure of 90 bar, chamber pressure of 1 bar,

chamber temperature of 298 K and spark delay time of 110 ms for equivalence ratios

of 0.6, 0.8 and 1.0 ...................................................................................................... 77

Figure 4.1. Refrigerant safety group classification ....................................................................... 81

Figure 4.2. Minimum ignition currents for a stoichiometric CH4–air mixture, at various initial

pressures and two electrode diameters [113] ............................................................. 83

Figure 4.3. Schematic of a spherical flame kernel ......................................................................... 85

Figure 4.4. MIE -1/3 vs. Sl for the twenty-nine values provided by Glassman, et al. [138] ............. 86

Figure 4.5. Adjusted fit of MIE -1/3 vs. Sl containing values from Table 4-5 ............................. 88

Figure 4.6. Adjusted fit of MIE -1/3 vs. Sl without Ammonia. ........................................................ 89

Figure 4.7. Adjusted fit of MIE -1/3 vs. Sl without HFC-152a. ....................................................... 89

Figure 4.8. Adjusted fit containing values from Table 4-6. .......................................................... 91

Figure 4.9. Adjusted fit containing values from Table 4-7. ........................................................... 92

Figure 4.10. Adjusted fit with Ammonia removed. ....................................................................... 93

Figure 4.11. Adjusted fit with HFC-152a removed. ...................................................................... 94

Figure 4.12. Average error of the fit as a function MIE of in HFC-152a ....................................... 95

Figure 5.1. Schematic of flame propagation model [104] .......................................................... 102

Figure 5.2. The effect of initial radius on air kernel temperature, Ti = 7000 K, discharge energy =

24 mJ [104] .............................................................................................................. 102

Figure 5.3. Specific heat at constant pressure for oxygen atom and its ions versus temperature for

three different pressures, 10-6, 1 and 100 atm. ........................................................ 112

15

Figure 5.4. Comparison between calculated data (solid line) and fitted data (symbols) for the

equilibrium specific heat at constant pressure 𝑐𝑝,eq of a stoichiometric H2/air plasma

mixture for P = 10−6, 1 and 102 atm. ...................................................................... 118

Figure 5.5. Comparison of values of the equilibrium specific heat at constant pressure 𝑐𝑝,eq

computed using our self-consistent method (solid line) and the so-called ground state

method (dashed line), for a stoichiometric H2/air plasma at three different pressures,

10-6, 1, and 100 atm ................................................................................................ 119

Figure 5.6. Comparisons of the values of the equilibrium specific heats at constant pressure 𝑐𝑝,eq

of air plasma mixture obtained with present study (solid line) and those obtained by

Capitelli et al (ο) [162], Hansen (×) [143], Sher (Δ) [156] , Cressault et al (□) [190]and

Bottin et al (+) [191] for three different pressures: (a)=10-2, (b)=1, and (c)=100 atm.

................................................................................................................................. 121

Figure 5.7. Comparisons of the selected species mole fraction of air plasma mixture obtained with

present study (dashed line) and those obtained by Gilmore (□) [139] and Hilsenrath

and Klein (ο) [186] at pressure of 1 atm .................................................................. 122

Figure 5.8. Mole fractions for selected species in a stoichiometric CH4/air plasma at atmospheric

pressure. ................................................................................................................... 123

Figure 5.9. (a)-Mean molar mass 𝑀𝑡 and (b)-degree of ionization 𝛬 at three different pressures

(10-6, 1, and 100 atm) for a stoichiometric H2/air plasma mixture. ....................... 124

Figure 5.10. (a)-Equilibrium and frozen specific heat at constant pressure 𝑐𝑝,eq and (b)-specific

enthalpy for a stoichiometric CH4/air plasma mixture at three different pressures,

10−6, 1 and, 100 atm ............................................................................................... 126

Figure 5.11. (a) Gibbs free energy and (b)-Equilibrium specific heat at constant pressure for a

H2/air plasma mixture at atmospheric pressure for three different equivalence ratio of

1, 3 and 5. ................................................................................................................. 127

Figure 5.12. Speed of sound in a stoichiometric H2/air plasma mixture at three different pressures,

10-6, 1 and 100 atm. ................................................................................................ 127

Figure 5.13. Specific heat ratio 𝛾off and isentropic exponent 𝛾𝑠,off for a stoichiometric CH4/air

plasma mixture at three different pressures of 10-6, 1, and 100 atm. ...................... 128

Figure 6.1. Schematic diagram of experimental facilities and Z-type Schlieren system ............ 134

Figure 6.2. Snapshots of the H2/CO/air flames for various initial pressures and wide range of

equivalence ratios at hydrogen concentration of 25%, initial temperature of 298 K and

flame radius of 60 mm ............................................................................................. 143

Figure 6.3. Effective Lewis number and flame thickness of the H2/CO/air flames corresponding to

the snapshots of Figure 6.2 ...................................................................................... 144

16

Figure 6.4. Snapshots of the stoichiometric H2/CO/air flames for various hydrogen concentration

at initial pressure of 2 atm and initial temperature of 450 K ................................... 145

Figure 6.5. Critical Peclet number of the stoichiometric H2/CO/air flames for various hydrogen

concentration at initial pressure of 2 atm and initial temperature of 450 K ............ 146

Figure 6.6. Critical pressures versus equivalence ratio for three different hydrogen concentration

................................................................................................................................. 148

Figure 6.7. Laminar burning speed versus stretch rates for two different equivalence ratios and

unburned gas conditions at hydrogen concentration of 5% ..................................... 149

Figure 6.8. Laminar burning speed of syngas/air mixture along isentropes at different (a)

equivalence ratios, (b) temperatures, (c) pressures and (d) hydrogen fractions ...... 152

Figure 6.9. Comparison of present experimental data versus published experimental data and

kinetic simulations for H2/CO/air laminar burning speed at atmospheric conditions, (a)

𝛼 = 5%, (b) 𝛼 = 10%, and (c) 𝛼 = 25%, ............................................................. 154

Figure 7.1. Schematic diagram of experimental facilities and Z-type Schlieren system ............ 160

Figure 7.2. Snapshots of the H2/CO/air/SEGR flames for various SEGR concentrations and

equivalence ratios at hydrogen concentration of 25%, initial temperature of 298 K and

initial pressure of 1 atm ........................................................................................... 161

Figure 7.3. Effective Lewis number and flame thickness of the H2/CO/air/SEGR flames

corresponding to the snapshots of Figure 7.2 .......................................................... 162

Figure 7.4. Snapshots of the H2/CO/air/SEGR flames for various initial pressures and flame radii

at hydrogen concentration of 25%, initial temperature of 298 K, SEGR concentration

of 10% and equivalence ratio of 2.0 ........................................................................ 163

Figure 7.5. Effective Lewis number and flame thickness of the H2/CO/air/SEGR flames

corresponding to the snapshots of Figure 7.4 .......................................................... 164

Figure 7.6. Snapshots of the stoichiometric H2/CO/air/SEGR flames for various hydrogen

concentration at initial pressure of 2 atm, SEGR concentration of 5% and initial

temperature of 298 K ............................................................................................... 165

Figure 7.7. Critical Peclet number of the stoichiometric H2/CO/air/SEGR flames for various

hydrogen concentration at initial pressure of 2 atm, SEGR concentration of 5% and

initial temperature of 298 K ..................................................................................... 165

Figure 7.8. Laminar burning speed versus stretch rates for three different cases with various

equivalence ratios, unburned gas conditions and SEGR concentrations at hydrogen

concentration of 5% ................................................................................................. 172

17

Figure 7.9. Laminar burning speed of H2/CO/air/SEGR mixture along isentropes at different

equivalence ratios for initial pressure of 0.5 atm, initial temperature of 298 K,

hydrogen concentration of 25% and SEGR concentration of 10% ......................... 174

Figure 7.10. Laminar burning speed of stoichiometric H2/CO/air/SEGR mixture along isentropes

at different initial pressures for initial temperature of 298 K, hydrogen concentration

of 5% and SEGR concentration of 10% .................................................................. 174


hydrogen concentrations for atmospheric initial pressure, initial temperature of 298 K,

equivalence ratio of 3.0 and SEGR concentration of 5% ........................................ 175


SEGR concentrations for initial pressure of 0.5 atm, initial temperature of 298 K,

equivalence ratio of 0.6 and hydrogen concentration of 10% ................................. 175

Figure 7.13. Comparison of present experimental laminar burning speed data versus published

experimental data [37,41,43,193,195,199,200,204] for H2/CO/air at atmospheric

temperature and pressure at hydrogen concentration of 5% and SEGR concentration

of 0% ........................................................................................................................ 176

Figure 7.14. Comparison of calculated laminar burning speeds versus two kinetic simulations

(Davis [221] and Li [222] mechanisms) for H2/CO/air/SEGR mixture at atmospheric

pressure and temperature, hydrogen concentration of 25% and three different SEGR

concentrations .......................................................................................................... 177

Figure 7.15. Normalized sensitivity coefficients of H2/CO/air/SEGR mixture at different SEGR

concentrations, initial pressure of 0.5 atm, initial temperature of 298 K, equivalence

ratio of 0.6 and hydrogen concentration of 25% ..................................................... 178

Figure 8.1. Overview of experimental facilities ......................................................................... 184

Figure 8.2. Schematic of multi-shell theoretical model .............................................................. 187

Figure 8.3. Snapshots of the H2/CO/O2/He flames for various equivalence ratios, hydrogen

concentration of 5%, initial pressure of 5 atm and initial temperature of 400 K .... 188

Figure 8.4. Effective Lewis number and flame thickness of the H2/CO/O2/He flames corresponding

to the snapshots of Figure 8.3 .................................................................................. 190

Figure 8.5. Cellular burning speed and mass burning rate of stoichiometric H2/CO/O2/He mixture

along two isentropes at different initial temperatures, initial pressure of 10 atm and

hydrogen concentration of 10% ............................................................................... 194

Figure 8.6. Cellularity factor and laminar burning speed of stoichiometric H2/CO/O2/He mixture

along two isentropes at different initial temperatures, initial pressure of 10 atm and


18


along isentropes at different initial pressure for initial temperature of 400 K and


Figure 8.8. Cellularity factor and flame area of stoichiometric H2/CO/O2/He mixture along three

isentropes at different initial pressure for initial temperature of 400 K and hydrogen

concentration of 25% ............................................................................................... 196

Figure 8.9. Cellular burning speed and mass burning rate of H2/CO/O2/He mixture along three

isentropes at different equivalence ratios for initial pressure of 12 atm, initial

temperature of 480 K and hydrogen concentration of 5% ....................................... 197

Figure 8.10. Cellularity factor, cellular and laminar burning speed of H2/CO/O2/He mixture for

three different equivalence ratios of 0.6, 1.0 and 2.0 at pressure of 23.5 atm,

temperature of 602 K and hydrogen concentration of 5% ....................................... 198


along three isentropes at different hydrogen concentration for initial temperature of

450 K and initial pressure of 2 atm .......................................................................... 199

Figure 8.12. Laminar and cellular burning speed of stoichiometric H2/CO/O2/He mixture along

three isentropes at different hydrogen concentration for initial temperature of 450 K

and initial pressure of 2 atm (laminar burning speeds are indicated with dashed lines)

................................................................................................................................. 199

Figure 8.13. Laminar and total flame area of stoichiometric H2/CO/O2/He mixture along isentropes

at different hydrogen concentration for initial temperature of 450 K and initial pressure

of 2 atm (laminar flame areas are indicated with dashed lines) .............................. 200

Figure 9.1. Overview of experimental facilities ......................................................................... 207

Figure 9.2. Comparison of pressure-time traces of auto-ignition of GTL/air mixture for three

different initial pressure of 8.6, 10 and 12 atm, at initial temperature of 450 K and

equivalence ratio of 0.8 and normal combustion with initial pressure of 2 atm ...... 209

Figure 9.3. Comparison of pressure rate-time traces of auto-ignition of GTL/air mixture for three

different initial pressure of 8.6, 10 and 12 atm, at initial temperature of 450 K and

equivalence ratio of 0.8 ............................................................................................ 210

Figure 9.4. Comparison of available GTL detailed kinetics mechanisms [66,258,261,262] with

experimental data [255] at equivalence ratio of 1 and pressure of 20 atm for a wide

range of temperatures .............................................................................................. 211

Figure 9.5. Theoretical ignition delay time for a wide range of pressures and temperatures using

Ranzi et al. [261] mechanism for stoichiometric GTL/air mixture ......................... 212

Figure 9.6. Experimental temperatures and pressures at the onset of auto-ignition for GTL/air

mixture at different equivalence ratios .................................................................... 213

19

Figure 9.7. Theoretical ignition delay times for GTL/air mixture at different equivalence ratios

versus (a) experimental temperatures and (b) experimental pressures at the onset of

auto-ignition ............................................................................................................. 214

Figure 10.1. Comparison of ignition delay time between available GTL chemical mechanisms

[66,258,261,262] and experimental data [255] at equivalence ratio of 1 and pressure

of 20 atm for a wide range of temperatures ............................................................. 222

Figure 10.2. Comparison of laminar burning speed between GTL chemical mechanisms

[66,262,261] and experimental data [254,257,270] for different equivalence ratios at

pressure of 1 atm and temperature of 400 K ............................................................ 223

Figure 10.3. Comparison of laminar burning speed between GTL chemical mechanisms

[66,261,262] and experimental data [254,270,271,274] for different equivalence ratios

at pressure of 1 atm and temperature of 473 K ........................................................ 224


Ranzi et al. [261] mechanism for stoichiometric GTL/air mixture ......................... 225

Figure 10.5. Theoretical ignition delay time for a wide range of temperatures at three different

equivalence ratios and a pressure of 10 atm using Ranzi et al. [261] mechanism for

GTL/air mixture ....................................................................................................... 226



GTL/air mixture ....................................................................................................... 226



GTL/air mixture ....................................................................................................... 227

Figure 10.8. Theoretical laminar burning speed and flame thickness for a wide range of

equivalence rations and different temperatures of 400, 500, 600, 700 and 800 K at

pressure of 1 atm using Ranzi et al. [261] mechanism for GTL/air mixture ........... 228

Figure 10.9. Theoretical laminar burning speed and flame thickness for a wide range of

equivalence ratios and different pressures of 1, 5, 10, 15, 20 and 25 atm at temperature

of 533 K using Ranzi et al. [261] mechanism for GTL/air mixture ........................ 229

20

List of Tables

Table 1-1- Hydrofluorocarbons Characteristics............................................................................ 27

Table 1-2- Specification properties of Synterleoum S-8 fuel ....................................................... 30

Table 2-1- Injector characteristics parameter, a, for fuel pressure of 90 bar as a function of chamber

pressure ...................................................................................................................... 45

Table 4-1-Summary of MIE data (mJ) .......................................................................................... 82

Table 4-2- Comparison of MESG values between several apparatuses [114] .............................. 83

Table 4-3- Source: Glassman, et al. [138] .................................................................................... 86

Table 4-4- Source: Minor, et al. [136] .......................................................................................... 87

Table 4-5- Fitted values of laminar burning speed for several adjustments contained in Table 4-4

................................................................................................................................... 87

Table 4-6- Predicted values of burning speed using Equation (4-4). Glassman, et al. [138] ....... 90

Table 4-7- Predictions of the multi-variable fit for several adjustments of MIE values .............. 91

Table 4-8- Errors of the fits for different values of MIE of HFC-152a ........................................ 94

Table 5-1- List of the 133 species considered in the present calculations for H2/Air and CH4/Air

plasma mixtures. ...................................................................................................... 103

Table 6-1- Critical pressures and temperatures of H2/CO/air mixtures at initial temperature of 450

K, different initial pressures, wide range of equivalence ratios and three hydrogen

concentration of 5, 10 and 25% ............................................................................... 147

Table 6-2- Power law fitting coefficients ................................................................................... 150

Table 7-1- Critical pressures and temperatures of H2/CO/air/SEGR mixtures at SEGR

concentration of 5%, initial temperature of 298 K, different initial pressures, wide

range of equivalence ratios and three hydrogen concentration of 5, 10 and 25% ... 166

Table 7-2- Critical pressures and temperatures of H2/CO/air/ SEGR mixtures at SEGR

concentration of 10%, initial temperature of 298 K, different initial pressures, wide

range of equivalence ratios and three hydrogen concentration of 5, 10 and 25% ... 167

Table 7-3- Power law fitting coefficients ................................................................................... 173

Table 8-1- Coefficients of cellular burning speed correlation for H2/CO/O2/He mixture .......... 192

Table 8-2- Coefficients of mass burning rate correlation for H2/CO/O2/He mixture ................. 192

21

Table 9-1- Specification properties of Syntroleum S-8 fuel ....................................................... 208

Table 9-2- Comparison of different chemical kinetics mechanisms for GTL fuel ..................... 211

Table 9-3- Experimental temperatures and pressures at the onset of auto-ignition for GTL/air

mixture ..................................................................................................................... 213

Table 10-1- Specification properties of Syntroleum S-8 fuel ..................................................... 220

Table 10-2- Comparison of different chemical mechanisms for GTL fuel ................................ 221

22

1. Introduction

23

1.1. INTRODUCTION

In one hand, combustion has a substantial role in our everyday life from cooking and heating at

home to power generation, chemical synthesis and transportation in industries. On the other hand,

its destructive effects on human and natural lives through pollutions, fires, global warming and

diseases push us to break the edge of knowledge in order to control these disadvantages. The only

way to get to that point is an in-depth fundamental study on important parameters and properties

which play significant roles on performance and emissions of advanced combustion devices such

as internal combustion engine and gas turbines. By doing that a new generation of combustion

devices and advanced technics which can satisfy our needs will be generated. Among these

important methods and properties are lean partially premixed combustion, high pressure direct

injection, laminar burning speed, flame instabilities, onset of auto-ignition and plasma formation.

Due to increasing concern over energy shortages and the advent of strict environmental

regulations, researchers in combustion and engine development have become motivated to

discover novel ways to improve fuel economy and reduce pollutant emissions. One of the

significant methods to achieve these goals is lean combustion of hydrocarbon fuels which has the

potential to obtain high thermal efficiency, high fuel economy and low pollutant emission,

particularly NOx. The antiknock capability of the lean mixture promotes the upper limit of the

compression ratio in spark ignition engines. However, in the case of lean mixture combustion,

most of the hydrocarbon fuels have the problem of combustion instability due to low burning speed

[1–4] and large cycle variations which lead to flame kernel extinction, loss in power output,

increase in fuel consumption and unburned hydrocarbon emissions [5,6]. To improve the lean-

burn capability, it is necessary to increase the turbulence intensity in-cylinder, optimize the ignition

timing and combustion chamber geometry to achieve the stable combustion. The most important

problem in lean mixture combustion for most hydrocarbon fuels is the low burning speed of the

flame kernel. One effective method to solve the problem is to enrich the region near the spark for

initiating the flame. This can be accomplished by high pressure fuel direct injection to create a

stratified mixture just before the spark which leads to a different combustion regime called partial

premixed combustion. Compressed natural gas spark-ignition direct-injection (CNG-SIDI)

engines today appear as the most promising way to achieve the two objectives of lowering

pollutant emission and improving fuel economy [7–10]. Compared to the conventional port fuel

injection (PFI), it permits the stable flame front to propagate for a wide range of equivalence ratios,

24

especially in ultra-lean modes by creating a mixture with high fuel concentration around the spark

plug. It also helps in reducing pollutant formation and the tendency towards engine knocking [11–

13]. In this work, the fundamentals of high pressure spray and partially premixed combustion

characteristics of directly injected methane in a constant volume combustion chamber (CVCC)

have been experimentally investigated. The effect of different characteristics parameters such as

spark delay time, stratification ratio, turbulence intensity, fuel injection pressure, chamber

pressure, chamber temperature, synthetic Exhaust Gas recirculation (SEGR) addition, hydrogen

addition and equivalence ratio on flame propagation and pollutant concentrations of lean partially

premixed turbulent combustion have been analyzed. As a part of this work and for the purpose of

control and calibration of high pressure injector, spray development and characteristics including

spray tip penetration (STP), spray cone angle (SCA) and overall equivalence ratio have been

evaluated under a wide range of fuel injection pressures of 30 to 90 atm and different chamber

pressures of 1 to 5 atm.

To improve efficiency and reduce pollutant formation in internal combustion engines [14],

knowledge of flame kernel development and flame propagation play important role. A plasma, at

very high temperature, will be generated at the onset of spark discharge. Accurate modeling of the

thermodynamic properties of plasma mixtures is essential to understand the evolution of the

plasma channel and its evolution into the formation of the flame kernel. During the spark discharge

in a fuel-air mixture, the electrical energy is injected in a constant volume process followed by a

sudden expansion which leads to the formation of fully ionized high temperature plasma through

the generation of a shock wave and the consequent dissociation and ionization of the mixture. The

plasma thermodynamic properties and its degree of ionization have important effects on flame

ignition, structure, and propagation and must be estimated by means of sophisticated models to

ensure accurate simulations of the plasma flow field. In addition to flame kernel in spark ignition

process, during the past decades a significant progress in plasma applications such as cutting,

spraying, arc heating, re-entry of space-vehicles, nuclear rockets and CFD simulation of high-

temperature flow fields has happened. So in this work, a new algorithm based on the complete

chemical equilibrium assumption and statistical thermodynamics is developed to calculate the

ultra-high temperature plasma composition and thermodynamic properties of any arbitrary gas

mixtures particularly hydrogen/air and methane/air plasma mixtures for a wide range of

temperatures (1,000 - 100,000 K), different pressures (10-6 - 100 atm), and different fuel/air

25

equivalence ratios within flammability limit. The calculated plasma properties are presented as

functions of temperature, pressure and equivalence ratio, in terms of a new set of

thermodynamically self-consistent mathematical correlations that are shown to provide very

accurate fits suitable for efficient use in CFD simulations.

Laminar burning speed and onset of auto-ignition are two important thermo-physical properties

of every fuel which can be used in turbulent combustion modeling and most importantly for

validating of chemical kinetics mechanisms. They are strongly influenced by mixture

characteristics and operational conditions such as equivalence ratio, diluents type, temperature and

pressure. Laminar burning speed is defined as the speed at which a planar, one-dimensional,

adiabatic flame travels relative to the unburned gas mixture. There are various methods to measure

laminar burning speed: 1- stationary flame methods, 2- propagating flame methods. In propagating

flames the methods used to measure burning speeds can be characterized as either constant

pressure [15–17] or constant volume [1–3,18–25]. The important point is to use a method by which

laminar burning speed can be measured in a wide range of pressures and temperatures with a high

accuracy. In this work, laminar burning speeds are measured by a new developed differential-

based multi-shell model using the pressure rise data collected through the flame propagation of

premixed fuel/air mixture inside a spherical constant volume combustion chamber. The onset of

auto-ignition is the set of thermodynamic conditions at which the combustion process occurs

spontaneously and simultaneously throughout the combustible mixture [26]. Using the

experimental facility developed in this study, a controlled combustion event in spherical constant

volume combustion chamber produces an increase in the pressure and temperature of the unburned

mixture. When auto-ignition conditions are reached, the unburned gas instantly and simultaneously

ignites and produces a series of pressure waves that can be detected by the pressure transducer.

The conditions of the unburned gas that initiates the pressure waves are the conditions at which

auto-ignition occurs, and are more representative of the varying conditions typically found in a

practical combustion systems such as internal combustion engines. Flame morphology and

instability can be also studied using the cylindrical vessel, which is installed in a Z-type Schlieren

system equipped with a high speed CMOS camera, in terms of the hydrodynamic and thermo-

diffusive effects. As a part of this work, the effect of Synthetic Exhaust Gas Recirculation (SEGR)

addition, a mixture of 14% CO2 and 86% N2, and substitution of nitrogen with helium in air on

26

flame morphology and laminar burning speeds are extensively studied at high temperatures and

pressures.

1.2. SELECTED FUELS

In this dissertation flame different alternative fuels including Compressed Natural Gas (CNG),

Hydrofluorocarbon (HFC) refrigerants, synthetic gas (syngas) and Gas-to-Liquid (GTL) have been

used. In following sub-sections a brief discussion of each fuel will be given.

1.2.1. Compressed Natural Gas (CNG)

Compressed natural gas is regarded as one of the most promising alternative fuels and it is

composed primarily of methane (CH4) [27] which has been extensively used in spark ignition

engines and power generation devices [28]. The benefits of CNG as an alternative fuel are that it

emits lower amounts of pollutants and it is very economical compared to conventional fuels

specially in countries with large natural gas resources [14,29]. Compressed natural gas has a high

research octane number (RON=110–130) and therefore can be easily employed in spark ignition

(SI) internal combustion engines. Due to the high RON of CNG, engines could be operated with a

higher compression ratio for better thermal efficiency [30]. Furthermore, since CNG has a low

carbon/hydrogen (C/H) ratio, it produces less CO2 emissions, a greenhouse gas which is largely

responsible for global warming trends [31], per unit of energy released. Therefore, CNG appears

to be an excellent alternative fuel for SI engines [32].

1.2.2. Hydrofluorocarbons (HFCs)

The need to replace high global warming potential (GWP) refrigerants with environmentally

friendly refrigerants has been motivated by concerns regarding climate change. Since the adoption

of the Montreal Protocol in 1989 and the Kyoto Protocol in 1997 there has been an ongoing phase-

out of chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) [33]. Refrigerant

companies are working to develop alternatives to CFC based chemicals such as CCl3F (CFC-11)

and CCl2F2 (CFC-12). Alternatives that are currently in use include hydrofluorocarbons (HFCs)

such as tetrafluoroethane (C2H2F4 or HFC-134a) which replaced CFC-12 used in automobile air

conditioning systems. Generally, HFCs have shorter lifetime in the atmosphere and so lower global

warming potential [34]. While the environment has been the primary driving force behind the

27

search for next generation refrigerants, safety considerations require thorough studies of the

combustion characteristics of these potential refrigerants. Some HFCs refrigerants like HFC-32

and HFC-152a are classified as flammable and so the potential for ignition must be evaluated very

carefully. Table 1-1 summarizes some of the characteristics of these two refrigerants at 23°C and

1 bar [35]. In considering the potential combustion hazard of any flammable gases, minimum

ignition energy and flammability limits are used for evaluating the possibility of ignition. The scale

of the fire disaster can be estimated in terms of burning speed and heat of combustion [34].

Table 1-1- Hydrofluorocarbons Characteristics

Refrigerant

Number Chemical Name

Chemical

Formula

Molar

Mass

(g/mol)

Heat of

Formation

(kJ/mol)

Heat of

Combustion

(MJ/kg)

Flammability

Limits (φ)

(ASTM-E681)

HFC-32 difluoromethane CH2F2 52.02 -452.3 9.4 0.83 – 1.7

HFC-152a 1,1-difluoroethane CH3CHF2 66.05 -497.0 17.4 0.62 – 2.47

ANSI/ASHRAE Standard 34–2010 [36] identifies the safety classification assigned to

refrigerants by ASHRAE SSPC 34, as shown in Figure 1.1. This classification has been made

based on the toxicity and the flammability.

Figure 1.1. Refrigerant safety group classification [36]

Class 1 refrigerants exhibit no propagating flame when tested for flammability in air at 60°C

and 101.3 kPa. Although having lower heats of combustion than Class 1, Class 2 refrigerants

28

exhibit lower flammability limits (LFL > 0.10 kg/m3) when tested in air at 60°C and 101.3 kPa

and also have a low heat of combustion (Δhc < 19,000 kJ/kg). Class 3 refrigerants exhibit higher

flammability limits (LFL ≤ 0.10 kg/m3) when tested at 60°C and 101.3 kPa and have a higher heat

of combustion (Δhc ≥ 19,000 kJ/kg). HFC-32 and HFC-152a are rank as A2. Flammability class 2

includes a wide range of moderately flammable substances and additional criterion based on the

burning speed is required for more precise scaling of flammability within this class. A subclass,

Class 2L, are refrigerants that meet the requirements for Class 2 and also have a burning speed

less than or equal to 10 cm/s, when tested at 23°C and 101.3 kPa. The 2L subclass, considered

“mildly” flammable, is an optional classification designed to better identify the flammability

characteristics of a Class 2 refrigerant.

1.2.3. Synthetic Gas (syngas)

Synthetic gas, also known as syngas, is the name of a combustible mixture predominantly

containing varying levels of hydrogen and carbon monoxide and in some instances some levels of

CO2, CH4, N2, and H2O and other higher order hydrocarbons [37]. Syngas has gained importance

as an alternative fuel for stationary gas turbines and internal combustion engines. Power plants

have been using syngas for more than a decade, citing increased energy efficiencies and less

emissions than conventional coal fired plants. Syngas is also increasingly being used in petroleum

refineries to help produce cleaner transportation fuels and improve overall efficiency of the plant

[38]. Syngas can be derived from the gasification of coal or biomass, including municipal waste,

agricultural residue, and herbaceous energy crops therefore reducing greenhouse gas (GHG)

emissions. This gas is considered to be an alternative fuel that is used to produce a wide range of

synthetic materials, solvents, and fertilizers and also is predicted to have an important role in the

future of renewable and environmentally friendly energies. One of the important applications of

this alternative fuel is as a reformer gas that can be used during engine cold start to reduce the

amount of HC emissions [39]. Synthetic gas also plays an important role in stationary power plants

that use the integrated gasification combined cycle (IGCC) [40]. Recently a large focus has been

cast on this fuel for its potential use in the gas turbine industry as a replacement for natural gas

[41–43]. Thus it is of utmost importance to study the flame structure and determine the

fundamental combustion characteristics of the fuel to fully understand how it behaves over a wide

range of operating conditions.

29

1.2.4. Gas-to-Liquid (GTL)

The urge for finding an alternative to oil-based transportation fuels is higher now than ever

before due to environmental impact and supply security. Alternative fuels obtained from feed

stocks such as biomass, natural gas and coal, are called Synthetic Paraffinic Kerosene (SPK) fuels.

Recently, the interest on SPK fuels as a viable alternative fuel for aviation transportation is

enormous as they do not warrant any major modifications to the existing fuel injection /combustor

system. Furthermore, the SPK fuels obtained through Fisher-Tropsch (F-T) synthesis are preferred

as the fuel composition can be appropriately tailored for specific applications. Among SPK fuels,

gas-to-liquid (GTL) fuel, owing to its cleaner combustion characteristics due to the near absence

of sulfur, and less aromatic content, is preferred over conventional jet fuels [44]. The GTL fuel

can also be surrogate for gasoline, diesel, and aviation fuels [45]. Over the years, the potential for

deriving high value products from natural gas [46,47] and its abundant availability have attracted

the pioneers in GTL production technology such as Syntroleum, Shell, Sasol, and Chevron to build

small and medium scale GTL plants across the globe. The availability of world’s third largest

natural gas reserve in Qatar (with proven reserves of about 890 trillion cubic feet [48]) has led to

the construction of world's largest GTL plant, Pearl GTL, jointly by Qatar-Petroleum and Shell at

a cost of about $18billion. This has enabled Qatar airways to attempt a commercial flight from

London to Doha using a 50-50% blend of GTL fuel and conventional Jet A-1 fuel [49].

The SPK fuels produced using F-T process are mainly composed of normal-alkanes, iso-

alkanes, and cyclic-alkanes, which is substantially different from those of conventional jet fuels

such as Jet A, Jet A-1, and JP-8. Synthetic fuels have a very small concentration of cyclo-alkanes

in comparing with conventional jet fuels and this small number varies based on the different

production processes and companies. Moses [50] has done a very good comparison between

different available synthetic fuels. He showed that among SPK fuels, Syntroleum aviation fuel

provided by Air Force Research Laboratory (AFRL), designated with S-8, has almost no cyclo-

alkanes. The difference in fuel chemical properties will have a significant influence on the

combustion and emission characteristics in combustors. Therefore, a complete knowledge on

fundamental combustion parameters for GTL fuel at combustor conditions is essential in order to

improve/optimize the combustor design and engine efficiency. Furthermore, these fundamental

combustion parameters are necessary to develop, validate, and to improve the prediction

capabilities of computational tools and chemical kinetics models. Among these fundamental

30

combustion parameters, investigation of onset of auto-ignition [51] for GTL fuel, is extremely

relevant and necessary for combustion community, particularly for gas turbine and internal

combustion engines in the transportation industry [14,52]. GTL has gained more and more

attention in recent years due to its clean combustion behavior comparing to the conventional fuels.

It not only contains less sulfur and aromatic compounds but also has less NOx and particular

formation [44,53]. The economics and benefits of producing GTL fuel from natural gas has been

studied by different groups [54,55]. The performance and emissions of GTL fuel as an alternative

fuel for engines were also investigated and compared with traditional fuels [56–64].

The GTL fuel used in this study and its detailed composition have been provided by the Air

Force Research Laboratory (AFRL) [50,65]. This fuel was produced in the U.S. from natural gas

through a Fischer-Tropsch process called low temperature Cobalt catalyst [50] in small pilot plant

by Syntroleum in Oklahoma. The specification properties of this fuel are presented in Table 1-2.

A blend of 32% of iso-octane, 25% n-decane and 43% n-dodecane [66] was employed as the

surrogates of GTL fuel for chemical kinetics study. The initial mixture composition for GTL/air

mixture is defined as Eq. (1-1). This surrogate mixture has an empirical formula of 𝐶10.22𝐻22.44,

𝐻 𝐶⁄ ratio of 2.196, an estimated Cetane number of 61 and a molecular weight of 145.37 g/mol.

𝜙(0.32 𝐶8𝐻18 + 0.25 𝐶10𝐻22 + 0.43 𝐶12𝐻26) + 15.83(𝑂2 + 3.76𝑁2) (1-1)

Table 1-2- Specification properties of Synterleoum S-8 fuel

Initial boiling point (K) 426

10% recovered (K) 444




Final boiling point (K) 533

Flash point (K) 321

Freezing point (K) 222

Density @ 15 oC (kg/L) 0.756

Viscosity @ -20 oC (mm2/s) 4.3

Net heat of combustion (MJ/kg) 44.1

Conductivity (pS/m) 128

Lubricity test (BOCLE) wear scar (mm) 0.59

Aromatics (% vol) 0.0

Total sulfur (% mass) <0.0003

Hydrogen content (% mass) 15.4

31

1.3. EXPERIMENTAL FACILITIES

1.3.1. Experimental Setup Configuration

The experimental facility has been optimized for efficiency, versatility, safety and ease of use,

as to make the transition to future researches as seamless as possible. Over the many years of

running experiments and tweaking the systems and processes the current laboratory facility is

considered state of the art. All the data acquisition and analysis can be done on-site by several

dedicated PCs using a high speed LabVIEW DAQ card and isolated input and output modules for

temperature, voltages and pressure measurements as well as automatic delayed firing via control

of the high voltage coil driving the spark plugs. The filling manifold mainly constructed of 304

and 316 Stainless steel Swagelok componentry and tubing is predisposed to accommodate inputs

from 5 simultaneous gas cylinders, thus allowing for an inventory of gas mixtures to be always

readily available for immediate use. Two vacuum pumps help evacuate the system faster and allow

for independent testing of the two vessels. The heater controllers are proportionally programmable

with redundant safety feature for over temperature protection and electric shock. The cylindrical

vessel with optical side ports and all its supporting system are rigidly mounted to an optical bench.

Using a focused light source and a series of mirrors the light is guided through the optically clear

Quartz sides and reflected to a high speed CMOS camera capable of capturing images at 40,000

frame per second. This shadowgraph effect is useful in visualizing the flame propagation, as well

as investigating the shape of the flame front. Another key element of the apparatus is the liquid

filling system where a slug of liquid fuel is allowed to enter and evaporate in a temperature

controlled portion of the manifold. A higher temperature pressure transducer closely coupled to

this section of the manifold is used to monitor the partial pressure of the vaporized fuel and hence

control the amount of fuel that will be used in the experiment. The experimental setup

configuration shown in Figure 1.2.

32

Figure 1.2. Experimental setup configuration

1.3.2. Combustion Spherical Chamber

The spherical combustion chamber is constructed from two hemispheres one-inch-thick that are

bolted together at their flanges with 6 bolts of 0.75 inch diameter to give a 6 inch spherical vessel

that can withstand 425 atm of pressure as shown in Figure 1.3. The chamber is fitted with two

ports for the spark plug electrodes, one for the piezoelectric pressure transducer (Kistler model

601B), one for filling and three additional ports that can be used either for ionization probes and

thermocouple. In the current set up one ionization probe mounted on top of the vessel and the other

diametrically opposed to one of the top probe. The location of the ports was strategically chosen

to allow the measurement of buoyancy and ignition misalignment.

1.3.3. Combustion Cylindrical Chamber for Laminar Burning Speed Measurement

The cylindrical combustion chamber is 13.5 cm in diameter and 13.5 cm in length and is capped

on both ends by 5.08cm thick fused quartz windows, which are used to record the flame

propagation with a high-speed camera, as shown in Figure 1.4. The windows are seated on the

33

body of the cylindrical chamber by using elastomer O-rings that also create a vacuum seal. The

cylindrical chamber is equipped with a piezoelectric pressure transducer, two band heaters, and

two extended spark plugs for central ignition with a gap of about 1mm. The spark energy is tuned

to minimize the effect of spark discharge on the propagation of the flame. The cylindrical chamber

is installed in a Z-shaped Schlieren system where flame propagation is captured by a high-speed

CMOS camera with capability of recording pictures up to 40,000 frame per second. Ignition,

pressure-time data and flame images are controlled, synchronized, and recorded using a LabVIEW

program and camera software. The cylindrical chamber is limited to a maximum of 50 atmospheres

due to the windows and a maximum of 500K due to the elastomer O-rings.

Figure 1.3. Spherical chamber design and placement of the ports

Figure 1.4. Different views of combustion cylindrical chamber and its components

34

1.3.4. Spray Cylindrical Chamber for High-Pressure Injection

This chamber has the same dimensions as combustion cylindrical chamber but different

configuration. A gasoline direct-injection (GDI) single hole injector, with 0.9 mm hole diameter

was installed on the top of the cylindrical chamber. Methane was injected into the combustion

chamber and then ignited by the extended spark plug placed in the center of the chamber as shown

in Figure 1.5.

Figure 1.5. Exploded view of spray cylindrical chamber and its components

1.3.5. High-Pressure Fuel Delivery System

The fuel supply system can provide a constant 10-150 bar pressure to the injector. The fuel

supply system consists of a high pressure injector, a methane tank with 99.5% purity, a high

pressure regulator, a stainless steel connecting tube with an inside diameter of 4 mm that can

tolerate maximum pressure of 300 bar, and a check valve and three ball valves for safety purposes

as shown in Figure 1.6. The injection pressure was adjusted by using a high pressure regulator.

35

Figure 1.6. High-pressure fuel delivery system schematic

1.3.6. Electronic Control Unit (ECU) and Data Acquisition System

All data exchanging activities have been done using National Instrument DAQ card PCI6036-E.

An injecting pulse signal from the DAQ card was fed into the DRIVVEN’s DI driver module kit

to generate the three-stage current (10/5.5/2.5 A) required by the injector. Then, the actuator coils

of the high pressure injector were charged by the dc 65V supply voltage to induce the

electromagnetic force to draw back the nozzle needle of the high pressure injector. For timing

adjustment CRIO-9076 chassis in conjunction with NI-9401 module have been used. The DAQ

and control systems are shown in Figure 1.7.

1.3.7. Z-shaped Schlieren Photography System

The Z-shaped Schlieren photography system is used in conjunction with the cylindrical chamber

and is shown schematically in Figure 1.8. Light is produced from a lamp that enters a pin hole and

is captured by the first concave spherical mirror. The beams reflect from the first spherical mirror,

pass through the cylindrical chamber’s windows and the medium of interest within (a gas), and

then reflect off of the second spherical mirror into the high-speed CMOS camera with a knife edge.

Tracing the rays from the light source to the camera creates the so called ‘Z-shaped’ setup. The

Schlieren setup is such that the beams travelling through the cylindrical chamber are initially

parallel to each other and but become deflected when passing through media with differing

36

densities, which result in a change in refractive index. Beams that are greatly deflected after

passing through the entire medium do not pass the knife edge and result in dark spots in the

captured images. The knife edge is the difference between a Schlieren setup and a shadowgraph

setup. A more detailed description of the Schlieren photography method can be found in [67,68].

Figure 1.7. Electronic Control Unit (ECU) and Data Acquisition System

Figure 1.8. Z-shaped Schlieren Photography System

37

1.3.8. Gas Supply System

Both spherical and cylindrical chambers are attached to a newly built gas delivery system that

is comprised of valves, high accuracy pressure transducers, a vacuum pump, constituent gases, and

a manifold, as shown in Figure 1.9. There are four pressure gauges, one of which is connected to

a thermocouple vacuum transducer and three of which are piezoelectric pressure transducers, each

suited for different pressure ranges. The thermocouple vacuum gauge is firstly used to determine

vacuum pressure within the manifold and combustion chamber (~100-120 milliTorr is considered

to be sufficiently close to vacuum pressure) and is secondly used to calibrate the piezoelectric

pressure transducers, since piezoelectric pressure transducers only measure dynamic pressure.

Once a vacuum pressure reading is chosen, the corresponding readings of the other three pressure

gauges are considered as offsets for subsequent pressure readings.

Figure 1.9. Gas supply system configuration

1.3.9. Gas Chromatography

A Varian CP-3800 Gas Chromatograph (GC) is used to verify the accuracy of the mixture

composition of the gases filled using the partial pressure method. Currently, the GC is equipped

with a Thermal Conductivity Detector (TCD) that is used in conjunction with a MolSieve 13x

packed column that can be used to identify some permanent gases (O2, N2, CH4, CO, but not CO2),

38

as well as a HayeSep DB porous polymer column and a CP-Sil 5B capillary column. Currently the

GC is configured to sample from gaseous flow and is calibrated using several calibration gases of

differing mixture compositions.

1.4. DISSERTATION STRUCTURE

The structure of this dissertation is based on the manuscripts published and submitted to the

journals during PhD years. Each chapter is represented by a paper. Chapter 2 and 3 discuss about

the fundamentals of high-pressure direct injection and lean partially-premixed combustion of

methane fuel as the representative of Compressed Natural gas (CNG). Chapters 4 discusses about

the alternative approaches to predict the laminar burning speed of refrigerants using the minimum

ignition energy. Chapters 5 discusses the thermodynamic properties of hydrocarbon/air plasma

mixtures at temperature range of 1,000-100,000 K, pressure range of 10-6-100 atm and different

equivalence ratios within the flammability limit. Chapter 6 describes a new developed differential-

based multi-shell model and its application to calculate the laminar burning speed with a detailed

study on flame structure and instability for syngas/air mixture at various temperatures, pressures,

equivalence ratios. Chapter 7 present the effect of Exhaust Gas Recirculation (EGR) on the flame

morphology and laminar burning speed of syngas/air mixture for a wide range of operating

conditions. Chapter 8 describes the cell formation effect on burning speed and flame front area for

syngas fuel at high temperatures and pressures. Chapter 9 and 10 present theoretical and

experimental study on laminar burning speed, ignition delay time and onset of auto-ignition for

Gas-to-Liquid fuel at high temperature and pressures for different equivalence ratios.

39

2. Fundamental Study of Spray and Partially

Premixed Combustion of Methane/Air Mixture

40

2.1. ABSTRACT

This study presents fundamentals of spray and partially premixed combustion characteristics of

directly injected methane in a constant volume combustion chamber (CVCC). The constant

volume vessel is a cylinder with inside diameter of 135 mm and inside height of 135 mm. Two

end of the vessel are equipped with optical windows. A high speed complementary metal oxide

semiconductor (CMOS) camera capable of capturing pictures up to 40,000 frames per second is

used to observe flow conditions inside the chamber. The injected fuel jet generates turbulence in

the vessel and forms a turbulent heterogeneous fuel–air mixture in the vessel, similar to that in a

compressed natural gas (CNG) direct injection engine. The fuel–air mixture is ignited by centrally

located electrodes at a given spark delay timing of 1, 40, 75 and 110 milliseconds. In addition to

the four delay times, a 5 minute waiting period was used in order to make sure of having laminar

homogeneous combustion. Spray development and characterization including spray tip

penetration, spray cone angle and overall equivalence ratio were investigated under 30-90 bar fuel

pressures and 1-5 bar chamber pressure. Flame propagation images and combustion characteristics

were determined via pressure-derived parameters and analyzed at a fuel pressure of 90 bar and a

chamber pressure of 1 bar at different stratification ratios (from 0% to 100%) at overall equivalence

ratios of 0.6, 0.8 and 1.0. Shorter combustion duration and higher combustion pressure were

observed in direct injection-type combustion at all fuel air equivalence ratios compared to those of

homogeneous combustion.

Keywords: methane, spray development, direct injection, stratified mixture, partially premixed

combustion

2.2. INTRODUCTION

Combustion of very lean premixed hydrocarbon-air mixtures exhibits low flame propagation

speeds leading to a loss in power output, and an increase in fuel consumption and hydrocarbon

emissions [5]. Due to these restrictions and also increasing the catalyst efficiency, spark ignition

engines always operate close to the stoichiometric mixture. Traditionally, to improve the lean-burn

capability of the hydrocarbon–air premixed charge, an increase of turbulence intensity in the

cylinder is needed. However, these measures are always accompanied by increases in energy loss

to the cylinder wall and fuel consumption. One effective method to solve the problem is to enrich

41

the region near the spark for initiating the flame. This can be accomplished by high pressure fuel

direct injection to create a stratified mixture just before the spark.

In order to achieve better fuel economy and meet the requirements of stringent emission

regulations, the development of four-stroke, spark-ignition engines to inject compressed natural

gas (CNG) directly into the combustion chamber is an important development in the automotive

and motorcycle industries [8–10,69,70]. Compressed natural gas is regarded as one of the most

promising alternative fuels and it is composed primarily of methane (CH4) [27].The benefits of

CNG as an alternative fuel are that it emits lower amounts of air pollutants and it is very

economical compared to conventional fuels [29]. Compressed natural gas has a high research

octane number (RON=110-130) and therefore can be easily employed in spark-ignited (SI) internal

combustion engines. Due to the high RON of CNG, engines could be operated with a higher

compression ratio for better thermal efficiency [30]. Furthermore, since CNG has a low

carbon/hydrogen (C/H) ratio, it produces less CO2 per unit of energy released. Therefore, CNG

appears to be an excellent fuel for SI engines [32].

In recent years, a direct injection (DI) gasoline engine has been developed for automobile

engines to improve fuel economy [69]. Direct injection technology strongly increases the engine's

volumetric efficiency, which permits the engine to run at higher speed and produce more overall

power. Direct injection technology also reduces the need for throttling for control purposes, thus

reducing the cycle pumping loss. During low loads and low engine speeds, the DI engines operate

with a stratified charge. The charge stratification in the combustion chamber permits extremely

lean combustion without high cycle-to-cycle variations and with high combustion efficiency,

although the problem of high nitrogen oxides (NOx) and particulate matter (PM) emissions remains

[6,71–73].

The spark-ignited direct injection (SIDI) CNG engine adopts DI technology in an SI engine,

and uses alternative fuel. Up until now, studies of SIDI CNG engines have concentrated on the

CNG homogeneous charge, and few reports can be found related to SIDI CNG engines with

stratified charge [74–79]. For the design and optimization of an SIDI CNG engine with stratified

charge, an examination of the essential features is needed. For the design and optimization of an

SI engine adopting DI technology with CNG fuel, it is necessary to investigate the spray

42

development process in order to develop more precise control of the overall equivalence ratio and

the combustion propagation process.

In this study, a visualization experimental system consisting of a combustion chamber, methane

fuel supply system representing CNG fuel, air supply system, electronic control unit (ECU), and

data acquisition system was designed and built. Spray development and investigation of fuel

injection characteristics including spray tip penetration, spray cone angle and overall equivalence

ratio have been conducted under 30-90 bar fuel pressures, 1-5 bar chamber pressure. Flame

propagation images and combustion characteristics via pressure-derived parameters have been

analyzed at a fuel pressure of 90 bar and a chamber pressure of 1 bar at different stratification

ratios (from 0% to 100%) at overall equivalence ratios of 0.6, 0.8 and 1.0.


A Hitachi gasoline direct injection (GDI) single hole injector, model number E7T05091, with

0.9 mm hole diameter was installed on the top of the combustion chamber. Methane was injected

into the combustion chamber and then ignited by the extended spark plug placed in the center of

the chamber as shown in Figure 2.1. This arrangement of the injector and spark plugs provided a

stratified charge of methane around the spark discharge position. A visualization experiment was

designed and set up to investigate methane spray and combustion characteristics. Pressure of the

vessel during the combustion process is recorded by a miniature piezoelectric Kistler absolute

dynamic pressure transducer. Figure 2.2 shows the experimental setup that is consisted of five

main parts [1,4]: a combustion chamber, an initial mixture supply system (filling system), a fuel

supply system, an electronic control unit (ECU) and an optical system (Z-type Schlieren setup

[67]).

The fuel supply system can provide a constant 10-150 bar pressure to the injector. The fuel

supply system consists of a high pressure injector, a methane tank with 99.5% purity, a high

pressure regulator, a stainless steel connecting tube with an inside diameter of 4 mm that can

tolerate maximum pressure of 300 bar, and a check valve and three ball valves for safety purposes.

The injection pressure was adjusted by using a high pressure regulator. Method of partial pressure

[80] was used to make the desired mixture. The electronic control unit (ECU) was used to generate

43

control signals including injection timing, injection duration, spark delay timing and camera timing

and was also used to collect pressure data, schlieren and shadowgraph images.

Figure 2.1. Cross sectional view of constant volume combustion chamber

Figure 2.2. Experimental arrangement

44

2.4. EXPERIMENTAL PROCEDURES

Two types of experiments were performed. The first experiment investigated the injection

characteristics and the second experiment studied the combustion process of a partial premixed

mixture under different turbulent intensities. In both cases the chamber was first evacuated and

then air was introduced into the vessel via the inlet valve at an initial temperature of 298 K. Mixture

in the vessel was allowed to settle for one minute to become quiescent. The first part of the

experiment was to measure the injector characteristics such as overall equivalence ratio, spray tip

penetration and spray cone angle. In this step, the range of pressures of the injected fuel and

chamber pressure were varied from 30-90 bar and 1-5 bar respectively. At each condition, various

injection durations were used and spray development images were recorded. The electronically

controlled injector is the key component in the high pressure fuel injection system. Therefore,

characterizing the dynamic performance of the high pressure injector was essential to the

implementation of CNG-DI engine air-fuel ratio [81,82]. The injector needed to be controlled in

order to achieve the precise air-fuel ratio control for the combustion experiments. The overall

equivalence ratio of the mixture was determined by exact information on the partial pressures of

the components.

The second part of the experiment dealt with the combustion characteristics of the partially

premixed mixtures. Fuel with a specific overall equivalence ratio was injected into the vessel. The

injection and chamber pressure was maintained constant at 90 bar and 1 bar, respectively. Methane

jet penetrated and air was entrained into the jet, leading to the expansion of the jet. The fuel jet

with high momentum collides with the opposite wall 2.1 ms from the beginning of the fuel

injection and diffuses rapidly in the constant volume vessel. The injected fuel generates turbulence

in the vessel and forms a turbulent heterogeneous fuel–air mixture in the vessel, similar to that in

a gas direct injection engine [73].

Fuel injection was divided into two parts in order to obtain the partially premixed direct-

injection combustion. First, a portion of fuel was injected into the vessel. The setup was allowed

to stabilize for five minutes to ensure the fuel air mixtures were homogeneous and remained

quiescent in the vessel. Then, the rest of fuel with a specific stratification ratio (S.R.) was injected

into the vessel. The stratification ratio is defined as the ratio of the amount of fuel injected in the

second part to the total amount of injected fuel. The second part of the injected fuel generates the

45

turbulence in the vessel while mixing with the homogeneous ultra-lean fuel-air mixtures formed

by first injected fuel. The fuel-air mixture in the vessel will be relatively richer in the bottom part

and leaner in the upper part before turbulence dies out. The fuel–air mixture was ignited by

centrally located electrodes at a given spark delay timing of 1, 40, 75 and 110 milliseconds after

fuel injection to reflect different turbulence intensity. In addition, homogeneous premixed mixture

was studied having five minutes spark delay time to provide information on laminar homogeneous

mixture combustion. At least three runs at each initial condition were made to provide a good

statistical sample. Based on statistical analysis, it was found that three runs are sufficient to achieve

a 95% confidence level [83].

2.5. RESULTS AND DISCUSSION

2.5.1. Fuel Injection Quantities Investigation

An injecting pulse signal from the ECU was fed into the DRIVVEN's DI driver module kit to

generate the three-stage current (10/5.5/2.5A) required by the injector. Then the actuator coils of

the high pressure injector were charged by the DC 65V supply voltage. The first section of current

command (10A peak current) was generated by high voltage DC 65V to induce the electromagnetic

force to draw back the nozzle needle of the high pressure injector. The overall equivalence ratio

was evaluated experimentally using partial pressure method in several injection durations and then

its relation as a function of injection duration using least square curve fitting method is considered

as linear function, Φ(Δ𝑡𝑖𝑛𝑗) = 𝑎Δ𝑡𝑖𝑛𝑗 , with regression factor greater than 0.9995. The overall

equivalence ratio coefficient, a, for four chamber pressures and a fuel pressure of 90 bar is shown

in Table 2-1.

Table 2-1- Injector characteristics parameter, a, for fuel pressure of 90 bar as a function of chamber pressure

𝑷𝒊𝒏𝒋 (𝒃𝒂𝒓) 𝑷𝒄𝒉 (𝒃𝒂𝒓) a

90 1 2.2650×10-2

90 2 1.1285×10-2

90 3 7.4467×10-3

90 5 4.3895×10-3

46

2.5.1.1. Effect of Fuel Pressure on Equivalence Ratio

The overall equivalence ratio between various fuel pressures ranging from 30 to 90 bar at the

chamber pressure of 1 bar is shown in Figure 2.3. As shown, increasing the injector duration time

increases the overall equivalence ratio. It is clear in this figure that we can achieve a greater

equivalence ratio in constant pulse duration by increasing the fuel injection pressure.

Figure 2.3. Comparison of the overall equivalence ratio for various fuel pressures at chamber pressure 1

bar as a function of injection duration.

2.5.1.2. Effect of Chamber Pressure on Equivalence Ratio

The overall equivalence ratio at different chamber pressures ranging from 1 to 5 bar at a fuel

pressure of 90 bar is shown in Figure 2.4. As shown in this figure, increasing chamber pressure

causes the overall equivalence ratio to be reduced while keeping the injection duration constant.

47

Figure 2.4. Comparison of the overall equivalence ratio for various chamber pressures at fuel pressure of

90 bar as a function of injection duration.

2.5.2. Spray Development Process

Figure 2.5 shows methane spray tip penetration (STP), defined as the distance from the injector

exit plane to the tip of the spray. The spray cone angle (SCA) is the angle at which the methane

spray expands in the radial direction. These two parameters, STP and SCA, are found by MATLAB

image processing code. Tip of the spray is its head and it is a foremost position that spray reaches.

The speed and extent to which the methane spray penetrates across the combustion chamber

strongly affects the air utilization and fuel–air mixing rates.

Figure 2.6 shows a sequence of Schlieren images of the methane spray development process for

injection pressure of 90 bar and an injection duration of 5 ms. The chamber temperature and

pressure are 298 K and 1 bar, respectively. As shown in Figure 2.6, methane spray rapidly

penetrates axially and also expands in the radial direction just after the injection begins.

48

Figure 2.5. Definitions of spray tip penetration (STP) and spray cone angle (SCA).

Figure 2.6. A sequence of Schlieren images of methane spray process.

49

2.5.2.1. Injection Pressure Effects

Figure 2.7 shows the effect of injection pressure on the methane spray process. The figure shows

the spray tip penetration and spray cone angle for four injection pressures of 30, 50, 70 and 90 bar.

It is found that spray tip penetration was significantly affected by the injection pressure. As the

injection pressure increased, the spray tip penetration increased. The spray cone angle is influenced

by the injection pressure for only the first 1.5 ms after the start of the injection. In these cases the

spray cone angle reaches 28o at 1.5 ms after injection.

Figure 2.7. (a) Spray tip penetration and (b) spray cone angle under different injection pressures and

chamber pressure 1 bar as a function of time.

50

2.5.2.2. Chamber Pressure Effects

The effect of chamber pressure on the methane spray process is shown in Figure 2.8. These data

were acquired for chamber pressures of 1, 2, 3, and 5 bar. It is shown that as chamber pressure

increases, the injected methane spray penetration decreases in both the axial and radial directions.

As shown in these figures, the chamber pressure has a significant effect on spray tip penetration

and the spray cone angle.

Figure 2.8. (a) Spray tip penetration and (b) spray cone angle under different chamber pressures and

injection pressure 90 bar as a function of time.

51

The injected methane under the 5 bar chamber pressure condition penetrates quite slowly, but

the penetration under the 1 bar was much faster. It took 2, 2.4, 3.2, and 4.4 ms for the methane

spray tip under chamber pressures of 1, 2, 3, and 5 bar, respectively, to penetrate 131 mm from the

injector exit (top of chamber) in the axial direction to bottom of chamber. In the early part of the

injection process, the spray cone angle increases and then becomes constant. After approximately

1.6, 2, 2.8, and 3.8 ms from the start of injection, the spray cone angle under the 1, 2, 3, and 5 bar

chamber pressure conditions increased to 28, 29.7, 31.2 and 34.1 degree, respectively, and then

remained constant.

2.5.3. Flame Propagation Process

The momentum of the fuel jet reduces due to collision with walls and interaction between the

fuel jet and the charge inside the vessel. Schlieren photographs show that the fuel–air mixtures in

the vessel become almost quiescent after 5 minutes from the end of fuel injection. The time interval

between the end of fuel injection and start of ignition, the spark delay timing (Tsd), reflects different

turbulence intensities in the vessel at ignition time. Short spark delay timing creates a high

turbulence intensity environment while long spark delay timing creates a low turbulence intensity

environment.

Figure 2.9 shows snapshots of methane-air combustion at the stratification ratio of 100% and

the overall equivalence ratio of 0.8 for different spark delay timings. The snapshots show the

burned and unburned gases at 1, 4, 7 and 10 milliseconds after spark ignition. The injection

pressure, chamber pressure and temperature were 90 bar, 1 bar and 298 K, respectively. Following

the spark discharge, an electrical arc expands between the electrodes. Then, a high temperature

plasma followed by a flame kernel is formed. For the homogenous case (Tsd = 5 minutes), the

flame becomes spherical and propagates outwardly toward the surfaces of the vessel. For non-

homogenous cases flame shape is a function of turbulence intensity which is inversely related to

the spark delay times. Flame is smooth and laminar at the beginning but becomes cellular as

pressure increases reducing flame thickness and increasing wrinkles. Turbulent flames at spark

delay timing of 40, 75, and 110 ms propagate outwardly from the center of the vessel with wrinkled

flame surfaces compared to the smooth flame front of homogeneous mixture combustion.

52

Figure 2.9. Snapshots of methane/air combustion for stratification ratio of 100% and overall equivalence

ratio of 0.8 as a function of spark delay timing (Tsd).

The effect of turbulence on the enhancement of combustion can be clearly observed from these

images, and the wrinkled flame front is the typical indication of turbulent combustion. The images

also show that the flame propagation speed of direct injection turbulent combustion is much higher

than that in the case of homogeneous mixture combustion. The increase of spark delay timing

decreases the turbulent flame propagation speed, and this is due to the reduction of turbulence

intensity generated by the fuel spray.

Flame images of the partially premixed direct-injection combustion of methane at the

equivalence ratio of 0.8, spark delay timing of 1 ms and different stratification ratio (S.R.) are

53

shown in Figure 2.10. It can be seen that the flame kernel grows faster as stratification ratio

increases. This is due to the increase in turbulence intensity as the stratification ratio increases. It

indicates that the burning rate is increasing with the increase of turbulence intensity within the

experimental range.

Figure 2.10. Snapshots of methane/air combustion for spark delay timing of 1 ms and overall equivalence

ratio of 0.8 as a function of stratification ratio (S.R.).

Figure 2.10 also shows that the flame propagation process in the 25% stratification condition is

much different than that of 100% stratification condition, where the latter is similar to that of

turbulent premixed flame [84]. This indicates that the spark ignition becomes more stable with the

decreasing of stratification ratio due to the compromise of relatively lower turbulence intensity

and richer mixture near the spark position at the spark timing [85].

In these experiments, the rate of pressure rise is proportional to the rate of energy release, which

is an important characteristic of the combustion process. Figure 2.11 shows the pressure (a) and

54

the rate of pressure rise (b) of methane/air combustion at different spark delay timings and the

overall equivalence ratio of 0.8. The pressure-time curve of the homogeneous mixture combustion

shows the slow increase compared to the turbulent flame, leading to the peak pressure of the

homogeneous mixture combustion being lower than those of turbulent flame. In the case of

turbulent combustion, only a slight decrease in peak pressure is observed at different spark delay

timings.

Figure 2.11. (a) Pressure and (b) rate of pressure rise at different spark delay timing and overall

equivalence ratio 0.8.

55

Meanwhile, turbulent combustion reaches its peak pressure earlier compared to homogeneous

mixture combustion, and turbulent combustion shortens main combustion duration compared to

homogeneous mixture combustion. Main combustion duration, that is defined as the time interval

from 10% of the pressure rise to 90% of the pressure rise, decreases with increasing turbulence

intensity. Peak pressures versus stratification ratio at different spark delay timings and overall

equivalence ratio of 0.6 and 1.0 are given in Figure 2.12.

Figure 2.12. Peak pressure versus stratification ratio at different spark delay timings, (a) Ф=0.6 and (b)

Ф=1.0

56

The high burning speed of the mixtures at the stoichiometric condition (Ф=1.0) leads to a

minimal influence on the peak pressure among various stratification ratios in the case of both

homogeneous mixture combustion and direct injection turbulent combustion. Peak pressure is

increased with the increase of turbulence intensity in the vessel at all equivalence ratios. The peak

pressure value of all mixtures gives the larger difference in the case of lean mixture combustion

(Ф=0.6), and this indicates that the influence of turbulence on combustion is larger in lean mixture

combustion than in rich mixture combustion. The turbulence intensity at the same spark delay

timing will decrease with the decrease of stratification ratio which would lead to the decrease of

combustion rate, peak pressure and charge stratification of the fuel-air mixture. Peak pressure is

increased with the decrease of spark delay timing at all stratification ratios.

This shows that the combustion of lean methane-air mixtures inside the CVCC can be enhanced

by advancing the spark delay timing. Maximum rate of pressure rise versus stratification ratio at

different spark delay timings and the overall equivalence ratio of 0.6 and 1.0 is illustrated in

Figure 2.13. At the stoichiometric mixture condition (Ф=1.0), the effect of the stratification ratios

on the maximum rate of pressure rise is weak. In the case of lean mixture combustion (Ф=0.6), the

maximum rate of pressure rise increases with increasing of stratification ratio. Since flame

propagation speed decreases during lean mixture combustion, increasing the stratification ratio can

increase the flame propagation speed due to increasing turbulence and leads to the increase in the

maximum rate of pressure rise.

The maximum rate of pressure rise changes remarkably as stratification ratio changes from 0 to

20% and then shows a slow increase as stratification ratio increases beyond 25%. For lean mixture

combustion, the effect of stratification ratio and spark delay timing has remarkable effects on the

maximum rate of pressure rise. The study also indicates that large improvement in combustion

occurs at a large stratification ratio combined with a short spark delay timing (high turbulence

intensity).

57

Figure 2.13. Maximum rate of pressure rise versus stratification ratio at different spark delay timings, (a)

Ф=0.6 and (b) Ф=1.0

The initial combustion duration (the time interval from the ignition timing to 10% of the

pressure rise) and the main combustion duration (the time interval from 10% of the pressure rise

to 90% of the pressure rise) versus stratification ratio at different spark delay timings for the overall

fuel air equivalence ratio of 0.6 and 1.0 are given in Figures 2.14 and 2.15, respectively.

58

Figure 2.14. Initial combustion duration versus stratification ratio at different spark delay timings, (a)

Ф=0.6 and (b) Ф=1.0

The results show that the initial and main combustion durations increase with decreasing

stratification ratio at an equivalence ratio of 0.6 and this is due to reduction of turbulence intensity.

Both the initial and main combustion durations decrease as spark delay timing decreases regardless

of the stratification ratio due to the combustion enhancement with high turbulence. The effect of

stratification ratio on combustion duration is more obvious at lean mixture condition (Ф=0.6) than

59

in stoichiometric mixture. Initial combustion duration and main combustion duration are slightly

influenced by the stratification ratio. The turbulence generated by fuel direct injection can

remarkably decrease the initial combustion duration and main combustion duration compared to

homogeneous mixture combustion. This effect is more obvious at lean mixture combustion, which

suggests that turbulence is an effective method to improve the lean mixture combustion.

Figure 2.15. Main combustion duration versus stratification ratio at different spark delay timings, (a)

Ф=0.6 and (b) Ф=1.0

60

NOMENCLATURE

a coefficient of overall equivalence ratio

�̇� fuel mass flow rate

P pressure

T time (ms)

Δt injection duration (ms)

Φ overall equivalence ratio

Subscripts

ch chamber

inj injection

sd spark delay

61

3. Lean Partially Premixed Combustion Investigation

of Methane Direct-Injection under Different

Characteristic Parameters

62

3.1. ABSTRACT

The effects of hydrogen addition, diluent addition, injection pressure, chamber pressure,

chamber temperature and turbulence intensity on methane–air partially premixed turbulent

combustion have been studied experimentally using a constant volume combustion chamber

(CVCC). The fuel–air mixture was ignited by centrally located electrodes at given spark delay

times of 1, 5, 40, 75 and 110 milliseconds. Experiments were performed for a wide range of

hydrogen volumetric fractions (0% to 40%), simulated diluent volumetric fractions (0% to 25% as

a diluent), injection pressures (30-90 bar), chamber pressures (1-3 bar), chamber temperatures

(298-432 K) and overall equivalence ratios of 0.6, 0.8, and 1.0. Flame propagation images via the

Schlieren/Shadowgraph technique, combustion characteristics via pressure derived parameters and

pollutant concentrations were analyzed for each set of conditions. The results showed that peak

pressure and maximum rate of pressure rise increased with the increase in chamber pressure and

temperature while changing injection pressure had no considerable effect on pressure and

maximum rate of pressure rise. The peak pressure and maximum rate of pressure rise increased

while combustion duration decreased with simultaneous increase of hydrogen content. The lean

burn limit of methane–air turbulent combustion was improved with hydrogen addition. Addition

of diluent increased combustion instability and misfiring while decreasing the emission of nitrogen

oxides (NOx).

Keywords: methane direct injection, transparent chamber, Schlieren/Shadowgraph, hydrogen,

simulated diluent, partially premixed combustion, NOx

3.2. INTRODUCTION

Due to increasing concern over energy shortages and the advent of strict environmental

regulations, researchers in combustion and engine development have become motivated to

discover novel ways to improve fuel economy and reduce pollutant emissions. One of the

significant methods to achieve these goals is lean combustion of hydrocarbon fuels which has the

potential to obtain high thermal efficiency, high fuel economy and low pollutant emission,

particularly NOx. The antiknock capability of the lean mixture promotes the upper limit of the

compression ratio in spark ignition engines. However, in the case of lean mixture combustion,

most of the hydrocarbon fuels have the problem of combustion instability due to low burning speed

63

[1–4] and large cycle variations which lead to flame kernel extinction, loss in power output,

increase in fuel consumption and unburned hydrocarbon emissions [5,6].

To improve the lean-burn capability, it is necessary to increase the turbulence intensity in-

cylinder, optimize the ignition timing and combustion chamber geometry to achieve the stable

combustion. The most important problem in lean mixture combustion for most hydrocarbon fuels

is the low burning speed of the flame kernel. One effective method to solve this problem is to

enrich the region near the spark plug to initiate the flame with greater speed using high pressure

fuel direct injection. Another effective method is to create an ultra-lean hydrogen-air premixed

mixture inside the chamber right before fuel injection.

Compressed natural gas (CNG) containing mostly methane has been extensively used in spark

ignition engines and power generation devices [28]. The high hydrogen-to-carbon ratio of natural

gas reduces CO2 emissions, a greenhouse gas which is largely responsible for global warming

trends [31]. Another advantage of CNG as an alternative fuel, in addition to lower quantities of air

pollutants, is that it is very economical compared to conventional fuels especially in countries with

large natural gas resources [14,29]. Compressed natural gas has a high research octane number

(RON=110-130) and therefore can be easily used in spark ignition engines to operate with higher

compression ratio for better thermal efficiency [30].

Compressed natural gas Spark-Ignition Direct-Injection (CNG-SIDI) engines today appear as

the most promising way to achieve the two objectives of lowering pollutant emission and

improving fuel economy [8–10,70]. Compared to the conventional port fuel injection (PFI), it

permits the stable flame front to propagate for a wide range of equivalence ratios, especially in

ultra-lean modes by creating a mixture with high fuel concentration around the spark plug. It also

helps in reducing pollutant formation and the tendency towards engine knocking [11–13].

The effects of hydrogen addition on the combustion and pollutant characteristics of natural gas

spark-ignition engines have been experimentally investigated and the results showed that the

concentrations of unburned hydrocarbons (UHC), carbon monoxide (CO) and carbon dioxide

(CO2) could be reduced [86–92]. However, NOx may increase for natural gas–hydrogen

combustion due to increased burned gas temperature. The lean-burn capability of natural gas could

be improved by hydrogen addition, leading to further improvement of engine thermal efficiency

and reduction in pollutant emission [93–97]. Moreover, hydrogen addition could increase the

64

tolerance of larger EGR while maintaining low cycle-to-cycle variations, reducing the engine NOx

production by 80% [98]. Studies of methane spark-ignition direct-injection engines to date have

concentrated on the methane-air homogeneous charge combustion and few reports can be found

related to stratified charge combustion [75–78]. In addition, many aspects of hydrogen and diluent

addition as well the effect of varying injection pressure, chamber pressure and chamber

temperature on methane SIDI stratified charge combustion in the presence of turbulence have not

been well understood and require further investigation.

The objectives of this study were to investigate combustion characteristics, flame stability and

pollutant concentrations for a wide range of hydrogen volumetric fractions (0% to 40%), diluent

volumetric fractions (0% to 25%), injection pressure (30-90 bar), chamber pressure (1-3 bar),

chamber temperature (298-432 K) and overall equivalence ratios of 0.6, 0.8 and 1.0 via

Schlieren/Shadowgraph optical technique and pressure-derived parameter using a constant volume

combustion chamber.

3.3. EXPERIMENTAL SETUP AND PROCEDURES

A schematic diagram of the experimental set-up and details of the constant volume combustion

chamber including the arrangement of the extended electrodes and fuel injector are shown by

Askari et. al. [46]. This arrangement of the injector and extended electrodes provided a

heterogeneous charge of methane around the spark discharge location [99]. The fuel volumetric

flow rate of the injector under various experimental conditions was calibrated and the relationship

between the fuel injection duration and the overall equivalence ratio were obtained based on the

partial pressure method [46]. The injection process was controlled by a driver module kit, which

generates peak and hold current pulses.

Six types of experiments were performed. In the first experiments the effect of spark delay times

on flame stability in lean combustion mode was investigated. The second, third and fourth

experiments investigated the effect of injection pressure, chamber pressure and chamber

temperature on combustion characteristics. In these cases the chamber was first evacuated and then

air was introduced into the vessel via the inlet valve and was allowed to settle down for one minute

to become quiescent. The fifth and sixth parts of the experiment dealt with the combustion

characteristics of methane injection into the hydrogen-air and diluent-air initial premixed mixture.

65

In these cases the chamber was first evacuated and then the initial mixture component (hydrogen

or diluent) with lower partial pressure than air was introduced into the vessel. The chamber then

was closed and filling lines were evacuated followed by introduction of air until the chamber

pressure reached the desired pressure.

For comparative study, the partial pressure of oxidizer (air plus diluents) was kept constant and

only the partial pressure of fuel mixture was changed to create various equivalence ratios. The

same duration (one minute) was maintained to allow the mixture in the vessel to become quiescent

and well mixed. Then the correct amount of methane for a given overall equivalence ratio was

injected into the vessel based on the injection duration as shown in Figure 3.1.

As methane is injected to the vessel, the methane jet collides with the opposite wall with high

momentum and diffuses rapidly in the combustion chamber. The injected fuel forms a turbulent

heterogeneous fuel–air mixture in the vessel, similar to that in a gas direct injection engine [13].

Then, the fuel–air mixture was ignited by centrally located electrodes at given spark delay times

of 1, 5, 40, 75 and 110 milliseconds after fuel injection to reflect varying turbulence intensity. At

least three runs at each initial condition were made to provide a good statistical sample. In order

to insure the accuracy of measurements, all instruments used in this study were calibrated before

the experiments. The best values reported for all measured parameters were averaged over 3

measurements to account for variations. The overall uncertainty ΔU of experimental result is

determined by combining the systematic (Bias) uncertainty and random (Precision)

uncertainty, ΔB and ΔA [100]. This is accomplished using the root-sum-square method providing

95% coverage of the true value.

∆𝑈 = √∆𝐵2 + ∆𝐴2

∆𝐵

𝑅= [∑(

1

𝑅

𝜕𝑅

𝜕𝑋𝑖∆𝑋𝑖)

2𝑛

𝑖=1

]

1 2⁄

∆𝐴

𝑅= [∑(

1

𝑅

𝜕𝑅

𝜕𝑋𝑖∆𝑋𝑖)

2𝑛

𝑖=1

]

1 2⁄

(3-1)

66

In above equations, R is the physical parameter that is dependent on variable, 𝑋𝑖. The

symbol ∆𝑋𝑖 denote the uncertainty of variable 𝑋𝑖. The uncertainty analysis has been implemented

throughout this research.

Figure 3.1. Injection duration setting for various (a) hydrogen fractions and (b) diluent fractions as a

function of equivalence ratio

67


3.4.1. Spark Delay Time Effects in Lean Combustion Mode

The effect of ignition delay timing on combustion characteristics has been reported previously

[46]. Reduction of spark delay time increased the turbulent flame propagation speed due to the

increase of turbulence intensity generated by the fuel spray. But in the lean combustion case (Φ =

0.6), especially for the spark delay time equal to 5 ms, there exists combustion instability in which

the flame kernel is quickly quenched after a few milliseconds.

As shown in Figure 3.2 (a) after the end of injection (EOI) there is a fuel cone which is moving

toward the lower zone of the chamber. After 1 ms from EOI the spark discharge location is still

inside the fuel cone which leads to the creation of a locally rich mixture around the spark electrode

tips. Therefore a strong flame kernel with a high burning speed and high energy release rate is

initiated and propagates inside the chamber without quenching. If the spark delay time is increased

to 5 ms as illustrated in Figure 3.2 (b) the vertex of the fuel cone passes the spark plug location

and most of the fuel concentrates in the lower half of the chamber. A very lean mixture will be

created locally at the spark electrode tips and the initiated flame kernel will be very weak with a

low burning speed. In this condition the energy release rate is reduced and after a while the flame

will be quenched.

Figure 3.2. Methane distribution around the spark discharge location at two different spark delay times (a)

Tsd = 1 ms and (b) Tsd = 5 ms at equivalence ratio of 0.6

68

3.4.2. Injection Pressure Effects

To investigate the effect of injection pressure on combustion characteristics, different injection

pressures of 30, 50, 70 and 90 bar at constant chamber pressure of 1 bar and chamber temperature

of 298 K were considered. As shown in Figure 3.3, peak pressure and maximum rate of pressure

rise are nearly constant at different injection pressures for a given equivalence ratio. At the given

overall equivalence ratio the effect of high injection velocity in the case of high injection pressure

could be compensated for by the effect of large injection duration in the case of low pressure

injection. Consequently in this case the turbulence intensity remains constant. In other words,

turbulence intensity created by fuel injection does not depend on injection pressure. Injection

pressure therefore has a very weak effect on peak pressure and maximum rate of pressure rise.

Figure 3.3. Effect of injection pressure on peak pressure and maximum rate of pressure rise at chamber

pressure of 1 bar, chamber temperature of 298 K and spark delay time of 1 ms for equivalence ratios of

0.6, 0.8 and 1.0

The only observed effect of injection pressure is related to initial combustion duration, which

is the time from the start of ignition to 10 percent of pressure rise due to combustion [84]. This is

more recognizable in lean mixtures and short spark delay times as shown in Figure 3.4. The initial

combustion duration will be increased slightly with decreasing injection pressure at an overall

69

equivalence ratio of 0.6 and spark delay time of 1 ms while significant changes are not seen in

other cases. The higher the injection pressure, the more stratified the mixture. The existence of a

stratified mixture creates a local rich mixture at the spark location increasing burning speed of the

flame kernel and decreasing the initial combustion duration. The flame does not propagate at a

spark delay time of 5 ms and overall equivalence ratio of 0.6 due to combustion instability as

described in the previous section. In the Figures 3.3 and 3.4, the maximum uncertainty of the peak

pressure, maximum rate of pressure rise and initial combustion duration were ±2.5%, ±9% and

±4%, respectively. The uncertainties of the other figures are within the mentioned appropriate

range.

Figure 3.4. Effect of injection pressure on initial combustion duration at different spark delay times at

chamber pressure of 1 bar and chamber temperature of 298 K for equivalence ratios of 1.0 and 0.6

3.4.3. Chamber Pressure and Temperature Effects

To evaluate the effect of chamber temperature and chamber pressure on combustion

characteristics, chamber pressures from 1 to 3 bar and chamber temperatures from 298 to 423 K

at injection pressure of 90 bar and spark delay time of 1 ms for different equivalence ratios from

0.6 to 1.0 were considered. Chamber pressure could be increased by increasing the mass of fuel-

air mixture which leads to increasing peak pressure and maximum rate of pressure rise as shown

70

in Figures 3.5 and 3.6 respectively. In these figures similar behavior is observed with increasing

chamber temperature due to increasing burning speed and higher flame temperature. However the

effect of the chamber pressure is more significant than that of the chamber temperature.

Figure 3.5. Effect of chamber temperature and chamber pressure on peak pressure at injection pressure of

90 bar, spark delay time of 1 ms and equivalence ratios of 0.6, 0.8 and 1.0

The main combustion duration, the time from 10 percent to 90 percent of pressure rise due to

combustion [84], is decreased with increasing chamber temperature and is increased with

increasing chamber pressure as shown in Figure 3.7. Main combustion duration is mainly

dependent on laminar burning speed and turbulence intensity. In this case the effect of laminar

burning speed is more significant than turbulence intensity because the laminar burning speed is

dependent on chamber pressure and chamber temperature while turbulence intensity is less

dependent on them and is nearly constant. The laminar burning speed of methane is increased with

increasing chamber temperature and is decreased with increasing chamber pressure.

71

Figure 3.6. Effect of chamber temperature and chamber pressure on maximum rate of pressure rise at

injection pressure of 90 bar, spark delay time of 1 ms and equivalence ratios of 0.6, 0.8 and 1.0

Figure 3.7. Effect of chamber temperature and chamber pressure on main combustion duration at injection

pressure of 90 bar, spark delay time of 1 ms and equivalence ratios of 0.6, 0.8 and 1.0

72

3.4.4. Hydrogen Addition Effects

Flame propagation images are an impressive way to go through the combustion details.

Figure 3.8 shows the effect of hydrogen addition on the flame propagation process at an injection

pressure of 90 bar, a spark delay time of 1 ms and an equivalence ratio of 0.8. The snapshots are

shown at 1.0, 2.4, 3.9 and 5.4 ms after spark ignition with various hydrogen percentages. Short

spark delay time produces a relatively lean mixture at the upper zone and a relatively rich mixture

at the bottom zone of the combustion chamber with a high degree of stratification and therefore

causes the flame to propagate first to the bottom rich mixture and then to the upper lean mixture.

H2 5.4 ms 3.9 ms 2.4 ms 1 ms

0%

10%

20%

30%

40%

Figure 3.8. Effect of hydrogen addition on flame propagating process at four different times after spark

ignition (1.0, 2.4, 3.9 and 5.4 ms), injection pressure of 90 bar, spark delay time of 1 ms and equivalence

ratio of 0.8

73

To compare the effect of hydrogen addition, it is necessary to assure that the overall equivalence

ratio is constant. For this reason the injection duration of methane should decrease with increasing

hydrogen content. Reduction of injection duration would lead to decreasing turbulence intensity

level which in turn decreases burning rate. On the other hand increasing the content of hydrogen

in the mixture could increase the burning speed and improve combustion efficiency. These two

factors behave inversely, but flame propagation images illustrate that the effect of hydrogen

addition on the burning speed is much greater than the decrease of turbulence intensity.

This indicates that the effect of turbulent flow and fuel-air stratified distribution in the chamber

generated by high-pressure methane injection on flame propagation becomes weak with increasing

hydrogen content. It could be seen that the flame kernel occupies a larger volume at the same time

after ignition with a higher amount of hydrogen in the mixture.

Peak pressure and maximum rate of pressure rise as a function of hydrogen addition is shown

in Figure 3.9. It can be seen that peak pressure and maximum rate of pressure rise would be

increased with hydrogen addition but the effect of hydrogen addition is more significant in lean

mixtures.

Figure 3.9. Effect of hydrogen addition on peak pressure and maximum rate of pressure rise at injection

pressure of 90 bar, chamber pressure of 1 bar, chamber temperature of 298 K and spark delay time of 1

ms for equivalence ratios of 0.6, 0.8 and 1.0

74

In other words, the lean burn limit of methane can be extended with increasing hydrogen in the

mixture. The methane-air mixture combustion with 40% hydrogen content at an overall

equivalence ratio of 0.6 gives nearly the same peak pressure as pure methane-air mixture

combustion at an equivalence ratio of 0.8.

The main combustion durations and NOx concentrations at different equivalence ratios are

shown in Figure 3.10. The main combustion durations decreased with increasing hydrogen content.

This would be due to the high reactivity and high diffusivity of hydrogen which enhances the

burning speed and consequently increases burning rate. The effect of hydrogen addition on

combustion duration is more remarkable at lean mixture condition. The NOx concentrations are

increased with increasing hydrogen fraction at all equivalence ratios due to increase of combustion

temperature but its effect is more significant in lean mixtures. The percentages of increase of NOx

concentration are 112.6, 10.4 and 11.58 in equivalence ratios of 0.6, 0.8 and 1.0 respectively. The

NOx concentration is dependent on two important factors: combustion temperature and air

availability. In the equivalence ratio around 0.8 the combined effect of the foregoing factors led to

significant NOx concentration.

Figure 3.10. Effect of hydrogen addition on main combustion duration and NOx concentration at injection

pressure of 90 bar, chamber pressure of 1 bar, chamber temperature of 298 K and spark delay time of 1

ms for equivalence ratios of 0.6, 0.8 and 1.0

75

3.4.5. Diluent Addition Effects

In this study a mixture of 14% carbon dioxide and 86% nitrogen, having the same specific heat

of burned gases, was used to simulate diluent. In this case there is no hydrogen addition. Diluent

addition has two remarkable effects as shown in Figure 3.11. First, peak pressures are decreased

with increasing diluent fractions at all equivalence ratios and all spark delay times due to reduction

of burned gas temperature. Second, diluent addition creates misfiring and combustion instability

in some conditions.

Figure 3.11. Effect of diluent addition on peak pressure at injection pressure of 90 bar, chamber pressure

of 1 bar, chamber temperature of 298 K and equivalence ratios of 0.6, 0.8 and 1.0 for different spark delay

times

76

Combustion instability indicates that the formed flame kernel is quenched since the energy loss

rate is greater than the energy release rate. For example, at an equivalence ratio of 0.8 there is no

flame propagation at spark delay times of 1, 5 and 40 ms for diluent fractions larger than 5, 10 and

25% respectively.

The snapshots in Figure 3.12 visualize the combustion instability as a function of time after

spark at a diluent fraction of 25% and spark delay time of 40 ms for stoichiometric mixture. In this

figure flame kernel position is indicated using a red closed curve. The flame kernel cannot

propagate as time goes on and after a while it will be extinguished due to the high energy loss

which is created by high turbulence intensity due to high pressure methane injection inside the

combustion chamber.

Maximum rate of pressure rise, main combustion duration and NOx concentration versus diluent

fractions at spark delay time of 110 ms for all equivalence ratios are shown in Figure 3.13.

Maximum rate of pressure rise is decreased and main combustion duration is increased with

increasing diluent fraction. In the case of lean mixtures (Φ = 0.6) for diluent greater than 10% there

is no combustion.

Figure 3.12. Snapshots of combustion instability as a function of time after spark in diluent fraction of

25%, spark delay time of 40 ms and equivalence ratio of 1.0

77

For low diluent fractions (smaller than 7%) NOx concentration at an equivalence ratio of 0.8 is

larger than that for an equivalence ratio of 1.0 and for diluent fractions greater than 7% it will be

reversed. This indicates that for diluent fractions greater than 7% the air availability has less effect

than combustion temperature and since the combustion temperature is larger in the stoichiometric

mixture (Φ = 1.0) it leads to an increase in NOx emission.

Figure 3.13. Effect of diluent addition on maximum rate of pressure rise, main combustion duration and

NOx concentration at injection pressure of 90 bar, chamber pressure of 1 bar, chamber temperature of 298

K and spark delay time of 110 ms for equivalence ratios of 0.6, 0.8 and 1.0

78

NOMENCLATURE

(dP/dt)max maximum rate of pressure rise (bar/ms)

Pch chamber pressure (bar)

Pmax peak pressure (bar)

Tch chamber temperature (K)

Tsd spark delay time (ms)

Δtmain main combustion duration (ms)

Φ overall equivalence ratio (-)

ΔU overall uncertainty

ΔB systematic uncertainty

ΔA random uncertainty

R physical parameter

ΔXi uncertainty of variable Xi

Abbreviations

CNG Compressed Natural Gas

CO Carbon Monoxide

CO2 Carbon Dioxide

CVCC Constant Volume Combustion Chamber

EOI End of Injection

H2 Hydrogen

HC Unburned Hydrocarbon

NOx Nitrogen Oxides

PFI Port Fuel Injection

RON Research Octane Number

SIDI Spark Ignition Direct Injection

79

4. Developing Alternative Approaches to Predicting

the Laminar Burning Speed of Refrigerants Using

the Minimum Ignition Energy

80

4.1. ABSTRACT

Measurement of laminar burning speed is complex and costly. Therefore, engineering

correlations of this thermo-chemical property with other simpler-to-measure fundamental

combustion properties such as Minimum Ignition Energy (MIE) are desired. Two different

correlations between laminar burning speed and minimum ignition energy have been developed.

The first correlation is of the form Sl = a MIE-1/3 and the second correlation of the form Sl =bMIEc,

where a, b and c are the fitting constants. The accuracies of these fits were close to each other.

4.2. INTRODUCTION

The need to replace high Global Warming Potential (GWP) refrigerants with environmentally-

friendly refrigerants has been motivated by concerns of climate change. While the environment

has been the primary driving force behind the search for next generation refrigerants, safety

considerations require thorough studies of the combustion characteristics of these potential

refrigerants. The burning speed, an important thermo-physical property of every fuel/oxidizer

mixture that characterizes how fast a flame burns through a premixed mixture, is one such

characteristic. Some refrigerants are classified as flammable and therefore, a leak from a

refrigeration system may result in a potentially dangerous situation.

ANSI/ASHRAE Standard 34–2010 [36] identifies the safety classification assigned to

refrigerants by ASHRAE SSPC 34 as shown in Figure 4.1. Class 1 refrigerants exhibit no

propagating flame when tested for flammability in air at 60°C and 101.3 kPa. Although having

lower heats of combustion than Class 1, Class 2 refrigerants exhibit lower flammability limits

when tested in air at 60°C and 101.3 kPa. A subclass, Class 2L, are refrigerants that meet the

requirements for Class 2 and also have burning speeds less than or equal to 10 cm/s in air and at

23°C and 101.3 kPa. Note that the 2L subclass, considered “mildly” flammable, is an optional

classification designed to better identify the flammability characteristics of a Class 2 refrigerant.

Class 3 refrigerants exhibit higher flammability limits at 60°C and 101.3 kPa and have a higher

heat of combustion.

81

Figure 4.1. Refrigerant safety group classification

Burning speed is defined as the speed at which a flame propagates normal to the flame front

and relative to the unburned gas ahead of it. In other words, considering a laminar one-dimensional

stationary flame, the speed of the incoming gas is the laminar burning speed (LBS) of the mixture.

There are several methods for measuring the LBS of a flammable mixture [2–

4,20,21,23,34,68,101–107].

Since measurement of LBS is costly, complex and time-consuming, engineering correlations

that relate this property to simpler-to-measure combustion parameters of refrigerants are desired.

In the absence of burning speed data, such correlations could provide quick predictive tools for

assessment and selection of new low GWP refrigerants. Flammability characteristics such as

Minimum Ignition Energy (MIE), Minimum Ignition Current (MIC), and Maximum Experimental

Safety Gap (MESG) may be used to predict burning speed. In this study, these flammability

characteristics have been reviewed. Their possible relationships to burning speed have also been

investigated and correlations between burning speed and minimum ignition energy have been

developed.

4.3. FLAMMABILITY CHARACTERISTICS

Flammability characteristics such as Minimum Ignition Energy (MIE), Minimum Ignition

Current (MIC) and Maximum Experimental Safety Gap (MESG) are introduced in this section.

82

4.3.1. Minimum Ignition Energy

Minimum Ignition Energy (MIE), as defined by ASTM-582-07 [108], is the electrical energy

discharged from a capacitor, which is just sufficient to effect ignition of the most easily ignitable

concentration of fuel in air under the specific test conditions. In the US, measurement of MIE is

conducted per ASTM-582-07. However, several other apparatuses and methods of measurement

exist. The variations in these measurement procedures have resulted in discrepancies in the

currently existing database of MIE data. The inconsistencies in the existing data are readily seen

in Table 4-1. As it can be seen, the MIE values vary by a factor of 3 for some of the fuels.

Table 4-1-Summary of MIE data (mJ)

Staggs [109] Lewellyn [110] Calcote [111] Babrauskak [112]

Acetone 1.15 0.6 1.15 1.15, 2.15

Acetaldehyde 0.38 -- 0.376 0.376, 0.58, 0.38

Benzene 0.55, 0.22, 0.2 0.5 0.55 0.55, 0.91, 0.22

Ethane 0.285, 0.42, 0.25 -- 0.285 0.285, 0.42, 0.26

Heptane 0.7, 1.15, 0.24 1.10 0.7 0.7, 1.15

Methane 0.47, 0.33, 0.21 -- 0.47 0.37, 0.71, 0.3

Propane 0.31, 0.29, 0.25 -- 0.305 0.305, 0.5, 0.26

4.3.2. Minimum Ignition Current

As defined by the International Electrotechnical Commission [113], the minimum ignition

current is the minimum current at which, in a specified spark test apparatus and under specified

conditions, the refrigerant, in it’s most easily-ignitable concentration, is capable of igniting.

Figure 4.2 shows the minimum ignition currents for a stoichiometric methane-air mixture at

various initial pressures and two electrode diameters.

4.3.3. Maximum Experimental Safe Gap

Maximum experimental safe gap (MESG) characterizes the ability of a confined gas mixture to

transmit a flame through a narrow gap into a surrounding atmosphere of the same gas mixture.

Table 4-2 shows values of MESG for different molecules as measured by different researches

using different apparatuses.

83

Figure 4.2. Minimum ignition currents for a stoichiometric CH4–air mixture, at various initial pressures

and two electrode diameters [113]

Table 4-2- Comparison of MESG values between several apparatuses [114]

Coast Guard

(mm)

Westerberg

(mm)

British

(mm)

NFPA 497

(mm)

AIT

(0C)

methanol 0.92 n/a 0.91 0.92 464

ethanol 1.02 n/a 1.02 0.89 363

acetaldehyde not listed 0.43 n/a 0.92 175

methane 1.17 1.12 1.17 1.12 537

butane 1.07 0.99 1.07 1.07 varies

n-pentane 1.02 0.56 0.99 0.93 260

diethyl ether 0.86 0.3 n/a 0.83 160

acetylene not listed 0.81 0.25 n/a 391

ammonia <0 .02 0.08 3.18 0.25 305

carbon monoxide 0.2 0.05 n/a 0.2 90

hydrogen 0.92 0.63 0.28 0.94 609

hydrogen sulfide 0.1 0.08 n/a 0.28 520

NFPA = National Fire Protection Association

Investigation was made to find relationships between the laminar burning speed and the three

flammability characteristics. However, the experimental data for MESG and MIC is scarce and

development of first-principle theoretical models to relate them to LBS is highly involved.

Therefore, the current study focuses on correlating LBS to MIE.

84

4.4. THEORETICAL CORRELATION AND RESULTS

Ignition by an electrical discharge is an extremely complex process and has been studied by

many researchers [113,115–135]. It involves three characteristically different stages. The first

stage, which occurs on a time scale of microseconds, involves the formation of a narrow spark

channel followed by the formation of plasma kernel with a radius of approximately 0.5 mm and a

temperature of 7000 K. The second stage, which occurs on a time scale of milliseconds, involves

the subsequent growth of a constant-mass plasma kernel of atomic ions and electrons due to the

input of additional electrical energy from the ignition system. The third and final stage involves

the ignition of the combustible gas mixture surrounding the hot plasma kernel to produce a

propagating flame. A physically correct energy balance, as shown in Figure 4.3, must include the

volumetric contributions of electric discharge, ionization and chemical reactions along with

appropriate boundary conditions on conductive, radiative and mass-diffusion energy transfers.

However, despite what is usually assumed in successful, yet simplified models [104], the plasma

kernel is non-spherical and the mass and energy boundary layers are present. As a result, the

complexity of the process makes the first-principle studies of ignition and transition to a self-

sustained propagating flame a difficult problem. However, based on phenomenological analysis,

several correlations have been proposed to relate MIE to various combustion parameters, e.g.

quenching distance, maximum experimental safety gap, minimum ignition current and laminar

burning speed (LBS). A complete report of such studies can be found in [112]. This article

investigates two potential correlations between MIE and Sl. The theoretical analysis of Minor [136]

and Jabbour [35,137] results in the following relation between MIE and the LBS:

𝑀𝐼𝐸~1

𝑆𝑙3 (4-1)

Nonetheless, it suggests a functional dependence of LBS on MIE. In the following sections, we

consider two different correlations. The first is a single variable correlation that fits the LBS data

to that of MIE based on the functional form suggested by relation (4-1). The second is a two

variable transcendental fit of LBS to the best MIE exponent and coefficient.

85

Figure 4.3. Schematic of a spherical flame kernel

4.5. SINGLE-VARIABLE ANALYSIS

Although several simplifying assumptions have been made to arrive at equation (4-1), this

equation suggests a functional dependence of LBS on MIE, namely

𝑆𝑙 = 𝑎𝑀𝐼𝐸−1 3⁄ (4-2)

In this analysis we determine the proportionality constant, a, in equation (4-2) by least-square

fitting the data in Table 4-3 to this function. In all fittings reported in this paper the average fitting

error, 𝜖𝑓, is defined by the following equation:

𝜖𝑓 =1

𝑛∑|(

𝑆𝑙𝑓− 𝑆𝑙

𝑚

𝑆𝑙𝑚 )

𝑘

|

𝑛

𝑘=1

(4-3)

where 𝑆𝑙𝑓 and 𝑆𝑙

𝑚 and n are the fitted and measured LBS’s and the number of fuels considered,

respectively. Table 4-3 contains measured values of MIE and 𝑆𝑙𝑚 that are used in this paper.

Figure 4.4 shows the result of this fit based on Table 4-3. The fit suggests a value of a to be 33.157,

and has an average error of 𝜖𝑓 = 12.91%..

86

Table 4-3- Source: Glassman, et al. [138]

Fuel Measured MIE (mJ) Measured Sl (cm/s)

Acetaldehyde 0.376 41.4

Acetone 1.15 42.6

Acrolein 0.137 65.9

Allyl chloride 0.775 32.4

Benzene 0.55 47.6

1,3-Butadiene 0.175 49.6

n-Butane 0.76 44.8

n-Butyl chloride 1.24 34.5

Diisopropyl ether 1.14 38.3

Dimethoxymethane 0.42 46.6

Dimethyl ether 0.33 48.4

Dimethyl sulfide 0.48 33

Ethane 0.285 44.5

Ethylamine 2.4 32.4

Furan 0.225 62.5

n-Heptane 0.7 42.2

Isopropyl alcohol 0.65 41.3

Isopropylamine 2 30.6

Isopropyl chloride 1.55 27.4

Isopropyl mercaptan 0.53 33

Methane 0.47 43.4

Methanol 0.215 48

Methyl ethyl ketone 0.68 43.3

n-Pentane 0.51 42.7

Propane 0.305 45.6

Propionaldehyde 0.325 49

n-Propyl chloride 1.08 27.5

Triethylamine 0.75 28.5

Vinyl acetate 0.7 41.4

Figure 4.4. MIE -1/3 vs. Sl for the twenty-nine values provided by Glassman, et al. [138]

87

Table 4-4- Source: Minor, et al. [136]

Fuel Measured MIE Range (mJ) Measured Sl (cm/s)

HFC-152a 0.38 23

Ammonia 100-300 7.2

HFC-32 30-100 6.7

HFO-1234yf 5000-10000 1.5

Also, Table 4-4 contains data of minimum ignition energy and laminar burning speed for four

refrigerants of interest that are used in this study. It can be seen that the measured MIE covers a

wide range of values. The values of MIE for Ammonia, HFC-32, and HFO-1234yf have been

reported to vary significantly. The uncertainty ranges provided in Table 4-4 can be used to fine-

tune the fit of MIE -1/3 for Sl.

Table 4-5 shows the fitted values of laminar burning speed for several adjustments of the values

contained in Table 4-4. As it can be seen, when the four refrigerants are added, the fit results in a

minimum average error of 15.45%, which is worse than that in Figure 4.4. Figure 4.5 shows the

fitted values for the best-case scenario resulting in the lowest average error (last set of data). This

implies that either the correlation presented in equation (4-1) is not accurate for slow burning fuels

and/or MIE and LBS data for low flame-speed refrigerants is not accurate. While additional data

points would improve the accuracy, there is still discrepancy due to the inconsistencies in

measurement procedures of MIE. Among the four refrigerants in Table 4-4, Ammonia is the only

one that does not contain carbon in its composition. It, therefore, suggests the possibility of

molecular structure dependent correlations. Figure 4.6 shows a slight increase in error when

Ammonia is removed from the plot. With Ammonia removed the fit results in an average error of

15.85%, showing Ammonia effect is negligible.

Table 4-5- Fitted values of laminar burning speed for several adjustments contained in Table 4-4

Fuel Measured MIE

(mJ)

Measured Sl

(cm/s)

Fitted Sl

(cm/s)

Average Error

for (29 +4)

fuels

HFC-152a 0.38 23 44.86

17.02% Ammonia 100 7.2 7.00

HFC-32 30 6.7 10.46

HFO-1234yf 5000 1.5 1.90

HFC-152a 0.38 23 44.86

17.63%

Ammonia 200 7.2 5.56

HFC-32 30 6.7 10.46

HFO-1234yf 5000 1.5 1.90

88

HFC-152a 0.38 23 44.87

17.92% Ammonia 300 7.2 4.86

HFC-32 30 6.7 10.46

HFO-1234yf 5000 1.5 1.90

HFC-152a 0.38 23 44.89

15.94% Ammonia 100 7.2 7.00

HFC-32 65 6.7 8.09

HFO-1234yf 5000 1.5 1.90

HFC-152a 0.38 23 44.86

16.53% Ammonia 100 7.2 7.00

HFC-32 30 6.7 10.46

HFO-1234yf 7500 1.5 1.66

HFC-152a 0.38 23 44.86

16.23% Ammonia 100 7.2 7.00

HFC-32 30 6.7 10.46

HFO-1234yf 10000 1.5 1.51

HFC-152a 0.38 23 44.89

16.06% Ammonia 200 7.2 5.56

HFC-32 65 6.7 8.09

HFO-1234yf 7500 1.5 1.66

HFC-152a 0.38 23 44.89

15.45% Ammonia 100 7.2 7.00

HFC-32 100 6.7 7.00

HFO-1234yf 5000 1.5 1.90

Figure 4.5. Adjusted fit of MIE -1/3 vs. Sl containing values from Table 4-5

89

HFC-152a is contributing a significant amount of error in the fit presented in Figure 4.5.

Removing this refrigerant from the database improves the accuracy of the fit from 15.85 in

Figure 4.5 to 13.24% in Figure 4.7.

Figure 4.6. Adjusted fit of MIE -1/3 vs. Sl without Ammonia.

Figure 4.7. Adjusted fit of MIE -1/3 vs. Sl without HFC-152a.

90

4.6. MULTI-VARIABLE ANALYSIS

Despite its relative success in correlating the measured LBS data with MIE, correlation (4-1)

suffers from inaccuracies. As noted in [134], since the burning speed varies by at least one order

of magnitude between the stoichiometric (45 cm/s) and the very lean (5 cm/s) mixtures for

propane-air mixtures, the ignition energy is predicted to vary by a factor of 103. The experimental

variation, however, is approximately by a factor of 105 for this fuel [134]. In this section we

consider the following power-law fit in order to investigate the possibility of a more accurate fit.

𝑆𝑙 = 𝑏𝑀𝐼𝐸𝑐 (4-4)

Table 4-6 shows predicted values of the laminar burning speed for data in Table 4-5 based on

the empirical correlation (4-4). The result of the fit is shown in Figure 4.8 with the average error

of 11.68%. Comparing this accuracy with the average error of predictions of correlation (4-2),

12.91%, the double variable fit is slightly more accurate than the single variable. The difference

in MIE’s exponent in Figure 4.8 is due to omitting the four refrigerants listed in Table 4-4. As

done in the single variable analysis, the four refrigerants will be added to the fit in order to

determine the prediction performance of the proposed multi-variable relationship over a wider

range of laminar burning speed values.

Table 4-6- Predicted values of burning speed using Equation (4-4). Glassman, et al. [138]

Fuel Measured MIE (mJ) Measured Sl (cm/s) Fitted Sl (cm/s) Error (%)

Acetaldehyde 0.376 41.4 44.977 8.64

Acetone 1.15 42.6 34.278 19.54

Acrolein 0.137 65.9 57.483 12.77

Allyl chloride 0.775 32.4 37.728 16.44

Benzene 0.55 47.6 41.007 13.85

1,3-Butadiene 0.175 49.6 54.163 9.20

n-Butane 0.76 44.8 37.908 15.38

n-Butyl chloride 1.24 34.5 33.656 2.44

Diisopropyl ether 1.14 38.3 34.351 10.31

Dimethoxymethane 0.42 46.6 43.784 6.04

Dimethyl ether 0.33 48.4 46.426 4.08

Dimethyl sulfide 0.48 33 42.386 28.44

Ethane 0.285 44.5 48.110 8.11

Ethylamine 2.4 32.4 28.666 11.52

Furan 0.225 62.5 50.955 18.47

n-Heptane 0.7 42.2 38.673 8.36

Isopropyl alcohol 0.65 41.3 39.375 4.65

91

Isopropylamine 2 30.6 29.965 2.07

Isopropyl chloride 1.55 27.4 31.880 16.35

Isopropyl mercaptan 0.53 33 41.377 25.39

Methane 0.47 43.4 42.603 1.83

Methanol 0.215 48 51.521 7.33

Methyl ethyl ketone 0.68 43.3 38.946 10.05

n-Pentane 0.51 42.7 41.766 2.19

Propane 0.305 45.6 47.324 3.78

Propionaldehyde 0.325 49 46.599 4.90

n-Propyl chloride 1.08 27.5 34.805 26.56

Triethylamine 0.75 28.5 38.030 33.44

Vinyl acetate 0.7 41.4 38.673 6.59

Figure 4.8. Adjusted fit containing values from Table 4-6.

Table 4-7 shows predictions of the multi-variable fit for several adjustments of MIE values of

the four refrigerants. Figure 4.9 shows the predicted values of the case corresponding to the lowest

average error (case with 15.33% average error).

Table 4-7- Predictions of the multi-variable fit for several adjustments of MIE values

Fuel Measured MIE (mJ) Measured Sl (cm/s) Fitted Sl (cm/s) Error (%)

HFC-152a 0.38 23 45.15

16.64% Ammonia 100 7.2 6.46

HFC-32 30 6.7 9.83

HFO-1234yf 5000 1.5 1.65

HFC-152a 0.38 23 45.04

17.48% Ammonia 200 7.2 5.38

HFC-32 30 6.7 10.24

92

HFO-1234yf 5000 1.5 1.81

HFC-152a 0.38 23 44.97

17.94% Ammonia 300 7.2 4.88

HFC-32 30 6.7 10.50

HFO-1234yf 5000 1.5 1.91

HFC-152a 0.38 23 45.25

15.72% Ammonia 100 7.2 6.70

HFC-32 65 6.7 7.76

HFO-1234yf 5000 1.5 1.75

HFC-152a 0.38 23 44.95

16.38% Ammonia 100 7.2 6.76

HFC-32 30 6.7 10.18

HFO-1234yf 7500 1.5 1.56

HFC-152a 0.38 23 44.83

16.22% Ammonia 100 7.2 6.97

HFC-32 30 6.7 10.42

HFO-1234yf 10000 1.5 1.50

HFC-152a 0.38 23 45.047

16.23% Ammonia 200 7.2 5.805

HFC-32 65 6.7 8.384

HFO-1234yf 7500 1.5 1.775

HFC-152a 0.38 23 45.28

15.33% Ammonia 100 7.2 6.85

HFC-32 100 6.7 6.85

HFO-1234yf 5000 1.5 1.82

Figure 4.9. Adjusted fit containing values from Table 4-7.

93

The multi-variable analysis shows 10% improvement in the average error over the -1/3 power

law correlation for faster burning fuels. As done in the single variable analysis, the multi-variable

plot has also been considered without Ammonia, which is chemically different than the other

refrigerants studied. Figure 4.10 shows a slight increase in the average error of the fit, from 15.33%

to 15.57% with Ammonia removed, showing negligible changes.

Again, it has been determined that HFC-152a is contributing a significant amount of error to

this fit. Eliminating HFC-152a from the fitting dataset reduces the average error from 15.33% to

12.75%. Figure 4.11 contains predictions corresponding to this case. A parametric study was made

by varying minimum ignition energy of HCF-152a from 0.1 mJ to 3 mJ as an input to the fit.

Table 4-8 and Figure 4.12 show the errors of the fits for different values of minimum ignition

energy of HFC-152a. As it can be seen the error reduces by 33% as MIE of HCF-152a is increased

from 0.1 mJ to 3mJ.

Figure 4.10. Adjusted fit with Ammonia removed.

94

Figure 4.11. Adjusted fit with HFC-152a removed.

Table 4-8- Errors of the fits for different values of MIE of HFC-152a

Fuel Measured MIE

(mJ)

Measured Sl

(cm/s)

Fitted Sl

(cm/s) Average Error

HFC-152a 0.1 23 66.023

19.52 % Ammonia 200 7.2 6.070

HFC-32 65 6.7 8.639

HFO-1234yf 7500 1.5 1.945

HFC-152a 0.5 23 41.324

15.70 % Ammonia 200 7.2 5.791

HFC-32 65 6.7 8.372

HFO-1234yf 7500 1.5 1.764

HFC-152a 1.0 23 33.154

14.50 % Ammonia 200 7.2 5.740

HFC-32 65 6.7 8.326

HFO-1234yf 7500 1.5 1.729

HFC-152a 1.5 23 29.098

13.91 % Ammonia 200 7.2 5.733

HFC-32 65 6.7 8.326

HFO-1234yf 7500 1.5 1.721

HFC-152a 2.0 23 26.524

13.55 % Ammonia 200 7.2 5.750

HFC-32 65 6.7 8.350

HFO-1234yf 7500 1.5 1.726

HFC-152a 2.5 23 24.685

13.30 % Ammonia 200 7.2 5.762

HFC-32 65 6.7 8.369

HFO-1234yf 7500 1.5 1.730

HFC-152a 3.0 23 23.303

13.13% Ammonia 200 7.2 5.803

HFC-32 65 6.7 8.419

HFO-1234yf 7500 1.5 1.749

95

Figure 4.12. Average error of the fit as a function MIE of in HFC-152a

NOMENCLATURE

a, b and c fitting constants

n number of fuels considered

Sl laminar burning speed

Slf fitted laminar burning speed

Slm measured laminar burning speed

εf average fitting error

Abbreviations

MIE Minimum Ignition Energy

GWP Global Warming Potential

LBS laminar burning speed

MESG Maximum Experimental Safety Gap

MIC Minimum Ignition Current

96

5. On the Thermodynamic Properties of Thermal

Plasma in the Flame Kernel of Hydrocarbon/Air

Premixed Gases

97

5.1. ABSTRACT

Thermodynamic properties of hydrocarbon/air plasma mixtures at ultra-high temperatures must

be precisely calculated due to important influence on the flame kernel formation and propagation

in combusting flows and spark discharge applications. A new algorithm based on the complete

chemical equilibrium assumption is developed to calculate the ultra-high temperature plasma

composition and thermodynamic properties, including enthalpy, entropy, Gibbs free energy,

specific heat at constant pressure, specific heat ratio, speed of sound, mean molar mass, and degree

of ionization. The method is applied to compute the thermodynamic properties of H2/air and

CH4/air plasma mixtures for different temperatures (1,000 - 100,000 K), different pressures (10-6

- 100 atm), and different fuel/air equivalence ratios within flammability limit. In calculating the

individual thermodynamic properties of the atomic species needed to compute the complete

equilibrium composition, the Debye-Huckel cutoff criterion has been used for terminating the

series expression of the electronic partition function so as to capture the reduction of the ionization

potential due to pressure and the intense connection between the electronic partition function and

the thermodynamic properties of the atomic species and the number of energy levels taken into

account. Partition functions have been calculated using tabulated data for available atomic energy

levels. The Rydberg and Ritz extrapolation and interpolation laws have been used for energy levels

which are not observed. The calculated plasma properties are then presented as functions of

temperature, pressure and equivalence ratio, in terms of a new set of thermodynamically self-

consistent correlations that are shown to provide very accurate fits suitable for efficient use in CFD

simulations. Comparisons with existing data for air plasma show excellent agreement.

Keywords: high temperature, ionized gas, thermal plasma, partition function, Debye-Huckel, local

thermodynamic equilibrium, thermodynamic properties, statistical thermodynamic, correlation,

fuel/air mixture, flame kernel formation

5.2. INTRODUCTION

To improve efficiency and reduce pollutant formation in internal combustion engines [14],

knowledge of flame kernel development and flame propagation play important role. A plasma, at

very high temperature, will be generated at the onset of spark discharge. Accurate modeling of the

thermodynamic properties of plasma mixtures is essential to understand the evolution of the

98

plasma channel and its evolution into the formation of the flame kernel. During the spark discharge

in a fuel-air mixture, the electrical energy is injected in a constant volume process followed by a

sudden expansion which leads to the formation of fully ionized high temperature plasma through

the generation of a shock wave and the consequent dissociation and ionization of the mixture. The

plasma thermodynamic properties and its degree of ionization have important effects on flame

ignition, structure, and propagation.

During the past decades a significant progress in plasma applications such as cutting, spraying,

arc heating, re-entry of space-vehicles, nuclear rockets, CFD simulation of high-temperature flow

fields and spark ignition has happened. To model and control the plasma flow in these applications,

energy, mass, and momentum transfer are very important. As a result, the thermodynamic

properties of plasma mixtures at high temperatures must be estimated by means of sophisticated

models to ensure accurate simulations of the plasma flow field. In many applications it is possible

to model plasma mixtures behavior by the equation of state of an ideal gas in local thermodynamic

equilibrium (LTE).

In the last six decades, many papers have been published on the thermodynamic properties of

plasma mixtures with particular attention to air species because of their importance in the aero-

thermodynamic analysis of hypersonic flows surrounding a space vehicle during its reentry into

the Earth's atmosphere. Gilmore [139,140] reported results for composition and thermodynamic

properties of air for temperatures between 1000 K and 24,000 K. Calculations assume a perfect

gas mixture in local thermodynamic equilibrium, including dissociation and ionization. Hansen et.

al. [141–143] studied the space-vehicle traveling at high speed which excite the air to high

temperature, resulting in dissociation and ionization of air. His method was valid to predict the

thermodynamic properties of air up to 15,000 K and considered dissociation and only first

ionization of nitrogen and oxygen. Rosenbaum and Levitt [144] derived expressions for the

composition, specific volume, enthalpy, and entropy of hydrogen plasmas up to 100,000 K.

Lick and Emmons [145] calculated the thermodynamic properties of helium plasmas at

temperatures up to 50,000 K. They considered a mixture composed of neutral helium atoms, singly

and doubly ionized helium atoms, and electrons. Brown calculated equilibrium high-temperature

thermodynamic properties of the atmospheres of Earth [146], Mars [147] and Venus [148] for

studying flights in planetary atmospheres in the shock and boundary layers. Drellishak et al. [149]

99

calculated equilibrium composition and the thermodynamic properties of argon plasma for five

pressures of 0.1, 0.5, 1.0, 2.0 and 5.0 atm, and for the temperature range from 5000 K to 35,000

K. Kubin and Presley [150] calculated the thermodynamic properties of hydrogen plasmas for a

temperature up to 20,000 K. Hydrogen atoms were assumed to have only six energy levels. They

neglected the reduction in the ionization potential and arbitrarily cut off the electronic partition

function at six terms.

Patch and McBride [151] obtained thermodynamic properties for H3+ and H2

+ at temperatures

between 298K and 10,000K. Patch [152] calculated the equilibrium composition of a hydrogen

plasma for pressures ranging from 1 to 100 atm at temperatures of 400 K to 40,000 K. Nelson

[153] calculated and tabulated thermodynamic properties of an atomic hydrogen-helium plasma

for temperatures from 10,000 K to 100,000 K. Pateyron et al. [154,155] calculated thermodynamic

properties such as specific enthalpy and specific heat of the Ar-H2 and Ar-He plasmas up to 30,000

K using partition functions of species. Sher et al. [156] calculated the specific heat capacity and

mole fractions of the air at high temperatures using a simplified thermodynamic model to study

the formation of spark channels. Capitelli et al. [157–161] calculated thermodynamic and transport

properties of air at high temperatures assuming that the plasma is in local thermodynamic

equilibrium (LTE) for temperatures up to 100,000 K. D’Angola et. al. [162] calculated

thermodynamic and transport properties of high temperature equilibrium air plasmas in a wide

range of pressure (0.01 atm to 100 atm) and temperature range (50 to 60,000 K). Rat et al. [163]

performed an alternate derivation of transport properties in a nonreactive two-temperature plasma

without Bonnefoi’s assumptions. They applied their model for a two-temperature argon plasma

and figured that the theory of transport coefficients of Devoto and Bonnefoi underestimates the

electron thermal conductivity. Murphy calculated the transport coefficients such as viscosity,

thermal conductivity and electrical conductivity of different species including hydrogen and

mixtures of argon-hydrogen [164] and helium and its mixture with argon [165] using local

thermodynamic equiblirium at atmospheric pressure in the temperature range from 300 to 30,00

K.

The above literature shows that most of the works dealt only with air and some fundamental

gases like, Hydrogen, Helium, Argon, and their mixtures. It also reveals a shortage of exact curve-

fit correlations of thermodynamic properties of fuel/air plasma mixtures such as hydrogen/air and

methane/air which have many important applications in automotive and aviation industries

100

[46,47], as well as in other studies dealing with plasma mixtures. The combustion community

suffers from lack of these kind of correlations which in CFD simulations of plasma mixture flows

can be easily implemented and effectively reduce numerical complications and computation time.

Curve-fit correlations have only been reported in few works with high emphasis on air plasma.

The purpose of this paper is to provide the thermodynamic properties and equilibrium

composition of hydrogen/air and methane/air plasma mixtures. The correlations we propose

provide the equilibrium composition and the thermodynamic properties such as enthalpy, entropy,

Gibbs free energy, specific heat at constant pressure, specific heat ratio, speed of sound, mean

molar mass, and degree of ionization for a wide range of temperatures (1,000 - 100,000 K),

pressures (10-6 – 102 atm) and different equivalence ratios within flammability limit (for

methane/air mixture flammability limit is 0.6 < 𝜙 < 1.4 and for hydrogen/air mixture

flammability limit is 0.5 < 𝜙 < 5.0). To calculate the thermodynamic properties of a plasma

mixture, it is necessary to evaluate the individual properties of the pure components and calculate

the equilibrium composition. For polyatomic molecules and molecular ions, which are the

dominant components during the dissociation phase, the individual thermodynamic properties are

extracted from the NASA database [166]. For monoatomic molecules, atomic ions, and electrons,

the individual thermodynamic properties are computed by statistical thermodynamic methods

using a rigorous calculation of the electronic partition functions. Griem's self-consistent model

[167] is used for the reduction of the ionization potential based on Debye-Huckel length. This

model uses a cut-off of the electronic partition function expansion series in order to prevent its

divergence problem. The effect of the number of energy levels on thermodynamic properties is

illustrated by comparing the results with the ground state method. In order to determine the

equilibrium composition, the complete equilibrium method based on Gibbs free energy

minimization assuming ideal gas equation of state, mass conservation, and electrical neutrality

[168,169] has been applied.

The paper is structured as follows. Section 3 discusses the importance of plasma study in flame

kernel modeling in the spark ignition process. Section 4 illustrates the model and the various

assumptions in detail. Section 5 presents and discusses the results. Section 6 gives some

conclusions. The Appendix gives the coefficients of the proposed correlations.

101

5.3. PLASMA APPLICATION IN SPARK IGNITION PROCESS

It is a well-known fact that in the spark and laser ignition, high temperature ionized gases is

the source of flame kernel formation and propagation. In conventional spark ignition, electrical

energy is supplied through an external source (e.g. a spark plug). A part of electrical energy is

converted to thermal energy by ionizing the gases. This conversion process involves the formation

of a plasma kernel which can potentially form a flame kernel. The formation of spark kernel

consists of two parts [104]. The first, the shorter stage involves a pressure wave emission; the

second stage which is longer is a constant pressure process. In the second stage the diffusion of

reactants and ions conclude the initial flame kernel [104]. In both stages the high density electrical

energy creates ions in an extremely high temperature environment. In our previous work, we

calculated the properties of the initial spark kernel by employing a thermodynamic model validated

by experiments [104]. For an initial plasma kernel the energy balance for the control volume shown

in Figure 5.1, is given by:

𝜕𝐸

𝜕𝑡= �̇�𝑏 (ℎ𝑢𝑓 + 𝑐𝑝𝑢𝑇𝑢) +

𝑑𝑆𝐸

𝑑𝑡− �̇�𝑐𝑜𝑛𝑑 − �̇�𝑟𝑎𝑑 − 𝑃�̇� (5-1)

𝐸 = 𝑚(𝑢𝑏𝑓 + 𝑐𝑣𝑏𝑇𝑏) (5-2)

where E is the energy of the burned gas region, m the mass of the gas, T the temperature, h the

specific enthalpy, u the specific internal energy, cp the specific heat at constant pressure, cv the

specific heat at constant volume, SE the supplied spark energy, t the time, Qcond the conductive

energy losses, Qrad the radiated energy losses, P the pressure and V the volume of the kernel, u, b

and f subscripts refer to unburned, burned and formation.

102

Figure 5.1. Schematic of flame propagation model [104]

Figure 5.2. The effect of initial radius on air kernel temperature, Ti = 7000 K, discharge energy = 24 mJ

[104]

By solving the Eqs. (5-1) and (5-2), the kernel temperature at several conditions was calculated.

Figure 5.2 shows the temperature of kernel at different initial radii. It can be seen that the

temperature is high enough for the formation of plasma ions. We have shown that at temperatures

higher than 6000 K the thermodynamic properties such as cv and cp in Eqs. (5-1) and (5-2) are

strong function of ionization processes [170]. In previous work [104] due to low concentration of

Time (ms)

Te

mp

era

ture

(K)

0 0.5 1 1.5 2 2.5 30

10000

20000

30000

40000

50000

60000

70000

ri = 0.45 mm

ri = 0.5 mm

ri = 0.55 mm

103

methane molecule the thermodynamic properties of methane/air plasma were approximated by

considering only air and neglecting methane in the mixture. This rough assumption can be

resolved by keeping all the components available in the real plasma mixture which will enhance

the accuracy of thermodynamic properties by including hydrogen, helium, carbon, argon and neon

ions in the computations. Laminar burning speed [22,24,25,171], an important thermo-physical

properties of combustible mixtures, can be calculated using the method introduced in previous

publication [104] in conjunction with exact plasma simulation of hydrocarbon/air premixed gases

in this study at ultra-high pressures at which the flame is always cellular and unstable.

5.4. METHOD OF CALCULATION

The calculations described here, and the resulting correlations, are based on the following three

assumptions, which are valid for many plasma mixtures: (1) the plasma is in local thermodynamic

equilibrium; (2) the plasma mixture is quasi-neutral; and (3) the plasma mixture and its individual

components obey the ideal gas equation of state. Under such conditions, Boltzmann statistics is

applicable. Calculations have been carried out in two different temperature ranges, called

dissociation and ionization. To obtain realistic calculations, all minor species have been

considered, for an overall of 133 species as listed in Table 5-1 for both methane/air and

hydrogen/air plasma mixtures.

Table 5-1- List of the 133 species considered in the present calculations for H2/Air and CH4/Air plasma

mixtures.

Plasma mixture Available species

H2/Air

and

CH4/Air1 [172]

𝐶𝐻, 𝐶𝐻+, 𝐶𝐻2, 𝐶𝐻2𝑂𝐻, 𝐶𝐻2𝑂𝐻+, 𝐶𝐻3, 𝐶𝐻3𝑂, 𝐶𝐻3𝑂𝐻, 𝐶𝐻4,

𝐶2𝐻, 𝐶2𝐻2, 𝐶𝐻2𝐶𝑂, 𝐶2𝐻3, 𝐶𝐻3𝐶𝑁, 𝐶𝐻3𝐶𝑂, 𝐶2𝐻4, 𝐶2𝐻4𝑂, 𝐶𝐻3𝐶𝐻𝑂, 𝐶2𝐻5, 𝐶2𝐻6, 𝐶3𝐻7, 𝐶3𝐻8, 𝐶𝑁, 𝐶𝑁

+, 𝐶𝑁−, 𝐶𝑁𝑁, 𝐶𝑂, 𝐶𝑂+, 𝐶𝑂2, 𝐶𝑂2+,

𝑁𝐶𝑂,𝐻𝐶𝑂,𝐻𝐶𝑂+, 𝐻𝐶𝑁,𝐻𝐶𝐶𝑁,𝐻𝐶𝐶𝑂,𝐻𝑁𝐶, 𝐻𝑁𝐶𝑂,𝐻𝑁𝑂, 𝑂𝐻,𝑂𝐻−, 𝑂𝐻+, 𝐻𝑂2, 𝐻𝑂2

−, 𝐻2𝑂,𝐻2𝑂+, 𝐻2𝑂2, 𝑁𝐻,𝑁𝐻

+, 𝑁𝐻2, 𝑁𝐻3, 𝑁𝑂,𝑁𝑂+,

𝑁𝑂2, 𝑁𝑂2−, 𝑁2𝑂,𝑁2𝑂

+, 𝐻2, 𝐻2−, 𝐻2

+, 𝐻, 𝐻−, 𝐻+, 𝐻𝑒, 𝐻𝑒+, 𝐻𝑒+2, 𝐶, 𝐶−, 𝐶2, 𝐶2

−, 𝐶2+, 𝐶+, 𝐶+2, 𝐶+3, 𝐶+4, 𝐶+5, 𝐶+6, 𝑁, 𝑁−, 𝑁2, 𝑁2

−, 𝑁2+, 𝑁+, 𝑁+2,

𝑁+3, 𝑁+4, 𝑁+5, 𝑁+6, 𝑁+7, 𝑂, 𝑂−, 𝑂2, 𝑂2−, 𝑂2

+, 𝑂+, 𝑂+2, 𝑂+3, 𝑂+4, 𝑂+5, 𝑂+6, 𝑂+7, 𝑂+8, 𝑁𝑒, 𝑁𝑒+, 𝑁𝑒+2, 𝑁𝑒+3, 𝑁𝑒+4, 𝑁𝑒+5, 𝑁𝑒+6, 𝑁𝑒+7, 𝑁𝑒+8, 𝑁𝑒+9, 𝑁𝑒+10, 𝐴𝑟, 𝐴𝑟+, 𝐴𝑟+2, 𝐴𝑟+3, 𝐴𝑟+4, 𝐴𝑟+5, 𝐴𝑟+6, 𝐴𝑟+7, 𝐴𝑟+8, 𝐴𝑟+9, 𝐴𝑟+10, 𝐴𝑟+11, 𝐴𝑟+12, 𝐴𝑟+13, 𝐴𝑟+14, 𝐴𝑟+15, 𝐴𝑟+16, 𝐴𝑟+17, 𝐴𝑟+18, 𝑒−

1 N2: 78.084%, O2: 20.946, Ar: 0.9335%, CO2: 0.03398%, Ne: 0.001818% and He: 0.000702%

104

5.4.1. Dissociation Temperature Range

Increasing the temperature of a gas mixture causes the molecules not only to vibrate but also to

dissociate into elemental atoms. Depending on the initial gas mixture composition the dissociation

temperature range is typically characterized by lots of chemical reactions all actively contributing

to determine the equilibrium composition. Under such conditions, the accurate approach to

compute the equilibrium composition for given temperature and pressure is a complete equilibrium

calculation [173], namely, Gibbs free energy minimization constrained by elemental conservation

and electrical neutrality. The minimization algorithm used here is based on Lagrange’s multipliers

as implemented in the RAND method [168,169] . The thermodynamic properties for the molecules

and molecular ions are taken from NASA database [166] up to 20,000 K.

5.4.2. Ionization Temperature Range

At even higher temperatures the gas mixture is characterized by the formation of positively

charged ions and unbound electrons created by the ionization reactions. Ions and electrons have a

significant effect on plasma properties at high temperatures and because of that a rigorous

statistical model which is described in the following subsections has been developed.

5.4.2.1. Thermodynamic Properties of Individual Monoatomic Species

The important step in calculating the high temperature properties of plasma mixtures is to

calculate the pure-substance thermodynamic properties of the individual monoatomic species

participating in the ionization reactions, i.e., neutral atoms, positive atomic ions, and electrons. For

gaseous species the thermodynamic functions may be calculated from spectroscopic constants

using the partition function concept [174]. Using the statistical thermodynamics formulation, the

partition functions and their first and second derivatives discussed in detail in subsection 5.4.2.2,

we can compute all the pure-substance thermodynamic properties. The specific enthalpy (kJ kg⁄ )

and specific entropy (kJ kg K⁄ ) of the pure ith species are given respectively by

ℎ𝑖𝑖(𝑇, 𝑃) = 2.5�̅�𝑇

𝑀𝑖+�̅�𝑇2

𝑀𝑖

1

𝑄𝑒𝑖∗

𝜕𝑄𝑒𝑖∗

𝜕𝑇 (5-3)

105

𝑠𝑖𝑖(𝑇, 𝑃) = 2.5�̅�

𝑀𝑖+�̅�𝑇

𝑀𝑖

1

𝑄𝑒𝑖

𝜕𝑄𝑒𝑖𝜕𝑇

+�̅�

𝑀𝑖ln [𝑄𝑒𝑖 (

2𝜋𝑀𝑖

𝑁𝐴)3 2⁄

(𝑘𝑇)5 2⁄ ℎ𝑝−3𝑃−1]

(5-4)

where, following Ref. [173] the double subscript 𝑖𝑖 in ℎ𝑖𝑖 and 𝑠𝑖𝑖 is used to denote pure-substance

specific properties, and to distinguish them from the partial properties ℎ𝑖 and 𝑠𝑖 of the same

component in the mixture; moreover,

𝑄𝑒𝑖∗ = 𝑄𝑒𝑖𝑒

−𝜖𝑖∗

𝑘𝑇 (5-5)

𝜕𝑄𝑒𝑖∗

𝜕𝑇= [

𝜕𝑄𝑒𝑖𝜕𝑇

+𝑄𝑒𝑖𝑘𝑇2

(𝜖𝑖∗ − 𝑇

𝜕𝜖𝑖∗

𝜕𝑇)] 𝑒

−𝜖𝑖∗

𝑘𝑇 (5-6)

where 𝜖𝑖∗ is the energy of formation of the ith species, 𝑄𝑒𝑖 is the electronic partition function of the

ith species, 𝑀𝑖 is its molar mass, �̅� the universal gas constant, 𝑁𝐴 Avogadro’s number, 𝑘 the

Boltzmann constant, ℎ𝑝 the Planck constant, 𝑃 the pressure and 𝑇 the gas temperature. The pure-

substance specific Gibbs free energy (kJ kg⁄ ) is calculated from enthalpy and entropy, 𝑔𝑖𝑖 = ℎ𝑖𝑖 −

𝑇𝑠𝑖𝑖, i.e.,

𝑔𝑖𝑖(𝑇, 𝑃) = 𝜇𝑖𝑖(𝑇, 𝑃) =�̅�

𝑘𝑀𝑖(𝜖𝑖

∗ − 𝑇𝜕𝜖𝑖

∗

𝜕𝑇) −

�̅�𝑇

𝑀𝑖ln [𝑄𝑒𝑖 (

2𝜋𝑀𝑖

𝑁𝐴)3 2⁄

(𝑘𝑇)5 2⁄ ℎ𝑝−3𝑃−1]

(5-7)

where the first equality is a reminder that for the pure substance the specific Gibbs free energy is

equal to the chemical potential. The pure-substance specific heat at constant pressure is evaluated

as the partial derivative of the specific enthalpy with respect to temperature,

𝑐𝑝𝑖𝑖(𝑇, 𝑃) = 2.5�̅�

𝑀𝑖+ 2

�̅�𝑇

𝑀𝑖

1

𝑄𝑒𝑖∗

𝜕𝑄𝑒𝑖∗

𝜕𝑇−�̅�𝑇2

𝑀𝑖(1

𝑄𝑒𝑖∗)

2

(𝜕𝑄𝑒𝑖

∗

𝜕𝑇)

2

+�̅�𝑇2

𝑀𝑖

1

𝑄𝑒𝑖∗

𝜕2𝑄𝑒𝑖∗

𝜕𝑇2

(5-8)

where

106

𝜕2𝑄𝑒𝑖∗

𝜕𝑇2= [

𝜕2𝑄𝑒𝑖𝜕𝑇2

+2

𝑘𝑇2(𝜖𝑖

∗ − 𝑇𝜕𝜖𝑖

∗

𝜕𝑇)𝜕𝑄𝑒𝑖𝜕𝑇

+1

𝑘2𝑇4(𝜖𝑖

∗ − 𝑇𝜕𝜖𝑖

∗

𝜕𝑇)

2

𝑄𝑒𝑖

−2

𝑘𝑇3(𝜖𝑖

∗ − 𝑇𝜕𝜖𝑖

∗

𝜕𝑇)𝑄𝑒𝑖 −

1

𝑘𝑇

𝜕2𝜖𝑖∗

𝜕𝑇2𝑄𝑒𝑖] 𝑒

−𝜖𝑖∗

𝑘𝑇

(5-9)

and we note that, differently from the standard ideal gas model, the enthalpy and the specific heat

here depend, though slightly, on pressure through the pressure-dependent cut-off criterion that we

adopt for the electronic partition function, as explained in the next subsection.

5.4.2.2. Partition Function

To calculate the pure-substance thermodynamic properties and the equilibrium mass fractions

of all the species present in the plasma, the knowledge of partition functions and their derivatives

are prerequisites. In general, the partition function of a molecular system can be expressed by

translational and internal contributions

𝑄 = 𝑄𝑡𝑟𝑄𝑖𝑛𝑡 (5-10)

The internal contribution may be due to the rotational, vibrational, and electronic motions

within the particle(𝑄𝑖𝑛𝑡 = 𝑄𝑟𝑄𝑣𝑄𝑒). For an atomic system (atoms, atomic ions and electrons) the

rotational and vibrational partition functions take the value of unity, so translational and electronic

partition functions for such species are:

𝑄𝑡𝑟 = (2𝜋𝑚𝑘𝑇

ℎ𝑝2)

3 2⁄�̅�𝑇

𝑃

(5-11)

𝑄𝑒 =∑𝑔𝑛𝑒−𝜖𝑛𝑘𝑇

𝑛

=∑(2𝐽𝑛 + 1)𝑒−𝜖𝑛𝑘𝑇

𝑛

(5-12)

where 𝑚 is the mass of the molecule, 𝜖𝑛 is the electronic energy of the 𝑛th level of the species

under consideration, 𝑔𝑛 its statistical weight, and 𝐽𝑛 the corresponding angular momentum

quantum number.

107

However, the summation in Eq. (5-12) diverges because the statistical weight increases rapidly

with the number of energy levels (e.g., for hydrogen atoms, 𝑔𝑛 ∝ 𝑛2). This behavior is correct just

for a hypothetical isolated atomic species, while interactions with other species in the plasma

mixture limit the number of energy levels. So an appropriate cut-off criterion is required for the

termination of electronic partition function of atomic species to define an upper limit for the

aforementioned series.

5.4.2.2.1. Cut-off Criteria

The only problem to calculate the pure-substance thermodynamic properties of plasma mixtures

is that the series for the electronic partition function of atomic species does not have an upper

bound. The exponential terms in Eq. (5-12) approach a finite limit corresponding to the ionization

potential, which is the upper bound to the energy but the statistical weight increases as the square

of the number of energy levels and consequently the series diverges. On the other hand, it has been

observed experimentally that as the temperature increases, due to a polarizing effect of neighboring

charged particles, the ionization potential of particles in a plasma is lowered [175]. In order to

prevent numerical divergence and match the empirically observed lowering of the ionization

potential, a criterion is needed for terminating the series of the electronic partition function. A

review of various cut-off criteria can be found in the literature [176,177]. These cut-off criteria

may be summarized as the following types:

1. No dependence on temperature or pressure [177,178]

2. Dependence on temperature only [177,179]

3. Dependence on temperature and pressure (or number density) [149,167]

The ionization potential of an atomic species in the presence of other ions and electrons is

decreased due to the action of the Coulomb fields. This reduction depends on the number densities

of the charged particles or the gas pressure. This means that the pure-substance thermodynamic

properties of single atomic species in the ionization range depend on both temperature and

pressure. The well-known Griem model [167,180] adopts the cut-off criterion to include only

energy levels below reduced ionization potential,

108

𝜖𝑛 ≤ 𝐼𝑃 − ∆𝐼𝑃 (5-13)

In current work the observed energy levels reported by Moore [181] and NIST [182] have been

completed with the Rydberg-Ritz formulas using the isoelectronic sequence method [183]. For the

atomic species including only one electron which are called hydrogenic species (H+, He+, C+6, N+7,

O+8, …) the statistical weight (𝑔𝑛) and energy (𝜖𝑛) of 𝑛th level have been evaluated using the

following relations,

𝑔𝑛 = 2𝑛2 (5-14)

𝜖𝑛 = 𝐼𝑃 (1 −1

𝑛2)

(5-15)

5.4.2.2.2. Reduced Ionization Potential

The reduced ionization potential, ∆𝐼𝑃 adopted by the Griem model [167,180] depends on the

plasma composition via the Debye-Huckel length 𝑙𝐷 and by making a self-consistent solution for

the problem. The reduction of the ionization potential of an atomic specie of charge 𝑧 is

∆𝐼𝑃𝑖 =(𝑧𝑖 + 1)𝑒

2

𝑙𝐷

(5-16)

where the Debye length is defined as

𝑙𝐷 = [𝑘𝑇

4𝜋𝑒2(∑ 𝑁𝑖𝑧𝑖2𝑁𝑆

𝑖=1 )]

1 2⁄

(5-17)

where 𝑒 is the charge of an electron, 𝑁𝑆 is the number of all species present in the plasma including

electrons and 𝑁𝑖 is the number density of 𝑖th species. Eq. (5-16) applies for densities and

temperatures for which the Debye theory is valid. Griem [167] and Cooper [184] derive the

criterion for the validity of the Debye theory as

∑𝑁𝑖

𝑁𝑆

𝑖=1

≥1

8𝜋𝑙𝐷3

(5-18)

109

5.4.2.3. Complete Equilibrium Solution Based On Gibbs Free Energy Minimization

This method is based on Gibbs free energy minimization under the assumption of Gibbs-Dalton

mixture of ideal gases [173] and subject to the constraints of element conservation and electrical

neutrality [168,169]. To determine complete equilibrium composition at a given temperature and

pressure, the Gibbs free energy of the mixture must be minimized, subject only to the constraints

of element conservation, electrical neutrality, and non-negativity of the mole numbers, i.e.,

{

∑ 𝑎𝑖𝑗𝑛𝑖 = 𝑞𝑗𝑛C𝑘Hℓ 𝑗 = 1,… ,𝑚𝑁𝑠

𝑖=1

∑ 𝑎𝑖0𝑛𝑖 = 0𝑁𝑠𝑖=1

𝑛𝑖 ≥ 0 ∀𝑖

(5-19)

where 𝑛C𝑘Hℓ is the mole number of hydrocarbon C𝑘Hℓ in the initial fuel-air mixture, 𝑛𝑖 is the mole

number of species 𝑖 in the equilibrium plasma mixture, 𝑁𝑠 the number of species present in the

plasma mixture, 𝑚 the number of different elements, 𝑎𝑖𝑗 represents the number of elements of type

𝑗 that compose the atom or molecule of species 𝑖 so that 𝑞𝑗 (dimensionless) represents the (fixed)

number of elements of type 𝑗 in the mixture per unit mole number of hydrocarbon in the initial

fuel-air mixture, and 𝑎𝑖0 represents the electrical charge of species 𝑖. In what follows we will

denote by 𝒒 the vector 𝑞1, … , 𝑞𝑚 of the given amounts of the elements in the mixture per unit

amount of initial fuel. For an initial C𝑘Hℓ-air mixture with equivalence ratio 𝜙 and molar

composition of air given by 𝑥N2a N2 + 𝑥O2

a O2 + 𝑥H2Oa H2O + 𝑥Ar

a Ar + 𝑥CO2a CO2 + 𝑥Ne

a Ne + 𝑥Hea He,

the values of the 𝑞𝑗 's are listed in Table A1 in Appendix.

Under the assumption of Gibbs-Dalton mixture of ideal gases, the Gibbs free energy of the

reacting mixture at a generic non-equilibrium composition can be written as

𝐺(𝑇, 𝑃, {𝑛𝑖}) = ∑𝑛𝑖𝜇𝑖,off(𝑇, 𝑃, {𝑛𝑖})

𝑁𝑠

𝑖=1

=∑𝑛𝑖 [𝜇𝑖𝑖0(𝑇) + 𝑅𝑇ln(

𝑛𝑖∑ 𝑛𝑗𝑁𝑠𝑗=1

) + 𝑅𝑇ln (𝑃

𝑃0)]

𝑁𝑠

𝑖=1

(5-20)

where, following [173], 𝜇𝑖,off(𝑇, 𝑃, {𝑛𝑖}) denotes the chemical potential of species i in the so-called

"surrogate system", namely, the frozen-composition non-reacting mixture (hence the "off"

110

subscript) at stable equilibrium with the same temperature 𝑇, pressure 𝑃, and composition {𝑛𝑖} as

the actual non-equilibrium state of the reacting mixture, and 𝜇𝑖𝑖0 is the chemical potential of pure

species 𝑖 at temperature 𝑇 and the standard pressure 𝑃0 = 1 atm, which we have defined in terms

of partition functions in the preceding subsection.

The minimization is done using an equilibrium composition solver based on the well-known

algorithm developed in [169] and convergence is considered satisfied based on the following

condition:

∆𝑛𝑖

𝑛𝑖< 10−15 ∀𝑖 (5-21)

As shown in [173], the solution can be formally expressed in terms of a set of 𝑚 + 1 Lagrange

multipliers 𝜆𝑗(𝑇, 𝑃, 𝒒), with 𝑗 = 0,1, … ,𝑚, so that the complete-equilibrium mole fractions are

given by

𝑥𝑖(𝑇, 𝑃, 𝒒) =𝑃0

𝑃exp [

1

�̅�∑𝜆𝑗(𝑇, 𝑃, 𝒒)𝑎𝑖𝑗 −

1

�̅�𝑇𝜇𝑖𝑖0(𝑇)

𝑚

𝑗=0

] (5-22)

Once the mole fractions 𝑥𝑖 are obtained, the mass fractions are readily found from 𝑦𝑖(𝑇, 𝑃, 𝒒) =

𝑥𝑖𝑀𝑖/∑ 𝑥𝑘𝑀𝑘𝑘 .

5.4.2.3.1. Iterative Solution

The iterative solution to find the mole fractions of all species at a given temperature, pressure,

and elemental composition proceeds as follows. Using the last calculated mole fractions, we

estimate the number densities 𝑁𝑖 using the ideal gas law

𝑁𝑖(𝑇, 𝑃, 𝒒) =𝑛𝑖𝑉=𝑛𝑖𝑛

𝑃

�̅�𝑇= 𝑥𝑖(𝑇, 𝑃, 𝒒)

𝑃

�̅�𝑇

(5-23)

to evaluate i) the Debye length, ii) the lowered ionization potential, and iii) the maximum number

of energy levels based on the cut-off criterion. Then the partition function is calculated by summing

over all such energy levels. The species mole fractions are then re-calculated using these partition

functions and the equilibrium composition solver. The new mole fractions are then used and a new

111

Debye length is determined. In general, the previous value of the Debye length and the new

calculated value do not agree. Therefore, the new value is used to compute again an improved

partition function, and the process is repeated until convergence is reached on the value of the

Debye length.

5.4.3. Mixture Thermodynamic Properties

Once the complete-chemical-equilibrium mole fractions of all the species are obtained, the

(mass) specific properties of the plasma mixture are determined using the Gibbs-Dalton mixture

model. Showing explicitly all dependences, we have

ℎ(𝑇, 𝑃, 𝒒) =∑𝑦𝑖(𝑇, 𝑃, 𝒒) ℎ𝑖𝑖(𝑇, 𝑃)

𝑁𝑆

𝑖=1

(5-24)

𝑠(𝑇, 𝑃, 𝒒) =∑𝑦𝑖(𝑇, 𝑃, 𝒒) (𝑠𝑖𝑖(𝑇, 𝑃) −�̅�

𝑀𝑖ln(𝑥𝑖(𝑇, 𝑃, 𝒒)))

𝑁𝑆

𝑖=1

(5-25)

𝑔(𝑇, 𝑃, 𝒒) = ℎ(𝑇, 𝑃, 𝒒) − 𝑇 𝑠(𝑇, 𝑃, 𝒒) (5-26)

The mean molar mass is calculated as

𝑀𝑡(𝑇, 𝑃, 𝒒) = [∑𝑦𝑖(𝑇, 𝑃, 𝒒)

𝑀𝑖

𝑁𝑆

𝑖=1

]

−1

(5-27)

The mass specific gas constant is

𝑅(𝑇, 𝑃, 𝒒) =�̅�

𝑀𝑡(𝑇, 𝑃, 𝒒) (5-28)

The density and the mass specific volume 𝑣(𝑇, 𝑃, 𝒒) = 1/𝜌(𝑇, 𝑃, 𝒒) can be obtained from the

relation

𝜌(𝑇, 𝑃, 𝒒) ≅𝑀𝑡(𝑇, 𝑃, 𝒒) 𝑃

�̅�𝑇 (5-29)

and therefore the (mass) specific internal energy is given by

112

𝑢(𝑇, 𝑃, 𝒒) =∑𝑦𝑖(𝑇, 𝑃, 𝒒) 𝑢𝑖𝑖(𝑇, 𝑃)

𝑁𝑆

𝑖=1

≅ ℎ(𝑇, 𝑃, 𝒒) −�̅�𝑇

𝑀𝑡(𝑇, 𝑃, 𝒒) (5-30)

In the last two relations we use the 'approximately equal to' symbol because the electronic

partition functions depend (slightly) on pressure through the cut-off criterion, and therefore neither

the individual species nor the mixture strictly obey the ideal gas equations of state. However, we

have verified that the departure is essentially negligible for all species. The specific heat for oxygen

atom and its ions versus temperature for three different pressures of 10-6, 1 and 100 atm are plotted

in Figure 5.3. As it is obvious, the effect of pressure is very negligible especially for the ions,

which are the main species at high temperatures.

Figure 5.3. Specific heat at constant pressure for oxygen atom and its ions versus temperature for three

different pressures, 10-6, 1 and 100 atm.

113

To compute specific heats at constant pressure and volume, 𝑐𝑝,off and 𝑐𝑣,off, the specific heat

ratio 𝛾off, the isoentropic exponent 𝛾𝑠,off, and the speed of sound 𝜒off, we must recall that according

to the standard model of chemical kinetics (again, for a fully explicit discussion see [173]) these

properties are generally defined at arbitrary compositions in terms of the so-called "surrogate

system". Here, the plasma composition is that of complete chemical equilibrium, hence the

surrogate system is the frozen-composition, non-reacting mixture at stable equilibrium with the

given temperature 𝑇 and pressure 𝑃, and the (fixed) composition {𝑦𝑖(𝑇, 𝑃, 𝒒)} . Therefore, the

partial derivatives with respect to temperature must be evaluated keeping the 𝑦𝑖 's fixed, so that we

have

𝑐𝑝,off(𝑇, 𝑃, 𝒒) = (𝜕ℎ

𝜕𝑇)𝑃,𝒚=∑𝑦𝑖(𝑇, 𝑃, 𝒒) 𝑐𝑝𝑖𝑖

(𝑇, 𝑃)

𝑁𝑆

𝑖=1

(5-31)

𝑐𝑣,off(𝑇, 𝑃, 𝒒) = (𝜕𝑢

𝜕𝑇)𝑣,𝒚=∑𝑦𝑖(𝑇, 𝑃, 𝒒) 𝑐𝑣𝑖𝑖(𝑇, 𝑃)

𝑁𝑆

𝑖=1

= 𝑐𝑝,off(𝑇, 𝑃, 𝒒) −�̅�

𝑀𝑡(𝑇, 𝑃, 𝒒) (5-32)

𝛾off(𝑇, 𝑃, 𝒒) =𝑐𝑝,off(𝑇, 𝑃, 𝒒)

𝑐𝑣,off(𝑇, 𝑃, 𝒒)= (1 −

�̅�

𝑀𝑡(𝑇, 𝑃, 𝒒) 𝑐𝑝,off(𝑇, 𝑃, 𝒒))

−1

(5-33)

𝛾𝑠,off(𝑇, 𝑃, 𝒒) =𝜌

𝑃(𝜕𝑃

𝜕𝜌)𝑠,𝒚

= 𝛾off

𝜌

𝑃(𝜕𝑃

𝜕𝜌)𝑇,𝒚

= 𝛾off(𝑇, 𝑃, 𝒒) (5-34)

𝜒off(𝑇, 𝑃, 𝒒) = √(𝜕𝑃

𝜕𝜌)𝑠,𝒚

= √𝛾off(𝑇, 𝑃, 𝒒) �̅�𝑇

𝑀𝑡(𝑇, 𝑃, 𝒒)

(5-35)

Where, of course, we used the Meyer relations, 𝑐𝑝𝑖𝑖 = 𝑐𝑣𝑖𝑖 + �̅�/𝑀𝑖. Equilibrium specific heats at

constant pressure will be calculated as:

𝑐𝑝,eq = (𝜕ℎ

𝜕𝑇)𝑃,𝒒

=∑𝑦𝑖 𝑐𝑝𝑖𝑖(𝑇, 𝑃)

𝑁𝑆

𝑖=1

+∑ℎ𝑖𝑖(𝑇, 𝑃)

𝑁𝑆

𝑖=1

(𝜕𝑦𝑖𝜕𝑇)𝑃,𝒒

(5-36)

All of the above properties can be easily computed if the following three properties are known as

functions of temperature 𝑇 and pressure 𝑃, for the given elemental composition 𝒒,

114

𝑔 = 𝑔(𝑇, 𝑃, 𝒒) (5-37)

𝑀𝑡 = 𝑀𝑡(𝑇, 𝑃, 𝒒) (5-38)

𝑐𝑝,off = 𝑐𝑝,off(𝑇, 𝑃, 𝒒) (5-39)

Indeed, for example, from the latter we can find

𝑠 = −𝜕𝑔(𝑇, 𝑃, 𝒒)

𝜕𝑇, 𝑐𝑝,eq

𝑇= (

𝜕𝑠

𝜕𝑇)𝑃,𝒒= −

𝜕2𝑔(𝑇, 𝑃, 𝒒)

𝜕𝑇2,

(𝜕𝑠

𝜕𝑃)𝑇,𝒒= −

𝜕2𝑔(𝑇, 𝑃, 𝒒)

𝜕𝑇𝜕𝑃

(5-40)

and similarly from ℎ = 𝑔 + 𝑇𝑠 and 𝑢 = ℎ − �̅�𝑇/𝑀𝑡 we may find all the other partial derivatives.

It is for this reason that in Section 5.4.5 we propose correlations for the Relations (5-37), (5-38),

and (5-39) [see Equations (5-47), (5-48) and (5-43) respectively]. The coefficients for these

correlations have been obtained by running the complete chemical equilibrium composition

calculations for various temperatures, pressures, and initial compositions, so as to compute the

mass fractions 𝑦𝑖(𝑇, 𝑃, 𝒒) needed in the Relations (5-26), (5-27) and (5-31), which lead to

Relations (5-37), (5-38), and (5-39). In Section 5.4.5 we discuss the functional forms chosen to

correlate efficiently these relations. The coefficients for hydrogen-air and methane-air plasmas are

listed in Appendix.

5.4.4. Ideal Gas Model Validation

As part of the preliminary computations, we checked the validity of the ideal gas model

assumption. In order to consider an ionized gas as an ideal one, it is necessary that the energy of

the Coulomb interaction between neighboring particles be small in comparison with the thermal

energy of the particles [185], meaning

𝑁𝑡 ≪ (𝑘𝑇

𝛬2𝑒2)3

= 2.2 × 1014 (𝑇

𝛬2)3

[m−3]

(5-41)

where 𝑁𝑡 is the number density of the plasma mixture, 𝛬 is the degree of ionization defined as

115

𝛬 =𝑁𝐼

𝑁𝐼 + 𝑁𝑛 (5-42)

where 𝑁𝐼 is the number density of ions and 𝑁𝑛 is the number density of neutral atoms. The virial

corrections to thermodynamic properties are negligible especially for temperatures higher than

2000 K and pressures up to 1000 atm [186,187]. Virial corrections have very significant effects

for very low temperatures and very high pressures [188] meaning far from plasma conditions.

Inequality (5-41) is comfortably satisfied for all plasmas at all pressure and temperatures

considered in this work.

5.4.5. Fitting of Thermodynamic Properties

It is desired to have analytical expressions to evaluate the thermodynamic properties of a plasma

mixture without iteration. Such expression would be valuable for example as a subroutine in a

computer program or a CFD code. Fitting thermodynamic functions for plasma mixture properties

in a wide range of temperatures (1,000 - 100,000 K) and pressures (10−6 – 102 atm) is a complicated

problem because of the non-monotonic behavior of some properties as functions of temperature,

in particular, the equilibrium specific heat 𝑐𝑝,eq . In order to correlate the computed values of 𝑐𝑝,eq,

we have chosen a modified Hill equation in conjunction with a modified Log-normal distribution

function. These functions provide the capability to capture the peaks and valleys of the equilibrium

specific heat. The number of terms for first (modified Hill) part of the 𝑐𝑝,eq correlation depends on

how well we can fit 𝑐𝑝,off to the exact data points and the number of terms for the second (modified

Log-normal) part depends on the number of peaks in 𝑐𝑝,eq.

The least squares fitting procedure is as follows. First we find the coefficients for 𝑐𝑝,eq, then we

find the coefficients for the integration constants of the specific enthalpy and the specific entropy

obtained by integration of the functional form of the correlation for 𝑐𝑝,eq according to ℎ =

∫ 𝑐𝑝,eq 𝑑𝑇 + const and 𝑠 = ∫(𝑐𝑝,eq 𝑇⁄ )𝑑𝑇 + const, respectively. The integration constants are

obtained by least square fitting the calculated data for enthalpy and entropy to the correlations

developed by integration. The advantage of this approach is that the main set of coefficients for

the equilibrium specific heat, the specific enthalpy and the specific entropy are the same and are

consistent with the thermodynamic relations provided in the previous sections.

116

Below, we present the analytical expressions that we propose for the correlations of the frozen

and equilibrium specific heat at constant pressure, the specific enthalpy, the specific entropy, the

specific Gibbs free energy, and the mean molar mass. The results of the least square fittings of our

calculated data using these correlations are given in the Appendix. The number of terms in the

summations have been chosen so that the relative errors of the correlations are always less than

2%.

Frozen specific heat at constant pressure (kJ/kg K)

𝑐𝑝,off =∑ 𝑎𝑖

off

1 + (𝑏𝑖off 𝑇⁄ )

𝑐𝑖off

8

𝑖=1

(5-43)

Equilibrium specific heat at constant pressure (kJ/kg K)

𝑐𝑝,eq =∑ 𝑎𝑖

off

1 + (𝑏𝑖off 𝑇⁄ )

𝑐𝑖off

8

𝑖=1

+∑𝑎𝑖eq exp [−(

𝑙𝑛(𝑇 𝑏𝑖eq⁄ )

𝑐𝑖eq )

2

]

16

𝑖=9

(5-44)

Specific enthalpy (kJ/kg)

ℎ = 𝜆1 + 𝑇∑𝑎𝑖off(1− 2𝐹1(1,

1

𝑐𝑖off, 1 +

1

𝑐𝑖off, − (

𝑇

𝑏𝑖off)

𝑐𝑖off

))

8

𝑖=1

−√𝜋

2∑𝑎𝑖

eq𝑏𝑖

eq𝑐𝑖

eq

16

𝑖=9

exp((𝑐𝑖

eq)2

4) erf (

𝑐𝑖eq

2−𝑙𝑛(𝑇 𝑏𝑖

eq⁄ )

𝑐𝑖eq )

(5-45)

Specific entropy (kJ/kg K)are right

𝑠 = 𝜆2 +∑𝑎𝑖

off

𝑐𝑖off

8

𝑖=1

𝑙𝑛 ((𝑏𝑖off)

𝑐𝑖off

+ (𝑇)𝑐𝑖off

) +√𝜋

2∑𝑎𝑖

eq𝑐𝑖

eq

16

𝑖=9

erf(𝑙𝑛(𝑇 𝑏𝑖

eq⁄ )

𝑐𝑖eq ) (5-46)

where erf and 2F1(𝑎, 𝑏, 𝑐, 𝑥) are the error function and the hypergeometric functions [189] ,

respectively. As a result of Eqs. (5-45) and (5-46), the specific Gibbs free energy is

117

𝑔 = 𝜆1 − 𝑇𝜆2 + 𝑇∑𝑎𝑖off (1− 2𝐹1(1,

1

𝑐𝑖off, 1 +

1

𝑐𝑖off, − (

𝑇

𝑏𝑖off)

𝑐𝑖off

))

8

𝑖=1

− 𝑇∑𝑎𝑖

off

𝑐𝑖off

8

𝑖=1

𝑙𝑛 ((𝑏𝑖off)

𝑐𝑖off

+ (𝑇)𝑐𝑖off

)

−√𝜋

2∑𝑎𝑖

eq𝑏𝑖

eq𝑐𝑖

eq

16

𝑖=9

exp((𝑐𝑖

eq)2

4) erf (

𝑐𝑖eq

2−𝑙𝑛(𝑇 𝑏𝑖

eq⁄ )

𝑐𝑖eq )

−𝑇√𝜋

2∑𝑎𝑖

eq𝑐𝑖

eq

16

𝑖=9

erf (𝑙𝑛(𝑇 𝑏𝑖

eq⁄ )

𝑐𝑖eq )

(5-47)

Mean molar mass (kg/kmol)

𝑀𝑡 = 𝜆3 −∑ 𝑎𝑖

M

1 + (𝑏𝑖M 𝑇⁄ )𝑐𝑖

M

8

𝑖=1

(5-48)

where the various coefficients are function of pressure and equivalence ratio using polynomial

surface (PS𝑚𝑛) of degree m in 𝜙 and degree n in ln(𝑃) as follows,

𝑃𝑆𝑚𝑛 = 𝜉00 +∑𝜉𝑖0𝜙𝑖

𝑚

𝑖=1

+∑𝜉0𝑗(𝑙𝑛(𝑃))𝑗

𝑛

𝑗=1

+

{

∑ ∑ 𝜉𝑘𝑙𝜙

𝑘(𝑙𝑛(𝑃))𝑙

𝑛−𝑘

𝑙=1

𝑚

𝑘=1

𝑓𝑜𝑟 𝑚 < 𝑛

∑ ∑𝜉𝑘𝑙𝜙𝑘(𝑙𝑛(𝑃))

𝑙𝑛−𝑙

𝑙=1

𝑛−1

𝑘=1

𝑓𝑜𝑟 𝑚 = 𝑛

∑ ∑ 𝜉𝑘𝑙𝜙𝑘(𝑙𝑛(𝑃))

𝑙𝑚−𝑙

𝑘=1

𝑛

𝑙=1

𝑓𝑜𝑟 𝑚 > 𝑛

(5-49)

𝑎, 𝑏, 𝑐 = 𝑒𝑥𝑝(𝑃𝑆𝑚𝑛) (5-50)

𝜆 = 𝑃𝑆𝑚𝑛 (5-51)

The degree of m and n for methane/air mixture are considered 2 and 5 respectively. For

hydrogen/air mixture we have two sets of degree, first one is m = 4 and n = 3 and the second one

is m = 5 and n = 2 to provide the best fit. In this way all the thermodynamic properties are expressed

118

as a function temperature, pressure and equivalence ratio. The values of the 𝜉𝑘𝑙 coefficients that

result from our least square fitting procedure are reported in Appendix for H2/air and CH4/air

plasma mixtures in Table 2 and Table 3, respectively. Figure 5.4 shows the comparison of the

equilibrium specific heat at constant pressure for H2/air plasma mixtures between calculated and

fitted data which indicates excellent agreement.

Figure 5.4. Comparison between calculated data (solid line) and fitted data (symbols) for the equilibrium

specific heat at constant pressure 𝑐𝑝,eq of a stoichiometric H2/air plasma mixture for P = 10−6, 1 and 102

atm.


In this section we present and discuss some of our calculated chemical equilibrium

compositions and thermodynamic properties for H2/air and CH4/air plasmas in the temperature

range 1,000 - 100,000 K, pressure range 10−6 - 102 atm, and for different equivalence ratios within

flammability limits (for methane/air mixture flammability limit is 0.6 < 𝜙 < 1.4 and for

hydrogen/air mixture flammability limit is 0.5 < 𝜙 < 5.0). Calculated values have been fitted

using the analytical correlations proposed in the previous section and the fitting coefficients are

tabulated in Appendix.

Figure 5.5 shows an important effect that must be carefully taken into account in the interest of

accuracy, namely, the effect of the excited energy levels on the specific heat at constant pressure

119

for stoichiometric H2/air plasma mixture. Figure 5.5 compares the results obtained using our self-

consistent method considering excited energy levels with those of the so-called ground state

method. As it can be seen, for temperatures below 15,000 K the effect of excited energy levels on

the values of the specific heat and hence all the properties is negligible, because at relatively low

temperatures the high order terms in the electronic partition function expansion are indeed

negligible. But for temperatures above 15,000 the effect is significant and, importantly, it exhibits

a strong pressure dependence. The reason is that, differently from the ground state method, our

self-consistent method takes into account the experimental observation that the number of excited

energy levels is a function of both temperature and pressure. In other words, Figure 5.5 shows that

considering just the ground state or fixing the number of excited energy levels independent of

pressure, may introduce very large errors in the estimated thermodynamic properties at high

plasma temperatures, especially for derivative properties like the specific heats.

Figure 5.5. Comparison of values of the equilibrium specific heat at constant pressure 𝑐𝑝,eq computed

using our self-consistent method (solid line) and the so-called ground state method (dashed line), for a

stoichiometric H2/air plasma at three different pressures, 10-6, 1, and 100 atm

120

In order to validate our calculations with data existing in the literature for high temperature

plasmas, due to lack of data for H2/air and CH4/air plasma mixtures at high temperatures, we make

a comparison with air plasma. The reasons to choose air are that first it forms a large portion of

typical fuel/air mixtures and also many researches have already been done on air plasma.

Figure 5.6 compares the equilibrium specific heat at constant pressure of air plasma calculated in

this study with those of Capitelli et al [162] (up to 60,000 K), Hansen [143] (up to 15,000 K), Sher

[156] (up to 50,000 K), Cressault et al [190] (up to 30,000 K), and Bottin et al [191] (up to 15,000

K) for three different pressures, 10-2, 1, and 100 atm. The data for Sher [156] and Cressault et al

[190] are available only for atmospheric pressure. The underestimate in Sher's results is due to the

very simple method he used to find individual properties.

The results of this study are shown an excellent agreement in low and high pressures with

Capitelli et al [162] (up to 60,000 K). Figure 5.7 compares the equilibrium compositions of air

plasma computed in this study with tabulated data by Hilsenrath and Klein [186] (up to 15,000 K)

and Gilmore [139] (up to 24,000 K) at atmospheric pressure for temperature range of 300 to 25,000

K. As it is obvious from Figures 5.6 and 5.7, the results of our calculations are in very good

agreement with existing data, in spite of the slight differences in air composition assumed in the

different studies. We are now in the position to examine our results to illustrate the important

effects of temperature and pressure on all properties. Figure 5.8 shows the mole fractions of the

neutral and ionized single species (only those with mole fractions greater than 2×10-6) for a

stoichiometric CH4/air plasma mixture at atmospheric pressure.

121

Figure 5.6. Comparisons of the values of the equilibrium specific heats at constant pressure 𝑐𝑝,eq of air

plasma mixture obtained with present study (solid line) and those obtained by Capitelli et al (ο) [162],

Hansen (×) [143], Sher (Δ) [156] , Cressault et al (□) [190]and Bottin et al (+) [191] for three different

pressures: (a)=10-2, (b)=1, and (c)=100 atm.

122

Figure 5.7. Comparisons of the selected species mole fraction of air plasma mixture obtained with present

study (dashed line) and those obtained by Gilmore (□) [139] and Hilsenrath and Klein (ο) [186] at

pressure of 1 atm

123

Figure 5.8. Mole fractions for selected species in a stoichiometric CH4/air plasma at atmospheric

pressure.

124

Figure 5.9 shows the mean molar mass 𝑀𝑡 and the degree of ionization 𝛬, over the temperature

range 1000–100,000 K for different pressures (10-6, 1, and 100 atm) for a stoichiometric H2/air

plasma. As shown in Figure 5.9(a), increasing the temperature at a given pressure leads to a

decrease in mean molar mass due to the increase in mole numbers resulting from dissociation. The

stepwise decrease in the molar mass is connected to the successive ionization of atomic species,

while the slope becomes zero in transitions from one ionization to another. This behavior is very

manifest at low pressures and becomes less evident at high pressures. The dissociation reactions

are significantly favored at low pressures and consequently the transition from partially ionized

gas (Λ < 1) to fully ionized gas (Λ = 1) takes place at lower temperature for low pressures than

for high pressure. This is seen in Figure 5.9(b), where the fully ionized condition for P = 10-6 atm

obtains around 10,000 K whereas for P = 100 atm it occurs around 50,000 K.

Figure 5.9. (a)-Mean molar mass 𝑀𝑡 and (b)-degree of ionization 𝛬 at three different pressures (10-6, 1,

and 100 atm) for a stoichiometric H2/air plasma mixture.

Figure 5.10(a) shows the equilibrium specific heat at constant pressure for a stoichiometric

CH4/air plasma mixture. It shows some distinct peaks with increasing temperature where the

temperature dependence of the complete chemical equilibrium composition is very high. These

peaks are connected first to dissociation of the molecules and then to successive ionization of the

125

atomic species. When pressure decreases the peaks become sharper and shift to lower temperature.

This effect, again, is due to the favorable effect of low pressure on dissociation and ionization

reactions. As a result, for each given temperature, more chemical energy is stored at low pressure,

resulting in the specific enthalpy of the plasma mixture being a decreasing function of pressure, as

shown in Figure 5.10(b). Figure 5.10(a) compares the frozen and equilibrium specific heats at

constant pressure, cp,off and cp,eq, defined by Eqs. (5-31) and (5-36), respectively, for a

stoichiometric CH4/air plasma at different pressures. As it can be seen, the effect of chemistry is

clearly visible and whenever dissociation and ionization start to play a role and become important,

cp,eq presents a peak. When maximum ionization is reached in the mixture, no further reactions

take place, so the rates of change of mole fractions with temperature, (∂yi ∂T⁄ )P,𝐪, become small

and values of equilibrium cp,eq decrease and reach the frozen cp,off values. This behavior is shown

in Figure 5.10(a) for the pressure of 10-6 atm around 75,000 K. It is important to emphasize again

that the pressure dependence of the mixture enthalpy and equilibrium specific heat has two

significant reasons. One is the pressure dependence of the complete chemical equilibrium

composition and its rate of change with temperature. In fact, chemical composition, computed with

the complete equilibrium method which is a function of pressure. The second reason is related to

the electronic partition functions of the individual species, which depend on the cut-off criteria

that determine the maximum number of energy levels that need to be considered. As discussed in

Section 2.2.2.1, our cut-off criteria are functions of the Debye length, which in turn is related to

number densities and, hence, to pressure.

Figure 5.11 shows the effect of equivalence ratio on the specific Gibbs free energy and the

equilibrium specific heat at constant pressure for H2/air plasma mixture. At each given

temperature, the Gibbs free energy is a decreasing function of equivalence ratio whereas the

equilibrium specific heat at constant pressure increases with equivalence ratio. The effect on the

specific heat is most significant at the first and third peaks, around 3,800 K and 15,000 K,

respectively. As already seen in Figure 5.8, the 3,800 K peak is due to the dissociation reaction to

create atomic hydrogen, while the 15,000 K peak is due to the ionization reaction to form ionic

hydrogen. Increasing the equivalence ratio is equivalent to increasing the hydrogen percentage in

the mixture and therefore the more hydrogen in the mixture the more hydrogen dissociation and

ionization reactions contribute to the mixture properties.

126

Figure 5.10. (a)-Equilibrium and frozen specific heat at constant pressure 𝑐𝑝,eq and (b)-specific enthalpy

for a stoichiometric CH4/air plasma mixture at three different pressures, 10−6, 1 and, 100 atm

Figure 5.12 shows speed of sound χoff defined by Eq. (5-35). Speed of sound is higher at low

pressures, leading to higher Mach numbers at low pressures for each given temperature. The

differences between frozen specific heat ratio 𝛾off defined by Eq. (5-33) and isentropic exponent

𝛾𝑠,off defined by Eq. (5-34) are shown in terms of pressure and temperature in Figure 5.13. As it

can be seen in Figure 5.13, the frozen specific heat ratio is higher at low pressures and the

isentropic exponent is always lower than its corresponding specific heat ratio. Under the condition

of non-reacting flows or when maximum ionization is reached in the mixture, the rates of change

of mass fractions with respect to temperature become negligible and the ratio of specific heats and

the isentropic exponent become identical as it is shown in Figure 5.13 for the pressure of 10-6 atm.

For higher pressures this convergence happens in higher temperatures.

127

Figure 5.11. (a) Gibbs free energy and (b)-Equilibrium specific heat at constant pressure for a H2/air

plasma mixture at atmospheric pressure for three different equivalence ratio of 1, 3 and 5.

Figure 5.12. Speed of sound in a stoichiometric H2/air plasma mixture at three different pressures, 10-6, 1

and 100 atm.

128

Figure 5.13. Specific heat ratio 𝛾off and isentropic exponent 𝛾𝑠,off for a stoichiometric CH4/air plasma

mixture at three different pressures of 10-6, 1, and 100 atm.

129

6. Laminar Burning Speed Measurement and Flame

Instability Study of H2/CO/Air Mixtures at High

Temperatures and Pressures Using a Novel Multi-

Shell Model

130

6.1. ABSTRACT

A new differential based multi-shell model has been developed in conjunction with schlieren

photography to measure laminar burning speeds and to investigate flame structures of H2/CO/air

mixtures. The experiments were carried out in two constant volume vessels; one spherical and one

cylindrical. Flame instability has been studied using the cylindrical vessel which was installed in

a Z-type Schlieren Shadowgraph system equipped with a high speed CMOS camera, capable of

taking pictures up to 40,000 frames per second. Flame instabilities such as cracking and wrinkling

have been observed during flame propagation and discussed in terms of the hydrodynamic and

thermo-diffusive effects. Laminar burning speeds were measured by a novel thermodynamic

model using pressure rise during flame propagation in the spherical chamber. Gases in the vessel

are divided into two parts; unburned and burned gases. The burned gases are in the center of sphere

surrounded by a small preheat zone followed by the unburned gases. The burned gases were

divided into multiple shells to determine the temperature gradient precisely. The following energy

transfers have been included in the model: Conductive energy loss to the chamber wall and

electrodes, energy transfer in the preheat zone, energy transfer between adjacent shells and

radiation energy loss from burned gases. The governing equations of unknown variables have been

defined by a set of nonlinear ordinary differential equations which were solved using CVODE

solver. Power law correlations have been developed for laminar burning speeds of smooth

H2/CO/air flames over a wide range of temperatures (298K up to 617K), pressures (from sub-

atmospheric up to 5.5atm), equivalence ratios (0.6-5) and three different hydrogen concentration

of 5%, 10% and 25% respectively. Experimental burning speeds of H2/CO/air mixtures have been

compared with available measurements as well as computed values obtained by 1D free flame

simulations using three chemical kinetics mechanisms. Comparisons show a very good agreement

for the conditions which data is available and the predicted results.

Keywords: Syngas, Laminar burning speed, flame instability, Schlieren photography, high

pressure, multi-shell

6.2. INTRODUCTION

Synthetic gas, also known as syngas, is the name of a combustible mixture predominantly

containing varying levels of hydrogen and carbon monoxide and in some instances some levels of

131

CO2, CH4, N2, and H2O and other higher order hydrocarbons [37]. Syngas can be produced through

the gasification of coal, biomass, and steam reforming of coke. This gas is considered to be an

alternative fuel that is used to produce a wide range of synthetic materials, solvents, and fertilizers

and also is predicted to have an important role in the future of renewable and environmentally

friendly energies. One of the important applications of this alternative fuel is as a reformer gas that

can be used during engine cold start to reduce the amount of HC emissions [39]. Synthetic gas also

plays an important role in stationary power plants that use the integrated gasification combined

cycle (IGCC) [40]. Recently a large focus has been cast on this fuel for its potential use in the gas

turbine industry as a replacement for natural gas [41–43]. Thus it is of utmost importance to study

the flame structure and determine the fundamental combustion characteristics of the fuel to fully

understand how it behaves over a wide range of operating conditions. The laminar burning speed

reliably characterizes a fuel as it contains essential information regarding the mixture’s reactivity,

exothermicity and diffusivity. It is used to validate chemical kinetics reactions and is strongly

influenced by mixture characteristics and operational conditions such as equivalence ratio, diluent

type, temperature and pressure.

Scholte et al. studied the effect on the laminar burning speed of hydrogen flames with the

addition of carbon monoxide at atmospheric conditions using the burner method [192]. McLean et

al. [193] measured the laminar burning speed of H2/CO mixtures using constant pressure spherical

flames and extrapolation method at atmospheric condition. Vagelopoulos et al. [194] used the

counter-flow twin-flame and laser Doppler velocimetry techniques to obtain laminar burning speed

and extinction strain rate data on hydrogen, carbon monoxide, methane, and air mixtures at

atmospheric conditions. Hassan et al. [195] measured burning speed of H2/CO/air mixtures over a

wide range of hydrogen ratios (3-50%), equivalence ratios (0.6-5.0) at atmospheric temperature

and pressure using constant pressure spherical flames and extrapolation method. Natarajan et al.

[37] employed the Bunsen and stagnation flame methods in conjunction with a linear extrapolation

method to find laminar burning speed at two different pressures (1atm, 5atm) and preheat

temperatures (300K-700K) with CO2 dilution limited to lean equivalence ratios. Sun et al. [41]

collected data at high pressures (up to 40atm) and atmospheric temperature using a dual-

chambered constant pressure cylindrical apparatus at atmospheric temperatures.

Dong et al. [196] used the Bunsen burner method to collect data on a wide range of hydrogen

concentration (0-100%) at atmospheric pressure and temperature. Burke et al. [197] measured

132

mass burning rates of hydrogen flames and syngas flames at elevated pressures (1-25atm) with

various diluents (He, Ar, CO2) at atmospheric temperature. Monteiro et al. [198] tested three

syngas mixtures that are typical products from wood gasification at atmospheric temperature and

pressure using the constant pressure method. Bouvet et al. [199,200] collected laminar burning

speed data over a wide range of equivalence ratios (0.4-5.0) and syngas mixtures (50:50 H2/CO to

5:95 H2/CO) at atmospheric pressure and temperature using the constant pressure method and

Bunsen burner configuration. Burbano et al. [201,202] used the burner configuration and Schlieren

imagery to study the laminar burning velocity and behavior of syngas at atmospheric pressure and

temperature considering different diluents (N2, CO2).

Liu et al. [203] investigated the effect of pressure on laminar and turbulent lean syngas flames

at atmospheric temperature. They observed a decreasing laminar burning speed with the increase

of pressure, while the turbulent burning speed increased with increasing pressure. Singh et al. [204]

collected data on four syngas mixture compositions (75%H2 – 5%H2) with moisture addition (up

to 40%) at atmospheric pressure and elevated temperatures (up to 500K) using the constant

pressure method. Wang et al. [205] investigated the behavior and laminar burning speed of oxyfuel

combustion in syngas mixtures (only H2-CO-O2-CO2 as reactants), as well as assessed the impact

of the increased CO2 presence as the sole diluent. Yepes and Amell [206] studied the effect of

increasing oxygen volume percent (21%–35% O2) on the behavior of syngas flames at 0.838atm

and 298K using the burner configuration. He et al. [207] investigated the effect of varying H2 and

CO content in a H2-CO-CH4-N2-CO2 mixture that is typical of coal-derived syngas using the heat

flux method at atmospheric conditions. Li et al. [208] focused on collecting lean and stoichiometric

syngas data while varying H2/CO ratios (0%-100% H2) using the outwardly propagating flame

method at room temperature. Zhang et al. [209] used non-linear extrapolation methods to extract

lean laminar burning speed data at atmospheric temperature and pressure over many H2/CO ratios

(2%-98% H2). Han et al. [210] employed the outwardly propagating flame method for CO2-diluted

syngas flames at atmospheric and elevated temperatures and pressures.

The purpose of this paper is: 1) To develop a new differential based model to calculate burning

speed of a propagating spherical flame in a constant volume vessel using pressure rise, 2) To

extend measurement of laminar burning speed of syngas/air mixtures for smooth flames, 3) To

investigate smooth and cellular flame structures of syngas/air mixtures and relate instabilities to

pressure and Peclet number. Measurements have been made over a wide range of temperatures

133

(from room temperature up to 617 K), pressures (from sub-atmospheric up to 5.5 atm), equivalence

ratios (0.6-5) and for three different hydrogen concentration of 5%, 10% and 25% in the syngas

mixture. In addition, correlations have been developed to calculate laminar burning speed as a

function operating conditions.


The experimental instruments comprised of a spherical vessel utilized for obtaining the laminar

burning speed measurement and a cylindrical vessel used in a Schlieren Shadowgraph system to

study flame shape and structure. The cylindrical vessel is equipped with two fused silica windows

that are sealed to the chamber with high temperature Parofluor O-rings. It is also equipped with

two band heaters to increase the initial gas temperature up to 500 K. The vessels are fitted with

two extended spark plugs that allow for central point ignition with a spark gap of about 0.9 mm,

and K-type thermocouples that measure the temperature of the gas and vessel walls. The spark

energy has been tuned to be sufficiently close to the minimum ignition energy to minimize the

effect of spark discharge on flame expansion [211].

The spherical vessel was used to measure pressure rise due to combustion processes using a

Kistler high sensitivity pressure sensor [23]. To be able to take optical recordings of the

combustion event the cylindrical vessel was installed in a Schlieren Shadowgraph system equipped

with a high speed CMOS camera, capable of taking pictures up to 40,000 frames per second

[46,47]. The vessel was filled by the method of partial pressures using a manifold supply system

comprised of valves, high accuracy pressure transducers, pipes connected to the respective mixture

constituents, and a vacuum pump. A gas chromatography (GC) system was used to verify the

composition of premixed fuel inside the vessel. A data acquisition system was utilized to record

the pressure-time data as well as the flame propagation images. A LabView program has been

written to find the exact initial composition and to initiate the combustion process. More

information about experimental facilities can be found in other studies [1,23,25,46,47,68].

Figure 6.1 shows a schematic of the experimental facilities. At each operational condition

experiments were done using both chambers. First, the cylindrical chamber was used to study the

shape and structure of the flame and then the same experiments were performed in the spherical

chamber to collect the pressure rise data. Only the portion of the pressure rise data where the flame

is completely smooth, laminar, and spherical has been used to calculate the laminar burning speed.

134

In this work each experiment was carried out at least three times at each working condition to

ensure that the confidence level of the experiments was above 95% [212].

Figure 6.1. Schematic diagram of experimental facilities and Z-type Schlieren system

6.4. MULTI-SHELL MODEL AND FORMULATION

One advantage of measuring the laminar burning speed using the pressure rise method over

other methods is that, from a single test, burning speeds can be calculated over a wide range of

temperatures and pressures. The other advantage is that it circumvents the need to define a constant

pressure phase as well as the use of unreliable extrapolation methods. In addition, the data

considered is not confined to small flame radii where the burning speed is affected by significant

stretch effects. However, two conditions should be satisfied for the accurate evaluation of the

laminar burning speeds from the pressure rise method: First, the pressure rise data due to flame

propagation must be recorded correctly and precisely. Second, flame radii should be large enough

to minimize the effect of stretch rate on the recorded data.

The two most well-known pressure rise methods are those of Lewis and von Elbe [213] and of

Metghalchi and Keck [20,101]. Lewis and von Elbe [213] assumed that the mass fraction burned

135

is proportional to the fractional pressure rise. Metghalchi and Keck [20,101] divided the closed

vessel into two zones consisting of burned and unburned fuel, and assumed a uniform temperature

and concentration in each zone. Metghalchi et al [3,23,25,171] have modified their method to take

into account the effect of the temperature gradient in the burned gas and energy transfer from the

vessel. They calculated the burning speeds by integrating the energy and mass conservation

equations all over the chamber. The new differential based model is an improvement to the integral

method by including energy exchange among shells in the system. The new model can predict

combustion characteristics such as laminar burning speed, flame front thickness, stretch rate,

Peclet number, thermal expansion ratio, and the Lewis number. In this model governing equations

of unknown variables have been defined by a set of nonlinear ordinary differential equations that

can be solved by using the CVODE solver from sundials package [214]. The governing equations

are derived by applying the differential form of mass and energy conservation equations over all

shells as well as the whole chamber.

The mixture is separated into a burned gas section and an unburned gas section with the flame

front as a jump discontinuity. The core burned gases are surrounded by a preheat zone having non-

uniform temperature, which is itself surrounded by the unburned gas. The burned gas is divided

into a number of domains called shells and pressure is assumed to have a uniform spatial

distribution. The gas mixture is assumed to be in local thermodynamic equilibrium (LTE) and

behave like an ideal gas. Chemical equilibrium composition has been evaluated using CANTERA

code combining with thermochemical properties of NASA correlations [215]. Twenty major

species (H2, N2, O2, CO, H, O, OH, HCO, HO2, H2O, H2O2, CO2, NO, NO2, CH2, CH3, CH4, CH2O,

CH3OH and C2H2) have been considered as products of combustion in order to cover the burning

of lean to very rich mixtures. All the energy losses to the electrodes, chamber walls, radiation from

the burned gas, and energy transfer between neighboring shells have been considered in current

model. The effect of energy transfer in the chamber wall and spark electrodes as well as preheat

zone is modeled by the thermal boundary layer and displacement thickness concept [216].

6.4.1. Governing Equations

The following model is for a spherical flame of one-dimensional geometry in the radial

direction. The chamber is filled with a combustible mixture and will be ignited at time t = 0 at the

center of the chamber by two extended electrodes. Upon ignition, an isotropic flame is created and

136

begins to propagate outwardly in the radial direction. The following assumptions are made in the

analysis of the combustion inside the vessel:

1. The unburned gas is initially at rest and has a uniform temperature, pressure and

composition.

2. The pressure is presumed to be uniform within the chamber at each time step.

3. The burned gas in each shell will be at a different temperature and a different composition

while it is in local thermodynamic equilibrium.

4. The gases are assumed to behave like an ideal gas.

5. The reaction zone has a negligible thickness.

The energy conservation equations for unburned, burned, and currently burning regions are

respectively:

�̇�𝑢 = −�̇�𝑏ℎ𝑢 + �̇�𝑢 − �̇�𝑢 (6-1)

�̇�𝑗 = �̇�𝑗 − �̇�𝑗 , 𝑗 = 𝑏1 − 𝑏𝑛−1 (6-2)

�̇�𝑏𝑛 = �̇�𝑏ℎ𝑢 + �̇�𝑏𝑛 − �̇�𝑏𝑛 (6-3)

𝑈 is the internal energy, �̇�𝑏 the mass burning rate, 𝑄 the energy transfer and 𝑊 the work. In these

equations the subscripts of 𝑗 denotes the already burned shells, 𝑢 and 𝑏 denotes the unburned and

burned gas conditions respectively, 𝑛 and 𝑏𝑛 denote the total number of shells in burned zone and

currently burning shell, respectively. The dot sign on top of the parameters refers to the complete

derivative with respect to time. Using thermodynamic relations [217] and concept of displacement

thickness [216] Eqs. (6-1)-(6-3) expand into the following format:

�̇�𝑢∞ =

𝐴𝑢∞�̇� +

𝜌𝑢∞ℎ𝑢

∞

1 − 𝑥𝑏𝑉𝑑𝑖𝑠𝑢�̇�𝑏 + 𝜌𝑢

∞ℎ𝑢∞�̇�𝑑𝑖𝑠𝑢 + �̇�𝑢

𝐵𝑢∞

(6-4)

�̇�𝑗∞ =

𝐴𝑗∞�̇� + 𝜌𝑗

∞ℎ𝑗∞�̇�𝑑𝑖𝑠𝑗 + �̇�𝑗

𝐵𝑗∞ , 𝑗 = 𝑏1 − 𝑏𝑛−1 (6-5)

137

�̇�𝑏𝑛∞ =

𝐴𝑏𝑛∞ �̇� + (𝑚(ℎ𝑢

∞ − ℎ𝑏𝑛∞ ) −

𝜌𝑢∞ℎ𝑢

∞

1 − 𝑥𝑏𝑉𝑑𝑖𝑠𝑢) �̇�𝑏 + 𝜌𝑏𝑛

∞ ℎ𝑏𝑛∞ �̇�𝑑𝑖𝑠𝑏𝑛 + �̇�𝑏𝑛

𝐵𝑏𝑛∞ (6-6)

𝜌 is the density, ℎ the enthalpy, 𝑥𝑏 = 𝑚𝑏 𝑚⁄ the burned gas mass fraction, 𝑉𝑑𝑖𝑠 the displacement

thickness, 𝑚 the total mass, 𝑝 the experimental pressure data and the superscript ∞ denotes the

region far from the thermal boundary layer with uniform temperature distribution. The 𝐴 and 𝐵 all

over the regions (𝑘 = 𝑢, 𝑏1, ⋯ , 𝑏𝑛−1, 𝑏𝑛) are defined as:

𝐴𝑘∞ = (ℎ𝑘

∞ − 𝑅𝑘∞𝑇𝑘

∞)𝑉𝑑𝑖𝑠𝑘 (𝜕𝜌𝑘

∞

𝜕𝑝) + (𝑉𝑑𝑖𝑠𝑘 −

𝑚𝑘

𝜌𝑘∞)

𝑇𝑘∞

𝜌𝑘∞ (

𝜕𝜌𝑘∞

𝜕𝑇𝑘∞) + 𝑉𝑑𝑖𝑠𝑘 (6-7)

𝐵𝑘∞ = 𝑚𝑘𝑐𝑝𝑘

∞ − 𝜌𝑘∞(𝑐𝑝𝑘

∞ − 𝑅𝑘∞)𝑉𝑑𝑖𝑠𝑘 − (ℎ𝑘

∞ − 𝑅𝑘∞𝑇𝑘

∞)𝑉𝑑𝑖𝑠𝑘 (𝜕𝜌𝑘

∞

𝜕𝑇𝑘∞) (6-8)

Total energy transfer rate for each region, �̇�𝑘, is the summation of all available rate of energy

transfers including wall and electrode boundary layers, preheat zone and radiation from the burned

gas. Therefore

�̇�𝑢 =4𝜋𝑝

(𝛾𝑢∞ − 1)𝜏(𝑟𝑐

2𝛿𝑤𝑏 + 𝑟𝑏𝑛2 𝛿𝑝ℎ + 𝛾𝑢

∞𝑝 (𝑟𝑐2𝑑𝛿𝑤𝑏𝑑𝑝

+ 𝑟𝑏𝑛2𝑑𝛿𝑝ℎ

𝑑𝑝)) (6-9)

is the rate of energy transfer from unburned region [216], γ is the specific heat ratio, 𝜏 =

𝑝 (𝑑𝑝 𝑑𝑡⁄ )⁄ is the characteristic time for the pressure rise, 𝛿𝑤𝑏 and 𝛿𝑝ℎ are the displacement

thickness of wall boundary layer [216] and preheat zone [68] respectively. 𝛿𝑤𝑏 and 𝛿𝑝ℎ are defined

as:

𝛿𝑤𝑏 = (𝛼𝑢∞𝜏

𝜋)

0.5

𝑧−1𝛾𝑢∞∫ (𝑧′ − 𝑧′

1𝛾𝑢∞)

𝑧

0

(∫ 𝑧"𝑑𝑧"𝑧

𝑧′

)

−0.5

𝑑𝑦′ (6-10)

𝛿𝑝ℎ = −(𝛼𝑢∞

�̇�𝑏𝑛)(𝑇𝑏𝑛∞

𝑇𝑢∞− 1) 𝑙𝑛 (

𝑇𝑏𝑛∞

𝑇𝑢∞) (6-11)

where 𝛼 is the thermal diffusivity, 𝑦 = 𝑡 𝜏⁄ is the dimensionless time and 𝑧 = 𝑝 𝑝𝑖⁄ is the

dimensionless pressure.

138

�̇�𝑖 =2𝜋𝑟𝑒𝑝(𝑟𝑖 − 𝑟𝑖−1)

(𝛾𝑖∞ − 1)𝜏

(𝛿𝑒𝑏𝑖 + 𝛾𝑖∞𝑝

𝑑𝛿𝑒𝑏𝑖𝑑𝑝

) + �̇�𝑟𝑖 , 𝑖 = 𝑏1 − 𝑏𝑛 (6-12)

is the rate of energy transfer from burned shells [216], 𝛿𝑒𝑏𝑖 is the displacement thickness of

electrode boundary layer [68] of each shell and �̇�𝑟𝑖 is the radiation energy loss rate from each

burned shell assuming an optically thin limit model and negligible radiation reabsorption [218].

𝛿𝑒𝑏𝑖 and �̇�𝑟𝑖 are defined as:

𝛿𝑒𝑏𝑖 =2

3(𝛼𝑖∞𝑟𝑖�̇�𝑖)

0.5

(𝑇𝑖∞

𝑇𝑤 − 1) (6-13)

�̇�𝑟𝑖 = 𝛼𝑝𝐴𝑖 (4𝜎(𝑇𝑖∞)4 −∫ 𝐼𝑑𝛺

4𝜋

) = 4𝜎𝛼𝑝𝐴𝑖(𝑇𝑖∞ − 𝑇𝑤)

4 (6-14)

where 𝑟 is the radius, 𝛼𝑝 the Planck mean absorption coefficient [219], 𝜎 the Stefan-Boltzmann

constant, 𝐼 the radiation intensity, Ω the solid angle of ray and 𝐴𝑖 = 4𝜋𝑟𝑖2 is the surface area of

each burned shell. The subscript 𝑤 refers to the chamber wall. The Planck mean absorption

coefficient is determined using statistical narrow-band (SNB) model [219] considering major

radiating species of CO2, H2O, CO and CH4. The total mass of the gas in unburned and burned

regions is

𝑚 = 𝑚𝑢 +∑𝑚𝑏𝑗

𝑛−1

𝑗=1

+𝑚𝑏𝑛 (6-15)

Due to the mass conservation the total mass is constant and also by assuming constant mass for

each already burned shells (�̇�𝑏1 = ⋯ = �̇�𝑏𝑛−1 = 0), so we have

�̇�𝑢 = −�̇�𝑏𝑛 (6-16)

The total volume of the gas inside the combustion chamber is

𝑉 = 𝑉𝑐 − 𝑉𝑒 = 𝑉𝑢 +∑𝑉𝑏𝑗

𝑛−1

𝑗=1

+ 𝑉𝑏𝑛 (6-17)

139

where

𝑉𝑢 = 𝑉𝑢∞ − 𝑉𝑑𝑖𝑠𝑢 =

𝑚𝑢

𝜌𝑢∞− 4𝜋(𝛿𝑤𝑏𝑟𝑐

2 − 𝛿𝑝ℎ𝑟𝑏𝑛2 ) (6-18)

𝑉𝑗 = 𝑉𝑗∞ − 𝑉𝑑𝑖𝑠𝑗 =

𝑚𝑗

𝜌𝑗∞ − 2𝜋𝑟𝑒(𝑟𝑗 − 𝑟𝑗−1)𝛿𝑒𝑏𝑗 , 𝑗 = 𝑏1 − 𝑏𝑛−1 (6-19)

𝑉𝑏𝑛 = 𝑉𝑏𝑛∞ − 𝑉𝑑𝑖𝑠𝑏𝑛 =

𝑚𝑏𝑛

𝜌𝑏𝑛∞ − 2𝜋𝑟𝑒(𝑟𝑏𝑛 − 𝑟𝑏𝑛−1)𝛿𝑒𝑏𝑏𝑛 (6-20)

The subscripts of 𝑐, 𝑓, 𝑒, 𝑤𝑏, 𝑝ℎ and 𝑒𝑏 denote the chamber, flame, electrode, wall boundary

layer, preheat zone and electrode boundary layer respectively. Since the chamber volume is fixed,

taking the derivative of Eq. (6-17) and applying Eqs. (6-4)-(6-6) yields the burned gas mass

fraction rate as

�̇�𝑏 = −(𝐶𝑢

∞ + ∑ 𝐶𝑘∞

𝑘 )�̇� + (𝐷𝑢∞ + ∑ 𝐷𝑘

∞𝑘 ) + (𝐸𝑢

∞ + ∑ 𝐸𝑘∞

𝑘 )

𝐹 , 𝑘 = 𝑢, 𝑏1, ⋯ , 𝑏𝑛−1, 𝑏𝑛 (6-21)

where

𝐶𝑘∞ = ((

𝜕𝜌𝑘∞

𝜕𝑝) + (

𝜕𝜌𝑘∞

𝜕𝑇𝑘∞)

𝐴𝑘∞

𝐵𝑘∞)

𝑚𝑘

(𝜌𝑘∞)2

(6-22)

𝐷𝑘∞ = (

ℎ𝑘∞𝑚𝑘

𝐵𝑘∞𝜌𝑘

∞ (𝜕𝜌𝑘

∞

𝜕𝑇𝑘∞) + 1) �̇�𝑑𝑖𝑠𝑘 (6-23)

𝐸𝑘∞ =

𝑚𝑘

𝐵𝑘∞(𝜌𝑘

∞)2(𝜕𝜌𝑘

∞

𝜕𝑇𝑘∞) �̇�𝑘 (6-24)

𝐹 =ℎ𝑢∞𝑚𝑢𝑉𝑑𝑖𝑠𝑢

𝐵𝑢∞𝜌𝑢∞(1 − 𝑥𝑏)(𝜕𝜌𝑘

∞

𝜕𝑇𝑘∞) +

𝑚𝑏𝑛

𝐵𝑏𝑛∞ (𝜌𝑏𝑛

∞ )2 (𝑚(ℎ𝑢

∞ − ℎ𝑏𝑛∞ ) −

𝜌𝑢∞ℎ𝑢

∞𝑉𝑑𝑖𝑠𝑢1 − 𝑥𝑏

)(𝜕𝜌𝑏𝑛

∞

𝜕𝑇𝑏𝑛∞)

+𝑚(1

𝜌𝑢∞−

1

𝜌𝑏𝑛∞ )

(6-25)

Eqs. (6-4), (6-6) and (6-21) form a set of nonlinear ordinary differential equations which contain

n + 3 unknowns: 𝑝(𝑡), 𝑥𝑏(𝑡), 𝑇𝑢∞ and 𝑇𝑏𝑖

∞ (i = 1 to n). Given experimental pressure as a function

140

of time, they can be solved numerically using CVODE method to find burned mass fraction and

temperature distribution. Finally, the laminar burning speed is calculated as:

𝑆𝑢 =𝑚�̇�𝑏𝜌𝑢∞𝐴𝑓

(6-26)

where 𝐴𝑓 is the flame front area. The initial mixture composition is defined as 𝜙(𝛼𝐻2 +

(1 − 𝛼)𝐶𝑂) + 0.5(𝑂2 + 3.76𝑁2), where 𝛼 is the hydrogen concentration of the fuel mixture and

𝜙 the equivalence ratio. The overall uncertainty of measured laminar burning speed data is

calculated by combining the systematic (Bias) and random (Precision) uncertainty [100], using the

root-sum-square method. More information about uncertainty mathematical formulations can be

found in our previous paper [47]. The range of overall uncertainty in the measured laminar burning

speed data was found to be between ±1% and ±3% with the average of ±1.51%. This range of

uncertainty is only valid for conditions which are covered in our experiments and numerical

analysis. For other conditions that are estimated using power law fitting especially atmospheric

conditions (except the tests with initial pressure of 0.5 atm) the average uncertainty is ±2.76%.

In order to compare experimental results with numerical results based on detailed kinetic

mechanisms, the steady, one-dimensional, laminar premixed free flame code from the CANTERA

package [220] has been used to solve the conservation equations of mass, momentum, energy and

species. The multi-component diffusion model has been used for evaluation of transport properties.

The computation usually led to higher burning speeds in comparison with the mixture-averaged

diffusion model. In the present paper, three detailed chemical kinetics mechanisms for syngas

combustion [221–223] have been selected and compared to the experimental laminar burning

speeds. Accuracy of the calculated burning speed is highly dependent on the number of grid points

used in calculations, especially for multi-component models. To lower the error in calculated

burning speeds and to make sure that convergence is attainable, a grid with between 800 and 1000

points is recommended.

141


6.5.1. Flame Structure and Instability Study

Besides the laminar burning speed, which is one of the most important thermo-physical

characteristics of premixed flames, the initiation and propagation of cellular instabilities over the

flame surface should be investigated in detail. The two most significant instabilities that occur in

premixed flames are hydrodynamic and thermo-diffusive instabilities [224]. Hydrodynamic

instability is caused by the density variation across the flame which is also associated to the thermal

expansion ratio (𝜍 = 𝜌𝑢 𝜌𝑏⁄ ) and flame thickness [225]. The flame thickness is defined by 𝛿𝑓 =

(𝑇𝑎𝑑 − 𝑇𝑢) (𝑑𝑇 𝑑𝑥⁄ )𝑚𝑎𝑥⁄ , where 𝑇𝑎𝑑 is the adiabatic flame temperature, 𝑇𝑢 the unburned

temperature and (𝑑𝑇 𝑑𝑥⁄ )𝑚𝑎𝑥 the maximum temperature gradient [226]. By reduction of flame

thickness as the pressure increases the propensity for cell formation is significantly enhanced. The

thermo-diffusive instability is due to the inequality of thermal diffusion from the flame and mass

diffusion towards the flame [227,228]. The non-dimensional parameter that distinguishes thermo-

diffusive instability is called the Lewis number. It is the ratio of thermal diffusivity of the mixture

to the mass diffusivity of the limiting reagent. The effective Lewis number for H2/CO/air mixtures

based on the works of Ai et al. [229] and Bouvet et al. [230] for a wide range of equivalence ratio

from lean (𝜙 = 0.6) to rich (𝜙 = 5.0) can be calculated by the following equation:

𝐿𝑒𝑒𝑓𝑓 =

{

𝐿𝑒𝑓𝑢𝑒𝑙 =

𝐷𝑇𝑥𝐻2𝐷𝐻2/𝑁2 + 𝑥𝐶𝑂𝐷𝐶𝑂/𝑁2

𝜙 ≤ 0.8

𝐿𝑒𝑓𝑢𝑒𝑙/𝑂2 = 1 +(𝐿𝑒𝐸𝑥 − 1) + (𝐿𝑒𝐷𝑒𝑓 − 1)𝐴

1 + 𝐴 0.8 < 𝜙 < 2

𝐿𝑒𝑂2 =𝐷𝑇

𝐷𝑂2/𝑁2 𝜙 ≥ 2

(6-27)

where 𝐷𝑇 = 𝜆 𝜌𝑢𝑐𝑝⁄ is the mixture thermal diffusivity, 𝐷𝑘/𝑁2 is the reactant-inert binary diffusion

coefficient both based on Davis mechanism [221] and 𝑥𝑖 the volumetric fraction of the 𝑖𝑡ℎ

component of the fuel blend. This relation proposes that the effective Lewis number for lean

mixtures is the Lewis number of the fuel blend (H2/CO), and for rich mixtures it is the Lewis

number of the oxidizer (O2) and for stoichiometric mixtures it is the weighted average of the Lewis

numbers of the fuel blend and oxidizer. The subscripts 𝐸𝑥 and 𝐷𝑒𝑓 refer to the excessive and

deficient reactants, respectively. The parameter 𝐴 which is also called “mixture strength” is

142

defined as 𝐴 = 1 + 𝑍𝑒(1 𝜙⁄ − 1), where 𝜙 is the mixture equivalence ratio and 𝑍𝑒 is the flame

Zel’dovich number which is calculated as follows:

𝑍𝑒 =𝐸𝑎(𝑇𝑎𝑑 − 𝑇𝑢)

�̅�𝑇𝑎𝑑2 (6-28)

where 𝐸𝑎 = −2�̅�[𝜕𝑙𝑛(𝜌𝑢𝑆𝑢) 𝜕(1 𝑇𝑎𝑑⁄ )⁄ ] is the global activation energy and �̅� is the universal gas

constant. The effects of initial pressure and equivalence ratio on the destabilization of the flame

front have been examined. Figure 6.2 shows the snapshots of the expanding spherical flame with

changing initial pressure and equivalence ratio at hydrogen concentration of 25%, initial

temperature of 298 K and flame radius of 60 mm. The time 𝑡, pressure ratio 𝑝/𝑝𝑖, thermal

expansion ratio 𝜎 and flame thickness 𝛿𝑓 are indicated under each image. As shown in these

images, only laminar and smooth flames are observed for 𝑝𝑖 = 0.5 atm, while the flame fronts

become cellular and unstable as initial pressure increases. Since the thermal and mass diffusivities

are inversely proportional to the pressure, the Lewis number is not sensitive to pressure variations

[231,232] as shown in Figure 6.3. It means that the tendency to destabilize the flame front by

increasing the initial pressure for a given equivalence ratio is not related to the thermo-diffusive

effect and doesn’t have any significant consequences on the effective Lewis number. The only

effect that can play a significant role on flame instability as the initial pressure increases is the

hydrodynamic effect due to the remarkable decrease in the flame thickness as shown in both

Figure 6.2 and Figure 6.3.

The reduction of flame thickness attenuates the influence of curvature, lowers its resistance to

perturbations associated with thermal expansion ratio, which promotes its destabilizing propensity

[233]. This same behavior is exhibited by flames of all equivalence ratios except for 𝜙 = 5, where

the flame remains completely smooth and laminar with the increase of pressure up to 5.5 atm. In

this case the hydrodynamic instability cannot deform the flame because its growth rate is smaller

than that of flame expansion [233]. Thermo-diffusive instability greatly impacts cell formation and

crack propagation in the initial stages of combustion where the radius is still small [226]. The

absence of cracks after ignition indicates that the thermo-diffusive instability can be neglected for

the remainder of the flame propagation. This and large flame thicknesses are the reasons why

flames are completely smooth and laminar at sub-atmospheric initial pressures and increasing

equivalence ratios.

143

𝒑𝒊 = 𝟎. 𝟓 𝒂𝒕𝒎 𝒑𝒊 = 𝟏 𝒂𝒕𝒎 𝒑𝒊 = 𝟐 𝒂𝒕𝒎

𝝓 = 𝟎. 𝟔

33.12, 1.74

5.07, 0.800

37.22, 1.80

5.05, 0.385

39.43, 1.65

5.16, 0.224

𝝓 = 𝟏. 𝟎

13.24, 1.82

5.86, 0.662

13.24, 1.90

5.89, 0.289

11.98, 1.75

6.07, 0.154

𝝓 = 𝟐. 𝟎

8.2, 1.86

5.38, 0.532

8.2, 2.10

5.23, 0.199

7.25, 1.88

5.37, 0.105

𝝓 = 𝟑. 𝟎

8.83, 1.74

4.80, 0.539

8.83, 1.90

4.71, 0.212

8.83, 1.86

4.73, 0.105

𝝓 = 𝟓. 𝟎

𝒕(𝒎𝒔), 𝒑/𝒑𝒊 𝝈, 𝜹𝒇(𝒎𝒎)

26.18, 1.72

3.96, 0.695

37.85, 1.79

3.92, 0.339

64.04, 1.74

3.93, 0.209

Figure 6.2. Snapshots of the H2/CO/air flames for various initial pressures and wide range of equivalence

ratios at hydrogen concentration of 25%, initial temperature of 298 K and flame radius of 60 mm

Increasing the initial pressure at lean conditions where the effective Lewis number is very small

causes the thermo-diffusive instability to come into effect by creating cracks. As it is shown in

Figure 6.2 for the case of atmospheric initial pressure at lean condition (𝜙 = 0.6), where the

144

effective Lewis number is very small and flame thickness is very large, the thermo-diffusive is the

only factor to create instability in the form of cracks. As the equivalence ratio increases thermo-

diffusive effects will be suppressed because the effective Lewis number increases. Simultaneously,

the reduction of flame thickness and growth of expansion ratio and burning speed cause the

hydrodynamic instability to come into effect when the flame thickness approaches to its local

minimum at 𝜙 = 2.0, the most unstable case will occur. Beyond 𝜙 = 2.0, since the growth rate of

hydrodynamic instability is proportional to burning speed and thermal expansion ratio, the

hydrodynamic effect is fading by increasing the flame thickness, decreasing the expansion ratio

and burning speed. It is also interesting to note that the time of flame arrival to the radius of 60

mm increases for equivalence ratios of 0.6 and 5.0, decreases for equivalence ratios of 1.0 and 2.0

and is almost constant for equivalence ratio of 3.0 as shown in Figure 6.2.

Figure 6.3. Effective Lewis number and flame thickness of the H2/CO/air flames corresponding to the

snapshots of Figure 6.2

Figure 6.4 shows a series of snapshots of H2/CO/air flames for equivalence ratio of 1.0, initial

pressure of 2 atm and hydrogen concentration of 5, 10 and 25%. The figure depicts the evolution

of flames and shows that the tendency for cell formation is increased with increasing pressures and

0 1 2 3 4 5

0.4

0.6

0.8

1

1.2

1.4

Effe

ctive

Le

wis

nu

mb

er

Equivalence ratio

0 1 2 3 4 50

0.2

0.4

0.6

0.8

0 1 2 3 4 50

0.2

0.4

0.6

0.8

0 1 2 3 4 50

0.2

0.4

0.6

0.8

Fla

me

th

ickn

ess (

mm

)

pinitial

= 0.5 atm

pinitial

= 1.0 atm

pinitial

= 2.0 atm

145

flame radii. As the hydrogen concentration in the fuel blend increases, the flame becomes much

more sensitive to instability. This can be explained by the reduction of Lewis number and flame

thickness amplifying the impact of thermo-diffusive and hydrodynamic instabilities, respectively,

as shown in Figure 6.4.

𝒕 = 𝟑. 𝟐𝟒 𝒎𝒔 𝒕 = 𝟖. 𝟎𝟗 𝒎𝒔 𝒕 = 𝟏𝟐. 𝟑𝟎 𝒎𝒔

𝜶 = 𝟓%

0.884, 1.00

4.79, 0.415

0.880, 1.03

4.77, 0.403

0.870, 1.10

4.69, 0.377

𝜶 = 𝟏𝟎%

0.858, 1.01

4.78, 0.353

0.852, 1.06

4.73, 0.336

0.829, 1.25

4.54, 0.284

𝜶 = 𝟐𝟓%

𝑳𝒆𝐞𝐟𝐟, 𝒑/𝒑𝒊 𝝈, 𝜹𝒇(𝒎𝒎)

0.816, 1.02

4.76, 0.285

0.784, 1.29

4.48, 0.222

0.672, 3.55

3.55, 0.085

Figure 6.4. Snapshots of the stoichiometric H2/CO/air flames for various hydrogen concentration at initial

pressure of 2 atm and initial temperature of 450 K

Figure 6.5 shows the experimentally derived critical Peclet number as a function of equivalence

ratio for three different hydrogen concentration at initial pressure of 2 atm and initial temperature

of 450 K. The non-dimensional critical Peclet number is defined as the ratio of critical radius to

flame thickness (𝑃𝑒𝑐𝑟 = 𝑟𝑐𝑟 𝛿𝑓⁄ ). The critical radius is the radius at which small cells appear

spontaneously and uniformly over the whole flame surface, which is defined as the onset of flame

instability. As shown in Figure 5, for the hydrogen concentration of 5% and 10%, as the

equivalence ratio increases, the critical Peclet number first decreases for lean mixtures, reaches a

minimum, and then increases for rich mixtures. The minimum critical Peclet number for the

𝛼 = 5% and 𝛼 = 10% cases occurs at 𝜙 = 2.0 and 𝜙 = 1.0 respectively, at which the flame

146

becomes cellular at smaller radii. With the addition of more hydrogen to the fuel (𝛼 = 25%) the

critical Peclet number increases linearly with respect to equivalence ratio, which means that

instability is lingered to larger radii. The flame instability is very sensitive to hydrogen fraction

variation at lean and around stoichiometric conditions as shown in Figure 6.5. In the present study

the laminar burning speeds are only reported for smooth, laminar and spherical flames.

Figure 6.5. Critical Peclet number of the stoichiometric H2/CO/air flames for various hydrogen

concentration at initial pressure of 2 atm and initial temperature of 450 K

For a given gas mixture, as the flame propagates, the pressure increases until eventually the

flame becomes cellular at a critical pressure and critical temperature at which point the cell

formation occurs over the entire flame surface. Table 6-1 shows the critical pressure and critical

temperature of H2/CO/air mixtures at different initial pressures and a wide range of equivalence

ratios for three hydrogen concentration of 5%, 10% and 25% and initial temperature of 450 K.

These parameters quantify the conditions at which small cells become visible over the whole flame

surface. It can be seen in Table 6-1 that cell formation strongly depends on the equivalence ratio

and hydrogen concentration. Initial pressure does not affect the critical pressure of flame

cellularity.

0 0.5 1 1.5 2 2.5 3 3.5100

150

200

250

300

350

400

Cri

tica

l P

ecle

t n

um

be

r

Equivalence ratio

= 5%

= 10%

= 25%

147

Table 6-1- Critical pressures and temperatures of H2/CO/air mixtures at initial temperature of 450 K,

different initial pressures, wide range of equivalence ratios and three hydrogen concentration of 5, 10 and

25%

𝒑𝒊(𝐚𝐭𝐦) 𝝓 = 𝟎. 𝟔 𝝓 = 𝟏. 𝟎 𝝓 = 𝟐. 𝟎 𝝓 = 𝟑. 𝟎 𝝓 = 𝟓. 𝟎

𝜶 = 𝟓%

0.5 𝑝𝑐𝑟(atm)~

𝑇𝑐𝑟(K)~ Smooth Smooth Smooth Smooth Smooth

1 𝑝𝑐𝑟(atm)~



𝑇𝑐𝑟(K)~

5.73

602

4.21

554

3.28

517

3.41

522 Smooth

𝜶 = 𝟏𝟎%




𝑇𝑐𝑟(K)~ Smooth

3.13

617

2.73

595

2.97

609 Smooth


𝑇𝑐𝑟(K)~

3.83

539

3.26

515

2.91

499

3.19

512 Smooth

𝜶 = 𝟐𝟓%




𝑇𝑐𝑟(K)~

2.80

598

2.43

576

2.55

584

2.85

602 Smooth


𝑇𝑐𝑟(K)~

2.91

500

2.62

485

2.71

490

3.07

507 Smooth

Figure 6.6 shows the critical pressures of H2/CO/air flames for all initial pressures, initial

temperatures and equivalence ratios from 0.6 up to 3.0 at three hydrogen concentration of 5%,

10% and 25 %. The critical pressure is defined as the pressure at the onset of flame cellularity. For

rich mixtures of 𝜙 = 4.0 and 𝜙 = 5.0 flames were smooth during experiments and critical

pressures were not measured. Pressures below the curve are related to smooth and laminar flames

whereas pressures above the curve are for cellular flames. Increasing the hydrogen concentration

shifts the local minimum of the curve, or vertex, to the left, decreasing the equivalence ratio at

which the vertex is found. The reason for the reduction of the critical pressure as equivalence ratio

increasing is that the flame instability happens earlier due to the considerable decrease of the flame

thickness and increase of laminar burning speed. Figure 6.6 shows that increasing hydrogen

concentration in the mixture decreases critical pressures and causes the flame to become cellular

at lower pressures.

148

Figure 6.6. Critical pressures versus equivalence ratio for three different hydrogen concentration

6.5.2. Stretch Effect Investigation

Flame stretch in spherically expanding flames can be defined as:

𝜅 =1

𝐴𝑓

𝑑𝐴𝑓

𝑑𝑡=2

𝑟

𝑑𝑟

𝑑𝑡 (6-29)

where 𝜅 is the stretch rate, 𝐴𝑓 is the flame front area, 𝑡 is time, and 𝑟 is the flame radius. Laminar

burning speed of stretched flames is different from zero stretch laminar burning speed. Zero stretch

laminar burning speed is usually estimated by extrapolating the stretched burning speed data to

zero stretch. This extrapolation process is considered as one of the major sources of discrepancies

among laminar burning speed data reported from different researchers. Various linear and

nonlinear extrapolations have been developed to measure zero stretch laminar burning speed

[41,193,195,197,203,210]. Recent paper by Wu et al [234] has reviewed different methods of

extrapolation and has shown great uncertainty of these methods. It is seen from Eq. (6-29) that as

the radius of flame increases the stretch rate decreases. Therefore, measured values of laminar

burning speed should be reported for large flame radii where there are very small stretch rates and

stretch effects can be considered negligible.

0 0.5 1 1.5 2 2.5 3 3.5

1

2

3

4

5

6

Cri

tica

l p

ressu

re (

atm

)

Equivalence ratio

= 5%

= 10%

= 25%

Cellular

Non-Cellular

149

In order to study the effect of stretch, laminar burning speeds of syngas and air mixtures have

been measured at different stretch rates and flame radii (𝑟 > 4cm) with similar unburned gas

properties such as temperature, pressure and equivalence ratios. To perform these experiments,

different tests have been arranged by changing the initial temperature and pressure of the mixtures

along specific isentropic lines. More information about this method can be found in previous

publications [1,3]. Figure 6.7 shows the variation of laminar burning speed versus stretch rate for

different equivalence ratios and unburned gas conditions at hydrogen concentration of 5%.

Figure 6.7. Laminar burning speed versus stretch rates for two different equivalence ratios and unburned

gas conditions at hydrogen concentration of 5%

As it can be seen the laminar burning speeds do not change for flame radii greater than 4 cm

and stretch rates lower than 80 s-1. Based on many studies in the literature [235–238] the stretch

rates higher than 100 s-1 can have significant effect on the laminar burning speeds. Therefore, in

this paper all the laminar burning speed data are reported for stretch rates of less than 80 s-1. This

observation is in agreement with prediction of Chen et al. [239] for low stretch rate flames.

30 40 50 60 70 80 900

20

40

60

80

100

120

140

160

180

La

min

ar

bu

rnin

g s

pe

ed

(cm

/s)

Stretch rate (1/s)

=1, T=460K, p=4.5atm

=3, T=410K, p=3.1atm

150

6.5.3. Laminar Burning Speed

All laminar burning speed data are reported in regions where 𝑟 > 4cm and stretch rate of less

than 80 s-1. In these regions the effects of stretch and spark energy discharge are negligible. The

measured laminar burning speeds have been used to develop a correlation for easy use. The laminar

burning speed correlation is a function of equivalence ratio, temperature and pressure as shown in

Eq. (30):

𝑆𝑢 = 𝑆𝑢0(1 + 𝑎(𝜙 − 1) + 𝑏(𝜙 − 1)2) (

𝑇

𝑇0)𝑐

(𝑝

𝑝0)𝑑

(6-30)

with Su0 as the laminar burning speed at reference point (ϕ = 1, T0 = 298K, p0 = 1atm) , ϕ the

equivalence ratio, T the temperature in K and p the mixture pressure in atm. Fitting coefficients,

a, b, c and d, have been found using a nonlinear least square method which are listed in Table 6-2

for three different hydrogen concentration. This correlation is only valid for non-cellular laminar

flames in the equivalence ratio range of 0.6 < 𝜙 < 5. The range of pressure and temperature is a

function of equivalence ratio and hydrogen fraction, which can be determined using Table 6-1 and

Figure 6.6. The maximum pressure for 𝜙 = 4.0 is 5.2 atm and for 𝜙 = 5.0 is 5.5 atm.

Table 6-2- Power law fitting coefficients

𝑺𝒖𝟎 𝒂 𝒃 𝒄 𝒅

𝜶 = 𝟓% 30.134 1.200 -0.311 1.912 -0.232

𝜶 = 𝟏𝟎% 40.596 1.232 -0.323 2.004 -0.275

𝜶 = 𝟐𝟓% 61.573 1.189 -0.325 2.100 -0.385

Figure 6.8 shows the laminar burning speeds of syngas and air mixtures at various initial

conditions and equivalence ratios and three different hydrogen fractions versus temperature along

many isentropes. As shown in Figure 6.8(a) by increasing the equivalence ratio from ϕ = 0.6 to

ϕ = 3.0 laminar burning speed increases. But increasing the equivalence ratio beyond ϕ = 3.0

leads to decrease in laminar burning speed. Initial temperature has a direct effect on laminar

burning speed and as it is shown in Figure 6.8(b) increasing the initial temperature causes an

increase in the laminar burning speed. This is the reason why the exponent of temperature term in

the power law correlation is positive. On the other hand the pressure has an inverse effect on

laminar burning speed as shown in Figure 6.8(c) and because of that its exponent in the power law

151

correlation is negative. As it can be seen in Figure 6.8(d), the laminar burning speed increases with

an increasing hydrogen concentration in the fuel mixture. The solid line is the laminar burning

speed data using the power law correlation.

(a)

(b)

152

Figure 6.8. Laminar burning speed of syngas/air mixture along isentropes at different (a) equivalence

ratios, (b) temperatures, (c) pressures and (d) hydrogen fractions

Measured laminar burning speeds from this study have been compared with experimental

available data in the literature as well as predicted laminar burning speeds using three detailed

chemical kinetics mechanisms for syngas combustion [221–223]. The comparisons have been

made only at standard ambient temperature and pressure for three different concentration of

(c)

(d)

153

hydrogen. It is seen from Figure 9 that the measured laminar burning speed agrees well with

available experimental data in literature. The results were within the expected experimental error

under the test conditions where comparisons were possible with other studies. As described earlier

in this paper the average uncertainty of ±2.76% is associated with the conditions which are

approximated from the power law fitting method such as atmospheric conditions (except for sub-

atmospheric initial pressure) as shown in Figure 6.9. From selected kinetics mechanisms, the Davis

mechanism [221] is in fairly good agreement with the obtained experimental data.

0 1 2 3 4 50

10

20

30

40

50

60

70

80

Equivalence ratio

La

min

ar

bu

rnin

g s

pe

ed

(cm

/s)

Present study

MClean et al [8]

Hassan et al [10]

Natarajan et al [1]

Sun et al [4]

Bouvet et al [14,15]

Singh et al [19]

Davis mechanism [47]

Li mechanism [48]

Keromnes mechanism [49]

(a) =5%

0 1 2 3 4 50

20

40

60

80

100

Equivalence ratio

La

min

ar

bu

rnin

g s

pe

ed

(cm

/s)

Present study

Hassan et al [10]

Dong et al [11]

Bouvet et al [14]

Bouvet et al [15]

Li et al [23]


Li mechanism [48]


(b) =10%

154

Figure 6.9. Comparison of present experimental data versus published experimental data and kinetic

simulations for H2/CO/air laminar burning speed at atmospheric conditions, (a) 𝛼 = 5%, (b) 𝛼 = 10%,

and (c) 𝛼 = 25%,

0 1 2 3 4 50

50

100

150

Equivalence ratio

La

min

ar

bu

rnin

g s

pe

ed

(cm

/s)

Present study

Hassan et al [10]

Sun et al [4]

Bouvet et al [14]

Burbano et al [16]

Burbano et al [17]

Singh et al [19]

Han et al [25]


Li mechanism [48]


(c) =25%

155

7. The Effect of Exhaust Gas Recirculation (EGR) on

Flame Structure and Laminar Burning Speeds of

H2/CO/Air Premixed Flame at High Pressures and

Temperatures

156

7.1. ABSTRACT

Experimental studies have been performed in conjunction with a novel differential based multi-

shell model to investigate the flame structure and measure laminar burning speed of

H2/CO/air/diluent premixed flames at high pressures and temperatures. This paper focuses on

synthetic gas (syngas) as the fuel blend, which is a mixture of H2 and CO, and investigates the

effect of synthetic EGR (SEGR) as the diluent on flame structure and laminar burning speed.

Synthetic EGR is a mixture of 14% CO2 and 86% N2. In these experiments two different SEGR

concentrations of 5 and 10% have been used. The experiments were performed in two constant

volume spherical and cylindrical chambers. The cylindrical chamber was set up in a Z-shape

Schlieren system equipped with a high speed CMOS camera, capable of taking pictures up to

40,000 frames per second, which was used to study the structure and stability of the flame. The

laminar burning speed of the combustion process was calculated from the pressure rise

measurement during flame propagation in spherical chamber. Power law correlations have been

developed for laminar burning speeds of smooth H2/CO/air/SEGR flames over a wide range of

temperatures (298K up to 450 K), pressures (from sub-atmospheric up to 5.5 atm), equivalence

ratios (0.6-3) and three different hydrogen concentration of 5, 10 and 25% in the fuel mixture.

SEGR lowers the laminar burning speed and has significant effect on the flame stability compared

to H2/CO/air, especially for very lean and very rich mixtures. Experimental burning speeds of

H2/CO/air/SEGR mixtures have been compared with available measurements as well as computed

values obtained by 1D free flame simulations using two chemical kinetics mechanisms. Very good

agreements have been observed with the experimental data available in the scientific literature as

well as computational burning speed calculation.

Keywords: syngas, exhaust gas recirculation, laminar burning speed, flame stability, schlieren

photography, high pressure and temperature, multi-shell

7.2. INTRODUCTION

Synthetic gas, also known as syngas, is fundamentally a mixture of hydrogen and carbon

monoxide gases along with various other higher-order hydrocarbons. Syngas is considered an

alternative fuel since it can be created through various sources such as biomass gasification,

reactions that involve natural gas and coal, as well as the recycling of stationary turbine

157

byproducts. With the advent of integrated gasification combined cycle (IGCC) technology, syngas

can be created from coal with lower emissions. Thus, the development and research pertaining to

syngas fuels are becoming more relevant amid growing concerns about pollutants and carbon

emissions.

Syngas is considered as a strong candidate to replace many fuels currently in use, therefore, it

is imperative to fully understand and characterize how syngas behaves in various conditions. The

laminar burning speed adequately characterizes a fuel and provides a good indicator of how a fuel

performs. It is widely used and contains information about a mixture’s exothermicity, diffusivity,

and reactivity. It is also important to study the laminar burning speed

[1,3,4,23,67,101,104,171,240–242] in a high pressure environment as well as with different

diluents, since those are normally gas turbine and I.C. engines [14] relevant conditions. One typical

form of diluent is the inert gas used in exhaust gas recirculation (EGR) technique commonly used

in automobile engines [14], which is primarily a mixture of carbon dioxide, nitrogen, water and

other products of combustion.

There is a wide assortment of literature on the laminar burning speed of syngas fuels with and

without diluent. Hassan et al. [195] measured the laminar burning speed of various hydrogen to

carbon monoxide ratios (3:97, 5:95, 10:90, 25:75, 50:50), sub-atmospheric to elevated pressures

(0.5-4 atm), atmospheric temperature, and wide equivalence ratio (0.6-5.0) in a spherical

combustion chamber. Sun et al. [41] used a dual-cylindrical chamber to extract laminar burning

speed data at atmospheric temperature from many different H2/CO ratios (1:99, 5:95, 25:75,

50:50), elevated pressures (up to 40 atm), and equivalence ratios (0.5-5.0). Sun et al. [41] also

replaced nitrogen with helium as the diluent in order to increase the stability of flames, which

allowed them to obtain data for much higher pressures. Natarjan et al. [37] used the burner and

particle velocimetry technique to measure laminar burning speed for 5:95, 50:50, and 95:5 syngas

percentages diluted with CO2 and later extended measurements to higher pressures with helium

substitution to reduce flame instability [43]. Prathap et al. [40] used the constant pressure method

to measure the laminar burning speed of 50:50 H2/CO mixtures diluted by N2 and later CO2 [243].

Vu et al. [244] compared the effects of CO2, N2, and He as diluents on the cellular instabilities in

syngas flames in a cylindrical chamber at elevated pressures for a 50:50 hydrogen to carbon

monoxide ratio, and found that He suppresses instabilities best and reduces the laminar burning

speed the least. Burbano et al. [202] used the burner method to extend the data on the effects of

158

CO2 and N2 dilution on laminar burning speed and stability over a wider equivalence ratio (0.6-

4.3). Lapalme and Seers [245] investigated the effect of initial temperature (up to 450K) and

carbon dioxide and methane dilution on the laminar burning velocities of syngas flames, as well

as provided a correlation based on their data. Han et al. [210] measured laminar burning speeds

for various CO2 diluent percentages (10%-40%) at elevated temperatures and pressures for

equivalence ratios of 𝜙 = 0.8 and 𝜙 = 1.0 using a dual-cylindrical setup. Wang et al. [246]

reported laminar burning speed data for a wide range of equivalence ratio (0.6-5.6), hydrogen

percentages (5%-75%), and N2 or CO2 percentages (0%-60%) using a heat flux burner as well as

a Bunsen flame in conjunction with OH-PLIF method. Askari et al. [22] measured the laminar

burning speeds of H2/CO/air flames using a new differential-based multi-shell model over a wide

range of temperatures (298K up to 617K), pressures (from sub-atmospheric up to 5.5atm),

equivalence ratios (0.6-5) and three different hydrogen concentration of 5%, 10% and 25%

respectively. They concluded when the initial pressure increases, the tendency for the flame to

destabilize takes place earlier due to a significant decrease of the flame thickness and enhancement

of hydrodynamic instability. They measured the laminar burning speeds for smooth flames using

the pressure rise method and developed power law correlations [22]. There is a wide range of

scientific literature that is currently available on the laminar burning speed of syngas flames diluted

with varying percentages of CO2 or N2, but no literature exists for syngas flames diluted exactly

with both 14% CO2 and 86% N2 to simulate the exhaust gas recirculation in I.C. engines.

The present study investigates the effect of Synthetic Exhaust Gas Recirculation (SEGR), with

the composition of 14% CO2 and 86% N2, on the stability and laminar burning speeds of H2/CO/air

flames. Since creating the real EGR, which is the engine post-combustion exhaust gases in our lab

is impossible, a synthetic EGR with aforementioned composition which has the same specific heat

as real EGR is used. The effect of SEGR addition (5 and 10%) to H2/CO/air on flame morphology,

flame stability and laminar burning speed has been studied in a wide range of temperatures,

pressures and equivalence ratios for three various hydrogen concentrations. In this paper laminar

burning speeds of H2/CO/air/SEGR mixtures and their correlations is reported over a wide range

of temperatures (298 K up to 450 K), pressures (from sub-atmospheric up to 5.5 atm), equivalence

ratios (0.6-3) and three different hydrogen concentration of 5, 10 and 25% in the fuel mixture.

159


Experiments have been performed using a cylindrical chamber in a Schlieren photography

system to study the morphology and stability of the flame and a spherical chamber for laminar

burning speed measurement. The cylindrical chamber is, 13.5 cm in diameter and 13.5 cm in

length. The cylindrical chamber is equipped with fused quartz windows that are sealed to the

chamber with two high temperature elastomer O-rings. The cylindrical chamber is set up in a Z-

shape Schlieren system equipped with a high speed CMOS camera, capable of taking pictures up

to 40,000 frames per second [46,47]. Two band heaters are installed in order to raise the initial

temperature of the system up to 500K. Both chambers are fitted with two extended automotive

spark plugs, and K-type thermocouples to measure the temperature of the inside gas mixtures. The

spark energy has been tuned to be sufficiently close to the minimum ignition energy to minimize

the effect of spark discharge on flame expansion [211]. Figure 7.1 shows the general configuration

of the experimental set up.

The spherical chamber is made of stainless steel that can withstand pressures up to 400 atm.

The spherical chamber is built using two hemispheres with a diameter of 15.24 cm. It is placed

inside an oven to heat up the chamber up to the initial temperature of 500 K. The pressure rise

inside the spherical chamber was measured using a Kistler high sensitivity pressure sensor [46,47].

The chambers were filled by the method of partial pressures using a manifold supply system

comprised of valves, high accuracy pressure transducers, pipes connected to the respective mixture

constituents, and a vacuum pump. A gas chromatography (GC) system was used to verify the

composition of premixed fuel inside the chamber. A data acquisition system collects and

synchronizes pressure-time data as well as flame propagation images. A LabView program

initiates the combustion process. After filling the chamber with fuel, air, and SEGR the system is

given at least 5 min to make sure that the mixture is completely still. At each operational condition

experiments were done using both chambers. Cylindrical chamber experiments yielded flame

images that were used to study the morphology and stability of the flame as well as to verify that

the flame is smooth, laminar, and spherical. The same experimental conditions were repeated in

the spherical chamber in order to collect the pressure rise data and check its reproducibility. In this

work each experiment was carried out at least three times at each initial condition to ensure that

the confidence level of the experiments were above 95% [212]. Only smooth, laminar, and

160

spherical flames were used to calculate the laminar burning speed. More information about

experimental facilities can be found in other studies [1,23,25,46,47,68,99].

Figure 7.1. Schematic diagram of experimental facilities and Z-type Schlieren system

7.4. FLAME MORPHOLOGY STUDY AND STABILITY ANALYSIS

The effect of SEGR addition on the formation and growth of cellular instabilities over the flame

surface of H2/CO/air mixtures was investigated in detail. Experiments with synthetic EGR (14%

CO2 + 86% N2) have been done with two different concentrations of 5% and 10%. The initial

conditions of the experiments were fixed at ambient temperature of 298 K, pressures of 0.5, 1, and

2 atm, equivalence ratios of 0.6, 1, 2 and 3 and three different hydrogen concentration of 5%, 10%

and 25%. Hydrodynamic and thermo-diffusive effects are two major kind of instabilities which

occur in premixed flames [22]. A complete flame structure and instability analysis including the

definitions and formulations on H2/CO/air mixtures has been explained in a previous publication

[22].

Figure 7.2 shows the snapshots of the expanding spherical flame for different concentration of

SEGR at hydrogen concentration of 25%, initial temperature of 298 K, initial pressure of 1 atm

161

and various equivalence ratios. The combustion duration times are indicated under each image. As

it can be seen in Figure 7.2 the addition of SEGR increases the flame stability for all equivalence

ratios except for stoichiometric case. Both hydrodynamic and thermo-diffusive instabilities have

a significant effect on flame structure as shown in Figure 7.3.

𝑺𝑬𝑮𝑹 = 𝟎 % 𝑺𝑬𝑮𝑹 = 𝟓 % 𝑺𝑬𝑮𝑹 = 𝟏𝟎 %

𝝓 = 𝟎. 𝟔

43.04 ms 47.89 ms 59.22 ms

𝝓 = 𝟏. 𝟎

15.21 ms 16.83 ms 20.39 ms

𝝓 = 𝟐. 𝟎

8.74 ms 10.36 ms 12.29 ms

𝝓 = 𝟑. 𝟎

10.03 ms 13.59 ms 16.18 ms

Figure 7.2. Snapshots of the H2/CO/air/SEGR flames for various SEGR concentrations and equivalence

ratios at hydrogen concentration of 25%, initial temperature of 298 K and initial pressure of 1 atm

For lean mixtures (𝜙 = 0.6) the effective Lewis number is less than unity (𝐿𝑒eff < 1) resulting

in a negative effect on stability. The amount of reduction of effective Lewis number by increasing

the SEGR concentration is negligible as shown in Figure 7.3. Simultaneously, the increase of flame

thickness and reduction of burning speed suppress the hydrodynamic instability and promote flame

stability. Figure 7.3 shows that increasing SEGR concentration has positive effect on flame

162

stability for lean mixtures (𝜙 = 0.6). Increasing SEGR concentration results in an increase in

flame thickness, which overcomes the thermo-diffusive instability and results in a more stable

flame. Figure 7.3 also shows that for the stoichiometric case (𝜙 = 1.0) the positive effect of flame

thickness and the negative effect of thermo-diffusive instability (𝐿𝑒eff < 1), which are similar in

magnitude, cancel each other out. For this reason the flame stability doesn’t drastically change

with increasing SEGR concentration. In the case of rich mixtures (𝜙 = 2.0 − 3.0) the effect of

thermo-diffusive instability will be gone due to the increase in effective Lewis number (𝐿𝑒eff > 1).

At the same time the hydrodynamic instability is fading by increasing the flame thickness which

enhances the tendency of the flame to stabilize by increasing SEGR concentration.

Figure 7.3. Effective Lewis number and flame thickness of the H2/CO/air/SEGR flames corresponding to

the snapshots of Figure 7.2

The effects of initial pressure and flame radius on the destabilization of the flame front are

shown in Figure 7.4. This figure shows the snapshots of the expanding spherical flame with

changing the initial pressures at hydrogen concentration of 25%, initial temperature of 298 K,

SEGR concentration of 10% and equivalence ratio of 2. As it can be seen in these snapshots, only

laminar and smooth flames are observed for 𝑝𝑖 = 0.5 atm, while the flame surfaces become

cellular and unstable as initial pressure increases. As discussed in detail in previous publication

0 5 10

0.5

0.7

0.9

1.1

1.3

Effe

ctive

Le

wis

nu

mb

er

SEGR (%)

0.1

0.2

0.3

0.4

0.5

Fla

me

th

ickn

ess (

mm

)

= 0.6

= 1.0

= 2.0

= 3.0

163

[22] and shown in Figure 7.5 the effective Lewis number is not sensitive to pressure changes. It

means that flame cellularity due to increase in initial pressure is not related to thermo-diffusive

instability. It is solely associated to hydrodynamic instability through the reduction of flame

thickness as shown in Figure 7.5. As pressure increases, flame thickness decreases, which reduces

its resistance to perturbations associated with thermal expansion ratio across the flame [2]. On the

other hand increase in flame radius promotes both thermo-diffusive and hydrodynamic instabilities

through the reduction in effective Lewis number and flame thickness, respectively. As shown in

Figure 7.4 and Figure 7.5, effect of hydrodynamic instability is greater than thermo-diffusive,

which appears in the form of small cells all over the flame surface.

𝒑𝒊 = 𝟎. 𝟓 𝒂𝒕𝒎 𝒑𝒊 = 𝟏 𝒂𝒕𝒎 𝒑𝒊 = 𝟐 𝒂𝒕𝒎

𝒓𝒇 = 𝟏𝟒 𝒎𝒎

𝒓𝒇 = 𝟑𝟑 𝒎𝒎

𝒓𝒇 = 𝟓𝟏 𝒎𝒎

𝒓𝒇 = 𝟔𝟓 𝒎𝒎

Figure 7.4. Snapshots of the H2/CO/air/SEGR flames for various initial pressures and flame radii at

hydrogen concentration of 25%, initial temperature of 298 K, SEGR concentration of 10% and

equivalence ratio of 2.0

164

Figure 7.5. Effective Lewis number and flame thickness of the H2/CO/air/SEGR flames corresponding to

the snapshots of Figure 7.4

Figure 7.6 shows a series of snapshots of stoichiometric H2/CO/air/SEGR flames for initial

pressure of 2 atm, SEGR concentration of 5%, initial temperature of 298 K and various hydrogen

concentration of 5%, 10% and 25%. The figure shows that the tendency for instability is increased

with increasing hydrogen concentration in the fuel blend. This can be explained by the reduction

of Lewis number and flame thickness which promotes the impact of thermo-diffusive and

hydrodynamic instabilities, respectively, as described earlier and previous publication [22].

Figure 7.7 shows the critical Peclet number as a function of equivalence ratio for three different

hydrogen concentration at initial pressure of 2 atm and initial temperature of 298 K. The critical

Peclet number, a non-dimensional parameter, is defined as the ratio of radius to flame thickness

(𝑃𝑒𝑐𝑟 = 𝑟𝑐𝑟 𝛿𝑓⁄ ) in onset of cell formation or flame instability [22]. The onset of cell formation is

defined when the small cells appear on flame surface. This phenomenon happens simultaneously

all over the spherical flame surface and can be captured preciously by our high speed CMOS

camera. Flame thickness is defined by 𝛿𝑓 = (𝑇𝑎𝑑 − 𝑇𝑢) (𝑑𝑇 𝑑𝑥⁄ )𝑚𝑎𝑥⁄ , where 𝑇𝑎𝑑 is the adiabatic

flame temperature, 𝑇𝑢 the unburned gas temperature and (𝑑𝑇 𝑑𝑥⁄ )𝑚𝑎𝑥 the maximum rate of

temperature [226].

10 20 30 40 50 60 70

0.9

1

1.1

1.2

1.3

1.4

Effe

ctive

Le

wis

nu

mb

er

Flame Radius (mm)

10 20 30 40 50 60 700

0.2

0.4

0.6

0.8

1

1.2

Fla

me

th

ickn

ess (

mm

)

pinitial

= 0.5 atm

pinitial

= 1.0 atm

pinitial

= 2.0 atm

165

𝒕 = 𝟑. 𝟖𝟖 𝒎𝒔 𝒕 = 𝟗. 𝟎𝟔 𝒎𝒔 𝒕 = 𝟏𝟕. 𝟒𝟖 𝒎𝒔

𝜶 = 𝟓%

𝜶 = 𝟏𝟎%

𝜶 = 𝟐𝟓%

Figure 7.6. Snapshots of the stoichiometric H2/CO/air/SEGR flames for various hydrogen concentration at

initial pressure of 2 atm, SEGR concentration of 5% and initial temperature of 298 K

Figure 7.7. Critical Peclet number of the stoichiometric H2/CO/air/SEGR flames for various hydrogen

concentration at initial pressure of 2 atm, SEGR concentration of 5% and initial temperature of 298 K

0 0.5 1 1.5 2 2.5 3 3.5

0

500

1,000

1,500

2,000

Cri

tica

l P

ecle

t n

um

be

r

Equivalence ratio

= 5%

= 10%

= 25%

Unstable

Stable

166

As shown in Figure 7.7, as the equivalence ratio increases, the critical Peclet number first

decreases for lean mixtures, reaches a minimum, and then increases for rich mixtures. This

minimum critical Peclet number for the 𝛼 = 5%, 𝛼 = 10% and 𝛼 = 25% takes place at ϕ = 2.0

and ϕ = 1.0 respectively. The area under each curve indicates the stable region which diminishes

with increasing hydrogen concentration, meaning that the flame becomes cellular at smaller radii.

In the present study laminar burning speeds are only reported for smooth, laminar and spherical

flames.

Upon ignition, as the flame propagates the pressure of the chamber increases until the pressure

reaches the critical pressure for cell formation. Table 7-1 and Table 7-2 show the critical pressure

and its corresponding temperature of H2/CO/air/SEGR mixtures at different initial pressures and a

wide range of equivalence ratios for three hydrogen concentration of 5%, 10% and 25%, initial

temperature of 450 K and SEGR concentration of 5% and 10%.

Table 7-1- Critical pressures and temperatures of H2/CO/air/SEGR mixtures at SEGR concentration of

5%, initial temperature of 298 K, different initial pressures, wide range of equivalence ratios and three

hydrogen concentration of 5, 10 and 25%

𝑬𝑫𝑮 = 𝟓% 𝒑𝒊(𝐚𝐭𝐦) 𝝓 = 𝟎. 𝟔 𝝓 = 𝟏. 𝟎 𝝓 = 𝟐. 𝟎 𝝓 = 𝟑. 𝟎

𝜶 = 𝟓%


𝑇(K)~

S - 1.07

S - 371

S - 1.36

S - 396

S - 1.55

S - 411

S - 1.31

S - 392


𝑇(K)~

S - 2.15

S - 371

S - 2.96

S - 405

S - 3.13

S - 412

S - 2.83

S - 401


𝑇(K)~

S - 4.19

S - 368

4.12

366

3.10

338

3.68

355

𝜶 = 𝟏𝟎%


𝑇(K)~

S - 1.17

S - 379

S - 1.50

S - 407

S - 1.55

S - 411

S - 1.38

S - 398


𝑇(K)~

S - 2.38

S - 381

3.41

422

3.19

414

3.30

418


𝑇(K)~

4.54

376

2.99

334

2.65

323

3.04

336

𝜶 = 𝟐𝟓%


𝑇(K)~

S - 1.29

S - 390

S - 1.61

S - 415

S - 1.51

S - 408

S - 1.59

S - 414


𝑇(K)~

2.03

364

2.13

369

2.39

382

3.13

412


𝑇(K)~

2.45

316

2.36

312

2.45

317

3.35

346

167

Table 7-2- Critical pressures and temperatures of H2/CO/air/ SEGR mixtures at SEGR concentration of

10%, initial temperature of 298 K, different initial pressures, wide range of equivalence ratios and three

hydrogen concentration of 5, 10 and 25%

𝑬𝑫𝑮 = 𝟏𝟎% 𝒑𝒊(𝐚𝐭𝐦) 𝝓 = 𝟎. 𝟔 𝝓 = 𝟏. 𝟎 𝝓 = 𝟐. 𝟎 𝝓 = 𝟑. 𝟎

𝜶 = 𝟓%


𝑇(K)~

S - 1.02

S - 365

S - 1.29

S - 389

S - 1.43

S - 401

S - 1.27

S - 388


𝑇(K)~

S - 1.86

S - 355

S - 2.76

S - 397

S - 2.85

S - 401

S - 2.65

S - 393


𝑇(K)~

S - 3.38

S - 346

4.61

377

3.13

338

4.19

367

𝜶 = 𝟏𝟎%


𝑇(K)~

S - 1.02

S - 365

S - 1.41

S - 399

S - 1.44

S - 402

S - 1.33

S - 394


𝑇(K)~

S - 2.07

S - 366

S - 2.98

S - 408

3.25

416

S - 2.69

S - 394


𝑇(K)~

S - 4.01

S - 363

3.68

354

3.01

335

3.84

359

𝜶 = 𝟐𝟓%


𝑇(K)~

S - 1.22

S - 384

S - 1.55

S - 410

S - 1.41

S - 400

S - 1.46

S - 404


𝑇(K)~

S - 2.39

S - 382

2.32

378

2.77

397

S - 2.89

S - 403


𝑇(K)~

2.57

320

2.50

318

2.56

320

4.37

372

These values serve as indicators when the flame has visibly reached the onset of cellularity. An

important issue in these experiments is that cells are formed at large radii; for all of reported cases

𝑟𝑐𝑟 𝑅⁄ > 0.5 where 𝑟𝑐𝑟is the flame radius where cellularity occurs. It can be seen in Table 7-1 and

Table 7-2 that cell formation strongly depends on the equivalence ratio and hydrogen

concentration. In the case that we have all smooth flames, the upper limit of pressures and

temperatures are the pressures and temperatures when flames hit the chamber wall and are reported

in Table 7-1 and Table 7-2 in shaded background started with letter S.

7.5. BURNING SPEED MEASUREMENTS

7.5.1. Burning Model

There are several methods for measuring the laminar burning speed [15,20,25,213,239,247].

The numerical model used in this work to calculate the laminar burning speed from the pressure

rise data is based on a newly developed multi-shell differential-based model by Askari et. al. [22].

Using this model, burning speeds can be calculated over a wide range of temperatures and

pressures without the need for extrapolation methods. Pressure rise must be accurately and

168

correctly measured, and flame radii must be large enough to minimize stretch effect on the laminar

burning speed. In this model governing equations of unknown variables have been defined by a

set of nonlinear ordinary differential equations that can be solved by using the CVODE solver

from sundials package [214]. The governing equations are derived by applying the differential

form of mass and energy conservation equations over all shells as well as the whole chamber.

The model divides the combustible mixture into an unburned gas section and a burned gas

section and considers the flame front as a jump discontinuity. The burned gas core is divided into

a number of shells, each shell with a uniform temperature in local chemical equilibrium.

Surrounding the outermost burned gas shell is a layer of unburned gas called the preheat zone that

has a non-uniform temperature, immediately followed by the outermost unburned gas shell.

Pressure is assumed to have no spatial gradient in the chamber at any particular instant in time.

The gas mixture is assumed to behave like an ideal gas and to be in local thermodynamic

equilibrium (LTE). Chemical equilibrium composition has been evaluated using CANTERA code

combined with thermochemical properties of NASA correlations [215]. In order to encompass the

burning of lean and rich mixtures, twenty major species (H2, N2, O2, CO, H, O, OH, HCO, HO2,

H2O, H2O2, CO2, NO, NO2, CH2, CH3, CH4, CH2O, CH3OH and C2H2) have been considered as

products of combustion. All the energy losses to the electrodes, chamber walls, radiation from the

burned gas, and energy transfer between neighboring shells have been added to the current model.

The effect of energy transfer in the chamber wall and spark electrodes as well as preheat zone is

modeled by the thermal boundary layer and displacement thickness concept [216].

This model simulates a one-dimensional spherical flame in radial direction. First chamber is

filled with a fuel/air/diluent mixture and will be ignited at the center of the combustion chamber

using two extended spark electrodes. After ignition, an isotropic flame is formed and propagates

outwardly in the radial direction. The following assumptions are made in the analysis of the

combustion inside the chamber:

1. The reactants are initially quiescent and have a uniform composition, pressure and

temperature.

2. The pressure is presumed to have a uniform spatial distribution within the chamber at each

time step.

169

3. The gases are assumed to behave like an ideal gas and to be in local thermodynamic

equilibrium (LTE).

The energy conservation equations for unburned, burned, and currently burning regions are

respectively:

�̇�𝑢 = −�̇�𝑏ℎ𝑢 + �̇�𝑢 − �̇�𝑢 (7-1)

�̇�𝑗 = �̇�𝑗 − �̇�𝑗 , 𝑗 = 𝑏1 − 𝑏𝑛−1 (7-2)

�̇�𝑏𝑛 = �̇�𝑏ℎ𝑢 + �̇�𝑏𝑛 − �̇�𝑏𝑛 (7-3)

where 𝑈 is the internal energy, �̇�𝑏 the mass burning rate, 𝑄 the energy transfer and 𝑊 the work.

In these equations the subscripts of 𝑗 refers the already burned shells, 𝑢 and 𝑏 denote the unburned

and burned gas conditions respectively, 𝑛 and 𝑏𝑛 denote the total number of shells in burned

section and currently burning shell, respectively. The dot sign on top of the parameters refers to

the complete derivative with respect to time. Using concept of displacement thickness [216] and

thermodynamic relations [217] Eqs. (7-1)-(7-3) expand into the following format:

�̇�𝑢∞ =

𝐴𝑢∞�̇� +

𝜌𝑢∞ℎ𝑢

∞


∞ℎ𝑢∞�̇�𝑑𝑖𝑠𝑢 + �̇�𝑢

𝐵𝑢∞

(7-4)

�̇�𝑗∞ =

𝐴𝑗∞�̇� + 𝜌𝑗

∞ℎ𝑗∞�̇�𝑑𝑖𝑠𝑗 + �̇�𝑗

𝐵𝑗∞ , 𝑗 = 𝑏1 − 𝑏𝑛−1 (7-5)

�̇�𝑏𝑛∞ =

𝐴𝑏𝑛∞ �̇� + (𝑚(ℎ𝑢

∞ − ℎ𝑏𝑛∞ ) −

𝜌𝑢∞ℎ𝑢

∞



𝐵𝑏𝑛∞ (7-6)

�̇�𝑏 = −(𝐶𝑢

∞ + ∑ 𝐶𝑘∞

𝑘 )�̇� + (𝐷𝑢∞ + ∑ 𝐷𝑘

∞𝑘 ) + (𝐸𝑢

∞ + ∑ 𝐸𝑘∞

𝑘 )

𝐹 , 𝑘

= 𝑢, 𝑏1,⋯ , 𝑏𝑛−1, 𝑏𝑛

(7-7)

where 𝜌 is the density, ℎ the enthalpy, 𝑥𝑏 the burned gas mass fraction, 𝑉𝑑𝑖𝑠 the displacement


region far from the thermal boundary layer with uniform temperature distribution. The parameters

170

𝐴𝑘∞ through 𝐸𝑘

∞ (𝑘 = 𝑢, 𝑏1, ⋯ , 𝑏𝑛−1, 𝑏𝑛) are defined in Askari et.al. [22] in terms of

thermodynamic properties. Eqs. (7-4)-(7-7) form a set of nonlinear ordinary differential equations

which contain n + 3 unknowns: 𝑝(𝑡), 𝑥𝑏(𝑡), 𝑇𝑢∞ and 𝑇𝑏𝑖

∞ (i = 1 to n). Given experimental

pressure as a function of time, they can be solved numerically using CVODE method to find

burned mass fraction and temperature distribution. Finally, the laminar burning speed is calculated

as:

𝑆𝑢 =𝑚�̇�𝑏𝜌𝑢∞𝐴𝑓

(7-8)

where 𝐴𝑓 is the flame front area. The initial mixture composition is defined as:

𝜙(𝛼𝐻2 + (1 − 𝛼)𝐶𝑂) +50

21(0.21𝑂2 + 0.79𝑁2) +

𝛽 (𝜙 +5021)

1 − 𝛽(0.14𝐶𝑂2 + 0.86𝑁2)

(7-9)

where 𝛼 is the hydrogen concentration of the fuel mixture, 𝜙 the equivalence ratio and 𝛽 the SEGR

concentration. Combination of the systematic (Bias) and random (Precision) uncertainty [100] in

conjunction with the root-sum-square method give us the overall uncertainty for calculated laminar

burning speed data [47]. The overall uncertainty varys between ±1% and ±3% with the average of

±1.51%. This range of uncertainty is only valid for conditions which are covered in our

experiments and numerical analysis. For other conditions which are estimated by power law

correlations such as atmospheric conditions (except sub-atmospheric pressure tests) the mean

uncertainty is ±2.76%.

A steady, one-dimensional, laminar premixed free flame code from the CANTERA package

[220] in conjunction with detailed kinetic mechanisms has been used to solve the conservation

equations of mass, energy and species to calculate the laminar burning speed. The multi-

component diffusion model has been used for evaluation of transport properties. In this paper, two

detailed chemical kinetics mechanisms for syngas combustion [221,222] have been selected and

compared to the experimental laminar burning speed data.

171

7.5.2. Stretch Effect Investigation

Stretched laminar burning speed is a function of the geometry of the flame and is not a

fundamental thermo-physical property. Stretched laminar burning speeds calculations from

spherical flames are usually corrected by means of extrapolation to zero stretch. Various linear and

nonlinear extrapolations have been developed to obtain the zero stretch laminar burning speed

[41,193,195,197,203,210]. However, a recent paper by Wu et al [234] has reviewed different

methods of extrapolation and has shown that there is great uncertainty in these methods. Flame

stretch in spherically expanding flames is defined as:

𝜅 =1

𝐴𝑓

𝑑𝐴𝑓

𝑑𝑡=2

𝑟𝑓

𝑑𝑟𝑓

𝑑𝑡 (7-10)

where 𝜅 is the stretch rate, 𝐴𝑓 is the flame front area, 𝑡 is time, and 𝑟𝑓 is the flame radius. It is seen

from Eq. (7-10) that as the radius of flame increases the stretch rate decreases. Therefore, it is

advantageous to consider data where flame radius is large, minimizing stretch and thus

circumventing the challenges associated with extrapolation to zero stretch.

The procedure used to investigate the stretch effects is briefly outlined below. Laminar burning

speeds have been measured at different stretch rates in order to study the effect of stretch on

H2/CO/air/SEGR mixtures. Given an isentrope that begins at an initial pressure and temperature,

different tests are selected from that isentrope such that the only difference in the initial conditions

of the subsequent tests are the initial pressure and temperature. The initial pressures and

temperatures selected must be constrained to lie on the isentrope of the first test. Finally, a

thermodynamic state (same pressure, temperature and equivalence ratio) that is shared by all tests

is chosen and the laminar burning speeds are compared at that chosen state for different stretch

rates. More information about this method can be found in previous publications [1,3]. Figure 7.8

shows the variation of laminar burning speed versus stretch rate for three different states with

various equivalence ratios, unburned gas conditions and SEGR percentages at hydrogen

concentration of 5%. As it can be seen the change of laminar burning speeds with respect to stretch

rate for flame radii greater than 4 cm and stretch rates lower than 90 s-1 is negligible which is in

agreement with Chen et al. [239].

172

Figure 7.8. Laminar burning speed versus stretch rates for three different cases with various equivalence

ratios, unburned gas conditions and SEGR concentrations at hydrogen concentration of 5%

7.5.3. Laminar Burning Speed

To reduce the effects of stretch and spark energy discharge all laminar burning speed data are

reported in regions where 𝑟𝑓 > 4cm and stretch rate of less than 90 s-1. The calculated laminar

burning speeds have been used to develop a correlation in terms of equivalence ratio, temperature,

pressure and SEGR concentration as shown in Eq. (7-11):

𝑆𝑢 = 𝑆𝑢0(1 + 𝑎(𝜙 − 1) + 𝑏(𝜙 − 1)2) (

𝑇

𝑇0)𝛼

(𝑝

𝑝0)𝜃

(1 − 𝛽)𝛾 (7-11)

where Su0 is the laminar burning speed at reference point (ϕ = 1, T0 = 298K, p0 = 1atm) , ϕ the

equivalence ratio, T the temperature in K, p the mixture pressure in atm and β the SEGR volumetric

fraction. To have a good fitting the temperature, pressure and SEGR fraction exponents are

considered as a linear function of equivalence ratio as shown in Eq. (7-12) -(7-14):

𝛼 = 𝛼1 + 𝛼2(𝜙 − 1) (7-12)

𝜃 = 𝜃1 + 𝜃2(𝜙 − 1) (7-13)

173

𝛾 = 𝛾1 + 𝛾2(𝜙 − 1) (7-14)

Coefficients, 𝑆𝑢0, a, b, c, α1, α2, θ1, θ2, γ1 and γ2, have been found using fminunc function in

MATLAB, an unconstrained minimization method, for three different hydrogen concentration as

listed in Table 7-3. This correlation is only valid for smooth laminar flames in the equivalence

ratio range of 0.6 < ϕ < 3 and SEGR fraction range of 0 < β < 0.1. The range of pressure and

temperature are function of equivalence ratio and hydrogen concentration, which can be

determined using Table 6-1 and Table 7-2 for SEGR concentration of 5 and 10%, respectively.

Table 7-3- Power law fitting coefficients

𝑺𝒖𝟎 𝒂 𝒃 𝜶𝟏 𝜶𝟐 𝜽𝟏 𝜽𝟐 𝜸𝟏 𝜸𝟐

𝜶 = 𝟓% 33.351 1.313 -0.410 1.884 -0.008 -0.136 -0.003 3.130 0.818

𝜶 = 𝟏𝟎% 47.433 1.337 -0.444 1.843 0.004 -0.173 0.019 3.579 0.429

𝜶 = 𝟐𝟓% 76.209 1.351 -0.510 1.842 0.008 -0.175 0.035 3.631 0.347

Figure 7.9 shows the laminar burning speeds of syngas/air/SEGR mixtures at various

equivalence ratios and SEGR concentration of 10% versus temperature along four isentropes. As

the equivalence ratio increases from ϕ = 0.6 to ϕ = 2.0 laminar burning speed increases. By

increasing the equivalence ratio beyond ϕ = 2.0, the laminar burning speed decreases. As it can

be seen the pressure exponent in Eq. (7-11) for whole range of equivalence ratio is always negative

which means the initial pressure has an inverse effect on laminar burning speed. This behavior is

shown in Figure 7.10 that by increasing the initial pressure, the laminar burning speed decreases.

Also, Figure 7.10 shows that the shrinking temperature range where laminar burning speed can be

calculated is becoming more narrow as initial pressure increases since flames become cellular.

Hydrogen addition has a significant direct impact on laminar burning speed. As shown in

Figure 7.11 the laminar burning speed increases with increasing hydrogen concentration in the fuel

mixture. SEGR addition to the syngas/air mixture has a very interesting effect on laminar burning

speed. SEGR acts as an energy sink, causing the flame temperature to decrease and consequently

lower the laminar burning speed as shown in Figure 7.12. More explanation using sensitivity

analysis will come later to show how SEGR addition lowers the laminar burning speed. In all these

figures, the solid line represents fitted laminar burning speed data using the power law correlation

in Eq. (7-11).

174

Figure 7.9. Laminar burning speed of H2/CO/air/SEGR mixture along isentropes at different equivalence

ratios for initial pressure of 0.5 atm, initial temperature of 298 K, hydrogen concentration of 25% and

SEGR concentration of 10%

Figure 7.10. Laminar burning speed of stoichiometric H2/CO/air/SEGR mixture along isentropes at

different initial pressures for initial temperature of 298 K, hydrogen concentration of 5% and SEGR

concentration of 10%

175

Figure 7.11. Laminar burning speed of H2/CO/air/SEGR mixture along isentropes at different hydrogen

concentrations for atmospheric initial pressure, initial temperature of 298 K, equivalence ratio of 3.0 and

SEGR concentration of 5%

Figure 7.12. Laminar burning speed of H2/CO/air/SEGR mixture along isentropes at different SEGR

concentrations for initial pressure of 0.5 atm, initial temperature of 298 K, equivalence ratio of 0.6 and

hydrogen concentration of 10%

176

Since there is no laminar burning speed data in the literature for the exact SEGR mixture

composition that has been considered in this paper (14% CO2 and 68% N2), laminar burning speeds

from this study have been compared with experimental data in the literature for no SEGR addition

at standard atmospheric temperature and pressure for hydrogen concentration of 5%, as shown in

Figure 7.13. The measured laminar burning speed agrees well with available experimental data in

literature. The results were within the expected experimental error under the test conditions where

comparisons were possible with other studies. As described earlier in this paper the average

uncertainty of ±2.76% is associated with the conditions which are approximated from the power

law fitting method such as atmospheric conditions (except for sub-atmospheric initial pressure).

Figure 7.14 shows a comparison of laminar burning speed calculated in this study by power law

correlation versus two detailed kinetic mechanisms, Davis [221] and Li [222] mechanisms, for

H2/CO/air/SEGR laminar burning speed at atmospheric conditions, hydrogen concentration of

25% and three different SEGR concentrations of 0%, 5% and 10%. From the selected kinetics

mechanisms, the Davis mechanism [221] is in fairly good agreement with the obtained

experimental data.

Figure 7.13. Comparison of present experimental laminar burning speed data versus published

experimental data [37,41,43,193,195,199,200,204] for H2/CO/air at atmospheric temperature and pressure

at hydrogen concentration of 5% and SEGR concentration of 0%

0 0.5 1 1.5 2 2.5 3 3.50

10

20

30

40

50

60

70

80

Equivalence ratio

La

min

ar

bu

rnin

g s

pe

ed

(cm

/s)

Present study

MClean et al [47]

Hassan et al [13]

Natarajan et al [15,16]

Sun et al [14]

Bouvet et al [53,54]

Singh et al [55]

177

Figure 7.14. Comparison of calculated laminar burning speeds versus two kinetic simulations (Davis

[221] and Li [222] mechanisms) for H2/CO/air/SEGR mixture at atmospheric pressure and temperature,

hydrogen concentration of 25% and three different SEGR concentrations

To show the effect of SEGR addition on the normalized sensitivity coefficients, computations

were performed for three different values of SEGR concentrations of 0, 5 and 10%. Davis et al.

mechanism [221], was employed for sensitivity analysis due to its good accuracy as shown in

Figure 7.14. The sensitivity of the predicted laminar burning speed with respect to each reaction

rate constant is calculated using CANTERA [220] code. Figure 7.15 gives the normalized

sensitivity coefficient of H2/CO/air/SEGR mixture for the most sensitive reactions in the

mechanism of Davis et al. [221] at three different SEGR concentrations of 0, 5 and 10%.

Chain propagation and branching reactions have positive sensitivity coefficients while

recombination and termination reactions have negative sensitivity coefficients. As shown in

Figure 7.15 the most dominant chain branching reactions are R1: H+O2 O+OH, R2: O+H2

H+OH and R16: HO2+H OH+OH, through increasing the concentrations of highly reactive

radical species, H and OH which promote the combustion. Reaction R28: CO+OH CO2+H is

identified as the most significant chain propagation reaction for syngas mixture due to high

concentration of CO in the reactants. The most dominant chain termination reaction is the third

body Reaction R12: H+O2(+M) HO2(+M) where reactive radical, H, is converted into stable

0 0.5 1 1.5 2 2.5 3 3.50

50

100

150

La

min

ar

bu

rnin

g s

pe

ed

(cm

/s)

Equivalence ratio

= 0 %

= 5 %

= 10 %


Li mechanism [46]

178

specie, H2O. As shown in Figure 7.15, the sensitivity coefficient of the chain termination reaction

R12 and the chain branching and propagation reactions R1, R2, R16 and R28 are increased with

the increase of SEGR concentrations in the mixture. It means that these five aforementioned

reactions are playing significant roles as SEGR concentration increases.

As mentioned earlier, with the increase of CO2 concentration, through addition of SEGR, flame

temperature and subsequently the H radical production via chain branching reaction R2 decreases.

On one hand, there is a competition between chain branching reaction R1 and chain termination

reaction R12 on the consumption of H radical. On the other hand, CO2 can act as a third body in

the chain termination reaction R12 and consumes the H radical produced from chain branching

reaction R2. By increasing the CO2 fraction, chain termination reaction R12 wins the competition

and suppresses the chain branching reaction R1. Through this competitive process, the

concentration of H and OH radicals in the reaction zone reduce drastically and therefore the other

significant chain branching and propagation reactions, R16 and R28, suppress and finally the

whole reaction process and most importantly the laminar burning speed decreases.

Figure 7.15. Normalized sensitivity coefficients of H2/CO/air/SEGR mixture at different SEGR

concentrations, initial pressure of 0.5 atm, initial temperature of 298 K, equivalence ratio of 0.6 and


179

8. Cell Formation Effect on the Burning Speed and

Flame Front Area of Synthetic Gas (Syngas) at

High Pressures and Temperatures

180

8.1. ABSTRACT

Cellular burning speeds and mass burning rates of premixed Syngas/oxidizer/diluent

(H2/CO/O2/He) have been determined at high pressures and temperatures over a wide range of

equivalence ratios. The experimental facilities consisted of two spherical and cylindrical chambers.

The spherical chamber, which can withstand high pressures up to 400 atm, was used to collect

pressure rise data due to combustion, to calculate cellular burning speed and mass burning rate.

For flame structure and instability analysis the cylindrical chamber was used to take pictures of

propagating flame using a high speed CMOS camera and a Schlieren photography system. A new

differential-based multi-shell model based on pressure rise data was used to determine the cellular

burning speed and mass burning rate. In this paper, cellular burning speed and mass burning rate

of H2/CO/O2/He mixture have been measured for a wide range of equivalence ratios from 0.6 to

2, temperatures from 400 to 750 K and pressures from 2 to 50 atm for three hydrogen

concentrations of 5, 10 and 25% in the syngas. The power law correlations for cellular burning

speed and mass burning rate were developed as a function of equivalence ratio, temperature and

pressure. In this study a newly developed parameter, called Cellularity Factor, which indicates the

cell formation effect on flame surface area and burning speed has been defined. The total flame

surface area and cellularity factor for syngas at high pressures and temperatures have been found

by combining the differential-based multi-shell model via the experimental pressure data with one

dimensional free flame simulation using detailed chemical mechanism. The results show that the

cellularity factor has a positive relation to pressure, equivalence ratio and hydrogen concentration

while it has a negative dependency to temperature.

Keywords: cellular burning speed, mass burning rate, Schlieren photography, syngas, cell

formation, cellularity factor, instability analysis, flame structure

8.2. INTRODUCTION

A study to comprehensively measure and investigate the cellular burning speed, mass burning

rate and cell formation effect of synthetic gas (syngas) at high pressures and temperatures is

relevant and necessary to the scientific and combustion community [41,248,249]. Syngas, a

mixture of H2 and CO, has gained importance as an alternative fuel for stationary gas turbines and

internal combustion engines. Power plants have been using syngas for more than a decade, citing

181

increased energy efficiencies and less emissions than conventional coal fired plants. Syngas is also

increasingly being used in petroleum refineries to help produce cleaner transportation fuels and

improve overall efficiency of the plant [38]. Syngas can be derived from the gasification of coal

or biomass, including municipal waste, agricultural residue, and herbaceous energy crops,

therefore, reducing greenhouse gas (GHG) emissions. Research studies into understanding the

cellularity effect on burning speed for syngas fuel, are extremely relevant particularly for use in

engineering combustion modelling, for stationary turbine based power plants and for internal

combustion engines in the transportation industry [14,192]. Mass burning rate is the rate at which

a combustible mixture is consumed by flame front and is also a measure of the energy release

during a combustion process. When the flame front is laminar and its area is simply obtainable a

more commonly used term is laminar burning speed [2,3,21,23,25,171].

Syngas mixtures have been studied and researched at atmospheric and elevated conditions.

Hassan et al. [195] measured the laminar burning speed of various hydrogen to carbon monoxide

ratios, sub-atmospheric to elevated pressures (0.5-4 atm), atmospheric temperature, and wide range

of equivalence ratios (0.6-5.0) in a spherical combustion chamber. Natarjan et al. [37] used the

burner and particle velocimetry technique to measure laminar burning speed for 5:95, 50:50, and

95:5 syngas percentages diluted with CO2 and later extended measurements to higher pressures

with helium substitution to reduce flame instability [43]. Vu et al. [244] compared the effects of

CO2, N2, and He as diluents on the cellular instabilities in syngas flames in a cylindrical chamber

at elevated pressures for a 50:50 hydrogen to carbon monoxide ratio. Han et al. [210] measured

laminar burning speeds for various CO2 diluent percentages (10%-40%) at elevated temperatures

and pressures for equivalence ratios of 0.8 and 1.0 using a dual-cylindrical setup. Askari et al. [22]

measured the laminar burning speeds of syngas/air mixtures using a new differential-based multi-

shell model over a wide range of temperatures (298K up to 617K), pressures (from sub-

atmospheric up to 5.5atm), equivalence ratios (0.6-5) and three different hydrogen concentration

of 5%, 10% and 25%. Recently Askari et al. [24] investigated the effect of synthetic EGR addition

on flame morphology and laminar burning speed of syngas/air mixture for a wide range of

equivalence ratios, temperatures and pressures. A comprehensive literature search of burning

speed measurements of all syngas composition exposed various gaps in the experimental data

especially at elevated pressure and temperature conditions [43,194,197,209,250]. Some data exist

but doesn’t comprehensively capture the whole range of conditions between 2-50 atm and 400-

182

750 K, with varying degree of stoichiometry and gas mixture compositions. Despite internal

combustion engines being subjected to high pressures, few studies have been performed under

comparable conditions. In a 2014 review of syngas research, Lee concluded that new

measurements on the burning speed were needed at elevated pressures [251]. At high pressure

conditions (higher than 2 atm) the syngas/air flame is cellular and calculating the laminar burning

speed due to lack of exact flame surface area is impossible. So instead, the other parameters such

as cellular burning speed and mas burning rate which are very useful in the modeling of

combustion systems can be calculated.

In this paper, cellular burning speed and mass burning rate of syngas/oxygen flame which was

diluted with helium, H2/CO/O2/He, were calculated for a wide range of equivalence ratios from

lean to rich (0.6 to 2), temperatures from 400 to 750 K and pressures from 2 to 50 atm. The structure

and effect of thermo-diffusive and hydrodynamic instabilities were studied at very high pressures

at which the flame is always cellular. Power law correlations as a function of equivalence ratio,

temperature and pressure for cellular burning speed and mass burning rate have been developed.

The effect of cell formation on burning speed and total flame front area has been investigated in

terms of a newly developed parameter, called cellularity factor. In addition to a complete

experimental data, the theoretical laminar burning speeds via a steady, one-dimensional and

laminar premixed free flame code from CANTER package [220] in conjunction with Davis et al.

mechanism [221] were calculated and used to determine the effect of cellularity.

8.3. EXPERIMENTAL SETUP AND PROCEDURES

The core component of the experimental setup includes a spherical combustion chamber that

enables the measurement of the pressure rise from a combustion process at high pressures and

temperatures. This chamber was mainly used to measure the pressure rise for calculating the

burning speed and mass burning rate. The spherical chamber was designed to withstand pressures

up to 400 atm and was located inside an oven which can be heated up to 500 K. The second

component of the experimental setup is a cylindrical chamber with optically clear sides which

enables visualization of flame propagation for the study of flame structure and instability analysis.

The cylindrical chamber with optical side ports and all its supporting system were rigidly mounted

on an optical bench. Using a focused LED light source and a series of mirrors the parallel light

was guided through the optically clear Quartz windows and was reflected to a high speed CMOS

183

camera capable of capturing images up to 40,000 frame per second. This Schlieren photography

method which works based on density gradient [242], is useful in visualizing flame propagation to

investigate flame front structure for instability analysis. A Kistler 601CA high-temperature

pressure transducer in conjunction with a Kistler 5010B charge amplifier was used to record the

dynamic pressure rise during flame propagation processes in both chambers. The filling manifold

mainly constructed of 304 and 316 Stainless steel Swagelok componentry and tubing is

predisposed to accommodate inputs from 5 simultaneous gas cylinders, thus allowing for an

inventory of gas mixtures to be always readily available for immediate use. Two vacuum pumps

help evacuate the system faster and allow for independent testing of the two chambers. The

composition of premixed fuel inside the spherical chamber was always checked and verified using

a gas chromatography (GC) system.

All the data acquisition and analysis can be done on-site by several dedicated PCs using a high

speed LabVIEW DAQ card and isolated input and output modules for temperature, voltage and

pressure measurements as well as automatic delayed firing via control of the high voltage coil

driving the spark plugs. The PID temperature controllers are proportionally programmable with

redundant safety feature for over temperature protection and electric shock. The raw pressure

signal produced by the high speed pressure transducer contains digitization noise resulting from

data acquisition system process of converting a voltage signal to a digital value. The digitization

noise is approximately 0.25 psi/bit which is certainly negligible for the range of pressure

measurements of interest. To minimize other experimental or human errors a data selection criteria

was developed. For any set of data to be deemed acceptable three consecutive experimental runs

have to yield the exact pressure curve to ensure that the confidence level of the experiments was

always greater than 95% [212]. The configuration of experimental facilities and their connections

are shown in Figure 8.1. More information about the experimental setup can be found in previous

publications [4,22,25,46,47,102,171].

184

Figure 8.1. Overview of experimental facilities

8.4. THEORITICAL MODEL

The numerical model used in this work to calculate burning speed and mass burning rate from

the pressure rise is based on a newly developed multi-shell differential-based model by Askari et.

al. [22]. The schematic of this theoretical model representing all available energy transfer and a

typical temperature distribution is shown in Figure 8.2. In the model, it is assumed that the

reactants are initially quiescent and have a uniform composition, pressure and temperature. The

fuel/air/diluent mixture inside the chamber is ignited at the center of the combustion chamber using

two extended spark electrodes. All gases are assumed to be ideal gases. The model divides the

chamber into unburned and burned gas sections which are separated by a reaction zone of

negligible thickness. The burned gas region is divided into a number of shells, each shell with a

uniform temperature different from other shells and in local thermodynamic equilibrium. Burned

gases are in chemical equilibrium in each shell. Composition of burned gases in each shell is

determined by using CANTERA [220] subroutines combined with the latest version of

thermochemical properties of NASA correlation [33]. Surrounding the outermost burned gas shell

185

is reaction zone with infinitesimal small thickness followed by a layer of unburned gas called the

preheat zone that has a non-uniform temperature. The preheat zone is surrounded by the core

unburned gas with uniform temperature. Pressure is assumed to have no spatial gradient in the

chamber at any particular instant in time. All the energy losses to the electrodes, chamber walls,

radiation from the burned gas, and energy transfer between neighboring shells have been added to

the current model. The effect of energy transfer in the chamber wall and spark electrodes as well

as preheat zone is modeled by the thermal boundary layer and displacement thickness concept

[216]. Using this model, burning rates can be calculated over a wide range of temperatures,

pressures and fuel air equivalence ratios at very high temperatures and pressures. In this model

governing equations of unknown variables have been defined by a set of nonlinear ordinary

differential equations that can be solved using the CVODE solver [214]. The governing equations

are derived by applying the differential form of mass and energy balance equations over all shells

as well as the whole chamber. The energy balance equations for unburned, burned, and currently

burning gases are respectively:

�̇�𝑢 = −�̇�𝑏ℎ𝑢 + �̇�𝑢 − �̇�𝑢 (8-1)

�̇�𝑗 = �̇�𝑗 − �̇�𝑗 , 𝑗 = 𝑏1 − 𝑏𝑛−1 (8-2)

�̇�𝑏𝑛 = �̇�𝑏ℎ𝑢 + �̇�𝑏𝑛 − �̇�𝑏𝑛 (8-3)

where 𝑈 is the internal energy, �̇�𝑏 the mass burning rate, 𝑄 the energy transfer and 𝑊 the work.

In these equations the subscript 𝑗 refers the already burned shells, 𝑢 and 𝑏 denote the unburned

and burned gas conditions respectively, 𝑛 and 𝑏𝑛 denote the total number of shells in burned

section and currently burning shell, respectively. The dot sign on top of the parameters refers to

the complete derivative with respect to time. Using concept of displacement thickness [216] and

thermodynamic relations [217] Eqs. (8-1)-(8-3)expand into the following format:

�̇�𝑢∞ =

𝐴𝑢∞�̇� +

𝜌𝑢∞ℎ𝑢

∞


∞ℎ𝑢∞�̇�𝑑𝑖𝑠𝑢 + �̇�𝑢

𝐵𝑢∞

(8-4)

186

�̇�𝑗∞ =

𝐴𝑗∞�̇� + 𝜌𝑗

∞ℎ𝑗∞�̇�𝑑𝑖𝑠𝑗 + �̇�𝑗

𝐵𝑗∞ , 𝑗 = 𝑏1 − 𝑏𝑛−1 (8-5)

�̇�𝑏𝑛∞ =

𝐴𝑏𝑛∞ �̇� + (𝑚(ℎ𝑢

∞ − ℎ𝑏𝑛∞ ) −

𝜌𝑢∞ℎ𝑢

∞



𝐵𝑏𝑛∞ (8-6)

�̇�𝑏 = −(𝐶𝑢

∞ + ∑ 𝐶𝑘∞

𝑘 )�̇� + (𝐷𝑢∞ + ∑ 𝐷𝑘

∞𝑘 ) + (𝐸𝑢

∞ + ∑ 𝐸𝑘∞

𝑘 )

𝐹 , 𝑘

= 𝑢, 𝑏1,⋯ , 𝑏𝑛−1, 𝑏𝑛

(8-7)

where 𝜌 is the density, ℎ the enthalpy, 𝑥𝑏 the burned gas mass fraction, 𝑉𝑑𝑖𝑠 the displacement


region far from the thermal boundary layer with uniform temperature distribution. All the energy

transfer terms in Eqs. (8-4)-(8-6) including conduction and radiation can be calculated using

proposed formulations in Askari et al. [22].

The parameters 𝐴𝑘∞, 𝐵𝑘

∞, 𝐶𝑘∞, 𝐷𝑘

∞, 𝐸𝑘∞ (𝑘 = 𝑢, 𝑏1, ⋯ , 𝑏𝑛−1, 𝑏𝑛) and 𝐹 are defined in terms of

thermodynamic properties which can be found in Askari et al. [22]. Eqs. (8-4)-(8-7) form a set of

nonlinear ordinary differential equations which contain n + 3 unknowns: 𝑝(𝑡), 𝑥𝑏(𝑡), 𝑇𝑢∞ and

𝑇𝑏𝑖∞ (i = 1 to n). Given experimental pressure as a function of time, the equations can be solved

numerically to find burned mass fraction and temperature distribution. Finally, the mass burning

rate and cellular burning speed are calculated as Eqs. (8-8) and (8-9), respectively:

�̇�𝑏 = 𝑚�̇�𝑏 (8-8)

𝑆𝑐 =�̇�𝑏

𝜌𝑢𝐴𝐿 (8-9)

where 𝜌𝑢 is the unburned gas density and 𝐴𝐿 = 4𝜋𝑟𝑓2 is the equivalent spherical flame area having

the same mass of burned gas, which is called hereafter laminar flame area.

187

Figure 8.2. Schematic of multi-shell theoretical model

The initial mixture composition for H2/CO/O2/He is defined as:

𝜙(𝛼𝐻2 + (1 − 𝛼)𝐶𝑂) + 0.5(𝑂2 + 3.76𝐻𝑒) (8-10)

where 𝛼 is the hydrogen concentration of the fuel blend and 𝜙 is the equivalence ratio. For

predicted laminar burning speed, a steady, one-dimensional and laminar premixed free flame code

from the CANTERA in conjunction with detailed chemical kinetic mechanism and multi-

component diffusion model has been used to solve the balance equations of mass, energy and

species. In this paper, Davis et al. mechanism [221] for syngas combustion has been selected due

to its good agreement with experimental results [22].

188


8.5.1. Flame Structure and Instability Study

The syngas fuel was combusted for a wide range of equivalence ratios of 0.6 – 2.0, in a lower

thermal capacity air (21% O2 and 79% He). By substituting the nitrogen in air with another inert

gas such as helium, the total heat capacity of the mixture is reduced, therefore for the same energy

of combustion the flame temperature and consequently mixture pressure are increased. The initial

pressure conditions were set to 2, 5, 10 atm and initial temperatures to 400 and 450 K. The effects

of equivalence ratio and flame propagation time on flame structure and instability of the flame

front are shown in Figure 8.3. This figure shows the snapshots of the expanding spherical flame

of H2/CO/O2/He mixture with varying the equivalence ratios at initial temperature of 400 K, initial

pressure of 5 atm and hydrogen concentration of 5%. As it can be seen in this figure, the flame

front is unstable and fully cellular during its propagation from the center of chamber until it hits

the chamber walls for all three different equivalence ratios of 0.6, 1.0 and 2.0. It is also shown in

this figure that the flame propagation rate increases as equivalence ratio increases.

𝝓 = 𝟎. 𝟔 𝝓 = 𝟏.𝟎 𝝓 = 𝟐.𝟎

𝒕 = 𝟓. 𝟏𝟎 𝒎𝒔

𝒕 = 𝟖. 𝟒𝟗 𝒎𝒔

𝒕 = 𝟏𝟏. 𝟐𝟎 𝒎𝒔

Figure 8.3. Snapshots of the H2/CO/O2/He flames for various equivalence ratios, hydrogen concentration

of 5%, initial pressure of 5 atm and initial temperature of 400 K

189

The effect of thermo-diffusive and hydrodynamic instabilities in terms of effective Lewis

number and flame thickness respectively, are shown in Figure 8.4. The flame thickness is defined

by 𝛿𝑓 = (𝑇𝑎𝑑 − 𝑇𝑢) (𝑑𝑇 𝑑𝑥⁄ )𝑚𝑎𝑥⁄ , where 𝑇𝑎𝑑 is the adiabatic flame temperature, 𝑇𝑢 the unburned

temperature and (𝑑𝑇 𝑑𝑥⁄ )𝑚𝑎𝑥 the maximum temperature gradient. The effective Lewis number

for a wide range of equivalence ratio can be computed by the following equation [22]:

𝐿𝑒𝑒𝑓𝑓 =

{

𝐿𝑒𝑓𝑢𝑒𝑙 =

𝐷𝑇𝑥𝐻2𝐷𝐻2/He + 𝑥𝐶𝑂𝐷𝐶𝑂/He

𝜙 ≤ 0.8

𝐿𝑒𝑓𝑢𝑒𝑙/𝑂2 = 1 +(𝐿𝑒𝐸𝑥 − 1) + (𝐿𝑒𝐷𝑒𝑓 − 1)𝐴

1 + 𝐴 0.8 < 𝜙 < 2

𝐿𝑒𝑂2 =𝐷𝑇

𝐷𝑂2/He 𝜙 ≥ 2

(8-11)

where 𝐷𝑇 = 𝜆 𝜌𝑢𝑐𝑝⁄ is the mixture thermal diffusivity, 𝐷𝑘/𝐻𝑒 the reactant-inert binary diffusion

coefficient that were found using Davis et al. mechanism [221] and 𝑥𝑖 the volumetric fraction of

the 𝑖𝑡ℎ component of the fuel blend [22].

The effective Lewis number in Figure 8.4 decreases as equivalence ratio and flame propagation

time increase. But the effective Lewis numbers are always greater than unity which makes the

flame independent from thermo-diffusive instability. It means that flame cellularity due to increase

in equivalence ratio and flame propagation time is not related to thermo-diffusive instability. As

shown in Figure 8.4, the higher the equivalence ratio, the lower the flame thickness, which

promotes the effect of hydrodynamic instability [2]. On the other hand increase in flame

propagation time promotes the hydrodynamic instability through the increase in pressure and flame

radius and reduction in flame thickness. The hydrodynamic instability makes a laminar and smooth

flame unstable by creating cells and wrinkles all over the flame front. These cells and wrinkles

increase the contact area between unburned gas and flame which leads to increase of the mass

entrained into the flame and consequently increase the mass burning rate. An in-depth analysis

about cell formation of H2/CO/O2/He mixture in terms of temperature, pressure, equivalence ratio

and hydrogen concentration is given in the next section.

190

Figure 8.4. Effective Lewis number and flame thickness of the H2/CO/O2/He flames corresponding to the

snapshots of Figure 8.3

8.5.2. Cell Formation Analysis

Askari et al. [22] showed that increase of hydrogen concentration, pressure and equivalence

ratio in the range of 0.6 to 2, promote flame destabilization propensity and enhance the chance of

cell formation over the flame front. Cellularity changes flame structure from a highly spherical,

laminar and smooth flame to an unstable flame with large number of cells and wrinkles in different

sizes all over the flame front. Therefore, the total exposed area of the unburned gas with the flame

or simply the total flame area increases rapidly and deviates from a laminar flame area which is

only a function of flame radius. In this case the total flame area becomes dependent to shape and

size of the cells. The mass burning rate can be evaluated in two different methods. The first, is

using the total flame area:

�̇�𝑏 = 𝜌𝑢𝐴𝑓𝑆𝐿 (8-12))

where 𝜌𝑢(𝑇𝑢, 𝑝) is the unburned gas density, 𝐴𝑓(𝑟𝑓 , 𝜉) the total flame area, 𝑆𝐿(𝑇𝑢, 𝑝, 𝜙) the laminar

burning speed, 𝑟𝑓 the flame radius, 𝑇𝑢 unburned gas temperature, 𝑝 the mixture pressure and 𝜙 the

fuel air equivalence ratio. The parameter 𝜉 which is called hereafter, Cellularity Factor includes

all information about the shape and size of cells over the flame front. Since the surface area of a

191

cellular flame cannot be measured directly, at least with current technologies, the laminar burning

speed cannot be calculated by previously discussed theoretical model using pressure rise method.

The other method is, to approximate the flame surface as the outer area of the spherical flame front

having the same mass of burned gas:

�̇�𝑏 = 𝜌𝑢𝐴𝐿𝑆𝑐 (8-13))

where 𝑆𝑐(𝑆𝐿 , 𝜉), the cellular burning speed, is a function of laminar burning speed and cellularity

factor. Since the mass burning rate is known, so the under-estimation of flame surface area will be

compensated by increase of the burning speed. This burning speed which includes the information

of cellularity is called hereafter the cellular burning speed. As discussed earlier, laminar burning

speed cannot be evaluated in cellular flames unless further knowledge regarding the shape and

area of the cellular flame becomes available, however cellular burning speed and mass burning

rate can be measured and evaluated using the same model and assumptions. To reduce the effects

of spark energy discharge, the results are reported in regions where 𝑟𝑓 > 4cm. The measurements

were taken at various equivalence ratios, pressures and temperatures and the calculated cellular

burning speeds and mass burning rates have been used to develop the correlations in terms of

equivalence ratio, temperature and pressure as shown in Eqs. (8-14) and (8-15) respectively:

𝑆𝑐 = 𝑆𝑐0(1 + 𝑎(𝜙 − 1) + 𝑏(𝜙 − 1)2) (

𝑇

𝑇0)𝛼

(𝑝

𝑝0)𝛽

(8-14)

�̇�𝑏 = �̇�𝑏0(1 + 𝑐(𝜙 − 1) + 𝑑(𝜙 − 1)2) (

𝑇

𝑇0)𝛾

(𝑝

𝑝0)𝜃

(8-15))

where 𝑆𝑐0 and �̇�𝑏0 are the cellular burning speed and mass burning rate at reference state

(ϕ = 1, T0 = 298K, p0 = 1atm) , 𝜙 the equivalence ratio, 𝑇 the temperature in K and 𝑝 the

mixture pressure in atm. To have an accurate fitting, the temperature and pressure exponents are

considered as a linear function of equivalence ratio as shown in Eqs.(8-16) - (8-19):

𝛼 = 𝛼1 + 𝛼2(𝜙 − 1) (8-16))

𝛽 = 𝛽1 + 𝛽2(𝜙 − 1) (8-17))

192

𝛾 = 𝛾1 + 𝛾2(𝜙 − 1) (8-18))

𝜃 = 𝜃1 + 𝜃2(𝜙 − 1) (8-19))

Coefficients, 𝑆𝑐0 , �̇�𝑏0 , 𝑎, 𝑏, 𝑐, 𝑑, 𝛼1, 𝛼2, 𝛽1, 𝛽2, 𝛾1, 𝛾2, 𝜃1 and 𝜃2, have been found using an

unconstrained minimization method for three different hydrogen concentration as listed in

Table 8-1 and Table 8-2. These correlations are only valid for the range of pressures, temperatures

and equivalence ratios that listed in those tables. Since correlations for hydrogen concentrations of

10 and 25% have been derived only for stoichiometric mixture (𝜙 = 1), the coefficients of

𝑎, 𝑏, 𝑐, 𝑑, 𝛼2, 𝛽2, 𝛾2 and 𝜃2 are non-applicable which are shown by “n/a” in Table 8-1 and Table 8-2.

Table 8-1- Coefficients of cellular burning speed correlation for H2/CO/O2/He mixture

𝑺𝒄𝟎 𝒂 𝒃 𝜶𝟏 𝜶𝟐 𝜷𝟏 𝜷𝟐 Validity Range

𝒑 (𝒂𝒕𝒎) 𝑻 (𝑲) 𝝓

𝜶 = 𝟓% 67.671 1.040 -0.500 1.545 -0.534 0.045 0.130 2 - 50 400 - 800 0.6 - 2

𝜶 = 𝟏𝟎% 88.443 n/a n/a 1.562 n/a 0.049 n/a 2 - 40 400 - 750 1

𝜶 = 𝟐𝟓% 139.70 n/a n/a 1.650 n/a 0.044 n/a 2 - 40 400 - 750 1

Table 8-2- Coefficients of mass burning rate correlation for H2/CO/O2/He mixture

�̇�𝒃𝟎 𝒄 𝒅 𝜸𝟏 𝜸𝟐 𝜽𝟏 𝜽𝟐 Validity Range

𝒑 (𝒂𝒕𝒎) 𝑻 (𝑲) 𝝓

𝜶 = 𝟓% 8.851 1.225 -0.529 1.943 0.947 1.010 -0.215 2 - 50 400 - 800 0.6 - 2

𝜶 = 𝟏𝟎% 10.111 n/a n/a 1.815 n/a 1.092 n/a 2 - 40 400 - 750 1

𝜶 = 𝟐𝟓% 15.038 n/a n/a 2.035 n/a 1.048 n/a 2 - 40 400 - 750 1

The cellularity factor is defined as,

𝜉 =𝐴𝑓 − 𝐴𝐿

𝐴𝐿=𝑆𝑐 − 𝑆𝐿𝑆𝐿

(8-20))

By combining Eqs. (8-12) and (8-13) and assuming the mass burning rate and laminar burning

speed are known respectively from experimental pressure data and 1D free flame simulation using

Davis et al. mechanism [221], the total flame surface area can be evaluated as,

𝐴𝑓 =�̇�𝑏

𝜌𝑢𝑆𝐿

(8-21))

Finally, using Eq. (8-20) the cellularity factor will be calculated as,

193

𝜉 =�̇�𝑏

𝜌𝑢𝐴𝐿𝑆𝐿− 1

(8-22))

The cellularity factor which includes the information regarding the shape and size of all cells

and wrinkles over the flame front is a function of unburned gas temperature, mixture pressure,

equivalence ratio and hydrogen concentration. To calculate the cellularity factor in Eq. (8-22),

mass burning rate (�̇�𝑏), laminar flame area (𝐴𝐿) and unburned gas density (𝜌𝑢) were calculated

from differential-based multi-shell model [22] using experimental pressure rise data and Laminar

burning speed (𝑆𝐿) was computed from 1-D free flame simulation using Davis et al. mechanism

[221]. In the following sections, the effect of temperature, pressure, equivalence ratio and

hydrogen concentration on cellular burning speed, mass burning rate and cellularity factor will be

investigated in details.

8.5.2.1. Effect of Temperature

The effect of two different preheat temperatures of 400 and 450 K on cellular burning speed

and mass burning rate of stoichiometric H2/CO/O2/He mixture at initial pressure of 10 atm and

hydrogen concentration of 10% is shown in Figure 8.5. As it was expected the cellular burning

speed and mass burning rate are directly proportional to temperature which also is demonstrated

through positive temperature exponents listed in Table 8-1 and Table 8-2. It means that the higher

the temperature, the higher the cellular burning speed and mass burning rate provided that all other

parameters such as pressure and mixture composition are fixed. As discussed earlier the cellular

burning speed is directly proportional to laminar burning speed and cellularity factor. The laminar

burning speed, calculated using free flame simulation, has a positive dependency to temperature

as shown in Figure 8.6 at a given pressure. Figure 8.6 shows that the cellularity factor which

indicates the percentage of increase of flame surface due to cell formation has a negative

relationship with temperature. In one hand increase in temperature, increases the laminar burning

speed and on the other hand it decreases the cell formation propensity and consequently the

cellularity factor. Since the laminar burning speed has a strong dependency to temperature than

cellularity factor, the overall effect of temperature on cellular burning speed would be positive as

shown in Figure 8.5. This strong dependency of laminar burning speed to temperature has been

proved through the large positive exponent in power law correlation by Askari et al. [22].

194

Figure 8.5. Cellular burning speed and mass burning rate of stoichiometric H2/CO/O2/He mixture along

two isentropes at different initial temperatures, initial pressure of 10 atm and hydrogen concentration of

10%

Figure 8.6. Cellularity factor and laminar burning speed of stoichiometric H2/CO/O2/He mixture along

two isentropes at different initial temperatures, initial pressure of 10 atm and hydrogen concentration of

10%

195

8.5.2.2. Effect of Pressure

Figure 8.7 shows the cellular burning speeds and mass burning rates of stoichiometric

H2/CO/O2/He mixture along three isentropes at varying initial pressures of 2, 5 and 10 atm for

hydrogen percentage of 25% and initial temperature of 400 K. As the pressure exponents of power

law correlations in Eqs. (8-14) and (8-15) are always positive, it indicates that the initial pressure

has a direct positive effect on both cellular burning speed and mass burning rate as shown in

Figure 8.7. It also shows that the positive effect of pressure on mass burning rate is much greater

than cellular burning speed. It is demonstrated through several scientific publications

[22,24,41,43,197,243] that the laminar burning speed has negative dependency with pressure. The

question is why the cellular burning speed which is proportional to laminar burning speed behaves

differently and has a minor positive dependence on pressure. This question can be answered by

considering the other important parameter that cellular burning speed depends on, cellularity

factor. Opposite to the laminar burning speed, the cellularity factor has a very strong and direct

relationship to pressure. As shown in Figure 8.8, pressure has a negligible effect on laminar flame

area which is only a function of flame radius. This figure also shows that the total flame area

increases as pressure increases. The reason is that, increasing pressure increases the tendency of

flame destabilization through the enhancement of hydrodynamic instability and reduction of flame

thickness [22] and promotes the cell formation tendency over the flame front and consequently

increases the total flame area and cellularity factor as shown in Figure 8.8. As the pressure

increases, since the positive effect of cell formation is slightly greater than negative effect of

laminar burning speed, then the cellular burning speed tends to increase. The increase in mass

burning rate as pressure increases is much more significant than cellular burning speed. Based on

Eq. (8-13) the mass burning rate is a function of laminar flame area, cellular burning speed and

unburned gas density. As shown in Figure 8.8 the laminar flame area doesn’t have impact on mass

burning rate as the pressure changes at a given temperature. Also based on above explanation and

Figure 8.7 the cellular burning speed has a minor positive effect on mass burning rate by increasing

the pressure at a given temperature. But unburned gas density increases by pressure based on ideal

gas law which is the only important term that explain the strong positive connection between mass

burning rate and pressure.

196


isentropes at different initial pressure for initial temperature of 400 K and hydrogen concentration of 25%

Figure 8.8. Cellularity factor and flame area of stoichiometric H2/CO/O2/He mixture along three

isentropes at different initial pressure for initial temperature of 400 K and hydrogen concentration of 25%

197

8.5.2.3. Effect of Equivalence Ratio

Cellular burning speeds and mass burning rates of H2/CO/O2/He mixture at various equivalence

ratios for hydrogen percentage of 5%, preheat temperature of 480 K and initial pressure of 12 atm

along three isentropes are shown in Figure 8.9. As the equivalence ratio increases from ϕ = 0.6

to ϕ = 2.0 both cellular burning speed and mass burning rate increase. Figure 8.10 shows the

effect of equivalence ratio on burning speed and cell formation. Increasing equivalence ratio from

0.6 to 2 leads to increase of the cell formation and laminar burning speed. The differences between

laminar and cellular burning speed at lean mixture (𝜙 = 0.6) is negligible because at this

stoichiometry there exist very few cells over the flame front. As equivalence ratio increases the

cell formation percentage increases and consequently the cellular burning speed deviate drastically

from laminar burning speed.

Figure 8.9. Cellular burning speed and mass burning rate of H2/CO/O2/He mixture along three isentropes

at different equivalence ratios for initial pressure of 12 atm, initial temperature of 480 K and hydrogen

concentration of 5%

198

Figure 8.10. Cellularity factor, cellular and laminar burning speed of H2/CO/O2/He mixture for three

different equivalence ratios of 0.6, 1.0 and 2.0 at pressure of 23.5 atm, temperature of 602 K and


8.5.2.4. Effect of Hydrogen Concentration

Hydrogen addition has a significant direct impact on cellular burning speed and mass burning

rate. As shown in Figure 8.11, the cellular burning speed and mass burning rate increase with

increasing hydrogen concentration in the fuel blend. Figure 8.12 compares the laminar and cellular

burning speeds of stoichiometric H2/CO/O2/He mixture for three different hydrogen

concentrations at preheat temperature of 450 K and initial pressure of 2 atm along isentropes. As

mentioned before, the laminar burning speed has been calculated from 1-D free flame simulation.

As it can be seen the difference between laminar and cellular burning speeds at the beginning of

flame propagation are negligible. As flame propagates and temperature and pressure increase, the

cellular burning speed starts to deviate from laminar burning speed. Deviation point varies by

changing the hydrogen concentration. As the hydrogen concentration increases, this deviation

point moves to smaller radii where the pressure and temperature are low. For the range that laminar

and cellular burning speeds are identical the cellularity factor is negligible and laminar and total

flame surface are similar as shown in Figure 8.13.

199


three isentropes at different hydrogen concentration for initial temperature of 450 K and initial pressure of

2 atm

Figure 8.12. Laminar and cellular burning speed of stoichiometric H2/CO/O2/He mixture along three

isentropes at different hydrogen concentration for initial temperature of 450 K and initial pressure of 2

atm (laminar burning speeds are indicated with dashed lines)

200

Also in this figure can be seen that the hydrogen concentration doesn’t have any significant

effects on laminar flame area which is indicated by dashed lines. Deviation points for each

hydrogen concentration are represented by arrows in both Figure 8.12 and Figure 8.13.

Figure 8.13. Laminar and total flame area of stoichiometric H2/CO/O2/He mixture along isentropes at

different hydrogen concentration for initial temperature of 450 K and initial pressure of 2 atm (laminar

flame areas are indicated with dashed lines)

201

9. Auto-Ignition Characteristics Study of Gas-to-

Liquid (GTL) Fuel at High Pressures and Low

Temperatures

202

9.1. ABSTRACT

Onset of auto-ignition of premixed GTL/air mixture has been determined at high pressures and

low temperatures over a wide range of equivalence ratios. The GTL fuel used in this study was

provided by Air Force Research Laboratory (AFRL), designated by Syntroleum S-8, which is

derived from natural gas via the Fischer–Tropsch process. A blend of 32% iso-octane, 25% n-

decane and 43% n-dodecane is employed as the surrogates of GTL fuel for chemical kinetics study.

A spherical chamber, which can withstand high pressures up to 400 atm and can be heated up to

500 K, was used to collect pressure rise data, due to combustion, to determine the onset of auto-

ignition. A gas chromatograph system working in conjunction with specialized heated lines were

used to verify the filling process. A liquid supply manifold was used to allow the fuel to enter and

evaporate in a temperature controlled portion of the manifold using two cartridge heaters. An

accurate high-temperature pressure transducer was used to measure the partial pressure of the

vaporized fuel. Pressure rise due to combustion process was collected using a high-speed pressure

sensor and was stored in a local desktop via a data acquisition system. Measurements for the onset

of auto-ignition were done in the spherical chamber for different equivalence ratios of 0.8 to 1.2,

different initial pressures of 8.6, 10, and 12 atm at initial temperature of 450 K. Critical pressures

and temperatures of GTL/air mixture at which auto-ignition takes place have been identified by

detecting aggressive oscillation of pressure data during the spontaneous combustion process

throughout the unburned gas mixture. To interpret the auto-ignition conditions effectively, several

available chemical kinetics mechanisms were used in modeling auto-ignition of GTL/air mixtures.

For low temperature mixtures, it was shown that auto-ignition of GTL fuel is a strong function of

unburned gas temperature and propensity of auto-ignition was increased as initial temperature and

pressure increased.

Keywords: onset of auto-ignition, GTL, Syntroleum S-8, spherical chamber, ignition delay time,

pressure rise, chemical kinetics mechanism

9.2. INTRODUCTION

The need for finding an alternative to oil-based transportation fuels is greater now than ever

before due to environmental impact and supply security. Alternative fuels obtained from feed

stocks such as biomass, natural gas and coal are called Synthetic Paraffinic Kerosene (SPK) fuels.

203

Recently, the interest on SPK fuels as a viable alternative fuel for aviation transportation is

enormous as they do not warrant any major modifications to the existing fuel injection /combustor

system. Furthermore, the SPK fuels obtained through Fisher-Tropsch (F-T) synthesis are preferred

as the fuel composition can be appropriately tailored for specific applications. Among SPK fuels,

gas-to-liquid (GTL) fuelis preferred over conventional jet fuels due to cleaner combustion

characteristics as a result of less aromatic content and the near absence of sulfur. [44]. The GTL

fuel can also be surrogate for gasoline, diesel, and aviation fuels [45]. Over the years, the potential

for deriving high value products from natural gas [46,47] and its abundant availability have

attracted the pioneers in GTL production technology such as Syntroleum, Shell, Sasol, and

Chevron to build small and medium scale GTL plants across the globe. The availability of the

world’s third largest natural gas reserve in Qatar (with proven reserves of about 890 trillion cubic

feet [48]) has led to the construction of world's largest GTL plant, Pearl GTL, jointly by Qatar-

Petroleum and Shell at a cost of about $18billion. This has enabled Qatar airways to attempt a

commercial flight from London, UK to Doha, Qatar, using a 50-50% blend of GTL fuel and

conventional Jet A-1 fuel [49].

The SPK fuels produced using F-T process are mainly composed of normal-alkanes, iso-

alkanes, and cyclic-alkanes, which is substantially different from those of conventional jet fuels

such as Jet A, Jet A-1, and JP-8. Synthetic fuels have a very small concentration of cyclo-alkanes

in comparing with conventional jet fuels and this small number varies based on the different

production processes and companies. Moses[50] has done a very good comparison between

different available synthetic fuels. He showed that among SPK fuels, Syntroleum aviation fuel

provided by Air Force Research Laboratory (AFRL), designated with S-8, has almost no cyclo-

alkanes. The difference in fuel chemical properties will have a significant influence on the

combustion and emission characteristics in combustors. Therefore, a complete knowledge of

fundamental combustion parameters for GTL fuel at combustor conditions is essential in order to

improve and optimize the combustor design and engine efficiency. Furthermore, these

fundamental combustion parameters are necessary to develop, validate, and to improve the

prediction capabilities of computational tools and chemical kinetics models. Among these

fundamental combustion parameters, the investigation of the onset of auto-ignition [51] for GTL

fuel is extremely relevant and necessary for the combustion community, particularly for gas

turbine and internal combustion engines in the transportation industry [14,52].

204

The onset of auto-ignition is the set of thermodynamic conditions at which the combustion

process occurs spontaneously and simultaneously throughout the combustible mixture [26]. For

any particular mixture of fuel, oxidizer and diluent, the temperature and the pressure are the key

parameters to consider as the drivers to auto-ignition [40]. Time is also a factor in driving auto-

ignition. A parameter called ignition delay time can be experimentally determined as the time a

mixture may remain at a temperature and pressure before auto-ignition occurs [252]. Typically,

rapid compression machines or shock tubes are used to determine the ignition delay times of a

mixture. The results from such experiments, even though widely accepted, do not represent the

conditions typically found in practical applications of combustion system where the pressure and

temperature are constantly changing due to flame propagation. Using the experimental facility

developed in this study, a controlled combustion event in spherical constant volume combustion

chamber produces an increase in the pressure and temperature of the unburned mixture [23]. When

auto-ignition conditions are reached, the unburned gas instantly ignites and produces a series of

pressure waves that can be detected by the pressure transducer. The conditions of the unburned

gas that initiate the pressure waves are the conditions at which auto-ignition occurs, and are more

representative of the varying conditions typically found in a combustion systems such as internal

combustion engines.

Kumar et al. [253] have done an experimental study of auto-ignition characteristics of GTL and

conventional fuel/air mixtures and observed two-stage ignition delay response. Their further study

on laminar burning speed indicated that S-8 GTL produces a robust flame compared to Jet-A

[254]. Wang et al. [255] have investigated the ignition behavior of several conventional and GTL

fuels using a heated shock tube. Their ignition delay time measurements were almost the same for

GTL and Jet-A at temperatures higher than 1000 K. However, at lower temperatures significant

differences were observed between those of GTL and Jet-A fuels. In order to simulate the

combustion behavior of GTL fuel, many groups tried to find a surrogate mixture for GTL fuels.

Huber et al. [256] provided surrogates for GTL fuel based on the thermo-physical properties

incorporating with volatility data. Naik et al. [66] developed a three component, iso-octane, n-

decane and n-dodecane, chemical kinetics model as a surrogate for GTL fuel and compared the

predictions with the experimental results reported by Ji et al. [257]. The comparison showed that

the model was able to accurately predict the laminar burning speeds of GTL fuels, but can only be

used for ignition delay time calculation at high temperatures. Dooley et al. [258] also developed a

205

chemical kinetic model based on the mixtures of iso-octane and n-dodecane to mimic the

combustion behavior of GTL fuels. The predictions of auto-ignition, extinction limits, and species

concentration profile were reported to agree well with experimental data. The ignition behaviors

have been evaluated using different experimental configurations such as counter flow burner [259],

rapid compression machine [253] and shock tubes [255]. The outcome of these studies highlighted

the fact that GTL fuel had a much larger resistance to flame stretch effects and robust combustion

behavior when compared to conventional jet fuels. The more notable combustion behavior was the

shorter ignition delay of GTL fuel than the conventional counterparts. However, it is important to

note that all of the above studies have been carried out either at atmospheric pressure or at discrete

intermediate pressures. The data for the onset of auto-ignition for GTL fuel has not

comprehensively been measured in the conditions which are identical to internal combustion

engines.

In this study, the onset of auto-ignition for GTL fuel/air mixtures have been measured for

different equivalence ratios of 0.8 to 1.2, different initial pressures of 8.6, 10, and 12 atm at an

initial temperature of 450 K. The GTL fuel used in this research was supplied by Air Force

Research Laboratory, designated by Syntroleum S-8, which was derived from natural gas via

Fischer-Tropsch process. The experiments have been done in a high pressure and temperature

spherical chamber and pressure rise has been collected using high-speed pressure transducer and

data acquisition systems. Critical pressures and temperatures of GTL/air mixture at which auto-

ignition takes place have been identified by detecting aggressive oscillation of pressure data during

the spontaneous combustion process throughout the unburned gas mixture. Several detailed

chemical kinetics mechanisms have been compared and used to study the onset of auto-ignition

conditions. A blend of 32% of iso-octane, 25% n-decane and 43% n-dodecane [66] was employed

as the surrogates of GTL fuel for chemical kinetics study and filling process.

9.3. EXPERIMENTAL SETUP

The core component of the experimental setup includes a spherical combustion chamber that

enables the measurement of the pressure rise during flame propagation. The spherical chamber is

designed to withstand pressures up to 400 atm and is located in an oven which can be heated up to

500 K. It includes three ionization probes to check the symmetry of the spherical flame. A Kistler

601CA high temperature pressure transducer in conjunction with a Kistler 5010B charge amplifier

206

are used to record the dynamic pressure rise during the combustion process. The chamber is also

equipped with two extended spark plugs for ignition at the center of chamber and a K-type

thermocouple to measure the mixture gas temperature. The gas supply manifold, mainly

constructed of 304 and 316 Stainless steel Swagelok fittings and tubing, is predisposed to

accommodate inputs from 5 simultaneous gas cylinders, thus allowing for an inventory of gas

mixtures to be always readily available for immediate use. Two vacuum pumps help evacuate the

system faster and allow for independent testing of the two chambers. The temperature controllers

are proportionally programmable with redundant safety feature for temperature protection and

electric shock.

Another key element of the apparatus is the liquid filling system where liquid fuel is allowed to

enter and evaporate in a temperature controlled portion of the manifold. A high-temperature

pressure transducer closely coupled to this section of the manifold is used to monitor the partial

pressure of the vaporized fuel and hence control the amount of fuel that will be used in the

experiment. A gas chromatograph (GC) system in conjunction with the specialized heated lines to

prevent condensation, was used to check the composition of premixed fuel/air mixture inside the

chamber to verify the filling process based on partial pressure method. The configuration of

experimental facilities and their connections are shown in Figure 9.1. All data acquisition and

analysis were done by several dedicated PCs using a high-speed DAQ card and isolated input and

output modules for temperature, voltages and pressure measurements as well as automatic delayed

firing via control of the high voltage coil driving the spark plugs. The raw pressure signal produced

by the high-speed pressure transducer contains digitization noise resulting from data acquisition

system process of converting a voltage signal to a digital value. The digitization noise is

approximately 0.25 psi /bit which is certainly negligible for the range of pressure measurements

of interest. For any set of data to be deemed acceptable three consecutive experimental runs have

to yield the exact pressure curve to ensure that the confidence level of the experiments are above

95% [212]. More information about the experimental setup can be found in previous publication

[2–4,21–25,46,47,102,171].

207

Figure 9.1. Overview of experimental facilities


As previously discussed, synthetic fuels produced by the Fisher-Tropsch method have become

increasingly popular as substitutes to the conventional hydrocarbon fuels such as diesel, gasoline,

and jet fuels [260]. The GTL fuel used in this study was provided by the Air Force Research

Laboratory (AFRL) [50,65]. This fuel was produced in the U.S. from natural gas through a Fischer-

Tropsch process called low temperature Cobalt catalyst [50] in a small pilot plant by Syntroleum

in Oklahoma. The Specification properties of this fuel are presented in Table 9-1. It can be seen

that the percentage of aromatic (cyclic) is zero. A blend of 32% iso-octane, 25% n-decane and

43% n-dodecane [66] was employed as the surrogates of GTL fuel for chemical kinetics study and

filling process. The initial mixture composition for GTL/air mixture is defined as:

𝜙(0.32 𝐶8𝐻18 + 0.25 𝐶10𝐻22 + 0.43 𝐶12𝐻26) + 15.83(𝑂2 + 3.76𝑁2) (9-1)

This surrogate mixture has an empirical formula of 𝐶10.22𝐻22.44, 𝐻 𝐶⁄ ratio of 2.196, an

estimated Cetane number of 61 and a molar mass of 145.37 g/mol.

208

Table 9-1- Specification properties of Syntroleum S-8 fuel

Flash point (oC) 48

Freezing point (oC) -51









In this study the propensity of GTL/air mixture to auto-ignite and the conditions that produce

the onset of auto-ignition were measured and analyzed for various equivalence ratios and initial

conditions. Measurements for the onset of auto-ignition of GTL/air mixture have been recorded in

the spherical chamber for different equivalence ratios of 0.8 to 1.2, different initial pressures of

8.6, 10, and 12 atm at initial temperature of 450 K. During the compression of unburned mixture

due to flame propagation, which acts as a piston, both temperature and pressure of the unburned

gas increases. At a specific condition, auto-ignition of all of the unburned gases occurs. The

temperature and pressure that instantaneously produce auto-ignition are measured and reported as

the onset of auto-ignition. To detect the onset of auto-ignition the derivative of the measured

pressure (𝑑𝑝 𝑑𝑡⁄ ) was evaluated and used as a non-subjective method to determine the auto-

ignition pressure. The measured pressure signal begins to oscillate once auto-ignition occurs due

to the shock waves bouncing around in the combustion chamber. The derivative with respect to

time of the pressure signal will oscillate very aggressively between positive and negative values

once auto-ignition occurs thus providing a convenient method to detect the onset of auto-ignition.

It was assumed that unburned gas is compressed isentropically up to the onset of auto-ignition and

the temperature at the onset of auto-ignition was determined using isentropic relation of

compression.

Figure 9.2 shows the pressure-time traces of combustion of GTL/air mixture for four initial

pressures of 2, 8.6, 10 and 12 atm at initial temperature of 450 K and equivalence ratio of 0.8. For

the case of initial pressure of 2 atm, no auto-ignition was observed, normal combustion process

occurred and the pressure curve is very smooth as shown by solid line in Figure 9.2. At the onset

of auto-ignition, a sudden oscillation in the pressure is detected as shown by points A, B and C in

209

Figure 9.2 for initial pressure of 8.6, 10 and 12 respectively, along with audible noise as a good

indication that unburned mixture was auto-ignited.

Figure 9.2. Comparison of pressure-time traces of auto-ignition of GTL/air mixture for three different

initial pressure of 8.6, 10 and 12 atm, at initial temperature of 450 K and equivalence ratio of 0.8 and

normal combustion with initial pressure of 2 atm

The auto-ignition pressure traces shown in Figure 9.2 are very similar to those in internal

combustion engines reported by Heywood [84]. The auto-ignition pressures were accurately

determined using pressure derivative technique and locating the point at which the pressure

derivative with respect to time becomes discontinuous as shown in Figure 9.3. It can be observed

visually in this figure that the oscillatory pressure waves caused by auto-ignition are easily detected

by this technique. As it was mentioned, the corresponding auto-ignition temperatures of unburned

gas were measured assuming that the unburned gas mixture was compressed isentropically.

210

Figure 9.3. Comparison of pressure rate-time traces of auto-ignition of GTL/air mixture for three different

initial pressure of 8.6, 10 and 12 atm, at initial temperature of 450 K and equivalence ratio of 0.8

While development of the chemical kinetics mechanism of GTL fuel is in its initial stage, there

are several mechanisms that can predict GTL combustion characteristics such as laminar burning

speed and ignition delay time [66,258,261,262]. These mechanisms are summarized in Table 9-2.

As shown in this table, in terms of computational time which is proportional to number of species

and reactions, Dooley et al. [258] is the most expensive mechanism due to the larger number of

species and Yu et al. [262] is the least expensive mechanism. All three surrogates of Iso-octane,

n-decane and n-dodecane are included in Naik et al. [66], Dooley et al. [258] and Ranzi et al. [261]

mechanisms except Yu et al. mechanism [262] which only has two surrogates of 2,5-

dimethylhexane (one of the octane’s isomers) and n-dodecane. The above proposed composition

of 32% iso-octane, 25% n-decane and 43% n-dodecane is applicable for the first three mechanisms

in Table 9-2. For Yu et al. mechanism [262], its own suggested composition of 41.9% 2,5-

dimethylhexane and 58.1 % n-dodecane has been used.

The ignition delay time computations were performed with assumption of constant

volume/constant internal energy using CANTERA solver [220]. The ignition delay time was

211

calculated when the temperature reached a value of 400 K above the initial temperature. Figure 9.4

shows a comparison of ignition delay times between available kinetics mechanisms of GTL fuel

with the heated shock tube experimental data of Wang et al. [255] at equivalence ratio of 1 and

pressure of 20 atm for a wide range of temperature from 700 K to 1300 K.

Table 9-2- Comparison of different chemical kinetics mechanisms for GTL fuel

Mechanism name Number of species Number of reactions Available GTL surrogates

Naik et al. [66] 753 7007 iso-octane, n-decane and n-dodecane

Dooley et al. [258] 3164 21671 iso-octane, n-decane and n-dodecane

Ranzi et al. [261] 484 19341 iso-octane, n-decane and n-dodecane

Yu et al. [262] 373 2037 2,5-dimethylhexane and n-dodecane

As it can be seen, Ranzi et al. [261] and Yu et al. [262] mechanisms have good agreement with

experimental results for both low and high temperatures. Since the agreement of Ranzi et al. [261]

mechanism with experimental data at intermediate temperatures is slightly better than those

predicted by Yu et al. [36] and also it includes all three surrogates of iso-octane, n-decane and n-

dodecane , it was used in this study.

Figure 9.4. Comparison of available GTL detailed kinetics mechanisms [66,258,261,262] with

experimental data [255] at equivalence ratio of 1 and pressure of 20 atm for a wide range of

temperatures

0.8 0.9 1 1.1 1.2 1.3 1.4 1.510

-3

10-2

10-1

100

101

102

103

1000/T (1/K)

Ign

itio

n d

ela

y tim

e (

ms)

Yu et al. [36]

Ranzi et al. [37]

Naik et al. [19]

Dooley at al. [21]

Wang et al. [17]

212


Ranzi et al. [261] mechanism for stoichiometric GTL/air mixture

As shown in Figure 9.5, at low temperature conditions (T < 800 K), both temperature and

pressure have a negative dependency to ignition delay time. It can be seen that for low temperature

and high pressure conditions indicated by dashed red box, as either temperature or pressure

increase the ignition delay time decreases or in other words the propensity of auto-ignition

increases. Figure 9.5 also shows that pressure has a minor effect on ignition delay time for low

temperatures and the effect of pressure on ignition delay time promotes as temperature increases.

It can be concluded from this figure that for low temperature conditions the ignition delay time is

a strong function of temperature.

The experimental critical temperatures and pressures in this work at the onset of auto-ignition

along with theoretical ignition delay time using Ranzi et al. [261] mechanism for GTL/air mixture

at different equivalence ratios are shown in Figure 9.6 and also listed in Table 9-3. In Figure 9.6,

as mixture pressure increases the temperature at which auto-ignition occurs decreases for all three

equivalence ratios. As shown in Figure 9.7, increasing the temperature while pressure is decreasing

causes the ignition delay time to decrease. The ignition delay time tends to keep its negative

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.510

-4

10-3

10-2

10-1

100

101

102

1000/T (1/K)

Ign

itio

n d

ela

y tim

e (

ms)

P = 10 atm

P = 20 atm

P = 30 atm

P = 50 atm

P = 100 atm

213

dependency only with temperature. These experimental runs produced auto-ignition conditions at

different pressures and only slightly different temperatures, indicating that the auto-ignition

characteristics are a strong function of the temperature of the unburned gases.

Figure 9.6. Experimental temperatures and pressures at the onset of auto-ignition for GTL/air mixture at

different equivalence ratios

Table 9-3- Experimental temperatures and pressures at the onset of auto-ignition for GTL/air mixture

Equivalence ratio Temperature (K) Pressure (atm)

0.8

699.63 53.11

694.51 59.92

687.90 69.14

1.0

705.59 54.90

699.51 61.76

692.55 71.05

1.2

696.41 52.13

691.11 58.71

685.28 68.02

50 55 60 65 70 75680

685

690

695

700

705

710

Pressure (atm)

Te

mp

era

ture

(K

)

=0.8

=1.0

=1.2

214

Figure 9.7. Theoretical ignition delay times for GTL/air mixture at different equivalence ratios versus (a)

experimental temperatures and (b) experimental pressures at the onset of auto-ignition

215

10. Theoretical Prediction of Laminar Burning

Speed and Ignition Delay Time of Gas-to-Liquid

Fuel

216

10.1. ABSTRACT

Gas to Liquid (GTL), an alternative synthetic jet fuel derived from natural gas through Fischer-

Tropsch process has gained significant attention due to its cleaner combustion characteristics when

compared to conventional counterparts. The effect of chemical composition on key performance

aspects such as ignition delay, laminar burning speed and emission characteristics have been

experimentally studied. However, the development of chemical mechanism to predict those

parameters for GTL fuel is still in its early stage. The GTL aviation fuel from Syntroleum

Corporation, S-8, is used in this study. For theoretical predictions, a mixture of 32% iso-octane,

25% n-decane and 43% n-dodecane, by volume is considered as the surrogate for S-8 fuel. In this

work, a detailed kinetics model (DKM) has been developed based on the chemical mechanisms

reported for the GTL fuel. The DKM is employed in a constant internal energy and constant

volume reactor to predict the ignition delay times for GTL over a wide range of temperatures,

pressures and equivalence ratios. The ignition delay times predicted using DKM are validated with

those reported in the literature. Furthermore, the steady one-dimensional premixed flame code

from CANTERA is used in conjunction with the chemical mechanisms to predict the laminar

burning speeds for GTL fuel over a wide range of operating conditions. Comparison of ignition

delay and laminar burning speed show that the Ranzi et al. mechanism has a better agreement with

available experimental data and therefore is used for further evaluation in this study.

Keywords: ignition delay time, laminar burning speed, detailed kinetics model, chemical

mechanism, gas-to-liquid, theoretical prediction, experimental data

10.2. INTRODUCTION

Gas-to-Liquid (GTL) fuel has gained considerable attention in recent years due to its clean

combustion behavior when compared to the conventional fuels. GTL fuel synthesized from natural

gas through Fischer-Tropsch (F-T) process not only contains less sulfur and aromatic compounds

but also contributes less NOx and Particulate formation [44,53]. Over the years, the scope for

deriving high value products from natural gas [14,46,47] has attracted the pioneers in GTL

production technology such as Syntroleum, Shell, Sasol and Chevron, to build GTL plants across

the globe [263]. GTL fuels from different companies may have difference in their chemical

compositions since they go through different F-T process, however, the fuel physical properties

217

are within the stipulated range for the aviation fuels. The economics and benefits of producing

GTL fuel from natural gas have been studied by different groups [54,55]. The different aspects of

the combustion performance and emissions of GTL fuel as an alternative fuel for automobile [56–

63] and aviation [264,265,253–255,266–268] engines were also investigated and compared with

those of the traditional fuels. In this work, the GTL fuel from Syntroleum Corporation, S-8, is

used. A brief review of literature pertaining to aviation GTL fuel (S-8) is presented next as it is of

interest to this work.

To investigate the effect of chemical composition on the combustion behavior, Kahandawala et

al. [264] measured the ignition and emissions characteristics of S-8, JP-8, 2-methylheptane and a

mixture of heptane and toluene using a single-pulse reflected shock tube. They observed similar

ignition delay times between the fuels, however, the soot and Polycyclic Aromatic Hydrocarbons

(PAHs) were reported to be lower for S-8 than those of JP-8. Balagurunathan et al. [265] used a

shock tube to measure the ignition delay time for JP-8 and its alternatives and got almost identical

ignition delays. Kumar et al. [253] have done experimental study of auto-ignition characteristics

of GTL and conventional fuel/air mixtures and have observed two-stage ignition delay response.

Their further study on laminar burning speed indicated that S-8 produces a robust flame comparing

with Jet-A [254]. Wang et al. [255] have investigated the ignition behavior of several conventional

and GTL fuels using a heated shock tube. Their ignition delay time measurements were almost the

same for GTL and Jet-A at temperatures higher than 1000 K. However, at lower temperatures

significant differences were observed between ignition delay time of GTL and Jet-A fuels. Kick

et al. [269] have focused on the laminar burning speed of different ratio of GTL and 1-hexanol

mixtures. Hui et al. [270] have compared the combustion characteristics of alternative jet fuels.

The laminar flame speeds measured for conventional and alternative jet fuels were similar,

although, the ignition delay times of the latter were shorter than those of the former. Vukadinovic

et al. [271] measured the laminar burning speed and Markstein number in a cubic vessel using the

optical laser method. Ji et al. [257] investigated the laminar burning speed of jet fuel and its

alternatives and found a 5-8% higher in laminar burning speed of synthetic and biofuels than

standard jet fuel-air flames at elevated temperatures of the unburned mixtures. Singh et al. [272]

measured the laminar flame speeds and Markstein lengths of n-decace, Jet-A and S-8 and got

similar laminar burning speed for equivalence ratio from 0.8 to 1.6.

218

In order to simulate the combustion behavior of GTL fuel, many groups tried to find a surrogate

mixture for GTL fuels. Huber et al. [256] provided surrogates for GTL fuel based on the thermo-

physical properties incorporating with the volatility data. Naik et al. [66] came up with three-

component surrogates (iso-octane, n-decane and n-dodecane) for S-8 and Shell GTL fuels. They

validated their chemical kinetic mechanism using the available experimental data from literature.

Dooley et al. [258] considered a mixture of iso-octane and n-dodecane as surrogates and validated

their predictions with the experimental data reported by Wang et al. [255]. Slavinskaya et al. [273]

came up with another surrogates for GTL composed of n-decane, n-propylcyclohexane and iso-

octane. The chemical mechanism for the surrogates is validated by comparing the ignition delay

time and laminar burning speed with experimental data from the literature. Yu et al. [262] created

a surrogate mixture of n-dodecane and 2,5-dimethyhexane (one of the octane’s isomers) and their

predictions compared well with the experimental data from literature. Dagaut et al. [260]

investigated the mole fraction of the major species, ignition delay times and the laminar burning

speed of GTL fuel. They also studied the kinetics of oxidation of Shell GTL blended with hexanol

both experimentally and theoretically [274]. Later, they compared the concentration profiles for

the oxidation of GTL and Jet-A and the calculated ignition delay times [275]. Zhu et al. [276]

studied the ignition delay times for conventional jet fuels, alternative fuels (derived from natural

gas and coal) and their blends using shock-tube/laser-absorption methods in various initial

conditions. They observed similar trends of ignition delay time between the fuels with a small and

evident differences in their activation energy.

Although there are some theoretical studies on the ignition delay time and laminar burning

speed of GTL fuels, they are all done under certain temperatures, pressures and equivalence ratios.

A comprehensive study on the behavior of ignition delay time and laminar burning speed over a

wide range of temperatures, pressures and equivalence ratios have not been studied yet. This is

serves as the motivation for the present study. The ignition delay time and laminar burning speed

of GTL/air mixtures are predicted over a wide range of operating conditions. The GTL fuel from

Syntroleum Corporation, S-8, is represented by a surrogate mixture in this study. The GTL fuel

properties and its chemical composition are based on the reports from Air Force Research

Laboratory (AFRL) [50,65]. In this work, a detailed kinetics model (DKM) has been developed

based on the existing information on the chemical kinetics for the GTL jet fuel. The DKM

predictions of ignition delay time and laminar burning speed are compared with those obtained

219

using different chemical mechanisms [66,258,262,261] for the GTL fuel to highlight the predictive

capabilities of different mechanisms with respect to the experimental data. The ignition delay time

is calculated with the assumptions of constant volume and constant internal energy using the

detailed kinetics model (DKM) [277]. For laminar burning speed prediction, the steady one-

dimensional premixed flame code from CANTERA [220] has been used.

10.3. DETAILED KINETICS MODEL

The most accurate way to determine the time-dependent behavior of the state of a reaction

system is developing a DKM for the reacting system [277]. In this study a constant internal energy

and constant volume DKM is created to calculate the ignition delay time. In this model, the

concentrations of all the species and the system temperature are time-dependent variables. This

model consists of a full set of nonlinear ordinary differential equations for the prediction of species

concentrations and temperature via species and energy balance equations, respectively. For a

reaction system, any chemical reactions can be written as follows

∑𝜈𝑗𝑖′ 𝑋𝑗 ↔

𝑛𝑠

𝑗=1

∑𝜈𝑗𝑖′′𝑋𝑗

𝑛𝑠

𝑗=1

, 𝑘 = 1,… , 𝑛𝑟 (10-1)

where 𝑿𝒋 is the symbol of species j, ns is the number of species, nr is the number of reactions,

𝝂𝒋𝒌′

and 𝝂𝒋𝒌′′ are the stoichiometric coefficients on the reactants and products side of the equation,

respectively, for species j in the reaction i. Then the rate equation of species j can be expressed as

𝑑[𝑋𝑗]

𝑑𝑡=∑𝜈𝑗𝑖𝑞𝑖

𝑛𝑟

𝑖=1

(10-2)

where

𝜈𝑗𝑖 = 𝜈𝑗𝑖′′ − 𝜈𝑗𝑖

′ (10-3)

𝑞𝑖 = 𝑘𝑓𝑖∏[𝑋𝑗]𝜈𝑗𝑖′

𝑛𝑠

𝑗=1

− 𝑘𝑟𝑖∏[𝑋𝑗]𝜈𝑗𝑖′′

𝑛𝑠

𝑗=1

(10-4)

220

where 𝑑[𝑋𝑗] 𝑑𝑡⁄ is the net molar concentration rate of species j, 𝑞𝑖 the rate-of-progress variable for

the ith elementary reaction, 𝑘𝑓𝑖 and 𝑘𝑟𝑖 are the elementary forward and reverse rate coefficients,

respectively. For temperature we need an additional rate equation which will be derived from

energy balance:

�̇� =−∑ �̇�𝑗𝑒𝑗(𝑇)

𝑛𝑠𝑗=1

∑ 𝑛𝑗𝑐𝑣𝑗(𝑇)𝑛𝑠𝑗=1

(10-5)

where 𝑛𝑗 is mole number of species 𝑗, 𝑒𝑗(𝑇) the specific internal energy (per mole) of species 𝑗 at

temperature 𝑇 and 𝑐𝑣𝑗 = 𝑑𝑒𝑗 𝑑𝑇⁄ the specific heat at constant volume for species 𝑗. Solving Eqs.

(10-1) and (10-4) simultaneously can give us the concentrations and temperature profiles versus

time, which describe the change of state of the system. The ignition delay time was calculated

when the temperature reached a value of 400 K above the initial temperature.

The GTL fuel properties and its chemical composition have been provided by the Air Force

Research Laboratory (AFRL) [50,65]. This fuel was produced in the U.S. from natural gas through

a Fischer-Tropsch process called low temperature Cobalt catalyst [50] in small pilot plant by

Syntroleum in Oklahoma. The specification properties of this fuel are presented in Table 10-1.

Table 10-1- Specification properties of Syntroleum S-8 fuel

Initial boiling point (K) 426





Final boiling point (K) 533

Flash point (K) 321

Freezing point (K) 222









221

A blend of 32% iso-octane, 25% n-decane and 43% n-dodecane [66] was employed as the

surrogate for the GTL fuel chemical kinetics study. The initial mixture composition for GTL/air

mixture is defined as:

𝜙(0.32 𝐶8𝐻18 + 0.25 𝐶10𝐻22 + 0.43 𝐶12𝐻26) + 15.83(𝑂2 + 3.76𝑁2) (10-6)

This surrogate mixture has an empirical formula of 𝐶10.22𝐻22.44, 𝐻 𝐶⁄ ratio of 2.196, an

estimated Cetane number of 61 and a molecular weight of 145.37 g/mol.


10.4.1. Chemical Mechanisms Comparison

While development of the chemical mechanism of GTL fuel is in its initial stage, there are

several mechanisms that can predict GTL combustion characteristics such as laminar burning

speed and ignition delay time [66,258,261,262]. These mechanism are summarized in Table 10-2.

As shown in this table, in terms of computational time, Dooley et al. [258] is the most expensive

mechanism due to the large number of species and Yu et al. [262] is the least expensive

mechanism. All three surrogates of iso-octane, n-decane and n-dodecane are included in Naik et

al. [66], Dooley et al. [258] and Ranzi et al. [261] mechanisms except Yu et al. mechanism [262]

which only has two surrogates of 2,5-dimethylhexane and n-dodecane. So the above proposed

composition of 32% iso-octane, 25% n-decane and 43% n-dodecane is applicable for the first three

mechanisms in Table 10-2. For Yu et al. mechanism [262], its own suggested composition of

41.9% 2,5-dimethylhexane and 58.1 % n-dodecane has been used.

Table 10-2- Comparison of different chemical mechanisms for GTL fuel Mechanism name Number of species Number of reactions Available GTL surrogates

Naik et al. [66] 753 7007 iso-octane, n-decane and n-dodecane

Dooley et al. [258] 3164 21671 iso-octane, n-decane and n-dodecane

Ranzi et al. [261] 484 19341 iso-octane, n-decane and n-dodecane

Yu et al. [262] 373 2037 2,5-dimethylhexane and n-dodecane

Figure 10.1 shows a comparison of ignition delay times between available chemical

mechanisms [66,258,262,261] of GTL fuel with the heated shock tube experimental data of Wang

et al. [255] at an equivalence ratio of 1 and a pressure of 20 atm for temperatures varying from 700

222

K to 1300 K. As it can be seen, Dooley et al. mechanism [258] overestimates the values of ignition

delay time especially for low and intermediate temperatures. For time-dependent calculations such

as ignition delay time, Naik et al. mechanism [66] is valid only for high temperature conditions

(𝑇 > 1000 𝐾) as shown in Figure 10.1, whereas for the time-independent calculations such as

laminar burning speed [24,25,171] it is valid for a wide range of temperatures, which will be

discussed later. Figure 10.1 also shows that both Ranzi et al. [261] and Yu et al. [262] mechanisms

have a good agreement with experimental results but the agreement of Ranzi et al. [261]

mechanism with intermediate temperature is slightly better.

Figure 10.1. Comparison of ignition delay time between available GTL chemical mechanisms

[66,258,261,262] and experimental data [255] at equivalence ratio of 1 and pressure of 20 atm for a wide

range of temperatures

For laminar burning speed prediction the steady one-dimensional premixed flame code from

CANTERA [220] has been used. Dooley et al. [258] mechanism due to large computational time

has not been considered in this comparison. Figure 10.2 and Figure 10.3show the comparison of

laminar burning speed for different chemical mechanisms [66,262,261] over a wide range of

equivalence ratios at 1 atm and at temperatures of 400 K and 473 K, respectively. As it can be seen

0.8 0.9 1 1.1 1.2 1.3 1.4 1.510

-3

10-2

10-1

100

101

102

103

1000/T (1/K)

Ign

itio

n d

ela

y tim

e (

ms)

Yu et al. [34]

Ranzi et al. [41]

Naik et al. [31]

Dooley at al. [32]

Wang et al. [21]

223

all the mechanisms are close to each other but Ranzi et al. [261] mechanism has slightly better

agreement with experimental data. Since the agreement of Ranzi et al. [261] mechanism with

experimental data for ignition delay time and laminar burning speed is slightly better and also it

includes all three surrogates of iso-octane, n-decane and n-dodecane, therefore, it is selected for

further analysis in this study.

Figure 10.2. Comparison of laminar burning speed between GTL chemical mechanisms [66,262,261] and

experimental data [254,257,270] for different equivalence ratios at pressure of 1 atm and temperature of

400 K

10.4.2. Ignition Delay Time

Figure 10.4 shows the ignition delay time predicated using Ranzi e al. [261] mechanism for a

wide range of temperatures of 650 to 1650 K at six different pressures of 1, 10, 20, 30, 50 and 100

atm. As it can be seen that increasing the pressure at a given temperature decreases the ignition

delay time or in other words, increases the auto-ignition propensity [278]. At low temperatures (T

< 800 K), the effect of pressure on ignition delay time is negligible, whereas it has a significant

effect at intermediate and high temperatures (T > 800 K). Temperature has a very interesting effect

on ignition delay time as shown in Figure 10.4.

0.7 0.8 0.9 1 1.1 1.2 1.3 1.435

40

45

50

55

60

65

70

Equivalence ratio

La

min

ar

bu

rnin

g s

pe

ed

(cm

/s)

P=1 atm, T=400 K

Hui et al. [26]

Kumar et al. [20]

Ji et al. [28]

Naik mechanism [31]

Yu mechanism [34]

Ranzi mechanism [41]

224

Figure 10.3. Comparison of laminar burning speed between GTL chemical mechanisms [66,261,262] and

experimental data [254,270,271,274] for different equivalence ratios at pressure of 1 atm and temperature

of 473 K

At high temperature conditions (T > 1000 K) for a given pressure, the ignition delay time

decreases with an increase in temperature. In this case, the temperature has a negative dependency

to ignition delay time. This trend is changed to positive dependency for intermediate temperatures

and again switched to negative dependency for low temperatures. The change in dependency

occurs at higher temperatures as pressure increases. Figure 10.4 also shows that pressure has a

minor effect on ignition delay time for low temperatures and the effect of pressure promotes by

increasing the temperature. It can be concluded from this figure that for low temperature conditions

the ignition delay time is a strong function of temperature.

0.7 0.8 0.9 1 1.1 1.2 1.3 1.440

50

60

70

80

90

Equivalence ratio

La

min

ar

bu

rnin

g s

pe

ed

(cm

/s)

P=1 atm, T=473 K

Dagaut et al. [36]

Hui et al. [26]

kumar et al. [20]

Vukadinovic et al. [27]

Naik mechanism [31]

Yu mechanism [34]

Ranzi mechanism [41]

225

Figure 10.4. Theoretical ignition delay time for a wide range of pressures and temperatures using Ranzi et

al. [261] mechanism for stoichiometric GTL/air mixture

The ignition delay time for GTL/air mixture for a wide range of temperatures and three different

equivalence ratios is predicted using the DKM model. The results are shown for three different

pressures of 10, 50 and 100 atm in Figure 10.5, Figure 10.6 and Figure 10.7, respectively. As

shown, at a given temperature, increasing the equivalence ratio decreases the ignition delay time

and increases the auto-ignition propensity. It is observed that there is also a shift in trends at high

temperature conditions. For a pressure of 10 atm this shift occurs around 1380 K as shown in

Figure 10.5. With an increase in pressure the location of the shift moves to higher temperatures.

This location is called the shifting point, where the ignition delay times are almost the same for

different equivalence ratio at a given pressure and temperature. Comparing Figure 10.5,

Figure 10.6 and Figure 10.7, it can be obviously found that the shifting point moves toward high

temperature direction as the pressure goes up.

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.510

-4

10-3

10-2

10-1

100

101

102

103

1000/T (1/K)

Ign

itio

n d

ela

y tim

e (

ms)

P = 1 atm

P = 10 atm

P = 20 atm

P = 30 atm

P = 50 atm

P = 100 atm

226


equivalence ratios and a pressure of 10 atm using Ranzi et al. [261] mechanism for GTL/air mixture



0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.510

-3

10-2

10-1

100

101

102

1000/T (1/K)

Ign

itio

n d

ela

y tim

e (

ms)

= 0.6

= 1.0

= 1.4

P = 10 atm

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.510

-4

10-3

10-2

10-1

100

101

102

1000/T (1/K)

Ign

itio

n d

ela

y tim

e (

ms)

= 0.6

= 1.0

= 1.4

P = 50 atm

227



10.4.3. Laminar Burning Speed and Flame Thickness

Figure 10.8 shows the theoretical laminar burning speed and flame thickness for a wide range

of equivalence ratios, from lean to rich, and different temperatures of 400, 500, 600, 700 and 800

K at pressure of 1 atm using Ranzi et al. [261] mechanism for GTL/air mixture. The flame

thickness is defined by 𝛿𝑓 = (𝑇𝑎𝑑 − 𝑇𝑢) (𝑑𝑇 𝑑𝑥⁄ )𝑚𝑎𝑥⁄ , where 𝑇𝑎𝑑 is the adiabatic flame

temperature, 𝑇𝑢 the unburned temperature and (𝑑𝑇 𝑑𝑥⁄ )𝑚𝑎𝑥 the maximum temperature gradient

[22]. As it can be seen, increasing the temperature at a given equivalence ratio increases the laminar

burning speed and decreases the flame thickness. Maximum laminar burning speed for all

temperature cases occurs at an equivalence ratio of 1.1 while the minimum of flame thickness

happens at an equivalence ratio of 1.2. It means that around equivalence ratio of 1.2, the flame is

very vulnerable to hydrodynamic instability through the reduction of flame thickness. The laminar

burning speed inceases from 66.8 cm/s to 267.2 cm/s as the temperature increases from 400 to 800

K at an equivalence ratio of 1.1.

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.510

-4

10-3

10-2

10-1

100

101

102

1000/T (1/K)

Ign

itio

n d

ela

y tim

e (

ms)

= 0.6

= 1.0

= 1.4

P = 100 atm

228

Figure 10.8. Theoretical laminar burning speed and flame thickness for a wide range of equivalence

rations and different temperatures of 400, 500, 600, 700 and 800 K at pressure of 1 atm using Ranzi et al.

[261] mechanism for GTL/air mixture

Effect of pressure on laminar burning speed and flame thickness is shown in Figure 10.9. As it

is shown, pressure has a negative relationship with both laminar burning speed and flame

thickness. As the pressure increases both laminar burning speed and flame thickness decrease. For

example, the laminar burning speed and flame thickness decrease from 112.8 to 53.8 cm/s and

0.28 to 0.028 mm, respectively as the pressure increases from 1 to 25 atm at an equivalence ratio

of 1.1. However, the rate of reduction of laminar burning speed and flame thickness become slower

as pressure increases.

0

50

100

150

200

250

300

La

min

ar

bu

rnin

g s

pe

ed

(cm

/s)

Equivalence ratio

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0.2

0.3

0.4

0.5

Fla

me

th

ickn

ess (

mm

)

T = 400 K

T = 500 K

T = 600 K

T = 700 K

T = 800 K

229

Figure 10.9. Theoretical laminar burning speed and flame thickness for a wide range of equivalence ratios

and different pressures of 1, 5, 10, 15, 20 and 25 atm at temperature of 533 K using Ranzi et al. [261]

mechanism for GTL/air mixture

0

25

50

75

100

125

La

min

ar

bu

rnin

g s

pe

ed

(cm

/s)

Equivalence ratio

0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

0.1

0.2

0.3

0.4

Fla

me

th

ickn

ess (

mm

)

P = 1 atm

P = 5 atm

P = 10 atm

P = 15 atm

P = 20 atm

P = 25 atm

230

11. Recommendations for Future Work, Summary

and Conclusions

231

Some recommendations for future work are:

The data analysis is currently executed in two major steps. One step involves a Fortran

subroutine in order to solve the conservation equations. The second step involves analyzing

the output of the first step which is essentially the mass fraction burned into LBS, or MBR,

this is typically done in Matlab. A better approach would be using Matlab to eliminate the first

step and achieve the final result in a very convenient format.

A higher temperature pressure transducer will enable higher initial temperature up to 325C (~

600K) using a Kalrez O-ring to seal the vessel.

A more extreme improvement to the facility would be a computer controlled filling system

using microprocessor controlled solenoid valves in the filling manifold.

More study on auto-ignition in spherical vessel is needed by running several experiments with

different initial pressure, temperature, equivalence ratio and the rate of pressure increase in the

vessel to learn about the characteristics of GTL auto-ignition. Using a thicker glass in

cylindrical vessel can be helpful to increase the limit of high pressure in this vessel with the

goal of observing auto-ignition to study this phenomenon.

Using the plasma simulation in conjunction with flame propagations images to find the laminar

burning speed in a region close to spark location especially at high pressure conditions.

Apply optical-thick radiation model to the code which can be used for heavy liquid

hydrocarbon.

The summary of this dissertation is described based on each individual chapter (paper) in following

sections.

11.1. Chapter 2

In this study, a visualization experimental system was designed and constructed to investigate

spray and lean burn methane direct-injection combustion by using a constant volume vessel. The

main conclusions are summarized as follows:

232

It was found that spray tip penetration was significantly affected by the injection pressure.

Under relatively higher chamber pressure conditions, the injected methane spray penetrated

at a very low rate in both the axial and radial directions.

A smooth flame front propagates in the case of homogeneous mixture combustion while a

wrinkled flame front is demonstrated in the case of direct injection turbulent combustion.

The rate of pressure rise of lean burn methane decreases with increasing of spark delay

timing while it increases with increasing of stratification ratio.

Fuel direct injection turbulent combustion results in higher peak pressure and maximum

rate of pressure rise, shorter initial combustion duration, and shorter main combustion

duration compared with homogeneous mixture combustion.

11.2. Chapter 3

In this study, a visualization experimental system was designed and constructed to investigate

the lean burn methane direct-injection combustion by using a constant volume vessel under

different characteristic parameters. The main conclusions are summarized as follows:

Injection pressure does not have a strong effect on peak pressure and maximum rate of

pressure rise but can change the initial combustion duration in lean mixtures and short

delay time conditions.

Increasing chamber temperature and chamber pressure lead to increasing peak pressure and

maximum rate of pressure rise but the effect of the chamber pressure is more significant

than that of the chamber temperature. The main combustion duration is decreased with

increasing chamber temperature and also is increased with increasing chamber pressure.

The sensitivity of the methane/hydrogen fuel mixture to the variation in turbulence

intensity was decreased with increasing the hydrogen addition.

The lean burn limit of methane can be extended by increasing the hydrogen fraction.

Diluent addition leads to reduced peak pressure and initiates combustion instability.

Combustion instability will be initiated earlier at small spark delay times due to high

turbulence intensity

233

11.3. Chapter 4

Thermo-physical properties such as laminar burning speed (LBS) and minimum ignition energy

(MIE) of hydrocarbon and refrigerants were reviewed. A fundamental model for ignition including

energy input (ignition energy), plasma, energy release, energy transfer and propagating flame has

been briefly described. A simple model showing minimum ignition energy to be inversely

proportional to cubic root of laminar burning speed has been cited. Two correlations have been

developed for laminar burning speed as a function of minimum ignition energy. The first

correlation fits the data to a functional form suggested by theoretical analysis, i.e. 𝑆𝑙 = 𝑎𝑀𝐼𝐸−1 3⁄ ,

and the second correlation relaxes that constraint and fits the data to a more general form, i.e.

𝑆𝑙 = 𝑏𝑀𝐼𝐸𝑐. The following conclusions were drawn:

There are significant discrepancies in the measured values of minimum ignition energy.

Laminar burning speed of low speed refrigerants have not been documented well.

Based on this analysis, it is recommended that minimum ignition energy of HFC-152a be

measured carefully since it is not consistent with other refrigerants.

For all practical purposes, both correlations have the same accuracy.

Both correlations demonstrate very accurate predictions for low burning speeds (Sl < 10

cm/sec) and high minimum ignition energies. The accuracy of the correlations for slow

burning fuels and refrigerants are however bound by the accuracy of the experimental data,

LBS and MIE.

In the absence of additional data, these correlations can be used to estimate laminar burning

speed of refrigerant once minimum ignition energies have been measure. The errors are about

15%

11.4. Chapter 5

A comprehensive model has been developed to calculate thermodynamic properties of

hydrogen/air and methane/air plasma up to 100,000 K for a wide range of pressures and fuel/air

equivalence ratios. The model is based on statistical thermodynamics and complete chemical

equilibrium of all species. For both hydrogen/air and methane/air plasma mixtures the model

234

considers 133 species. Properties such as enthalpy, entropy, Gibbs free energy, specific heat at

constant pressure, specific heat ratio, speed of sound, mean molar mass, and degree of ionization

have been calculated. The results have been compared to available experimental data and the

agreement is excellent. For each mixture and fuel/air equivalence ratio considered, the properties

have been summarized in the form of curve-fitted correlations as suitably defined functions of

temperature, pressure and equivalence ratio. In addition, the results have also allowed the

following conclusions relevant for other existing state-of-the-art models of thermodynamic

properties:

Considering just the ground state or fixing the number of energy levels independently of the

temperature and the pressure produces very large errors in the estimates especially for

second order properties at high temperature conditions. In particular, the accuracy of the

ground state method accuracy decreases with increasing the pressure and temperature.

Transition from partially ionized gas (𝛬 < 1) to fully ionized gas (𝛬 = 1) takes place at

relatively low temperatures.

The speed of sound is higher at low pressures, leading to higher Mach numbers at low

pressures for each given temperature.

11.5. Chapter 6

Laminar burning speeds of different mixtures of H2/CO and air for a wide range of equivalence

ratios (0.6-5) have been measured by the pressure rise during spherical flame propagations using

a new differential-based model. Burning speed measurements covered a wide range of

temperatures and pressures up to 670 K and 5.5 atm, respectively. The laminar burning speeds of

H2/CO/air flames decrease with the increase of initial pressure. When the initial pressure increases,

the tendency for the flame to destabilize takes place earlier due to a significant decrease of the

flame thickness and enhancement of hydrodynamic instability. Laminar burning speeds of syngas

mixtures increase with an increasing hydrogen concentration in the fuel. The onset of cell

formation in spherically expanding flames for all test conditions has been identified. Increasing

hydrogen concentration causes the flame to become cellular at lower pressures. Power law

correlations have been developed for laminar burning speeds of H2/CO/air mixtures at different

235

hydrogen concentration. Measured laminar burning speed data agreed well with available

experimental data in literature at standard ambient temperature and pressure.

11.6. Chapter 7

Laminar burning speed of syngas that has been diluted with synthetic EGR has been presented

in this paper using constant volume spherical and cylindrical chambers with a novel burning model

based on the pressure rise due to combustion process. An analysis shows that the stretch effects on

laminar burning speed are minimum for flames with radii larger than 4 cm and stretch rate of less

than 90 s-1. The stability of propagating flames has been analyzed using several key parameters,

including the Lewis number, flame thickness, and Peclet number. Increasing SEGR concentration

has a stabilizing effect on flames due to the combination effect of hydrodynamic and diffusive-

thermal instability and tends to decrease the laminar burning speed. Carbon dioxide behaves as an

inhibitor due to the competition of the reaction of R1: H+O2 O+OH and R12: H+O2(+M)

HO2(+M) on H radical. Laminar burning speeds of H2/CO/air/SEGR mixture increase with the

increase of hydrogen fraction which also promote the cellular flame structure. A power law fit

correlation has been developed for hydrogen concentrations of 5, 10 and 25% over equivalence

ratios of 0.6 to 3.0 and SEGR concentrations of 0 to 10% for smooth flames only. Flame critical

pressures and its corresponding temperatures can be determined using Table 6-1 and Table 7-2 for

SEGR percentages of 5 and 10%. Laminar burning speed results agree with the available data in

the literature.

11.7. Chapter 8

In this study, mass burning rate and cellular burning speed of syngas/O2/He were calculated for

a wide range of equivalence ration from 0.6 to 2, temperature from 400 to 750 K and pressure from

2 to 50 atm using a new differential-based multi-shell model based on pressure rise. The structure

and effect of thermo-diffusive and hydrodynamic instabilities were studied at very high pressures

at which the flame was always cellular. The power law correlations were also developed as a

function of equivalence ratio, temperature and pressure for cellular burning speed and mass

burning rate. The effect of cell formation on burning speed and total flame front area were

investigated in terms of a newly developed parameter called cellularity factor. In addition to a

236

complete experimental data, the theoretical laminar burning speeds via a steady, one-dimensional

free flame code in conjunction with detailed chemical mechanism were also used to calculate the

cellularity factor. The results showed that the cellularity factor has a positive relation to pressure,

equivalence ratio and hydrogen concentration while it has a negative dependency to temperature.

Cellular burning speed and mass burning rate have both positive relation to temperature, pressure,

equivalence ratio and hydrogen concentration. Pressure increase at a given temperature doesn’t

have significant effect on laminar flame area while it increase the total flame area. Reduction in

hydrogen concentration makes the flame stable and delays the onset of cell formation.

11.8. Chapter 9

In this study, the onset of auto-ignition of GTL fuel was measured for a wide range of

equivalence ratios from 0.8 to 1.2 and initial pressure of 8.6, 10 and 12 atm at initial temperature

of 450 K using aggressive oscillation of pressure data during the spontaneous combustion process

throughout the unburned mixture. The experiments were done in a high pressure and temperature

spherical chamber and pressure rise due to combustion was collected using high-speed pressure

transducer and data acquisition systems. Several detailed kinetics mechanisms have been

compared for ignition delay time calculations and it was found that Ranzi et al. mechanism [261]

is a better agreement with available experimental results in literature. It was shown that at low

unburned gas temperatures both temperature and pressure have a negative dependency on the

ignition delay time and auto-ignition characteristics are also a strong function of the unburned gas

temperature.

11.9. Chapter 10

In this study, the ignition and laminar burning speed characteristics of GTL fuel were predicted

by developing a detailed kinetics model (DKM) from the existing mechanisms for the GTL fuel.

A mixture of 32% iso-octane, 25% n-decane, and 43% n-dodecane, was used as the surrogate fuel

to mimic the chemical composition of the GTL jet fuel (S-8) from Synroleum Corporation.

Different chemical kinetic mechanisms reported in the literature were tested over a wide range of

operating conditions. Among them, the Ranzi et al chemical mechanism was found to have a better

agreement with the experimental data. Therefore, in this study, the laminar burning speed and

237

ignition delay time were investigated using CANTERA and DKM respectively using Ranzi’s

mechanism. The key highlights of the predictions are,

Starting from low temperature, the ignition delay time for GTL first decreases as the initial

temperature increases for low temperature (T < 800K), then increases at intermediate

temperature (800 ~ 1000 K) and finally decreases again for high temperature range (T >

1000K). Higher pressure increases the ignition propensity.

A shift in trends for different equivalence ratio is observed for GTL auto-ignition. If initial

temperature is lower than the shifting temperature, higher equivalence ratio decrease the

ignition delay time. After temperature passed the shifting point ignition delay time increases

as equivalence ration increases.

The laminar burning speed reaches its maximum value at equivalence ratio equal to 1.1. The

highest laminar burning speed of GTL increases from 66.8 cm/s to 267.2 cm/s as the

temperature increases from 400 to 800 K.

The minimum of flame thickness happens at equivalence ration of 1.2, where the flame is

very vulnerable to hydrodynamic instability because of the reduction in flame thickness.

Initial pressure has a negative effect on the laminar burning speed. The laminar burning

speed drops from 112.8 cm/s to 53.8 cm/s as the pressure increases from 1 to 25 atm.

238

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239

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266

13. Appendix

267

Fitting coefficients for hydrogen-air and methane-air plasma mixtures

In this supplementary material we present the coefficients to calculate frozen and equilibrium

specific heat at constant pressure, specific enthalpy, specific entropy, and mean molar mass,

according to Eqs. (5-43), (5-44), (5-45), (5-46) and (5-48), respectively, for hydrogen-air and

methane-air plasma mixtures. For our calculations and correlations, we assumed the following

molar composition of air (no water vapor): 𝑥N2

a = 0.78084, 𝑥O2

a = 0.20946, 𝑥H2Oa = 0, 𝑥Ar

a =

0.009335, 𝑥CO2

a = 0.0003398, 𝑥Nea = 0.00001818, 𝑥He

a = 0.00000702. Table A1 gives the

corresponding values of the 𝑞𝑗 's that we considered, as functions of the equivalence ratio 𝜙. Tables

A2 and A3 show the fitting coefficients of hydrogen/air and methane/air plasma mixture,

respectively.

Table A1- Values of the 𝑞𝑗 's as a function of the equivalence ratio 𝜙

Elemental atom

numbers CkHl /air mixture

H2/air mixture

(𝑘 = 0, ℓ = 2)

CH4/air mixture

(𝑘 = 1, ℓ = 4)

𝑞N 1

𝜙(𝑘 +

ℓ

4)2𝑥N2

a

𝑥O2a

0.78084

0.20946𝜙

4 × 0.78084

0.20946𝜙

𝑞O 1

𝜙(𝑘 +

ℓ

4) (2 +

𝑥H2Oa

𝑥O2a +

2𝑥CO2a

𝑥O2a )

1

𝜙+0.0003398

0.20946𝜙

4

𝜙+4 × 0.0003398

0.20946𝜙

𝑞C 𝑘 +1

𝜙(𝑘 +

ℓ

4)𝑥CO2

a

𝑥O2a

0.5 × 0.0003398

0.20946𝜙 1 +

2 × 0.0003398

0.20946𝜙

𝑞H ℓ +1

𝜙(𝑘 +

ℓ

4)2𝑥H2O

a

𝑥O2a 2 4

𝑞Ar 1

𝜙(𝑘 +

ℓ

4)𝑥Ar

a

𝑥O2a

0.5 × 0.009335

0.20946𝜙

2 × 0.009335

0.20946𝜙

𝑞Ne 1

𝜙(𝑘 +

ℓ

4)𝑥Ne

a

𝑥O2a

0.5 × 0.00001818

0.20946𝜙

2 × 0.00001818

0.20946𝜙

𝑞He 1

𝜙(𝑘 +

ℓ

4)𝑥He

a

𝑥O2a

0.5 × 0.00000702

0.20946𝜙

2 × 0.00000702

0.20946𝜙

Table A2 – H2/air plasma

𝒄𝒑,𝐨𝐟𝐟(𝒌𝑱/𝒌𝒈𝑲), 𝒄𝒑,𝐞𝐪(𝒌𝑱/𝒌𝒈𝑲), 𝒉 (𝒌𝑱/𝒌𝒈), 𝒔 (𝒌𝑱/𝒌𝒈𝑲)

𝝃𝟎𝟎 𝝃𝟏𝟎 𝝃𝟎𝟏 𝝃𝟐𝟎 𝝃𝟏𝟏 𝝃𝟎𝟐 𝝃30 𝝃21 𝝃12 𝝃03 𝝃40 𝝃31 𝝃𝟐2 𝝃𝟏3

𝒂𝟏𝐨𝐟𝐟 0.325766 0.295999 -0.010454 0.17606 0.016251 0.000125 -7.51E-02 -0.004551 -0.000141 2.02E-06 0.007738 3.92E-04 1.55E-06 6.11E-07

𝒂𝟐𝐨𝐟𝐟 -0.356532 0.20411 -0.014564 -0.321786 0.053117 -0.009868 0.087119 -0.021719 0.004184 -0.00035 -0.006685 2.42E-03 -1.63E-04 1.05E-04

𝒂𝟑𝐨𝐟𝐟 0.149062 0.482639 0.01784 -0.141731 -0.005376 0.004729 0.031576 0.002638 -0.001093 0.000193 -2.84E-03 -2.99E-04 3.68E-05 -4.42E-05

𝒂𝟒𝐨𝐟𝐟 0.492105 -0.027053 0.009439 -0.07043 -0.016436 3.66E-04 0.02252 0.001266 -0.001508 4.44E-05 -2.13E-03 -6.75E-05 3.66E-05 -5.54E-05

𝒂𝟓𝐨𝐟𝐟 0.495306 0.046521 -0.027897 -0.065072 0.005746 -1.37E-04 0.017576 -0.000864 9.96E-04 2.38E-05 -0.001632 -4.31E-05 -7.25E-05 3.74E-05

𝒂𝟔𝐨𝐟𝐟 -0.246024 0.260661 -0.111618 -0.240513 0.032134 -0.019551 0.072196 0.000282 5.70E-03 -0.000876 -6.88E-03 -2.39E-04 -1.77E-04 2.08E-04

𝒂𝟕𝐨𝐟𝐟 -0.052569 0.500379 0.008356 -0.295294 0.039514 -0.000679 0.058712 -0.015687 0.000776 -6.94E-05 -4.01E-03 1.57E-03 -0.000109 2.49E-05

𝒂𝟖𝐨𝐟𝐟 -1.316139 -0.63594 0.002881 0.208148 -0.047142 -0.005715 -0.021114 0.0235 0.003315 -0.000247 -0.000488 -2.87E-03 -4.53E-05 1.69E-04

𝒃𝟏𝐨𝐟𝐟 5.723293 1.02107 -0.002698 -0.511197 0.005373 -4.85E-05 0.109718 -0.00247 0.000164 6.60E-06 -0.008195 3.12E-04 -5.76E-05 -4.07E-06

𝒃𝟐𝐨𝐟𝐟 8.952488 -0.065389 0.038513 0.044519 0.007632 -0.001154 -0.013942 -0.005278 0.002049 -7.46E-05 1.74E-03 7.08E-04 -1.66E-04 7.60E-05

𝒃𝟑𝐨𝐟𝐟 9.591297 0.005342 0.060889 -0.004212 -0.000505 -8.48E-05 0.00092 -0.000135 1.79E-05 -5.08E-05 -5.58E-05 2.63E-05 4.00E-06 4.05E-06

𝒃𝟒𝐨𝐟𝐟 10.31002 -0.003176 0.061256 0.00335 0.000614 0.000559 -0.000694 1.23E-04 6.00E-05 -1.52E-05 5.39E-05 -7.52E-06 2.53E-06 1.05E-06

𝒃𝟓𝐨𝐟𝐟 10.75484 -0.004941 0.066266 -0.00014 -0.000329 0.001644 0.000297 1.07E-04 3.33E-05 2.87E-05 -3.99E-05 -1.43E-05 -1.69E-06 1.81E-06

𝒃𝟔𝐨𝐟𝐟 11.09656 0.005438 0.054597 -0.00577 0.002364 0.000248 0.001791 -0.00011 3.96E-04 -2.90E-05 -1.80E-04 -1.59E-05 -1.85E-05 1.46E-05

𝒃𝟕𝐨𝐟𝐟 11.33268 0.059837 0.043133 -0.035995 0.00807 -0.001844 0.008301 -0.001454 8.33E-04 -0.000124 -6.66E-04 1.10E-04 -3.54E-05 3.12E-05

𝒃𝟖𝐨𝐟𝐟 11.03422 1.089476 -0.009898 -0.513685 0.109938 0.001625 0.083932 -0.041693 1.03E-03 0.000145 -0.004116 4.20E-03 -3.60E-04 -3.94E-05

𝒄𝟏𝐨𝐟𝐟 0.124054 0.840514 0.040843 -1.210174 -0.072285 -5.72E-05 0.385634 0.019032 0.000658 5.78E-06 -3.67E-02 -1.57E-03 -3.99E-05 1.01E-06

𝒄𝟐𝐨𝐟𝐟 2.271393 -0.172845 -0.019733 0.074026 0.032179 -0.003477 -0.021718 -0.009678 0.00277 -0.00016 0.001756 4.71E-04 -1.35E-04 8.93E-05

𝒄𝟑𝐨𝐟𝐟 2.48469 -0.032591 -0.045116 0.046243 -0.00277 -0.006517 -0.01555 -0.000701 0.000415 -0.000372 1.63E-03 1.44E-04 -1.90E-05 2.07E-05

𝒄𝟒𝐨𝐟𝐟 2.601802 0.023603 -0.043885 0.047296 0.010316 -0.003402 -0.016312 -0.001063 7.96E-04 -1.53E-04 1.57E-03 8.14E-05 -9.97E-06 3.36E-05

𝒄𝟓𝐨𝐟𝐟 2.593675 -0.043896 -0.053577 0.029797 -0.008094 -0.000805 -0.006784 0.001325 -0.001015 5.52E-05 0.000612 1.13E-05 7.98E-05 -3.51E-05

𝒄𝟔𝐨𝐟𝐟 2.82907 0.023139 -0.028702 0.007746 -0.004316 0.003463 -0.007304 -0.002063 -1.31E-03 0.000248 0.000934 2.58E-04 3.88E-05 -3.72E-05

𝒄𝟕𝐨𝐟𝐟 2.617703 0.025931 -0.032416 -0.096552 -0.031419 -0.001768 0.042323 0.012062 -0.000329 -5.35E-05 -4.70E-03 -9.89E-04 0.000225 3.05E-05

𝒄𝟖𝐨𝐟𝐟 2.679309 0.188426 -0.078739 -0.038423 0.023823 -0.003399 -0.007311 -0.009759 0.001192 -8.77E-05 0.001749 0.001131 -5.83E-06 8.23E-05

𝒂𝟏𝐞𝐪

1.258564 1.515934 -0.133356 -0.585117 -0.005996 -0.00369 1.15E-01 0.001849 4.65E-05 -5.48E-05 -8.53E-03 -1.75E-04 -2.57E-05 -6.61E-06

𝒂𝟐𝐞𝐪

2.495274 -0.006412 -0.101442 -0.001124 0.003565 -0.001871 -0.00025 -0.000344 0.000359 -2.60E-05 7.38E-05 5.31E-05 9.25E-07 1.44E-05

𝒂𝟑𝐞𝐪

2.92697 0.351267 -0.135045 -0.065859 0.001769 -0.004247 0.009786 -0.001006 0.000225 -1.01E-04 -6.42E-04 1.15E-04 -5.05E-05 2.72E-06

𝒂𝟒𝐞𝐪

3.23209 0.015997 -0.105329 -0.018725 0.002379 -0.003153 0.003897 -0.000443 0.000244 -7.84E-05 -2.79E-04 3.82E-05 -2.06E-05 5.12E-06

𝒂𝟓𝐞𝐪

3.412773 -0.011158 -0.09399 -0.004827 0.002356 -2.24E-03 0.000617 -0.000623 1.46E-04 -3.84E-05 -1.19E-05 3.66E-05 -3.67E-05 -2.98E-06

𝒂𝟔𝐞𝐪

3.506561 0.018226 -0.102517 -0.02345 0.006194 -0.002934 4.86E-03 -0.001432 6.05E-04 -7.96E-05 -3.46E-04 1.08E-04 -5.72E-05 1.65E-05

𝒂𝟕𝐞𝐪

3.506037 0.000662 -0.097295 -0.017872 0.00285 -0.002919 0.004808 -0.000183 6.17E-04 -7.51E-05 -4.27E-04 8.78E-06 -3.07E-05 2.47E-05

𝒂𝟖𝐞𝐪

2.14331 -0.000928 -0.119999 -0.005795 0.002536 -0.005078 1.39E-03 0.000209 2.93E-05 -1.36E-04 -0.000108 -2.71E-05 -4.82E-06 -1.16E-05

𝒃𝟏𝐞𝐪

8.185678 0.002758 0.05985 0.014419 0.001688 0.001762 -4.70E-03 -7.83E-05 5.58E-05 4.30E-05 4.34E-04 -1.54E-05 -9.05E-06 -1.08E-06

𝒃𝟐𝐞𝐪

8.869649 -0.029608 0.058091 0.005957 -0.001627 0.001486 -8.59E-04 0.000281 -8.09E-05 3.46E-05 5.13E-05 -3.39E-05 -6.57E-06 -6.29E-06

𝒃𝟑𝐞𝐪

9.604007 0.009 0.072687 -0.002042 0.00139 0.002126 0.000147 -0.000341 3.96E-05 5.06E-05 4.92E-06 1.75E-05 -1.67E-05 -2.44E-06

𝒃𝟒𝐞𝐪

10.31207 -0.010974 0.070462 0.005786 -0.00021 0.001827 -0.00126 3.72E-05 -2.44E-05 3.44E-05 9.09E-05 -7.28E-06 1.50E-06 3.19E-08

𝒃𝟓𝐞𝐪

10.76373 -6.69E-03 0.06755 0.003914 0.000246 0.001925 -1.20E-03 -2.92E-04 -7.93E-05 4.45E-05 1.22E-04 3.83E-05 4.07E-06 -2.29E-06

𝒃𝟔𝐞𝐪

11.08908 0.010521 0.064075 -0.005576 0.002253 0.001883 0.000692 -0.000794 7.33E-05 4.34E-05 -2.40E-06 8.67E-05 -4.31E-06 2.28E-06

𝒃𝟕𝐞𝐪

11.35902 -0.003179 0.0643 0.000868 0.000499 0.001791 -1.99E-04 -0.000105 3.21E-05 4.11E-05 1.58E-05 1.03E-05 9.71E-07 1.59E-06

𝒃𝟖𝐞𝐪

11.71941 -0.000954 0.100886 -0.001549 2.59E-04 0.00645 7.09E-04 2.13E-05 5.01E-05 2.10E-04 -7.91E-05 -6.90E-06 -7.80E-06 -6.52E-07

𝒄𝟏𝐞𝐪

-1.39116 -0.143516 0.094047 0.009853 -0.010312 0.001449 0.004833 0.000999 -0.000667 -5.16E-05 -6.10E-04 -3.78E-05 4.79E-05 -8.85E-06

𝒄𝟐𝐞𝐪

-1.596411 -0.187092 0.054767 0.141901 -0.007228 -0.001475 -0.037177 0.004669 0.000588 -0.000139 3.23E-03 -5.96E-04 5.60E-06 4.05E-05

𝒄𝟑𝐞𝐪

-1.547451 0.066859 0.063709 -0.025208 0.007269 0.002743 0.004076 -0.002569 -0.000272 9.58E-05 -2.28E-04 2.57E-04 1.90E-05 -1.54E-05

𝒄𝟒𝐞𝐪

-1.736177 -0.04716 0.047029 0.017783 -0.016571 0.001021 -0.002458 0.004972 -0.000898 -7.14E-06 6.98E-05 -4.15E-04 1.60E-04 -1.63E-06

𝒄𝟓𝐞𝐪

-1.878835 0.080386 0.044049 -0.038666 0.005369 0.002548 0.006026 -0.002326 -0.000166 9.20E-05 -2.34E-04 2.80E-04 1.95E-05 -5.85E-06

𝒄𝟔𝐞𝐪

-1.965198 -0.013076 0.034078 0.006134 0.002581 -0.000673 -0.000811 -9.27E-05 3.39E-04 -5.09E-05 7.59E-06 1.78E-05 2.91E-05 2.19E-05

𝒄𝟕𝐞𝐪

-2.131654 0.394373 -0.001909 -0.264532 0.01199 -0.003503 0.066224 -0.005314 -4.40E-05 -0.000177 -0.005564 6.30E-04 7.24E-06 -3.33E-07

𝒄𝟖𝐞𝐪

-1.65582 -0.068852 0.082272 0.020623 -0.001633 4.78E-04 -0.001202 0.0018 7.33E-04 -0.000106 -1.01E-04 -2.24E-04 -4.79E-05 2.43E-05

𝝀𝟏 1136593 162278.7 4919.263 -110923.4 8700.356 -739.1671 27501.84 -2420.642 563.6006 -58.36081 -2283.962 270.0947 -15.16192 22.36501

𝝀𝟐 -55.03018 -0.340312 -1.206588 -4.652112 -1.127481 0.090793 1.5362 0.172984 -0.055993 0.003532 -0.148127 -0.010352 0.003772 -0.001654

269

𝑴𝒕(𝒌𝒈/𝒌𝒎𝒐𝒍)

𝝃𝟎𝟎 𝝃𝟏𝟎 𝝃𝟎𝟏 𝝃𝟐𝟎 𝝃𝟏𝟏 𝝃𝟎𝟐 𝝃30 𝝃21 𝝃12 𝝃03 𝝃40 𝝃31 𝝃𝟐2 𝝃𝟏3

𝒂𝟐𝐌 2.266963 -1.096096 -0.00123 0.274652 0.000149 -0.000236 -0.049081 0.000282 0.000132 -8.47E-06 0.003594 -6.94E-05 -1.16E-05 5.00E-06

𝒂𝟑𝐌 1.952006 -0.361525 -0.000424 0.058866 0.000428 1.37E-05 -0.007083 -0.000103 -8.02E-06 4.53E-07 3.93E-04 8.17E-06 -8.19E-07 -8.75E-07

𝒂𝟒𝐌 0.860893 -0.665758 -0.001402 0.100323 -0.001688 -4.65E-05 -0.012112 0.000394 1.11E-05 -6.33E-07 6.88E-04 -1.66E-05 1.54E-05 5.34E-06

𝒂𝟓𝐌 0.223394 -0.453833 0.004065 0.051948 0.000174 1.46E-04 -0.005189 -5.49E-05 2.46E-06 -4.52E-06 0.00026 3.92E-06 -7.20E-07 1.74E-07

𝒂𝟔𝐌 -0.348842 -0.356119 0.003212 0.036125 -0.000909 0.000266 -0.003732 0.000157 -5.25E-05 7.32E-06 2.11E-04 -5.94E-06 8.96E-06 2.05E-07

𝒂𝟕𝐌 -0.638468 -0.255556 0.000653 0.007127 0.001264 -0.000129 0.001732 -0.00061 -1.02E-05 -8.16E-06 -1.75E-04 8.45E-05 2.33E-06 -4.67E-07

𝒂𝟖𝐌 -2.52645 -0.153855 -0.005414 -0.021514 0.007352 -0.000151 0.004023 -0.002828 1.26E-05 -1.37E-05 -6.67E-05 3.33E-04 4.95E-06 2.77E-07

𝒃𝟏𝐌 8.195886 -0.093007 0.060415 0.073774 2.14E-05 0.00176 -0.019171 0.000454 2.97E-05 3.99E-05 0.00163 -6.28E-05 7.70E-07 7.93E-07

𝒃𝟐𝐌 8.823667 0.004928 0.057076 -0.010969 -0.000867 0.001424 0.00319 3.94E-05 -6.04E-05 2.70E-05 -2.85E-04 3.19E-06 1.84E-06 -1.82E-06

𝒃𝟑𝐌 9.543688 0.007416 0.071456 -0.001467 0.000837 0.002073 0.000139 -0.000143 1.26E-05 4.41E-05 -3.76E-06 9.93E-06 -1.08E-06 3.43E-08

𝒃𝟒𝐌 10.29095 0.006853 0.068933 -0.001976 5.13E-05 0.00178 0.000386 1.07E-05 -4.35E-06 3.41E-05 -3.05E-05 -1.12E-06 5.31E-07 -2.14E-07

𝒃𝟓𝐌 10.74839 -0.001804 0.064935 0.000328 -0.000475 0.001479 3.66E-05 1.32E-04 -9.45E-06 2.44E-05 -9.88E-06 -8.94E-06 3.74E-06 6.27E-07

𝒃𝟔𝐌 11.08649 -0.001236 0.062025 0.000507 0.000623 0.001417 -0.000169 -0.000108 6.86E-05 2.29E-05 1.46E-05 7.81E-07 -7.16E-06 1.70E-06

𝒃𝟕𝐌 11.38418 -0.042498 0.072513 0.017401 -0.009966 0.002303 -0.002689 0.00227 -6.96E-04 4.41E-05 1.42E-04 -1.34E-04 8.13E-05 -1.28E-05

𝒃𝟖𝐌 11.67614 -0.107179 0.067361 0.050281 -0.012522 0.002773 -0.009217 0.003612 -4.74E-04 0.000103 0.000578 -3.14E-04 5.95E-05 -5.90E-06

𝒄𝟏𝐌 2.474094 -0.375539 -0.073192 0.316855 -0.003339 -0.001935 -0.088337 0.002056 4.14E-05 -2.63E-05 7.90E-03 -2.46E-04 -5.79E-06 -6.65E-07

𝒄𝟐𝐌 2.455022 0.080699 -0.048362 -0.068114 0.000985 -0.000758 0.018978 -0.000135 4.51E-05 -8.30E-06 -0.001707 8.17E-06 -8.60E-06 -1.34E-06

𝒄𝟑𝐌 2.301124 -0.035348 -0.066133 0.011457 -0.000816 -0.001908 -0.001977 0.000224 1.39E-05 -3.94E-05 1.33E-04 -2.00E-05 6.87E-07 1.28E-06

𝒄𝟒𝐌 2.595419 0.032911 -0.048502 -0.00837 0.001987 -0.001769 0.001646 -0.000276 1.13E-04 -4.01E-05 -1.31E-04 1.56E-05 -5.02E-06 4.55E-06

𝒄𝟓𝐌 2.611683 0.00722 -0.047775 -0.007095 -0.002323 -1.15E-03 0.002062 0.000398 -0.000167 -7.77E-06 -0.000172 1.46E-05 3.49E-05 6.33E-07

𝒄𝟔𝐌 2.703058 0.027752 -0.052293 -0.025826 -0.007296 -0.00201 0.007507 0.000979 -6.81E-04 -8.67E-05 -0.000656 4.40E-05 9.27E-05 -8.63E-06

𝒄𝟕𝐌 2.646768 -0.070787 -0.059517 0.0409 -0.00632 -0.005176 -0.009092 0.00191 -0.000245 -0.000216 6.85E-04 -1.89E-04 2.53E-05 -3.52E-06

𝒄𝟖𝐌 2.672429 0.133919 -0.069491 -0.019029 0.03175 -0.001516 -0.0143 -0.014129 0.000213 -1.69E-05 0.002694 0.001664 -3.16E-05 6.88E-06

𝜉00 𝜉10 𝜉01 𝜉20 𝜉11 𝜉02 𝜉30 𝜉21 𝜉12 𝜉40 𝜉31 𝜉22 𝜉50 𝜉41 𝜉32

𝒂𝟏𝐌 1.368591 2.493734 -0.002591 -2.266136 0.006045 -3.62E-05 0.86761 -0.004278 4.14E-05 -0.153462 0.001101 -2.28E-05 0.010227 -9.39E-05 2.96E-06

𝝀𝟑 24.93836 9.344645 -0.000745 -14.97752 0.001263 -6.51E-05 6.456078 -7.67E-05 0.000129 -1.197114 -0.000104 -4.37E-05 0.081749 1.55E-05 4.21E-06

270

Table A3 – CH4/air plasma

𝒄𝒑,𝐨𝐟𝐟(𝒌𝑱/𝒌𝒈𝑲), 𝒄𝒑,𝐞𝐪(𝒌𝑱/𝒌𝒈𝑲), 𝒉 (𝒌𝑱/𝒌𝒈), 𝒔 (𝒌𝑱/𝒌𝒈𝑲) 𝜉00 𝜉10 𝜉01 𝜉20 𝜉11 𝜉02 𝜉21 𝜉12 𝜉03 𝜉22 𝜉13 𝜉04 𝜉23 𝜉14 𝜉05

𝒂𝟏𝐨𝐟𝐟 0.497235 -0.010146 0.006146 0.132319 -0.004705 -0.004655 -1.32E-04 0.003779 -0.000401 -0.002773 0.000293 -7.41E-06 -0.000171 4.80E-06 2.97E-08

𝒂𝟐𝐨𝐟𝐟 -0.492009 0.063951 0.024955 -0.078895 0.003734 -0.00132 -0.002522 0.005689 -0.000704 -0.001277 -0.000208 -4.84E-05 1.82E-05 -2.40E-05 1.58E-08

𝒂𝟑𝐨𝐟𝐟 0.136237 0.30128 0.001404 -0.062065 0.013145 0.004856 -0.00231 -0.003133 0.000619 0.001107 -1.73E-04 2.66E-05 4.72E-05 -1.79E-06 9.90E-09

𝒂𝟒𝐨𝐟𝐟 0.47622 0.009606 0.000554 -0.020947 -0.008987 7.70E-05 -0.001349 -0.000732 0.000153 -1.31E-04 1.17E-05 8.17E-06 -5.66E-06 1.79E-06 1.49E-08

𝒂𝟓𝐨𝐟𝐟 0.458757 0.064372 -0.036187 -0.058107 0.024215 -2.26E-04 -0.010297 0.003277 -1.71E-05 -0.000196 0.000329 -4.02E-06 2.24E-05 1.37E-05 4.95E-09

𝒂𝟔𝐨𝐟𝐟 0.042087 -0.479118 -0.001569 0.330713 -0.10352 -0.00276 0.081911 -0.008013 4.78E-05 0.004647 -7.12E-04 1.67E-05 2.07E-05 -3.79E-05 -3.17E-08

𝒂𝟕𝐨𝐟𝐟 -0.271327 1.338115 -0.010471 -0.884048 0.233342 0.004274 -0.168054 0.005653 -0.000159 -0.003721 4.97E-04 -3.69E-05 0.000314 6.16E-05 -3.07E-08

𝒂𝟖𝐨𝐟𝐟 -0.999978 -1.01828 0.045122 0.448092 -0.054759 -0.007118 0.019203 0.014534 -0.000117 -0.008288 0.00084 5.80E-05 -0.000528 -9.81E-06 2.21E-06

𝒃𝟏𝐨𝐟𝐟 4.883268 0.768414 -0.076613 -0.185001 0.068064 0.018553 -0.020469 0.004553 0.002715 -0.008897 -0.000384 1.02E-04 -0.000601 -4.57E-05 7.92E-09

𝒃𝟐𝐨𝐟𝐟 8.911241 -0.007505 0.048443 0.003303 -0.001354 0.000606 -0.000434 0.000603 -0.0002 7.85E-05 -1.69E-04 -1.52E-05 4.24E-05 -7.02E-06 -1.09E-08

𝒃𝟑𝐨𝐟𝐟 9.582611 0.006211 0.061922 -0.003823 -0.002991 0.000358 0.000438 -0.000227 -4.85E-05 1.27E-04 4.07E-05 -1.56E-06 7.02E-06 3.13E-06 -5.94E-09

𝒃𝟒𝐨𝐟𝐟 10.31256 -0.005942 0.06253 0.000768 0.001855 0.000335 -0.000259 8.38E-06 -8.29E-05 -4.33E-05 -3.87E-05 -3.42E-06 -4.93E-07 -2.00E-06 4.95E-09

𝒃𝟓𝐨𝐟𝐟 10.75312 -0.000119 0.067008 -0.002887 -0.002425 0.001812 0.000917 -3.54E-04 3.02E-05 2.64E-04 6.82E-06 -5.10E-07 1.33E-05 1.41E-06 -8.91E-09

𝒃𝟔𝐨𝐟𝐟 11.11139 -0.039429 0.065116 0.022776 -0.013731 0.002108 0.008991 -0.001642 6.94E-05 0.001096 -6.15E-05 1.00E-06 3.98E-05 -2.02E-07 -8.91E-09

𝒃𝟕𝐨𝐟𝐟 11.36593 0.012699 0.057597 -0.010485 0.005624 -0.000397 -0.002071 0.001757 -2.00E-04 -0.000238 1.92E-04 -1.02E-05 -1.17E-05 6.28E-06 -1.34E-07

𝒃𝟖𝐨𝐟𝐟 11.77548 -0.302768 0.09083 0.085835 -0.091709 0.002191 0.024234 -0.005771 -2.15E-05 0.001765 0.000206 1.69E-05 3.23E-05 1.86E-05 1.18E-06

𝒄𝟏𝐨𝐟𝐟 -0.876133 1.031048 -0.060732 -0.620664 0.053666 0.025566 -0.013877 -0.005611 0.002462 0.002339 -5.60E-04 6.32E-05 8.08E-05 -2.37E-05 -2.67E-08

𝒄𝟐𝐨𝐟𝐟 2.425062 -0.144835 -0.026844 0.052425 0.01215 -0.005304 0.002111 -0.007377 0.000853 0.002406 -0.000305 6.90E-05 6.77E-05 1.03E-05 1.68E-08

𝒄𝟑𝐨𝐟𝐟 2.500415 -0.049854 -0.003852 0.024875 -0.007965 -0.008848 0.000644 0.001835 -0.002085 -0.00087 6.60E-05 -9.87E-05 -3.34E-05 -2.23E-07 1.78E-08

𝒄𝟒𝐨𝐟𝐟 2.602944 -0.01988 -0.043329 0.016452 0.015017 -0.002515 -0.000861 0.000504 -7.73E-06 -1.39E-04 -1.79E-04 4.55E-06 -4.68E-06 -1.12E-05 -2.93E-20

𝒄𝟓𝐨𝐟𝐟 2.618781 -0.05165 -0.054351 0.032002 -0.006586 -0.002731 0.001594 -0.001001 -0.000112 -8.64E-04 -0.000215 -2.74E-06 -6.33E-05 -1.25E-05 1.88E-08

𝒄𝟔𝐨𝐟𝐟 2.72428 0.297453 -0.024522 -0.225509 -0.032982 0.004284 0.00253 -0.01505 -3.87E-04 0.009669 -0.000112 -4.88E-05 0.000627 5.25E-05 -8.91E-09

𝒄𝟕𝐨𝐟𝐟 2.680191 -0.391015 -0.126438 0.292187 0.07528 -0.0136 -0.02482 0.01997 0.000791 -0.014036 5.88E-05 1.45E-04 -0.000799 -6.41E-05 3.87E-06

𝒄𝟖𝐨𝐟𝐟 1.407622 3.445276 -0.266793 -1.881354 0.570463 -0.004332 -0.318174 0.011754 -0.000518 -0.004998 -0.000233 -0.000116 0.000618 4.80E-05 -3.57E-06

𝒂𝟏𝐞𝐪

1.170969 1.120215 -0.127371 -0.290187 -0.00863 -0.004768 1.97E-03 0.001474 -1.02E-04 -0.000784 1.44E-04 8.11E-06 -7.37E-05 -2.36E-07 3.77E-07

𝒂𝟐𝐞𝐪

2.497633 -0.04266 -0.102196 0.001199 0.005102 -0.003285 -0.001957 0.002736 -0.000177 -0.001204 0.000256 1.18E-06 -9.81E-05 2.61E-06 2.41E-07

𝒂𝟑𝐞𝐪

2.924353 0.173386 -0.131045 -0.022048 -0.00109 -0.004527 0.000571 0.000517 -0.000182 -3.34E-04 9.14E-05 4.76E-06 -5.03E-05 -5.83E-08 4.25E-07

𝒂𝟒𝐞𝐪

3.23299 0.011512 -0.101949 -0.013172 0.000824 -0.003726 0.000295 0.000233 -0.000272 -3.82E-05 9.75E-05 -8.38E-06 -2.75E-05 2.16E-06 -2.69E-08

𝒂𝟓𝐞𝐪

3.40678 0.007096 -0.090306 -0.009632 0.000805 -1.80E-03 0.000367 -0.000274 -5.18E-05 4.74E-05 -5.80E-07 -6.50E-08 -2.12E-05 -2.04E-06 -4.10E-09

𝒂𝟔𝐞𝐪

3.5286 -0.049264 -0.082688 0.008316 -0.030457 -0.000632 1.40E-02 -0.004309 -1.80E-04 0.00196 -8.91E-05 -1.71E-05 5.38E-05 2.03E-06 -4.50E-07

𝒂𝟕𝐞𝐪

3.493682 -0.019162 -0.089302 -0.013282 0.002382 -0.00152 0.000374 0.000427 -3.25E-04 0.000234 1.16E-04 -4.35E-05 -7.39E-06 3.60E-06 -1.68E-06

𝒂𝟖𝐞𝐪

2.221276 -0.051149 -0.110099 0.023218 0.004878 -0.008491 8.82E-05 0.001525 -5.01E-04 -1.05E-03 0.000105 1.30E-05 -8.85E-05 -1.67E-06 1.29E-06

𝒃𝟏𝐞𝐪

8.160764 0.009346 0.053899 0.004648 0.001257 0.00155 3.23E-04 -2.58E-04 1.16E-04 -0.000153 -8.74E-05 4.70E-06 -1.78E-05 -5.41E-06 -2.27E-08

𝒃𝟐𝐞𝐪

8.864583 -0.011165 0.058248 -0.000784 -0.001456 0.000767 6.02E-04 0.000983 -5.82E-05 -0.000331 1.21E-04 -1.75E-06 -3.50E-05 1.97E-06 1.10E-08

𝒃𝟑𝐞𝐪

9.603162 0.003438 0.072201 0.000246 0.000946 0.001924 -0.000184 0.000369 6.66E-05 -2.40E-04 2.87E-05 4.79E-06 -2.57E-05 -9.79E-07 1.44E-07

𝒃𝟒𝐞𝐪

10.31104 -0.004258 0.06884 -0.001763 0.002344 0.001749 -0.001341 8.23E-05 2.57E-05 3.70E-05 -1.26E-05 -3.95E-06 1.86E-05 1.00E-06 -1.69E-07

𝒃𝟓𝐞𝐪

10.76042 -6.32E-06 0.064195 -0.000807 0.003713 0.001876 -1.42E-03 6.13E-05 1.26E-04 -2.21E-05 -4.38E-05 5.93E-06 1.17E-05 -1.31E-06 1.14E-07

𝒃𝟔𝐞𝐪

11.09144 0.004937 0.059122 -0.004803 0.005487 0.001355 -0.00263 0.000751 1.87E-04 -2.38E-04 4.55E-05 2.21E-05 -3.35E-06 1.51E-06 8.09E-07

𝒃𝟕𝐞𝐪

11.36394 -0.01719 0.062897 0.007962 0.000936 0.002702 -5.42E-04 0.000573 4.03E-04 -0.000279 3.66E-05 3.55E-05 -1.28E-05 6.56E-07 1.08E-06

𝒃𝟖𝐞𝐪

11.74009 0.043901 0.156427 -0.019666 -1.06E-03 0.013143 1.13E-03 -1.62E-03 -1.61E-03 6.79E-04 -1.07E-04 -3.17E-04 2.78E-05 -2.13E-06 -1.24E-05

𝒄𝟏𝐞𝐪

-1.783352 0.805418 0.068536 -0.466204 0.076076 0.010183 -0.040024 -0.013165 0.000133 0.00822 -8.66E-04 -6.44E-05 0.000685 1.87E-05 -2.42E-06

𝒄𝟐𝐞𝐪

-1.557631 -0.214399 0.06253 0.138516 -0.00792 -0.001643 -0.000699 -0.00013 -0.000346 -0.001717 -5.50E-05 4.25E-06 -3.66E-05 5.23E-06 1.46E-06

𝒄𝟑𝐞𝐪

-1.470337 -0.066531 0.056063 0.038827 0.01101 0.001449 -0.004332 0.001059 0.000399 -0.000154 -1.55E-04 2.76E-05 9.46E-05 -1.36E-06 6.27E-07

𝒄𝟒𝐞𝐪

-1.706674 -0.059008 0.054224 0.028781 -0.024559 0.003532 0.011096 -0.007019 -0.000268 3.36E-03 -4.55E-04 -6.42E-05 2.06E-04 -1.26E-06 -2.39E-06

𝒄𝟓𝐞𝐪

-1.911221 0.169039 0.018469 -0.067678 0.030464 0.001369 -0.014073 0.00137 0.000797 -5.98E-04 -9.66E-05 9.02E-05 5.35E-05 1.06E-06 3.30E-06

𝒄𝟔𝐞𝐪

-1.885694 -0.150879 0.018103 0.06549 0.01824 -0.005356 -0.012393 0.0079 -7.68E-06 -2.96E-03 0.000568 4.62E-05 -1.04E-04 1.46E-05 2.08E-06

𝒄𝟕𝐞𝐪

-1.94994 -0.021065 0.048714 0.019304 0.015672 0.00562 -0.004887 0.005064 -1.48E-05 -0.00335 0.000149 -6.81E-05 -0.00024 -1.39E-05 -3.61E-06

𝒄𝟖𝐞𝐪

-1.68478 0.440727 0.126274 -0.230738 -0.022052 3.49E-03 0.008164 -0.019807 -1.60E-04 0.01056 -1.31E-03 5.80E-05 7.24E-04 2.37E-06 4.86E-06

𝝀𝟏 1239204 60992.76 47304.83 -39281 9894.682 4912.507 -4368.546 -643.2869 -347.3295 492.5372 -47.39907 -75.06363 46.37552 1.862041 -2.774747

𝝀𝟐 -54.8455 -6.450537 -1.453109 3.333452 -2.885249 0.039988 1.890681 -0.423165 -0.012156 0.281657 -0.017091 -0.001429 0.01251 0.000145 -3.64E-05

271

𝑴𝒕(𝒌𝒈/𝒌𝒎𝒐𝒍)

𝜉00 𝜉10 𝜉01 𝜉20 𝜉11 𝜉02 𝜉30 𝜉21 𝜉12 𝜉03 𝜉40 𝜉31 𝜉22 𝜉13

𝒂𝟏𝐌 6.430346 -20.59475 -0.017419 35.11529 0.044612 -0.000621 -2.49E+01 -0.03549 0.001003 -7.65E-06 6.314178 8.50E-03 -0.000481 1.21E-06

𝒂𝟐𝐌 0.779075 6.190502 0.026094 -11.17136 -0.067616 0.000817 7.919848 0.047522 -0.001904 -5.45E-06 -2.006626 -8.69E-03 1.04E-03 8.13E-06

𝒂𝟑𝐌 2.088849 -0.834086 -0.004443 1.099449 0.013696 -1.81E-05 -0.772545 -0.010785 0.000183 4.29E-06 1.99E-01 2.74E-03 -1.19E-04 -3.00E-06

𝒂𝟒𝐌 1.116831 -1.149791 0.034983 0.786855 -0.12332 1.10E-05 -0.167662 0.119168 -0.001175 -2.39E-05 -3.73E-02 -3.63E-02 7.07E-04 1.18E-05

𝒂𝟓𝐌 -3.863098 16.34086 -0.164651 -23.84476 0.560625 -1.19E-03 14.62394 -0.585652 1.10E-03 -9.48E-05 -3.236748 1.96E-01 1.37E-04 7.46E-05

𝒂𝟔𝐌 -0.416964 -0.0106 -0.009535 -0.2598 -0.055112 -0.005661 0.115142 0.000311 -6.48E-03 -0.000509 7.73E-03 2.54E-02 5.66E-03 2.30E-04

𝒂𝟕𝐌 5.776032 -27.2272 0.116906 41.33618 -0.35928 0.000245 -27.22584 0.382244 0.002239 6.91E-05 6.54E+00 -1.34E-01 -0.001828 -4.60E-05

𝒂𝟖𝐌 13.85832 -58.67581 1.188396 78.08012 -2.825995 0.037822 -45.97701 2.148978 -0.068526 -6.65E-06 10.12679 -5.17E-01 0.029907 -3.87E-05

𝒃𝟏𝐌 7.444697 3.301052 0.061611 -5.526276 -0.008931 0.001712 3.898451 0.005058 -0.000182 3.80E-05 -0.983131 -4.80E-04 4.03E-05 -4.05E-06

𝒃𝟐𝐌 9.025076 -0.916142 0.053798 1.511813 0.007276 0.001327 -1.063918 -0.005827 0.000139 2.71E-05 2.69E-01 1.10E-03 -1.04E-04 -2.37E-06

𝒃𝟑𝐌 9.511017 0.144884 0.071576 -0.234187 0.00052 0.002108 0.160985 -0.000379 -9.20E-06 4.56E-05 -3.99E-02 1.94E-04 6.09E-06 -4.66E-07

𝒃𝟒𝐌 10.3085 -0.057311 0.071718 0.049994 -0.009018 0.00182 -0.00862 8.97E-03 -1.07E-04 3.46E-05 -3.79E-03 -2.78E-03 4.71E-05 -1.17E-06

𝒃𝟓𝐌 10.27879 1.961269 0.053431 -2.951855 0.037831 0.001387 1.896233 -4.22E-02 -2.16E-04 1.01E-05 -4.42E-01 1.51E-02 2.10E-04 1.03E-05

𝒃𝟔𝐌 9.069924 8.464317 0.013068 -12.75324 0.154179 0.000207 8.213707 -0.173727 -9.82E-04 -9.69E-05 -1.92E+00 6.37E-02 1.22E-03 7.36E-05

𝒃𝟕𝐌 9.371168 7.821829 -0.043865 -10.85418 0.332449 -0.000782 6.305907 -0.37113 -2.14E-03 -0.000184 -1.30E+00 1.33E-01 2.07E-03 9.99E-05

𝒃𝟖𝐌 14.27568 -9.973113 0.20604 13.80429 -0.433682 0.001587 -8.447706 0.334434 -9.77E-03 -0.000242 1.929861 -7.85E-02 5.46E-03 1.14E-04

𝒄𝟏𝐌 -5.088415 33.71181 -0.055369 -55.33903 -0.046527 -0.001838 38.7386 0.035283 -0.000213 -1.91E-05 -9.77E+00 -8.64E-03 6.75E-06 -2.36E-06

𝒄𝟐𝐌 4.049066 -7.209922 -0.063165 11.87222 0.041731 -0.000969 -8.333286 -0.030271 0.000294 -9.04E-06 2.105179 6.81E-03 -2.37E-04 -5.66E-06

𝒄𝟑𝐌 2.106554 0.875651 -0.061822 -1.515111 -0.011044 -0.001861 1.078719 0.009621 -0.000308 -4.53E-05 -2.76E-01 -2.34E-03 1.37E-04 -1.23E-06

𝒄𝟒𝐌 2.549737 -0.02525 -0.075129 0.430601 0.094872 -0.001649 -0.550828 -0.088378 8.70E-04 -9.93E-06 1.95E-01 2.63E-02 -6.33E-04 -1.76E-05

𝒄𝟓𝐌 4.538237 -7.541132 0.06812 10.25639 -0.386149 -9.54E-05 -5.870282 0.393446 -0.002188 3.09E-05 1.193258 -1.28E-01 8.23E-04 -3.53E-05

𝒄𝟔𝐌 -1.122953 15.04155 -0.261769 -20.71645 0.715889 -0.001494 11.94269 -0.754682 -6.12E-04 -6.70E-05 -2.441927 2.53E-01 2.62E-05 -1.82E-05

𝒄𝟕𝐌 4.53999 -7.576703 0.063945 10.15983 -0.393544 0.000465 -5.50541 0.455627 0.002179 0.000287 1.00E+00 -1.73E-01 -0.004106 -3.14E-04

𝒄𝟖𝐌 3.054484 -1.366852 -0.132466 2.481974 0.271218 -0.00386 -2.315441 -0.307614 0.005328 -8.13E-05 0.753935 0.099294 -0.00235 1.38E-04

𝝀𝟑 70.23199 -189.2254 -0.005767 309.2387 0.02949 0.000516 -217.1366 -0.045316 -0.001592 -1.83E-05 54.62963 0.021279 0.001129 2.35E-05

Documents

On the experimental and theoretical investigations of lean ...cj82nd62b/fulltext.pdftemperatures, laminar flames and flame morphology of synthetic gas (syngas) and Gas-to-Liquid (GTL)