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Experimental and kinetic modeling studies of flames of H₂, CO, and C₁-C₄ hydrocarbons
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Experimental and kinetic modeling studies of flames of H₂, CO, and C₁-C₄ hydrocarbons
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EXPERIMENTAL AND KINETIC MODELING STUDIES OF FLAMES OF H 2 , CO, AND C 1 -C 4 HYDROCARBONS by Okjoo Park A Dissertation Present to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements of the Degree DOCTOR OF PHILOSOPHY (AEROSPACE ENGINEERING) DECEMBER 2013 Copyright 2013 Okjoo Park i Acknowledgements First and foremost, I would like to thank my advisor Prof. Fokion Egolfopoulos for his constant support and guidance throughout my doctoral work. I was granted the opportunity to work under his supervision in an exciting and productive research environment. Without his guidance, this work would not have been possible. I would like to extend a special thanks to Prof. Hai Wang for his kindness, concern, and for sharing his insight into science and giving me additional guidance. I also want to thank my dissertation committee members Profs. Paul Ronney, Veronica Ellison, and Katherine Shing. Thank you Dr. Peter Veloo who was a mentor, providing me with valuable advice about research and life during my doctoral studies. He happily shared his research ideas with me and reviewed all my papers as well as this dissertation. Special thanks for Dr Yang Lee Wang, Hugo Burbano, Jagannath Jayachandran, Vyaas Gururajan, Dr. Adam Fincham, Dr. David Sheen, Rei Tango, Steven McCornell, Dexing Du (Dr. Du), and Kevin Kellogg. Many thanks to combustion colleagues at University of Sothern California Roe Burrell, Christodoulos Xiouris, Dong Joon Lee, Runhua Zhao, Abtin Ansari, Tailai Ye, Aydin Jalali, Jennifer Smolke, Dr. Chunsheng Ji, Dr. Kian Eisazadeh-Far, Dr. Bret Windom, Dr. Bikau Shukla, Dr. Francesco Carbone, Dr. Enoch Dames, and Joaquin Camacho. I also want to thank my friends Gauri Khanolkar, Shanling Yang, Sydnie Lieb, Angie Cho, Jihyun Kim and Najung Kim. The administrator and staff members at the Aerospace and Mechanical Engineering department have been amazing. Thank you Samantha Graves, Silvana Martinez, Jorge Castilla, and April Mundy. I would like to thank to Professor Elizabeth Fisher at Cornell University to give me a chance to work in the field of combustion. I have learnt the joy of experimental research from her. Special acknowledgements go to Drs. Gareth Oskam and Pryank Saxena. ii There are no words to express my gratitude to my parents Jiwoo Park and Hyeonsoon Kim for their endless love, constant support, and encouragement. They always encouraged me to believe that I could do anything that I put my mind to and provided me with the best support no matter what I have chosen to do. Finally I want to thank to my brother Sangyeop Park and sister Jeonghee Park. Thank you, Hitam. iii Table of Contents Acknowledgements i List of Tables v List of Figures vi Abstract xv Chapter 1. Introduction 1 1.1. Background 1 1.1.1 Laminar flames 5 1.2. Significance and objectives 6 1.3. Chemical kinetic uncertainty minimization through laminar flame speeds 7 1.4. Thesis organization 10 1.5. References 12 Chapter 2. Methodology 13 2.1. Experimental approach 13 2.1.1 Vaporization system 16 2.1.2 Particle image velocimetry 20 2.1.3 Laser Doppler velocimetry 23 2.1.4 Experimental determination of laminar flame speeds 24 2.1.5 Experimental determination of extinction limits of premixed and non- premixed flames 27 2.1.6 Experimental uncertainties 30 2.2. Numerical approach 34 2.3. Uncertainty quantification and minimization 40 2.4. References 45 Chapter 3. Studies of Premixed and Non-premixed Hydrogen Flames 48 3.1. Introduction 48 3.1.1 Theory of three body reactions 52 3.2. Experimental approach 54 3.3. Numerical approach 56 3.4. Laminar flame speeds of H 2 /oxidizer mixtures 58 3.4.1 A brief consideration of numerical uncertainties 65 3.5. Experimental results and kinetic modeling of stretched flames 67 3.6. Extinction limits of premixed and non-premixed flames 72 3.6.1 Extinction limits of premixed H 2 /air flames 72 3.7. Sensitizing three-body reactions in H 2 flames 82 3.7.1 ‘Wet’ H 2 /air flames 82 3.7.2 ‘Wet’ non-premixed H 2 flames 84 3.8. Concluding remarks 86 3.9. References 88 iv Chapter 4. Combustion Characteristics of Alternative Gaseous Fuels 91 4.1. Introduction 91 4.2. Experimental and numerical approach 94 4.3. Results and discussion 96 4.4. Concluding remarks 110 4.5. References 111 Chapter 5. Studies of C 2 Hydrocarbons 114 5.1. Introduction 114 5.2. Experimental and numerical approach 116 5.3. Results and discussion 117 5.4. Concluding remarks 128 5.5. References 129 Chapter 6. Flame Propagation of C 3 and C 4 hydrocarbons with air mixtures 131 6.1. Introduction 131 6.2. Experimental and numerical approach 134 6.3. Results and discussion 135 6.4. Concluding remarks 151 6.5. References 153 Chapter 7. Chemical Kinetic Model Uncertainty Minimization through Laminar Flame Speed Measurements 155 7.1. Introduction 155 7.2. Reaction model 158 7.3. Active rate parameters 161 7.4. Uncertainty propagation 168 7.5. Uncertainty minimization 178 7.6. Consistency analysis for data set 184 7.7. Uncertainty minimization on reaction rate parameters 192 7.8. Prediction uncertainties for laminar flame speed 203 7.9. Uncertainty propagation into application 211 7.10.Concluding remarks 220 7.11.References 222 Chapter 8. Concluding Remarks and Recommendations 226 8.1. Concluding remarks 226 8.1.1 Hydrogen 226 8.1.2 Fuel mixtures 227 8.1.3 C 2 hydrocarbons 228 8.1.4 C 3 -C 4 hydrocarbons 228 8.1.5 Chemical kinetic model uncertainty minimization 229 8.2. Recommendations 230 Bibliography 233 v List of Tables Table 2.1. Main sources of uncertainties and accuracy in determining and mole fraction. ....................................................................................................... 30 Table 2.2. List of DPIV uncertainties [13,23]. ............................................................ 31 Table 2.3. K ext against the number of grid points for H 2 /air mixtures at = 0.35 with multi-component transport using a Model by Li et al. [37]. ............... 37 Table 3.1. Experimental configuration and conditions. ............................................... 54 Table 3.2. Kinetic models used to simulated present data. .......................................... 56 Table 3.3. List of reactions and associated uncertainties. ............................................ 57 Table 4.1. Composition of fuel blends on molar basis. ............................................... 95 Table 7.1. Experimental data set considered for optimization. .................................. 160 Table 7.2. Selected active reactions discussed in the sensitivity analysis section and their uncertainty factors [20]. ............................................................. 164 Table 7.3. Optimization targets and their associated uncertainties for posterior Model I. ..................................................................................................... 179 Table 7.4. List of optimization targets. ...................................................................... 185 Table 7.5. Selected rate parameter values for H 2 /CO subset reactions for posterior Model I and Movel IV. ............................................................................. 195 Table 7.6. Selected rate parameter values for C 1 -C 4 chemistry of the posterior Model I and Movel IV. ............................................................................. 198 Table 7.7. List of various models. .............................................................................. 204 Table 7.8. Experimental target uncertainty effect on prediction uncertainty in the model, C 3 H 8 /air, =1.2. ............................................................................ 206 vi List of Figures Figure 1.1. Sources of alternative gas; coke oven gas, landfill gas, and associated gas [9]. .......................................................................................................... 2 Figure 1.2. Landfill gas collection System [10] .............................................................. 3 Figure 1.3. Hierarchical structure of oxidation mechanism. ........................................... 4 Figure 1.4. 2 standard deviation uncertainties of CH 4 /air mixtures. ............................. 8 Figure 2.1. A Schematic of the counterflow configuration. .......................................... 13 Figure 2.2. Schematics of (a) a counterflow burner and (b) variable pressure chambers. .................................................................................................... 14 Figure 2.3. A schematic of experimental configuration with DPIV system (twin flame configuration). .................................................................................. 16 Figure 2.4. A schematic of the vaporization system. .................................................... 17 Figure 2.5. A schematic of a nebulizer [8]. ................................................................... 18 Figure 2.6. Schematics of vaporization chambers. ........................................................ 19 Figure 2.7. Time interval and image acquisition. .......................................................... 21 Figure 2.8. A schematic of a twin flame in the counterflow configuration. ................. 24 Figure 2.9. Typical axial velocity profile along the centerline. .................................... 25 Figure 2.10. Variation of S u, ref with K and the determination of S u o using non-linear extrapolation for 1-C 4 H 8 /air flames. Symbols: experimental S u,ref ; Solid black lines: linear extrapolation; Dotted lines: non-linear extrapolation. Numerical S u,ref vs. K was computed using USC Mech II. ................................................................................................................. 27 Figure 2.11. A schematic of a premixed flame. .............................................................. 28 Figure 2.12. A schematic of a non-premixed flame. ....................................................... 29 Figure 2.13. Determination of S u o for a stoichiometric C 2 H 6 /air flame at = 1.4, P = 1 atm and T u = 298 K. Symbols: experimental data; Lines: nonlinear extrapolation (―), 2 uncertainty band of sampling errors (- - -). ............................................................................................................... 33 Figure 2.14. Computed responses of maximum H radical mass fraction to strain rate by using mixture-averaged and multicomponent transport formulations for non-premixed (a) C 2 H 6 /N 2 -air flame, X F = 0.25 and (b) H 2 /N 2 -air flames X F = 0.145, for T u = 298 K, P = 1 atm. (simulation using USC Mech II [36]). .............................................................................................. 36 vii Figure 2.15. Computed responses of maximum H radical mass fraction to strain rate for dependence of grid points for (a) premixed H 2 /air flames for = 0.35 (Simulation by kinetic model of Li et al. [37]) and (b) non- premixed C 2 H 6 /N 2 -air flames (Simulation by USC Mech II [36]) at T u = 298 K, and P = 1 atm. ......................................................................... 38 Figure 3.1. Rate coefficient of reaction H+O 2 +M HO 2 +M at 1200 K for M = Ar, N 2 , H 2 O as a function of pressure. Data and theoretical high and low pressure limit rate coefficients are taken from Bates et al. [58]. ................ 53 Figure 3.2. A schematic of the experimental apparatus, including the vaporization system, setup for non-premixed flames in the high pressure chamber using LDV. .................................................................................................. 55 Figure 3.3. Comparison of experimental and numerical ’s for H 2 /air mixture with literature experimental data [14,15,16,17,18,19,20,29] at T u = 298 K, and P = 1 atm. Numerical simulations using Model I ( ), Model II ( ), and Model III ( ). ........................................... 59 Figure 3.4. Comparison of experimental and numerical ’s of (a) H 2 /(9.5%O 2 +90.5%N 2 ) and (b) H 2 /(7.7%O 2 +92.3%N 2 ) taken from Refs. 18 and 32. T u = 298 K, and P = 1 atm. Numerical simulations using Model I ( ), Model II ( ), and Model III ( ). .................... 61 Figure 3.5. Normalized logarithmic sensitivity coefficients of to reaction rate coefficients at = 1.1 and 1.75, for H 2 /air flames and H 2 /(9.5%O 2 +90.5%N 2 ) flames computed using Model I, II, and III for T exit = 298 K, and P = 1 atm. ....................................................................... 63 Figure 3.6. Comparison of species mass fraction and reaction rate for H 2 /air and H 2 /(9.5%O 2 +90.5%N 2 ) flames at = 1.1, T u = 298 K, and P = 1 atm computed using Model III. .......................................................................... 65 Figure 3.7. Probability density function and 2 uncertainty band of the predicted ’s of H 2 /(9.5%O 2 +90.5%N 2 ) flames using Model I. .............................. 66 Figure 3.8. Comparison of non-linear and linear extrapolation techniques for H 2 /air and H 2 /(9.5%O 2 +90.5%N 2 ). ....................................................................... 68 Figure 3.9. Sample case for cellular flame observed from counterflow configuration at lower strain rate for H 2 /air flame at = 0.28, T u = 298 K, and P = 1 atm. ......................................................................... 69 Figure 3.10. Comparison of experimental raw data and numerical predictions for stretched flame speeds for H 2 /air at = 0.32, 0.35 and 0.45, and H 2 /(9.5%O 2 +90.5%N 2 ) mixtures at = 1.1, 1.75, and 2.4, for T u = 298 K and P = 1 atm. Numerical simulation by Model I( ), Model II( ), Model III ( ). ............................................................... 71 S u o S u o S u o S u o viii Figure 3.11. K ext ’s of premixed H 2 /air flames at T exit = 298 K and P = 1 atm. Numerical simulation by Model I ( ), Model II ( ), and Model III ( ). ..................................................................................................... 73 Figure 3.12. Normalized Logarithmic sensitivity coefficients of K ext to reaction rate coefficients for premixed H 2 /air flames at = 0.28, T u = 298 K, and P = 1 atm using Model I, Model II, and Model III. .................................... 74 Figure 3.13. Branching ratio between R2 and R1. .......................................................... 76 Figure 3.14. K ext ’s of non-premixed H 2 /N 2 -air flames at T exit = 298 K, and P = 1, 4, and 7 atm. Lines: Model I ( ), Model II ( ), Model III ( ), and Model Ia( ). .................................................................................. 79 Figure 3.15. K ext ’s of premixed H 2 /H 2 O/air flames at = 0.38, T exit = 343 K, and P = 1 atm. Numerical simulations by Model I: ( ), Model II ( ), Model III: ( ). ........................................................................................ 82 Figure 3.16. Normalized Logarithmic sensitivity coefficients of S u o with respect to reaction rate coefficients for premixed H 2 /air/H 2 O flames computed using Model I at = 0.38, T exit = 343 K, and P = 1 atm using Model I. .... 83 Figure 3.17. K ext ’s of non-premixed H 2 /N 2 flames with water added to the oxidizer jet at (a) T exit = 353 K, P = 1 atm, and X F =0.17, and (b) T exit = 393 K, P = 4 atm, and X F = 0.15. Numerical simulations by Model I ( ), Model II ( ), Model III ( ) and Model Ia ( ). ....................... 85 Figure 4.1. Comparison of measured and estimated ’s using the mixing rule proposed by Ref. [37] as a function of equivalence ratio for methane- ethane binary fuel mixtures with air flames. Opened symbols: experimental data by author; Closed symbols: predictions by the mixing rule. ................................................................................................. 93 Figure 4.2. Experimental and computed ’s of (a) Fuel-1/air and Fuel-3/air flames and (b) Fuel-1/air and Fuel-4/air flames at P = 1 atm, T u = 298 K, and < 1.0. Symbols: experimental data; Lines: numerical results. The error bars indicate 2 standard deviations. ............................ 97 Figure 4.3. Experimental and computed K ext ’s of (a) Fuel-1/air and Fuel-3/air flames at P = 1 atm, T u = 298 K, and < 1.0. Symbols: experimental data; Lines: numerical results. The error bars indicate 2 standard deviations. ................................................................................................... 98 Figure 4.4. Experimental and computed K ext ’s of H 2 /air and Fuel-2/air flames at P = 1 atm, T u = 298 K, and < 1.0. Symbols: experimental data; Lines: numerical results. The error bars indicate 2 standard deviations. ................................................................................................... 99 Figure 4.5. Experimental and computed ’s of (a) Fuel-1/air, Fuel-1a/air, and Fuel-1b/air flames and (b) Fuel-2/air, Fuel-2a/air, and Fuel-2b/air flames at P = 1 atm, T u = 298 K, and < 1.0. Symbols: experimental S u o S u o S u o ix data; Lines: numerical results. The error bars indicate 2 standard deviations. ................................................................................................. 100 Figure 4.6. Pseudo-Arrhenius plot of mass flux computed for Fuel-2/air and Fuel- 2a/air mixtures = 0.65, P = 1 atm, and T u = 298 K. The lowest temperature results correspond to a fuel-air mixture without Ar substitution; the variation of the adiabatic flame temperature is accomplished through N 2 substitution by Ar. ........................................... 102 Figure 4.7. Computed CH 3 and H mole fraction profiles for = 0.6 (a) Fuel-1/air, Fuel-1a/air, and Fuel-1b/air flames and (b) Fuel-2/air, Fuel-2a/air, and Fuel-2b/air flames at P = 1 atm and T u = 298 K. ...................................... 103 Figure 4.8. Reaction path analysis of (a) Fuel-2a/air and (b) Fuel-2b/air flames at T u = 298 K, P = 1 atm, and = 0.6 using USC Mech II. The numbers indicate the conversion percentage. .......................................................... 106 Figure 4.9. Experimental and computed ’s of CH 4 /air, Fuel-5/air, and Fuel-6/air flames at P = 1 atm and T u = 298 K. The error bars indicate 2 standard deviations. .................................................................................. 107 Figure 4.10. Experimental and computed K ext ’s of CH 4 /air, Fuel-5/air, and Fuel- 6/air flames at P = 1 atm and T u = 298 K. The error bars indicate 2 standard deviations. .................................................................................. 108 Figure 4.11. Experimental and computed ’s of (a) CH 4 /air flames (b) Fuel-5/air flames at T u = 298 K and P = 1, 2, and 4 atm. .......................................... 109 Figure 5.1. ’s of C 2 H 6 /air mixtures at T u = 298 K and P = 1 atm. (a) Comparison with literature experimental data; (b) Comparison with simulations. ...... 118 Figure 5.2. Variation of S u,ref against K for C 2 H 6 /air mixtures at (a) = 0.8 (b) = 1.4. ............................................................................................................ 120 Figure 5.3. Ranked logarithmic sensitivity coefficients of with respect to kinetics for C 2 H 6 /air flames at = 1.0, computed using USC Mech II. ... 121 Figure 5.4. ’s of C 2 H 4 /air mixtures at T u = 298 K and P = 1 atm. (a) Comparison with literature experimental data; (b) Comparison with simulations. ...... 123 Figure 5.5. Experimental and computed ’s of C 2 H 2 /air mixtures at T u = 298 K and P = 1 atm. ........................................................................................... 125 Figure 5.6. Experimental and computed ’s of C 2 H 2 /O 2 /N 2 mixtures at T u = 298 K and P = 1 atm. ........................................................................ 125 Figure 5.7. Ranked logarithmic sensitivity coefficients of with respect to kinetics for a = 1.4 C 2 H 2 /O 2 /N 2 flames. ................................................. 126 Figure 6.1. Experimentally determined ’s of C 3 H 6 /air and C 3 H 8 /air mixtures, T u = 298 K and P = 1 atm. (a) Present experimental results and (b) Experimental results from Ref. [3]. .......................................................... 136 S u o S u o S u o S u o S u o S u o S u o S u o S u o x Figure 6.2. Literature data and present measurements for ’s of (a) C 3 H 8 /air and (b) C 3 H 6 /air flames compared to computed results. Lines: simulation results using USC Mech II. ....................................................................... 137 Figure 6.3. Variation of S u,ref vs. K for C 3 H 8 /air mixtures. Lines: simulation results using USC Mech II. .................................................................................. 139 Figure 6.4. Variation of S u,ref vs. K for C 3 H 6 /air mixtures. Lines: simulation results using USC Mech II. .................................................................................. 140 Figure 6.5. Experimentally determined ’s of C 4 -alkanes with air mixtures, T u = 298 K and P = 1 atm. ........................................................................ 141 Figure 6.6. Experimentally determined and numerical calculations for ’s of C 4 - alkanes with air mixtures (T u = 298 K and P = 1 atm). Lines: simulation results using USC Mech II. ..................................................... 142 Figure 6.7. Experimentally determined (a) ’s of butene isomers with air mixtures (b) S u,ref vs. K of butene isomer/air mixtures at = 1.0 (T u = 298 K and P = 1 atm). ...................................................................... 144 Figure 6.8. Computationally determined ’s of butene isomers with air mixtures using (a) USC Mech II [23], (b) Galway model [5], (c) Nancy model [8], (d) Ranzi model [26] (T u = 298 K and P = 1 atm). ............................ 145 Figure 6.9. Experimentally determined ’s of 1-C 4 H 8 /air and 2-C 4 H 8 /air mixtures compared to computed results (T u = 298 K and P = 1 atm). Lines: simulation results using USC Mech II. ..................................................... 147 Figure 6.10. Experimentally determined ’s of i-C 4 H 8 /air mixtures compared to computed results (T u = 298 K and P = 1 atm). Lines: simulation results using USC Mech II. .................................................................................. 148 Figure 6.11. Experimentally determined ’s of 1,3-C 4 H 6 /air mixtures compared to computed results (T u = 298 K and P = 1 atm). Lines: simulation results using USC Mech II. .................................................................................. 149 Figure 6.12. Nonlinear and linear extrapolation of present data and Davis and Law [2]. ............................................................................................................. 150 Figure 7.1. Logarithmic sensitivity coefficients of with respect to kinetic rate parameters, computed for flames of CH 4 /air. ........................................... 162 Figure 7.2. Logarithmic sensitivity coefficients of with respect to kinetic rate parameters, computed for flames of C 2 -C 4 alkanes and branched alkanes with air. ........................................................................................ 163 Figure 7.3. Logarithmic sensitivity coefficients of with respect to kinetic rate parameters, computed for flams of C 2 H 4 /air and C 3 H 6 /air mixtures. ....... 165 Figure 7.4. Logarithmic sensitivity coefficients of with respect to kinetic rate parameters, computed for flames of C 2 H 2 /O 2 /N 2 mixtures. ...................... 166 S u o S u o S u o S u o S u o S u o S u o S u o S u o S u o S u o S u o xi Figure 7.5. Logarithmic sensitivity coefficients of with respect to kinetic rate parameters, computed for flames of C 4 unsaturated hydrocarbons with air. ............................................................................................................. 167 Figure 7.6. 45° Diagonal plot of response surface predictions versus directly computed laminar flame speeds for the flames of C 1 -C 4 hydrocarbons. .. 168 Figure 7.7. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of CH 4 /air mixtures using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), and UCSD (San Diego Mech, [31]); The shaded bands indicate the 2- model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. ............................................................. 170 Figure 7.8. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of C 2 H 6 /air and C 3 H 8 /air mixtures using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), Nancy (Nancy model [32]) and UCSD (San Diego Mech, [31]); The shaded bands indicate the 2 model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. ........................................................................................ 171 Figure 7.9. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of n-C 4 H 10 /air and i-C 4 H 10 /air mixtures using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), and Nancy (Nancy Model, [32]); The shaded bands indicate the 2- model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. .......................................... 173 Figure 7.10. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of C 2 H 4 /air and C 2 H 2 /(13%O 2 +87%N 2 ) mixtures using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), and UCSD (San Diego Mech, [31]); The shaded bands indicate the 2- model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. .............................................................................................. 174 Figure 7.11. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of C 3 H 6 /air mixtures using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), and Nancy (Nancy model, [32]); The shaded bands indicate the 2- model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. ............................................................. 176 Figure 7.12. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of C 4 - hydrocarbon with air using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), and Nancy (Nancy model, [32]); The shaded S u o S u o S u o S u o S u o S u o S u o xii bands indicate the 2- model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. .................................................. 177 Figure 7.13. Comparison of prediction uncertainties of the prior model (top panel) and those of the posterior model I (bottom panel) for CH 4 /air mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are the experimental data [34]. ............................................................................. 180 Figure 7.14. Comparison of prediction uncertainties of the prior model (top panel) and those of the posterior model I (bottom panel) for (a) C 2 H 6 /air and (b) C 3 H 8 /air mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are the experimental data for (a) C 2 H 6 /air by Ref. [3] and for (b) C 3 H 8 /air by present data. ................................................... 181 Figure 7.15. Comparison of prediction uncertainties of the prior model (top) and those of the posterior model I for (a) n-C 4 H 10 /air and (b) i-C 4 H 10 /air mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are present experimental data. ........................................................................ 181 Figure 7.16. Comparison of prediction uncertainties of the prior model (top panel) and those of the posterior model I (bottom panel) for (a) C 2 H 4 /air and (b) C 2 H 2 /(13%O 2 +87%N 2 ) mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are the experimental data [3]. .................................... 182 Figure 7.17. Comparison of prediction uncertainties of the prior model (top panel) and those of the posterior model I (bottom panel) for C 3 H 6 /air mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are present experimental data. ........................................................................ 182 Figure 7.18. Comparison of prediction uncertainties of the prior model (top) and those of the posterior model for C 4 unsaturated hydrocarbon/air mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are present experimental data. ........................................................................ 183 Figure 7.19. Consistency analyses for (a) posterior Model II (b) posterior Model II (C 2 H 2 ). ....................................................................................................... 187 Figure 7.20. Consistency analysis for posterior Model III using Davis and Law [35]. 190 xiii Figure 7.21. Posterior Model III using optimization target only by Davis and Law [35]. ........................................................................................................... 191 Figure 7.22. Covariance matrix of Model I reactions involving H 2 /CO/C 1 - hydrocarbon species. ................................................................................. 194 Figure 7.23. Covariance matrix of Model I reactions involving C 1 - and C 2 - hydrocarbon species. ................................................................................. 199 Figure 7.24. Covariance matrix of Model I reactions involving C 2 - and C 3 - hydrocarbon species. ................................................................................. 201 Figure 7.25. Covariance matrix of Model I reactions involving C 3 - and C 4 - hydrocarbon species. ................................................................................. 201 Figure 7.26. Predicted uncertainties for ’s of (a) C 3 H 8 /air and (b) C 3 H 6 /air mixtures at T u = 298 K and p = 1 atm for the prior model and posterior Models Ia-1d. ............................................................................................ 205 Figure 7.27. Predicted uncertainties for ’s of (a) n-C 4 H 10 /air and (b) i-C 4 H 10 /air mixtures at T u = 298 K and p = 1 atm for the prior model and posterior Models Ia through Ic. ................................................................................ 207 Figure 7.28. Predicted uncertainties for ’s of (a) 1-C 4 H 8 /air and (b) 1,3-C 4 H 6 /air mixtures at T u = 298 K and P = 1 atm. ..................................................... 208 Figure 7.29. Predicted uncertainties for ’s of (a) n-C 4 H 9 OH/air, (b) i- C 4 H 9 OH/air, and (c) t-C 4 H 9 OH mixtures at T u = 298 K and P = 1 atm. .. 210 Figure 7.30. Variations of OH (a, b) and H 2 O (c, d) mole fraction with mean residence time in a simulated PSR in which n-C 4 H 10 is oxidized in stoichiometric air at a constant temperature of 1500 K and 1 atm pressure. The predictions for (a, c) the prior model and (b, d) the posterior model IV. Lines are model calculation and symbols are the uncertainty calculated using Monte Carlo sampling of the uncertainty space. ......................................................................................................... 212 Figure 7.31. Variations of OH (a, b) and H 2 O (c, d) mole fraction with mean residence time in a simulated PSR in which CH 4 is oxidized in stoichiometric air at a constant temperature of 1600 K and 1 atm pressure. The predictions for the prior model (a, c) are compared with the posterior Model IV (b, d). Lines are model calculation and symbols are the uncertainty calculated using Monte Carlo sampling of the uncertainty space. ................................................................................ 213 Figure 7.32. First order sensitivity coefficients of OH concentration with respect to reaction rate coefficients for CH 4 /air mixtures PSR at constant temperature of 1600 K and 1 atm pressure at = 1.0 using Model IV. (At residence time = 226 s) .................................................................. 214 Figure 7.33. Variations of OH (a, b) and H 2 O (c, d) mole fraction with mean residence time in a simulated PSR in which C 2 H 4 is oxidized in S u o S u o S u o S u o xiv stoichiometric air at a constant temperature of 1400 K and 1 atm pressure. The predictions for the prior model (a, c) are compared with the posterior Model IV (b, d). Lines are model calculation and symbols are the uncertainty calculated using Monte Carlo sampling of the uncertainty space. ................................................................................ 215 Figure 7.34. First order sensitivity coefficients of OH concentration with respect to reaction rate coefficients for C 2 H 4 /air mixtures PSR using Model IV for constant temperature of 1400 K and 1 atm pressure at = 1.0 at residence time (a) 7.28 s (lower branch near ignition point) and (b) 380 s (middle branch near ignition point). ............................................. 216 Figure 7.35. Variations of OH mole fraction with mean residence time in a simulated PSR in which n-butanol is oxidized in stoichiometric air at a constant temperature of 1500 K and 1 atm pressure. The predictions for (a) the prior model are compared with (b) the posterior Model IV and (c) Model VI. Lines are model calculation and symbols are the uncertainty calculated using Monte Carlo sampling of the uncertainty space. ......................................................................................................... 218 xv Abstract Developing reliable chemical kinetic models is a key ingredient in current and future efforts to develop science-based predictive tools, which will be used for the design of more efficient, less polluting, and flexible-fuel combustion systems. While a variety of combustion properties are needed for the comprehensive validation of detailed kinetic models, a minimum requirement for a model’s validity is the prediction of fundamental mixture properties including the laminar flame speed that is a measure of the heat release rate, and thus the driving force of dilatation that leads to power production. In this study, the combustion characteristics of hydrogen/carbon monoxide/C 1 -C 4 hydrocarbons were investigated both experimentally and numerically in laminar premixed and non-premixed flames. These characteristics included laminar flame speeds and extinction limits. Experimentally, flames were established in the counterflow configuration and flow velocity measurements were made using the particle image and laser Doppler velocimetry. Numerically, laminar flame speeds and extinction limits were simulated using quasi-one-dimensional codes, which integrated the conservation equations with detailed descriptions of molecular transport and chemical kinetics. Although the hierarchical importance of hydrogen chemistry to the modeling of combustion kinetics has long been recognized, there exist notable discrepancies between experimental and computed fundamental combustion properties especially in flames. Hydrogen/air mixtures are flammable for a wide range of equivalence ratios, with reactivity that ranges quite notably from near-limit to near-stoichiometric conditions. Among others, the extent of reactivity is manifested by the laminar flame speed that could vary from several cm/s to few m/s under atmospheric conditions. Additionally, due xvi to the very low molecular weight of hydrogen, its lean mixtures with nitrogen containing oxidizers are thermo-diffusionally unstable due to the sub-unity Lewis numbers. In the present investigation, accurate experimental data were determined for hydrogen/oxygen/nitrogen flames and compared against computed results. The novelty of this investigation is that reference flame speeds that are raw experimental data obtained in positively stretched flames were compared against computed results, which eliminates issues related to cellular flames and linear or non-linear extrapolations. In addition, uncertainties still exist in modeling of important three-body recombination reactions, such as for example the H-terminating H + O 2 + M → HO 2 + M. The collision efficiency of the water molecule is known to be large, and as a result its presence at conditions of high density can have a notable effect on various combustion phenomena. The influence of water vapor addition on the extinction of premixed and non-premixed H 2 /air flames was investigated experimentally and numerically in low temperature flames. One of the critical elements towards accurate predictions of combusting flows is to characterize and minimize the uncertainties associated with predictions of fundamental flame properties. In this work, a large set of laminar flame speed data, systematically collected for C 1 -C 4 hydrocarbons with well-defined uncertainties, were used to demonstrate how well-characterized laminar flame speed data can be utilized to explore and reduce the remaining uncertainties in a reaction model for small hydrocarbons. The USC Mech II kinetic model was used as a case study. The method of uncertainty minimization using polynomial chaos expansions (MUM-PCE) was employed to constrain the model uncertainty in laminar flame speed prediction. In addition, the types xvii of hydrocarbon fuels with the greatest impact on model uncertainty reduction are identified along with the attendant accuracy that is needed in flame measurements to facilitate better reaction model development. Results demonstrate that a reaction model constrained only by laminar flame speeds of methane/air flames reduces notably the uncertainty in the predictions of the laminar flame speeds of C 3 and C 4 alkanes, because the key chemical pathways of all of these flames are similar to each other. However, the uncertainty in the model predictions for flames of unsaturated C 3 -C 4 hydrocarbons remains significant without considering their laminar flames speeds in the constraining target data set, because the secondary rate controlling reaction steps are different from those in methane flames. 1 Chapter 1 Introduction 1.1. Background Government energy mandates are increasingly driven by the need to improve combustion efficiency, reduce emissions (e.g., particulates, CO 2 ), and diversify a countries existing energy portfolio. As such, there has been an observable increase in the production and utilization of alternative gaseous fuels. Alternative gaseous fuels include, but are not limited to; synthesis gas, coke oven gas, landfill gas, and associated gas. Integrated gasification combined cycle (IGCC) power generation has been proposed as a clean coal power initiative [1,2]. The gasification of coal results in the production of synthesis gas (syngas), which consists mainly of H 2 and CO. IGCC power generation utilizing syngas results in lower particulate emissions relative to conventional pulverized coal power stations. Additionally, CO 2 sequestration is simplified for IGCC power stations. The composition of coal-based syngas can vary depending on the source of the feedstock (e.g., lignite or anthracite coal) and processing technique (e.g., fixed or fluidized bed gasification). Since gasification involves partial oxidation of the coal, significant amounts of H 2 O can also be present in syngas (e.g., between 0 to 40%) with variability that depends on the processing technique (e.g., [3,4]). Syngas can be produced also via reforming or partial oxidation of natural gas (e.g. [5,6,7]). 2 Coke oven gas is the byproduct of the coke manufacturing process via coal carbonization. It is notable because this manufacturing technique results in large quantities of ‘waste’ H 2 . Coke oven gas additionally contains methane (CH 4 ), CO, and CO 2 . The desire to eliminate coke oven gas flaring (shown in Fig. 1.1) has led to the utilization of coke oven gas as an onsite power generation fuel (e.g., [8]). Figure 1.1. Sources of alternative gas; coke oven gas, landfill gas, and associated gas [9]. Landfill gas is produced via the anaerobic decomposition of solid waste that is deposited in landfills. Figure 1.2 demonstrates a schematic of a potential landfill gas production facility. Landfill gas consists primarily of CH 4 and CO 2 alongside trace quantities of organic compounds, such as paper, garden wastes, and food [10]. Natural gas that is extracted from crude oil wells alongside crude oil is called associated gas. Associated gas can exist either separately from the crude oil in the underground formation or it can be dissolved into the crude oil. The release of these gases into the atmosphere is not only a cause of air pollution and contributes to global warming, but is associated gas coke oven gas landfill gas 3 also a tremendous waste of valuable energy resources. Associated gas typically contains C 1 -C 4 hydrocarbons in various proportions and it can also include trace amounts of C 5 -C 8 hydrocarbons [11]. Figure 1.2. Landfill gas collection System [10] Developing reliable chemical kinetic models is a key ingredient in current and future efforts to develop science-based predictive tools, which will be used for the design of more efficient, less polluting, and flexible-fuel combustion systems that utilize the aforementioned alternative gaseous fuels. The computer-aided design of advanced combustors will require well-characterized, detailed kinetic models as their foundation. The development of kinetic models is an iterative process requiring experimental validation. While a variety of combustion properties are needed for the comprehensive validation of detailed kinetic models, a minimum requirement for a model’s validity is the prediction of the laminar flame speed, , of a reacting mixture as it is a measure of a mixture’s reactivity, exothermicity, and diffusivity. Gavel Packed Well Impermeable Landfill liner system Landfill Trash Landfill gas flared or converted to energy Gavel Packed Well Gas collection wells Vegetable on top of Landfill Leachate collection system S u o 4 High-temperature chemical kinetic oxidation models have a hierarchical dependence on the chemistry of small fuel molecules, as depicted schematically in Fig. 1.3. The combustion of a hydrocarbon fuel at high temperatures consists primarily of the sequential fragmentation of the initial fuel molecule into smaller intermediate species [12], e.g., methane, ethylene, etc. In other words, in order for a chemical model to predict accurately the combustion properties of alcohols or large molecular weight paraffins, the oxidation chemistry of the small intermediate species subset must be well characterized. Therefore, not only are the chemical kinetics of H 2 , CO, and C 1 -C 4 hydrocarbons relevant to alternative gaseous fuels, these kinetics are essential in the development of kinetic models of all practical fuels conventional and alternative alike. Figure 1.3. Hierarchical structure of oxidation mechanism. H 2 Oxidation CO-H 2 Oxidation CH x O y , C 2-4 H x Oxidation Gasoline, Diesel, … Alcohol, Bio-diesel, … CH 4 CH 3 OH 5 1.1.1 Laminar flames A flame is thin non-equilibrium region where a rapid conversion of reactants to products takes place resulting in heat release. In this thin region, there exist large gradients of species concentrations and temperature. In laminar flames, the effects of kinetics, fluid mechanics, and molecular transport can be assessed simultaneously and thus kinetic models can be validate for a wide range of temperatures and species concentrations. is defined as the propagation speed of a steady, one-dimensional, planar, adiabatic, and laminar premixed flame. It is a fundamental characteristic property of a particular mixture measuring of the mass-burning rate of an ideal flame that is free from external influences. A flame established in a laboratory cannot conform to the requirements of the aforementioned flame model, as a stabilization mechanism is required. For example, flames established using a Bunsen burner are stabilized via heat loss at the burner rim. Throughout this dissertation a burner configuration referred to as the counterflow configuration is utilized to study flame properties of fuel/oxidizer mixtures. The external mechanism stabilizing such flames is stretch. The general definition of stretch, K, at any point on the surface of the flame is given as the rate of change of any differential surface flame element scaled by the surface element area [13,14]. In other words, assuming the flame surface moves tangential to itself, K is defined as the change of the tangential component of velocity along the flame surface. Flames undergoing excessive degrees of stretch are prone to extinction. Extinction of flames established in the counterflow configuration is a result of a combination of factors dictated by the stretch rate. If the rate of diffusion of reactants into the flame zone is S u o 6 exceeded by the rate of heat diffusion from the reaction zone, the flame will extinguish. Additionally, if the residence time within the reaction zone is such that it is slower than the required time for combustion, the flame will extinguish. The counterflow configuration readily lends itself to the determination of extinction limits of premixed and non-premixed flames. The value of flame stretch, K at which extinction occurs is defined as the extinction strain rate, K ext . 1.2. Significance and objectives The importance of accurate flame measurements of H 2 /oxidizer and C 1 -C 4 hydrocarbons/oxidizer mixtures have been highlighted and emphasized in this thesis as a key component to validate kinetic models. The counterflow configuration provides a venue for the direct comparison between experimental data and numerical predictions. The reference flame speed, , which will be discussed in detail in the next chapter, can be determined readily using these burners. Numerical codes exist that model this experimental configuration directly. Given the accuracy of the physical model, the kinetic model can be validated using a direct measurement, i.e. free from extrapolations. The first objective of this study was to provide accurate archival experimental data, namely ’s, K ext ’s, and S u,ref for alternative gaseous fuels, H 2 /CO/H 2 O and CO 2 flames, and unblended or neat C 3 - and C 4 -hydrocarbons. Although there exists a relatively large set of experimental data for ’s of flames of low molecular weight hydrocarbons, the uncertainties associated with literature data has rarely been quantified accurately or systematically. In this thesis, it will be demonstrated that there remains a large degree of variation in measured and computed ’s of fuel rich hydrocarbon/air flames. S u o S u o S u o 7 Additionally a direct comparison between S u,ref ’s and kinetic model predictions will be presented to discuss in detail and resolve these differences. Finally, a large set of ’s, systematically collected for C 1 -C 4 hydrocarbons/air flames, with well-defined uncertainties are used to demonstrate how well-characterized data can be utilized to explore and reduce the uncertainties remaining in a kinetic model for low molecular weight hydrocarbons. This thesis explores important questions regarding the type of hydrocarbon fuels that have the greatest impact on model uncertainty reduction and the accuracy needed in the flame measurement to better facilitate model development and constrain model prediction uncertainties. 1.3. Chemical kinetic uncertainty minimization through laminar flame speeds Developing a detail kinetic model involves compiling a set of elementary reactions. Reaction rate parameters can be determined from experimental measurements, theoretical analysis, or estimations from analogous reactions. However, there exist uncertainties associated with each rate constant present within a chemical kinetic reaction model [15], the cumulative effect of all the rate constant uncertainties is manifested as the uncertainty in model predictions of combustion phenomena. As an example, consider the main chain branching reaction in high temperature combustion of hydrocarbon fuels H + O 2 O + OH. (R1) This ‘most understood’ reaction in combustion, until most recently, had an associated uncertainty of 25 % and has been reduced to 10~15 % by Hong et al. [16]. This is still a significant prescribed uncertainty. A calculation of using a kinetic model will result S u o S u o S u o 8 in 4~6 % contribution in the prediction uncertainty from R1 alone. Considering the remaining reaction rate parameters, and their associated uncertainties, of which there are hundreds (or thousands) in a typical kinetic model, the standard deviation of a predicted becomes substantial [17]. An example of such a calculation is presented in Fig. 1.4 for ’s of CH 4 /air mixtures. The nominal prediction of the model is given as the solid line, while the dashed lines represent the 2 uncertainties of the predictions. What Fig. 1.4 attempts to convey is that the predicted resides within the area between the two dashed lines with a 95 % confidence. Figure 1.4. 2 standard deviation uncertainties of CH 4 /air mixtures. Using experimental data with well-quantified experimental uncertainties, it is possible to constrain a kinetic model and as a result reduce the overall uncertainty in its predictions. One such uncertainty minimization methodology is the so-called method of S u o S u o S u o 9 uncertainty minimization using polynomial chaos expansions (MUM-PCE) developed by Sheen and Wang [17]. The mathematical background for this methodology was presented in Ref. [18]. A more detailed outline of MUM-PCE will be presented in Chapter 2. In this thesis, importance of experimental data and their accuracy to validate kinetic model were demonstrated and emphasized using MUM-PCE. 10 1.4. Thesis organization Chapter 2 is organized into three sections describing in detail the experimental and numerical methodologies utilized in this thesis. In the first section, the experimental approach using counterflow burners to determine laminar flame speeds, reference flame speeds, and extinction strain rates is presented. Following which the computational methodology and attendant codes used to model the aforementioned experimental data is introduced. Finally, in the third section, the mathematical background of MUM-PCE is introduced. Chapter 3 will present a comprehensive study of premixed and non-premixed flames of H 2 /oxidizer mixtures. The intent of this chapter is to perform flame type experiments that sensitize three body reactions. Experiments were performed also at elevated pressures to study the pressure dependent kinetics of hydrogen flames. Continuing from Chapter 3, in Chapter 4 includes an investigation of flame properties of realistic alternative fuel mixtures. The laminar flame characteristics of binary fuels containing significant H 2 fractions were studied also. Flame studies of C 2 hydrocarbons including; ethane, ethylene, and acetylene are presented in Chapter 5. This chapter highlights the large discrepancies that remain between kinetic model predictions and experimental results for flame properties of C 2 hydrocarbons especially at fuel rich conditions. A detailed explanation and suggested changes to existing kinetic models is proposed. Chapter 6 investigates the flame characteristics of mixtures C 3 and C 4 hydrocarbons with air. Insight into the effect of chemical structure of an isomer on a mixture’s reactivity is detailed. 11 Finally chapter 7 addresses chemical kinetic uncertainty minimization through laminar flame speeds for mixtures of air and C 1 -C 4 hydrocarbons. 12 1.5 . References [1] G.A. Richards, M.M. McMillian, R.S. Gemmen, W.A. Rogers, S.R. Cully, Prog. Energy Combust. Sci., 27 (2001) 141–169. [2] http://www.netl.doe.gov/technologies/coalpower/gasification/gasifipedia/6-apps/6- 2_IGCC.html. [3] M. Chaos, F. Dryer, Combust. Sci. and Tech, 180 (2008) 1053-1096. [4] M. Moliere, ASME Paper No. GT-2002-30017 (2002). [5] T. Leiuwen, V. McDonell, E. Petersen, D. Santavicca, ASME J. Eng. Gas Turbines Power 130 ASME Paper No. GT2008-011506 (2008). [6] J.R. Rostrup-Nielsen, J. Sehested, J.K. Nørskov, Adv. Catal. 47 (2002) 65–139. [7] J.R.H. Ross, Catal. Today 100 (2005) 151–158. [8] https://mysolar.cat.com/cda/layout?m=299939&x=7&id=1709677 [9] http://www.gereports.com/five-percent-of-worlds-gas-is-wasted-through-flaring/ [10] S. King, SAE, Paper No. 920593 (1992). [11] V.S. Arutyunov, ISSN 1070-3632, Russian Journal of General Chemistry 81 (2011) 2557–2563. [12] C.K. Westbrook, F.L. Dryer, Prog. Energy Combust. Sci. 10 (1984) 1-57. [13] M. Matalon, Combust. Sci. Tech. 31 (1983) 169-181. [14] C.K. Law, Proc. Combust. Inst. 22 (1988) 1381-1402. [15] M. Frenklach, H. Wang, M.J. Rabinowitz, Prog. Energy Combust. Sci. 18 (1992) 47-73. [16] Z. Hong, D.F. Davidson, R.K. Hanson, Combust. Flame 158 (2011) 633-644. [17] D.A. Sheen, X. You, H. Wang, T. Løvås, Proc. Combust. Inst. 32 (2009) 535–542. [18] D.A. Sheen, H. Wang, combust. Flame 158 (2011) 2358-2374. 13 Chapter 2 Methodology 2.1. Experimental approach All experiments in this study were conducted in the counterflow configuration (e.g., [1,2]) that results steady, axisymmetric, and planar flames. The flames established in the counterflow configuration can be modeled using a quasi-one dimensional numerical model. The opposed jets impinge on each other and create a stagnation-type flow. The location where the two jets impinge upon one another is referred to as the stagnation plane. A schematic of the flow streamlines are depicted in Fig. 2.1. Figure 2.1. A Schematic of the counterflow configuration. Experiments were performed at both atmospheric and elevated pressures. To vary the ambient pressure, counterflow burners were installed in a variable pressure chamber (e.g. 14 [1-4]). A schematic of the counterflow burners and variable pressure chambers is shown in Fig. 2.2. (a) Counterflow burner (b) Pressure chambers Figure 2.2. Schematics of (a) a counterflow burner and (b) variable pressure chambers. co-flow inlet Straight Burner Nozzle co-flow cap nozzle screen Gas inlet 1 mm 0.5 mm DETAIL F Pressure Chamber (II) Bottom Burner Top Burner cooling coil N 2 co-flow N 2 co-flow Pressure Chamber (I) 15 Figure 2.2 depicts the newly designed straight-tube nozzles used in all counterflow flame studies performed at elevated pressures discussed in this thesis. The length of the straight burner in pressure chamber I is 21 cm with a 7 mm diameter. Pressure chamber II is a second-generation pressure chamber, designed with the knowledge gained from using chamber I. The length of the burner in chamber II is longer at 29 cm and of the same diameter, 7 mm. The co-flow is fed from outside the pressure chamber. Experiments performed at atmospheric pressure utilized contour-type nozzles discussed in detail in Refs. [5,6,7]. Figure 2.3 depicts the overall experimental setup for gaseous fuel experiments. Two fine-wire mesh screens or honeycombs are placed within the burners to achieve nearly uniform radial velocity profile at the exit. Screens were used with the contour nozzles and either screens or honeycombs with the straight burners. The nozzle diameter, D, and the separation distance, L, depicted in Fig. 2.1, were varied in order to obtain a wide range of experimental conditions. L was kept equal to D, i.e., L/D ≈ 1 for all flame propagation experiments. Burners with D’s of 7, 10, 14, and 20 mm were utilized for both flame propagation and extinction measurements. Selection of burner diameter will be discussed in more detail later in this section. Sonic nozzles (or sonic orifices) from O’Keefe Controls Co.® were used for the accurate metering of gaseous flow such as N 2 , air, H 2 , CO, and C 1 -C 3 hydrocarbons. Depending on the desired mass flow rate of fuel, oxidizer, or diluent, sonic orifices with orifice diameters between 0.025 mm to 0.2 mm were used. C 4 hydrocarbon fuels (e.g. n- butane or iso-butene) have low vapor pressures at room temperature; as a result it is difficult to meter their mass flow rate using sonic nozzles. For such fuels, the Teledyne® Hastings mass flow controller (MFC) was utilized. Both sonic nozzles and mass flow 16 controller are calibrated using wet-test meter (Sinagawa Corporation® W-NK Type wet gas meter), soap-bubble flow meter, and dry piston calibrator (Bios ® Definer 220). Figure 2.3. A schematic of experimental configuration with DPIV system (twin flame configuration). 2.1.1. Vaporization system Experiments in which H 2 O was introduced into the gas phase involved a vaporization system. The vaporization system consists of a syringe pump, nebulizer, and heated vaporization chamber shown in Fig. 2.4. Liquid flow rates were controlled using high precision syringe pumps; a Harvard Apparatus® PHD 2000 for 1 atm experiments and a Chemyx® Nexus 6000 syringe pump for elevated pressure experiments. The Nexus pump can generate up to about 500 lbs (nominal 450 lbs) of linear force, effectively pushing pressure, on the syringe plunger. Using a 100 ml syringe with inner diameter of 34.9 mm, the Nexus pump generates 337 psi. On the other hand, the Harvard pump produces a nominal pushing force of 50 lbs. The Nexus pump was used for both the generation of seeding particles (discussed later in this section) and for the delivery of H 2 O to the nebulizer for high-pressure experiments. Optics Air Fuel Laser sheet Pressure Chamber Silicon oil Sonic nozzle Pressure Gauge Nebulizer 17 Figure 2.4. A schematic of the vaporization system. To ensure steady vaporization, H 2 O was delivered as a stream of atomized micron sized droplets into the vaporization chamber. Atomization was achieved using borosilicate concentric glass nebulizers. A Meinhard® Type A, TR-50-A3 nebulizer was used for experiments at 1 atm and a High Efficiency Nebulizer (HEN), HEN-170-A0.3 was used for experiments performed at elevated pressures. Concentric nebulizers have a central capillary, within which the liquid is delivered, and an outer capillary for a carrier gas, as shown in Fig. 2.5. The exit of the nebulizer was designed such that the carrier gas flow is effectively chocked; therefore the velocity of the gas escaping the annulus is sonic. The high velocity carrier gas shears the emerging liquid creating fine mist of atomized, micron-sized droplets. Air Pre-heater Sonic nozzle Pressure Gauge Nebulizer Vaporization chamber High pressure syringe pump Nebulizer Silicon oil To the bottom burner Heating tape Water 18 Figure 2.5. A schematic of a nebulizer [8]. The HEN produces droplets with a mean diameter between 1.2 ~ 1.5 m. The TR- 30-A3 nebulizer produces droplets with a mean diameter between 12 ~ 15 m [8-10]. Liu and Montaser [10] performed two phase-Doppler diagnostic studies to measure droplet size and droplet velocity distributions of H 2 O atomized by a TR-50-A4 and HEN- 170-AA. 95% of water droplets produced by the HEN and 50 % of the droplets produced by the TR-50-A4 had a diameter less than 8 m for a liquid flow rate of 0.085 ml/min. 95% of the droplets produced by the TR-50-A4 had a diameter less than 21 m. Note that droplet diameter will vary with the state of the liquid and carrier gas (e.g., temperature and pressure). Physical properties of liquid such as surface tension, viscosity, and density are important factors that additionally affect droplet size. In this study, typical liquid flow rates were between 0.2~2 ml/min for water and 0.03~0.1 ml/min for silicon oil. Figure 2.6a and 2.6b depict the schematics of the vaporization chambers used for atmospheric pressure and elevated pressure experiments respectively. A ~1200 cm 3 glass nozzle shoulder capillary annulus seal radius Liquid input gas input Nozzle end surface Sample passage capillary 19 vaporization chamber (Fig 2.6a) was used for the atmospheric experiment and an ~80 cm 3 of stainless steel cylindrical chamber (Fig 2.6b) was used for high-pressure experiments. It was determined, through trial and error that a large volume vaporization chamber causes instabilities in the flow at high pressures resulting in unsteady flames. Additionally, approximately half the total volume of the stainless steel chamber was filled with glass beads for elevated pressure experiments. (a) Glass atmospheric pressure vaporization system [5]. (b) Stainless steel high pressure vaporization system. Figure 2.6. Schematics of vaporization chambers. To assist vaporization, air or N 2 preheated above the boiling temperature of the liquid was co-flowed into the vaporization chamber (see Fig. 2.6). Additionally, the walls of Glass Chamber Preheated Air Nebulizer to burner Air Water Stainless steel Chamber Preheated Air Air Water to burner 20 the vaporization chamber were maintained at least 50 K above the liquid boiling temperature using a combination of heating tapes, insulation, and thermocouples. The vaporization chamber was connected to the burner using stainless steel heated and insulated tubing. The temperature of the gas was elevated throughout the system to the nozzle exit such that the partial pressure is consistently below the vapor pressure at the prevailing ambient temperature and pressure. 2.1.2 Particle image velocimetry For a large majority of the experiments discussed herein, flow velocities were measured using Particle Image Velocimetry (PIV). The flow was seeded with droplets of silicone oil atomized by a HEN using air as the carrier gas. PIV provides temporal and spatial resolution of the instantaneous flow field by tracking the spatial displacement of particles. Particles are illuminated by a double-pulsed laser with a specified (100 ~ 150 s) time interval, t between pulses as shown in Fig. 2.7. The double pulsed laser and camera were synchronized by the timing controller. Light scattered by the illuminated particles was captured by a Charged Couple Device (CCD) camera. The duration each laser pulse must be sufficiently short that the motion of the particles is “frozen” during each individual exposure to avoid blurred images [11]. A dual head Nd:YAG laser provided the light source for the flow field illumination and a high performance digital 12 bit CCD camera with 1392 1024 pixels of resolution was used to acquire the DPIV images. The Nd:YAG laser has two resonators and is frequency doubled, to achieve light with a wavelength of = 532 nm. A Thorlabs® FL-532-3 bandpass (laser line) filter was used to filter out light generated by the flame, and only 21 capture on the camera sensor, light generated by the flow seeding particles illuminated by the laser. Figure 2.7. Time interval and image acquisition. Time delay between illumination pulse needs to be long enough to determine the displacement between the two images of the tracer particles with sufficient resolution and short enough to avoid particles with an out of plane velocity component leaving the light sheet between subsequent illuminations [11]. Flow velocities are then computed using the correlation image velocimetry (CIV) technique developed by Fincham and coworkers [12,13] implemented through the DaVis software suite version 7.2.2. Proper flow seeding is integral to accurate DPIV measurements, especially with regards to the size of the seeding particles. The diameter of these particles should be sufficiently small to ensure accurate tracking of the flow velocity (i.e., u particle = u flow ). When the particle’s Reynolds number (Re) is much less than unity, Stokes’ drag law is applicable. Since actual drag is larger, it can be assumed that the particle velocity will equal the flow velocity. Additionally, there is a minimum particle diameter below which Laser #1 Laser #2 Q-switch Delay t Laser pulse Camera frame 1 st frame 2 nd frame Flash lamp pulse Q-switch pulse Laser pulse 22 the light scattering properties of the particle will no longer allow for effective PIV measurements [11]. Even when using high laser pulse energies, the distribution of this energy over a laser sheet leads to an energy density that is low relative to other laser diagnostic instruments, say laser Doppler velocimetry (LDV). Therefore, PIV requires a much greater seeding density than LDV. Finally, particle scattering efficiency is very important. Silicone oil droplets were selected to provide seeding for the entire flow field upstream of the flame from the exit of the burner nozzle for all experiments within this thesis. Silicone oil has a boiling point of ~570 K, as a result, a silicone oil droplet will not vaporize until it is well past the start of the preheat zone upstream of a steady flame established in the counterflow configuration. This allows for an accurate characterization of the flow velocity at the minimum point of the flow velocity prior to the flame. The regions upstream of the flame will be discussed in more depth in the section discussing the experimental determination of ’s later in this chapter. Finally, the seed particles should not affect the flame properties under consideration in this thesis. For example, the seeding density must be small enough such that it does not enhance or retard the reactivity of the original fuel/oxidizer mixture. The same HEN used to atomize water, discussed in the previous section (Fig 2.5), was used to generate a stream of micron sized silicone oil droplets that were then injected into the bulk flow. A Chemyx® Nexus 6000 syringe pump is used to deliver the silicone oil into the nebulizer for atomization at an approximate flow rate of ~0.1 ml/min for high- pressure conditions. For atmospheric pressure experiment, Razel scientific instruments® Model R-E single speed pump was used. The flow rate of silicone oil was selected such S u o 23 that the total mass of silicone oil in the bulk gaseous flow submitted to the burner is no more than 1 % resulting in no observable effect on flame propagation or extinction. 2.1.3 Laser Doppler velocimetry For elevated pressure flame studies, a laser Doppler velocimetry (LDV), MSE® MiniLDV™ system was utilized also. LDV is a point based velocity measurement technique as opposed to PIV that instantaneously determines the flow velocities across a specified area. LDV was used also to determine the velocity profile along the stagnation streamline. The LDV system consists of a transceiver probe, processing engine, and burst processor. A probe is mounted on an automated transverse mechanism that moves the probe vertically along the centerline. The probe consists of a laser, miniature beam shaping optics, receiving optics, and a detection system. The sensor is 32 mm in diameter and 165 mm long, and the fixed distance between the sensor and the center of burner nozzle diameter (which is the probe volume) is 150 mm. Laser power is 140 mW at a wavelength of 658 nm. Two coherent laser beams are crossed and form the probe volume to generate interference fringes. As the particle travels through the probe volume, it reflects bursts of light into the receiver only when it crosses a region of constructive interference. The reflected light fluctuates in intensity with a frequency equivalent to the Doppler shift between the incident and scattered light and is proportional to the component of particle velocity which lies in the plane of two laser beams. The sinusoid is isolated by a band-pass (frequency) filter and since the spacing between the fringes is known, the velocity of the particle can be calculated from the frequency of the reflected bursts [14]. 24 Flow seeding required for LDV measurements was achieved using the same methodology discussed above for DPIV measurements. Since LDV is a point based measurement the required seeding density can be much lower when compared to the seeding density required for effective DPIV measurements. 2.1.4 Experimental determination of laminar flame speeds All ’s were determined using the twin flame configuration as shown in Fig. 2.8. Two symmetrical and planar flames are established between the counterflow burners. A typical axial velocity profile along the centerline is shown in Fig. 2.9. The radial velocity varies linearly along the radius [2]. From the nozzle exit, the velocity decreases before reaching the preheat region. As the flow enters the preheat region, the velocity starts to increase by thermal expansion due to conductive heating from the flame. Downstream of the flame, the axial velocity once again decreases as it approaches the stagnation plane. Figure 2.8. A schematic of a twin flame in the counterflow configuration. S u o Fuel + Air Fuel + Air 25 The minimum axial flow velocity upstream of the flame is defined as the reference flame speed, S u,ref and the maximum absolute value of the velocity gradient upstream of the flame in the hydrodynamic zone is defined as the imposed strain rate, K, (e.g. [1,2,15,16]). The velocity at the point of initial temperature rise is located very close to the location of S u,ref [2]. This measured minimum velocity is taken, strictly by definition, to represent a characteristic velocity at the beginning of the preheat zone. Figure 2.9. Typical axial velocity profile along the centerline. Therefore, a stretched flame speed, S u,ref , and the magnitude of its local strain rate K have been defined and can be experimentally determined. For a given mixture and equivalence ratio, , the measured S u,ref ’s are plotted as a function of K. By extrapolating S u,ref to zero stretch, i.e., K = 0, is determined [2]. For weakly stretched flames, there exists a linear relationship between and S u,ref [17,18]. However, it has been Flow direction Axial Velocity, u, cm/s Distance from nozzle exit, x, cm 0 40 80 120 160 200 0 0.1 0.2 0.3 0.4 0.5 0.6 Nozzle exit dx du K max Hydrodynamic zone Preheat zone Reaction zone S u,ref Stagnation plane S u o S u o 26 demonstrated that the variation of S u,ref with K as K 0 is non-linear because S u,ref is affected by the heat conduction from the flame located further upstream (e.g., [19]). Recently, a non-linear extrapolation using a computationally-assisted approach was developed by Egolfopoulos and coworkers (e.g., [15,16]) to determine ’s. There exist non-linear extrapolation techniques based on asymptotic analysis that use simplified one- step chemistry and global transport (e.g., [19]). In this study the computationally assisted non-linear extrapolation technique was utilized which employs actual simulations of the opposed-jet experiments using detailed descriptions of chemical kinetics and molecular transport (e.g., [15,16,20]). Fig. 2.10 depicts the experimentally determined S u,ref vs. K for flames of 1-butene (1- C 4 H 8 )/air mixtures at different . The value of S u o ’s determined through the computationally assisted non-linear extrapolations of S u,ref to zero stretch are denoted using dashed lines. Linear extrapolations of the experimental results are depicted using solid lines. For fuel rich conditions, there is an observable difference between S u o ’s determined using the linear and non-linear extrapolation. These differences will be discussed in detail in chapters 3 and 6. It has been demonstrated, exhaustively, that the chemical kinetics and associated transport parameters of a reaction model do not have an effect on the shape of the extrapolation curve (e.g., [15,16,20]). This is expected since the balance of momentum and heat, upstream of the preheat zone where S u,ref is determined, should not depend to the first order on kinetics or transport of the chemical kinetic model [15]. S u o 27 Figure 2.10. Variation of S u, ref with K and the determination of S u o using non-linear extrapolation for 1-C 4 H 8 /air flames. Symbols: experimental S u,ref ; Solid black lines: linear extrapolation; Dotted lines: non-linear extrapolation. Numerical S u,ref vs. K was computed using USC Mech II. 2.1.5 Experimental determination of extinction limits of premixed and non-premixed flames The extinction strain rates, K ext , of premixed flames were measured using a single- flame configuration that results from counterflowing a fuel/air mixture against a room temperature N 2 jet (e.g., [21,22]) as illustrated schematically in Fig 2.11. This configuration is less resistant to extinction, resulting in lower measured K ext ’s, compared to a symmetric twin flame (Fig. 2.8) at the same As K ext ’s are directly proportional to the flow velocity, lower flow velocities result in lower Re’s, minimizing the effects of intrinsic instabilities that are present in the flow systems (e.g., [17,18]). The flow rate of the ambient temperature N 2 is accurately metered at the top jet and its mass flow rate is = 1.4 = 0.8 = 1.2 1-C 4 H 8 /air S u o 28 such that the momentum fluxes from the bottom and top jet are equal. A flame is established for a near-extinction conditions, i.e., ‘small’ perturbations in the deficient reactant will cause extinction, and the prevailing K is measured just upstream of the flame (e.g., [15,16]). Figure 2.11. A schematic of a premixed flame. K ext for non-premixed flame involved an air jet counterflowing against a fuel/N 2 jet as shown in Fig. 2.12. Similar to premixed flames, the flow rate of the air stream is determined such that the momentum fluxes from the bottom and top jet are equal. A flame is established for near-extinction conditions, and the prevailing K is measured just upstream of the flame. Extinction was achieved by slightly modifying the fuel concentration until extinction is achieved. Fuel + Air N 2 29 Figure 2.12. A schematic of a non-premixed flame. The burner diameters used were D = 14 mm for K ext ≤ 400 s -1 and D = 10 mm for K ext > 400 s -1 . L was kept equal to D, i.e., L/D ≈ 1 for P = 1 atm. The strain rate is directly proportional to the flow exit velocity from the nozzle, U exit . Stronger flames have large K ext requiring in turn large U exit that can be achieved more easily for a fixed mass flow rate by varying D. If U exit is increased for a fixed D, Re will increase to the point where the flow can no longer be considered laminar. Varying D alleviates this problem as mentioned previously. Air Fuel + N 2 30 2.1.6 Experimental uncertainties Accurate quantification and characterization of experimental uncertainties is necessary for meaningful chemical kinetic model validation (or development) and optimization. Dependent and independent parameters associated with an experimental measurement can characterize the dispersion (spread or uncertainty) in this measurement. By explicitly accounting for these parameters, we can determine, accurately, the uncertainties in the measured values. A variety of independent factors affect the uncertainty of the experimental results reported throughout this thesis. Table 2.1 listed the main sources of uncertainties in and mole fraction, typically the so-called x-axis of a reported experimental result. These uncertainties relate to the inherent accuracy of pressure gauges, mass flow controllers, liquid fuel pumps, and calibration devices. Overall, the uncertainties in and mole fraction were estimated to be less than 0.5 %. Source of uncertainties accuracy Pressure gauge ±0.25 % Mass flow controller ±1 % in full scale Liquid Fuel Pump ±0.35 % Calibration device Dry piston calibrator ±0.75 % of reading Wet gas meter ±1 % Bubble meter ±1 % Table 2.1. Main sources of uncertainties and accuracy in determining and mole fraction. The main sources of uncertainties in the experimentally determined are derived from PIV measurements and extrapolation to zero stretch. The uncertainty associated with the PIV measurements can be estimated by considering various parameter settings S u o 31 such as timing errors, particle (flow seeding) slip, as well as error that arise from the PIV data processing algorithm. Table 2.2 lists the uncertainties of PIV. Source of uncertainty Description Vibration Particle slip Flow irregularities DPIV system calibration Optical alignment, Reference scale, Optical distortion Image quality and particle seeding Image noise, Dynamic range, Discretization, Particle image size, Particle number of density Laser timing and synchronization errors Laser pulse synchronization, choice of inter- frame time interval DPIV processing errors Influenced by the general particle image properties and local fluid properties such as velocity gradients and cross-flow Table 2.2. List of PIV uncertainties [13,23]. The precision of the pressure gauge used to control the ambient pressure, P, and the thermocouples controlling the unburned reactant temperature, T u , can introduce additional uncertainties in the measured flow velocity. Fluctuation in T u and P affects the density of the unburned gas and velocity of the flow at the nozzle exit. T u was measured at the center of the burner exit and it was found to vary by as much as ±2 K in the radial direction. , as discussed previously, results from the extrapolation of the stretched flame speed to zero stretch. Therefore, when accounting for uncertainties in the derived it is necessary to quantify the contribution from the extrapolation methodology. When presented, the nominal, experimentally derived represents the extrapolation of the mean S u, ref , depicted as the solid line in Fig. 2.13. The uncertainty in the experimentally S u o S u o S u o 32 determined value of can be thought of as extrapolation from the upper and lower bounds of the 95 % confidence interval of the S u, ref to zero stretch, depicted as the dashed lines in Fig. 2.13. More precisely, the standard error of , ) ( , , i ref u S , has been defined as [21,22]: 1 ) ( ) ( 1 2 , , , , , , N S S S N i i ref u i ref u i ref u . (2.1) N is total number of PIV measurement data sets, S u,ref,i is the reference flame speed of the i th measurement and i ref u S , , is the calculated reference flame speed at strain rate K i using the polynomial function fitted by the nonlinear extrapolation methodology. The confidence interval of is generally given as an interval centered on the results and can be found only if the probability distribution of the result is known [22]. S u o S u o S u o 33 Figure 2.13. Determination of S u o for a stoichiometric C 2 H 6 /air flame at = 1.4, P = 1 atm and T u = 298 K. Symbols: experimental data; Lines: nonlinear extrapolation ( ―), 2 uncertainty band of sampling errors (- - -). PIV and LDV measurement determine the velocity of the flow field. The determination of the strain rate requires a polynomial fitting of this measured velocity field and a subsequent differentiation. The uncertainty of K depends on the uncertainty of velocity measurements and fitting methodology. The standard error of the strain rate is computed using a similar methodology used previously for . K is the mean strain rate and ) ( i K is the standard deviation, 1 ) ( ) ( 1 2 N K K K N i i i i . (2.2) The 2 standard deviation is indicated with uncertainty bars on all K ext data presented in this study. Mean reference flame speed, ref u S , 2 band of DPIV measurement S u o 34 2.2. Numerical approach ’s are computed using the PREMIX code [26,27] developed by Kee and coworkers. The governing equations for numerically simulating steady, isobaric, quasi one-dimensional laminar flames include the conservation of mass, conservation of species, and conservation of energy. This system is additionally constrained by the equation of state. Stretched flames in the counterflow configuration are numerically modeled using the opposed jet code developed by Kee and coworkers [28]. This CHEMKIN (CHEMical KINetics) based opposed jet code was used to generate non- linear extrapolation curves and determine K ext . The governing equations required to accurate simulate the counterflow configuration are similar to those in PREMIX with the addition of conservation of momentum. The original opposed jet code has been modified to allow for the simulation of asymmetric boundary conditions [29]. Both PREMIX and opposed-jet codes have also been modified to account for thermal radiation from CH 4 , CO, CO 2 , and H 2 O at the optically thin limit (e.g., [29,30]). The code is integrated with CHEMKIN [31] and the Sandia Transport [32] subroutine libraries. H and H 2 diffusion coefficients of several key pairs are based on a recently updated set of Lennard-Jones parameters [21,33]. K ext is computed by first establishing a vigorously burning flame at a given K. K is then increased by increasing the flow velocities at the burner exits to the point of extinction. At the extinction state, the response of any flame property to K is characterized by a turning-point behavior as shown in Figs. 14 and 15 that introduces a singularity, if K is considered as the independent variable (e.g., [34,35]). The opposed-jet code has been modified to capture this singular behavior, and to allow for the accurate S u o 35 determination of K ext [34]. More specifically, a two-point continuation approach is implemented by imposing a predetermined temperature or species mass fraction at two points in the flow field; thus the strain rate is solved for, rather than being imposed as a boundary condition. Locations where the temperature or species concentrations have maximum increasing and decreasing gradients are chosen as the two points [35]. In order to compute K ext properly, the experimental values of L (e.g., [29]) and the axial velocity gradient at the nozzle exit, , (e.g., [16]) were accounted for in the simulation using the opposed-jet code. Egolfopoulos [29] has demonstrated numerically that K ext increases with nozzle separation distance as a result of the reduction of the strain rate distribution within the reaction zone. In a recent study by the Ji et al. [16], α was found to have a considerable effect on the numerically determined K ext . Ref. [16] demonstrated that it is essential that be included as a boundary condition in all opposed-jet simulations. Full multi-component transport coefficient formulations were used in all simulations for ’s, S u,ref ’s, and K ext ’s along with a complete account of thermal diffusion (the Soret effect). All simulation results are determined to be grid independent. It should be noted that around 2000 grid points are necessary for grid independent calculations of flames involving H 2 . The largest variation in a numerical calculation emphasizing the importance of using full multi-component transport formulation as opposed to the mixture average formulation can be demonstrated in numerical calculations of the extinction limits of non- premixed flames. Figure 2.14 compares the computed K ext ’s using both mixture average and multi-component transport formulations for non-premixed C 2 H 6 (Fig 2.14a) and H 2 S u o 36 (Fig 2.14b) flames. Using the mixture average formulation, the calculated K ext was 15 % higher in flame (a) and 25 % higher for flame (b). Figure 2.14. Computed responses of maximum H radical mass fraction to strain rate by using mixture-averaged and multicomponent transport formulations for non-premixed (a) C 2 H 6 /N 2 -air flame, X F = 0.25 and (b) H 2 /N 2 -air flames X F = 0.145, for T u = 298 K, P = 1 atm. (simulation using USC Mech II [36]). Ethane/N 2 -air X F =0.25 K ext Multi-component Mixture Averaged ~16% (a) H 2 /N 2 -air X F =0.145 K ext ~26% Multi-component Mixture Averaged (b) 37 Table 2.3 depicts the computed K ext against number of grid points in calculations using the opposed-jet code of premixed H 2 /air flames. Above 1800 grid points, the differences in the calculations become negligible. # of grid points Computed K ext 800 692 1200 714 1800 730 2100 735 2500 739 Table 2.3. K ext against the number of grid points for H 2 /air mixtures at = 0.35 with multi- component transport using a model by Li et al. [37]. Figure 2.15 shows the computed response of maximum H mass fraction to strain rate for grid dependency (2.15a) and for various transport formulations (2.15b) for premixed H 2 /air flames at = 0.35. In this particular case a larger number of gird point results in a higher K ext . Similar to non-premixed flames, the computed K ext using multi-component transport formation is notably lower compared to the same calculation using the mixture average formulation. 38 Figure 2.15. Computed responses of maximum H radical mass fraction to strain rate for dependence of grid points for (a) premixed H 2 /air flames for = 0.35 (Simulation by kinetic model of Li et al. [37]) and (b) non-premixed C 2 H 6 /N 2 -air flames (Simulation by USC Mech II [36]) at T u = 298 K, and P = 1 atm. Although the computation of premixed and non-premixed flames of H 2 required a notably large (~2000) number of grid points, typical hydrocarbon flames considered in this study do not require such an excessive number of grid points. For example, the 2500 pts 2100 pts 1800 pts 1200 pts 800 pts H 2 /air = 0.35 800 pts, GRAD : 0.06, CURV :0.07 1200 pts, GRAD : 0.06, CURV :0.05 1800 pts, GRAD : 0.06, CURV :0.04 2100 pts, GRAD : 0.06, CURV :0.03 2500 pts, GRAD : 0.06, CURV :0.03 (a) Ethane/N 2 -air X F =0.25 1200pts 800pts 400pts 1200 pts, GRAD : 0.06. CURV : 0.04 400 pts, GRAD : 0.06. CURV : 0.11 800 pts, GRAD : 0.06, CURV : 0.06 (b) 39 calculation of K ext of non-premixed C 2 H 6 flames was determined to be grid independent at ~500 grid points. Sensitivity analysis is a technique used to understand quantitatively how the solution calculated using a model depends on the model parameters [26]. Sensitivity analysis is used to provide deeper insight into simulation results of both flame propagation and extinction limits to help to interpret the results of a flame model. The PREMIX and opposed-flow codes used to simulate and K ext , have the capability to determine sensitivities of these two computed quantities to both the pre-exponential factors of rate constants, A i , and to binary diffusion coefficients, D ij . The ability to determine the effects of chemical kinetics and molecular diffusion on K ext was first established by Dong et al. [21]. The ability to determine the sensitivity of ’s or K ext ’s to the binary diffusion coefficients was further developed by Holley et al. [38]. The codes calculate the normalized or logarithmic sensitivity coefficients, i.e., (2.3) . (2.4) Equations 2.3 and 2.4 are the mathematical formulation for the normalized logarithmic sensitivity coefficients of to both reaction rate coefficients and to binary diffusion coefficients respectively. The sensitivity coefficients of K ext on both these model parameters follow an identical formulation. S u o S u o i o u o u i A S S A ij o u o u ij D S S D S u o 40 2.3. Uncertainty quantification and minimization The method of uncertainty minimization using polynomial chaos expansions (MUM- PCE) [35-37] was employed to evaluate the prior model against experimental datasets of ’s of mixtures of C 1 -C 4 hydrocarbons with air. The model was represented by a multivariate polynomial response surface at each selected experimental condition. The polynomials were obtained from a sensitivity-analysis based method [38]. Active parameters were determined using sensitivity analysis. The reaction pre-factors were ranked in order of their uncertainty-weighted sensitivity coefficients for each selected experimental target. Uncertainties in numerical predictions were quantified by a stochastic spectral expansion method (e.g., [39-41]) and the model is constrained by experimental data. It should be noted that the model posterior uncertainty space strongly depends on the uncertainties of the experimental measurements [42]. The posterior model uncertainties were quantified by MUM-PCE. In MUM-PCE, each Arrhenius pre-factor is normalized as a factorial variable i i i i f k k x ln / ) / ln( 0 , [43], where k i is the Arrhenius pre-factor of the i th reaction, k i,0 is its nominal value, and f i is its span or the uncertainty factor of the rate coefficient. Thus x i = 0 represents the nominal rate value for x i and x i = -1 and +1 are the lower k i = k i,0 / f i and upper k i = k i,0 × f i bounds of uncertainty in k i,0 respectively. The kinetic parameter and its associated uncertainty can be expressed as a polynomial expansion of m basis random variables, m j j ij i i x x 1 ) 0 ( . (2.5) S u o 41 α is the expansion coefficient, ξ j is the i th basis variable, m is the number of basis variables considered in the expansion, and x (0) is the vector of normalized rate coefficients, which are zero for a reaction model as assembled or the optimal values upon model optimization. For flame simulations, direct Monte Carlo sampling is computationally expensive. MUM-PCE uses the method of solution mapping [43] and assumes that the dependence of a model prediction on the factorial variables, ) (x r η , can be approximated by a second- order polynomial [36,42]: . (2.6) N r represents the number of active parameters determined by a one-at-a-time sensitivity analysis [44]. The coefficients a i and b ij can be determined by a regression test against computational experiments from the Sensitivity-Analysis-Based (SAB) method [38]. Combining solution mapping and spectral expansion methods for uncertainty propagation, Eq. (2.7) provides predictions of ’s with their association uncertainties contributed by each rate coefficient uncertainty in the model, . (2.7) The model prediction uncertainty r is determined from the coefficients in Eq. (2.7) as S u o 42 . (2.8) Through optimization against the experimental target set, the factorial variables are updated to the values best able to fit the given experimental measurements, denoted as x * . These best-fit values will have an expansion in terms of the basis random variables, that is, * (0)* * 1 m i i ij j j xx . (2.5a) The best-fit factorial variables x (0)* are found by solving the least-squares optimization problem, 0 2 2 0 0 0* 11 min e r obs N N rr n obs x rn rn x x x . (2.9) In the first term on the right hand side of Eq. 2.9, obs r is the r th experimental , and obs r is its uncertainty, and N e is the number of experimental measurements. x (0)* is then an optimal set of rate coefficients by minimizing the least-squares difference between the model predictions and the experimental measurements, weighted by the experimental uncertainty. The second term comes from treating each rate parameter value as an experiment in its own right, with uncertainty n equal to 1/2. The matrix of expansion coefficients for the optimized model, α * , can be estimated by interpreting Eq. (2.9) as the joint probability density function for x, 1 2 ( ) exp p x . This is approximately equal S u o 43 to a multivariate normal distribution, which has the joint probability density function 1 * (x) exp 2 T p x μ Σ x μ with mean 0* μx , obtained from Eq. (2.9), and covariance matrix * * * T Σ α α [36]. can be approximated by linearizing the response surfaces in the vicinity of x (0)* , which gives 1 2 ** * 1 4 e N T rr obs r r JJ ΣI . (2.10) * r J is the gradient of the r th model response with respect to the factorial variables, evaluated at x (0)* and I is the identity matrix. Then, * α is calculated from the Cholesky factorization of . Simple multipliers for Arrhenius pre-factors were used for optimization, although temperature and pressure dependence in the rate expression may be equally important for consideration. Here and as in previous studies [35,36,42], these dependencies were not considered because does not give enough resolution to warrant such an exercise. Constraining the uncertainty of a kinetic model is a two-stage process. Firstly, the model is constrained by minimizing the least-squares difference between the model prediction and the experimental measurements, weighted by the experimental uncertainty, obs r . Following which, MUM-PCE also checks for inconsistencies in the experimental target dataset by calculating the contribution of the r th experiment to the objective function [36], obs r r obs r r x F 2 ) ( * 0 . (2.11) S u o 44 If 1 r F , the r th experiment is inconsistent with the constrained factorial vector x * , and that the initially constrained model will fall outside the r th experimental target’s uncertainty bounds. The effect of a particular experiment on the constrained model is measured by the normalized scalar product S r between the response surface gradient ) ( * x r and the constrained factorial vector or the change in the response caused by model constrain [36], * * * * ) ( ) ( x x x x S r r r . (2.12) Therefore, the target with the greatest effect on the posterior model will have the largest value of S r . If only one target has F r > 1, it will be removed from the optimization data target set and the model is re-constrained. However, when multiple targets have F r > 1, MUM- PCE [36] uses a weighted scalar product W r calculated by r r r F S W . (2.13) The single target that has the greatest r W is removed and the model is then re- constrained. This procedure is continued until an x * is calculated such that all F r are smaller than unity. These tests are referred to as F and W tests, respectively. 45 2.4. References [1] G. Yu, C.K. Law, C.K. Wu, Combust. Flame 63 (1986) 339-347. 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O’Connell, Linear Statistical Models: An Applied Approach, 2 nd ed., PWS-KENT, Boston, 1990, Chaps 5,6. [25] C. Ji, Y.L. Wang, F.N. Egolfopoulos, J. Propul.Power 27 (2011) 856-863. [26] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, A FORTRAN Program for Modeling Steady Laminar One-Dimensional Premixed Flames, Report No. SAND85-8240, Sandia National Laboratories, 1985. [27] J.F. Grcar, R.J. Kee, M.D. Smooke, J.A. Miller, Proc. Comb. Inst. 21 (1986) 1773- 1782. [28] R.J. Kee, J.A. Miller, G.H. Evans, G. Dixon-Lewis, Proc. Combust. Inst. 22 (1988) 1479–1494. [29] F.N. Egolfopoulos, Proc. Combust. Inst. 25 (1994) 1375–1381. [30] H. Zhang, F.N. Egolfopoulos, Proc. Combust. Inst. 28 (2000) 1875-1882 [31] R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics, Report No. SAND89- 8009, Sandia National Laboratories, 1989. [32] R.J. Kee, J. Warnatz, J.A. Miller, A FORTRAN Computer Code Package for the Evaluation of Gas- Phase Viscosities, Conductivities and Diffusion Coefficients, Report No. SAND83-8209, Sandia National Laboratories, 1983. [33] P. Middha, H. Wang, Combust. Theor. Model. 9 (2005) 353-363. [34] F.N. Egolfopoulos, P.E. Dimotakis, Proc. Combust. Inst. 27 (1998) 641–648. [35] M. Nishioka, C.K. Law, T. Takeno, Combust. Flame 104 (1996) 328–342. [36] H. Wang, X. You, A.V. Joshi, S. G. Davis, A. Laskin, F. Egolfopoulos, C.K. Law, USC Mech Version II. High Temperature combustion Reaction Model of H 2 /CO/C 1 -C 4 Compound. http://ignis.usc.edu/USC_Mech_II.htm, May 2007. 47 [37] J.Li, Z.Zhao, A. Kazakov, M. Chaos, F.L. Dryer, Int. J. Chem. Kinet. 36 (2004) 566-575. [38] A.T. Holley, X. You, E. Dames, H. Wang, F.N. Egolfopoulos, Proc. Combust. Inst. 32 (2009) 1157-1163. [39] D.A. Sheen, X. You, H. Wang, T. Løvås, Proc. Combust. Inst. 32 (2009) 535-542. [40] D.A. Sheen, H. Wang, Combust. Flame 158 (2011) 2358-2374. [41] D.A. Sheen, Spectral Optimization and Uncertainty Quantification in Combustion Modeling. PhD thesis, University of Southern California, 2011 [42] S.G. Davis, A.B. Mhadeshwar, D.G. Vlachos, H. Wang, Int. J. Chem. Kinet. 36 (2004) 94-106. [43] M.T. Reagan, H.N. Najm, R.G. Ghanem, O.M. Kino, Combust. Flame 132 (2003) 545-555. [44] M.T. Reagan, H.N. Najm, B.J. Debusschere, O.P. Le Maitre, O.M. Kino, R.G. Ghanem, Combust. Theor. Model. 8 (2004) 607-632. [45] M.T. Reagan, H.N. Najm, P.P. Pebay, O.M. Kino, R.G. Ghanem, Int. J. Chem. Kinet. 37 (2005) 368-382. [46] D.A. Sheen, H. Wang, Combust. Flame 158 (2011) 645-656. 48 Chapter 3 Studies of Premixed and Non-premixed Hydrogen Flames 3.1. Introduction The study and development of kinetic models for the oxidation of hydrogen has long been motivated by its hierarchical importance in combustion chemistry. As discussed in Chapter 1, recent interest in utilizing syngas as a fuel for stationary gas turbines will require a comprehensive revalidation of existing chemical kinetic reaction models for hydrogen oxidation at elevated pressures and low-temperatures (e.g., [1,2]). Adding to challenges in accurately modeling syngas oxidation is the possibility of significant H 2 O vapor present in the fuel stream after coal gasification. Nitrogen oxide (NO x ) mitigation strategies for stationary gas turbines include H 2 O vapor injected into gas turbine combustors or the utilization of exhaust gas recirculation (e.g., ([3-6]). Therefore the kinetics of H 2 oxidation in the presence of notable H 2 O concentration needs additional validation. Recent efforts to developing accurate syngas (and H 2 ) oxidation chemical kinetic models include, but are not limited to Refs. [7-12]. With regards to understanding the kinetics of hydrogen oxidation at elevated pressures, Burke et al. [2], demonstrated a negative pressure dependence of the mass burning rate at 25 atm, particularly for mixtures with low flame temperatures. Ref. [2] additionally demonstrated that 49 predictions made using the majority of existing models for H 2 oxidation failed to reproduce their experimental observations. More recently, Burke et al. [12] published an updated H 2 /O 2 kinetic model incorporating recent improvements in elementary rate coefficients, specifically developed to reproduce the trends observed in their experimental results by a wide margin. The inability of recently developed reaction models to reproduce the results from Burke et al. [2] has been a source of contention. Sheen [13] demonstrated that this inability stemmed from the uncertainties inherent in the rate parameters and not from errors in kinetic pathways. Using an existing kinetic model [10] optimized using MUM-PCE, Sheen [13] was able to reproduce the experimental measurements from Burke et al. [2]. Regardless, these studies highlight the need for additional flame data for hydrogen oxidation to better constrain existing, and aid in the development of new, kinetic models for hydrogen combustion. measurements with accurately quantified uncertainties for H 2 /oxidizer flames are a key component for the ongoing foundational fuel effort into validating and constraining H 2 oxidation chemistry. There is a large body of literature results for H 2 /air flames at atmospheric pressure (e.g., [14-20]). The difficulty with utilizing this data is the large spread in these measurements. There is little consensus between values at a fixed in each of these studies. The primary difficult encountered in experimental measurements of H 2 /air flames is that, for such mixtures range from few cm/s to few m/s. At such large flow field velocities, there is notable uncertainty in any flow velocity quantification methodology (PIV or LDV). Additionally, the extrapolation of these results to zero stretch will introduce uncertainties depending on the methodology used, e.g., linear or non-linear extrapolation. Fuel lean H 2 /air mixtures have a sub-unity Le and therefore are S u o S u o S u o S u o 50 thermo-diffusionally unstable. This add uncertainty to the so-called measured ’s of fuel lean H 2 /air flames which cannot physically exist at the zero stretch limit due to cellular instabilities. The first goal of the present study was to provide data for hydrogen oxidizer mixtures with accurately quantified uncertainties. Using a modified O 2 /N 2 oxidizer with a larger N 2 dilution ratio relative to air, ’s of H 2 /O 2 /N 2 flames at near stoichiometric conditions were measured. Such mixtures avoided the large flow velocities needed to stabilize H 2 /air flames. Both extrapolated ’s and directly measured S u,ref ’s were used to evaluate a number of recently developed kinetic models for H 2 oxidation. Syngas combustion in stationary gas turbines at elevated pressures and in the presence of notable quantities of vapor phase H 2 O will readily result in the production of the hydroxyl radical (HO 2 ). The main source of HO 2 is via a three-body main termination reaction between H and O 2 . H 2 O is a very efficient three body collisional molecule, and as such its presence will only serve to enhance the overall rate for the main termination reaction. There is a large uncertainty associated with the rate parameter used to express this three-body reaction in existing H 2 oxidation models. Additionally, the associated collisional efficiency of three body molecules, especially H 2 O, has a notable uncertainty. Reducing this uncertainty has driven recent studies into wet H 2 oxidation (e.g., [21-26]). With the above discussion in mind, the second goal of this study was to perform systematic flame type experiments in the counterflow configuration that would highly sensitize three-body reactions. The target reaction was the main termination reaction involving H 2 O as the third body, i.e., H + O 2 +H 2 O HO 2 + H 2 O. There are three S u o S u o S u o S u o 51 common methods to sensitize three body reactions, increasing the ambient pressure, reducing flame temperature, or adding gases known for their strong collision efficiency. All three methods were employed in this study. The extinction limits of ultra-lean H 2 /air flames were determined experimentally. The flame temperature of these ultra-lean flames lies between 1000 and 1400 K. In addition to sensitizing three-body reactions, at these temperatures, the H 2 oxidation system is at the cross over point between the main chain branching reaction and the main chain termination reaction. These data are useful in validating this cross over behavior in various H 2 oxidation kinetic models. The sensitivity of the main termination reaction involving H 2 O is also increased in “wet” premixed and non-premixed H 2 flames. H 2 O is introduced into the reaction zone in the vapor phase as part of the reactant, oxidizer, or diluent jet. The extinction limits of premixed and non-premixed H 2 /H 2 O/air flames were determined experimentally. The final goal of this study relates to the overall scarcity of elevated pressure H 2 flame measurements with systematically quantified uncertainties. This data is essential to improve the understanding and kinetic modeling of the pressure dependence in H 2 flames. In the counterflow configuration steady non-premixed H 2 flames are more readily established at elevated pressures compared to premixed H 2 /oxidizer flames. Based on these constraints, the extinction limits of non-premixed H 2 flames at atmospheric and elevated pressures over a wide range of fuel concentrations were measured. 52 3.1.1 Theory of three body reactions As mentioned previously, syngas production can result in notable quantities of H 2 O and CO 2 , that are efficient colliders when participating in three-body reactions. The notable presence of such molecules increases an oxidation system’s overall sensitivity to three body reactions, such as the main termination reaction producing HO 2 can be denoted as A + B + M ↔ AB + M. (R1) R1 is essentially a global representation of an elementary chemical reaction mechanism that begins with the collision of two species, A and B, and results in the formation of a new species, AB. The behavior of this reaction requires a combination of unimolecular and bimolecular reaction rate theories. At very high pressures or at the high-pressure limit, the overall reaction behaves like a bimolecular reaction and is only temperature dependent. At very low pressures or at the low-pressure limit, the overall reaction is unimolecular in nature and is both pressure and temperature dependent. Between the high and low pressure limits is the fall-off regime typically estimated from reaction rate theory. The Lindeman Mechanism explains most of the trends of unimolecular reactions qualitatively well. The effectiveness of different third bodies (any non-participating molecule in the reacting mixture) at transferring energy away from AB as it is formed is species dependent. H 2 O and CO 2 being more efficient collisional partners relative to say Ar or N 2 . The rate parameter for H+O 2 +M ↔HO 2 +M has been studied both in shock tubes and flow reactors over a range of temperatures (e.g., [53-59]). Recently, Petersen and coworkers [59] determined third-body collision efficiencies from shock tube ignition 53 delay time studies of syngas mixtures. The reported collision efficiency of H 2 O relative to N 2 was 12.2. Ashma and Haynes [60] estimated the relative collision efficiencies near 800 K to be of the order of 1 : 2.4 : 10.6 for M = N 2 , CO 2 , and H 2 O respectively. The reaction rate for the main termination reaction involving H 2 O at room temperature was theoretically derived by Michael et al. [55] and can be scaled relative to N 2 as H 2 O : N 2 = 11.6 : 1. Finally, Bates et al. [58] used 10.3 : 1 for M = H 2 O : N 2 between the temperature range of 1081 - 1262 K. Figure 3.1 depicts the rate constant for the main termination reaction as a function of pressure at 1200 K for M = Ar, N 2 , and H 2 O taken from Ref. [58]. The effectiveness of different third bodies on the overall rate parameter is apparent. Figure 3.1. Rate coefficient of reaction H+O 2 +M HO 2 +M at 1200 K for M = Ar, N 2 , H 2 O as a function of pressure. Data and theoretical high and low pressure limit rate coefficients are taken from Bates et al. [58]. 10 0 10 1 10 2 10 3 10 11 10 12 10 13 10 14 k ∞ k o (H 2 O)[M] Reaction constant, k, cm 3 mol -1 s -1 Pressure (bar) k o (N 2 )[M] k o (Ar)[M] H + O 2 + M HO 2 + M (1200 K) 54 3.2. Experimental approach Experiments were carried out at various pressures between 1 to 7 atm and unreacted fuel-carrying temperature of 298 K, water-carrying temperature from 343 K to 393 K as listed in Table 3.1. Mixture P [atm] T u [K] D [mm] L [mm] L/D Premixed H 2 /O 2 /N 2 1 298 10 11 ~ 1.1 H 2 /air 1 298 10, 14 10, 14 ~ 1 H 2 /air/H 2 O 1 343 10, 14 10, 14 ~ 1 Non-premixed H 2 /N 2 -air 1 298 10 10 ~1 4 298 7 9 ~1.29 7 298 7 9 ~1.29 H 2 /N 2 - air/H 2 O 1 353 10 10 ~1 4 393 7 9 ~1.29 Table 3.1. Experimental configuration and conditions. K ext ’s of premixed flames were measured using the single-flame configuration by counterflowing fuel/air mixtures against an ambient temperature N 2 jet. For H 2 /air flames, a flame was established at a near extinction condition and the oxidizer flow rate was slightly modified to achieve extinction and determine thus K ext (e.g., [27]). For H 2 /air/H 2 O mixtures, a flame was established at a fixed and a given strain rate, water concentration was slightly increased to achieve extinction and determine thus K ext . D = 14 mm for K ext ≤ 400 s -1 and D = 10 mm for K ext > 400 s -1 for atmospheric conditions. 55 K ext , are also measured for non-premixed H 2 flames. Experiments are carried out by counterflowing preheated air or air/water jet against H 2 /N 2 jet at room temperature. H 2 O was added to the oxidizer (air) stream to conduct the experiment under conditions for which the sensitivity of the extinction state to the main termination reaction was enhanced. Extinction was achieved by slightly modifying H 2 concentration for dry H 2 flames. To determine K ext ’s for water addition experiments, the water concentration was slightly increased until extinction occurs. 10 mm burner diameter was used at P = 1 atm. For elevated pressure conditions, P = 4 and 7 atm, a burner with a D = 7 mm were used and L = 9 mm. The H 2 O vaporization system is consisting of a high precision syringe pump and nebulizer that are used to deliver ultra-fine droplets of H 2 O into a vaporization chamber as shown in Fig. 3.2. Figure 3.2. A schematic of the experimental apparatus, including the vaporization system, setup for non-premixed flames in the high pressure chamber using LDV. Laser beam Pressure Chamber cooling coil Top Burner N 2 Fuel Air Pre-heater Sonic nozzle Pressure Gauge Nebulizer Vaporization chamber Nebulizer Silicon oil Heating tape High pressure syringe pump Water Light source for colorless H 2 flame Laser Bottom Burner 56 3.3 . Numerical approach All simulation results are grid independent and utilized approximately 2100 grid points. Four kinetic models were used to simulate experimental data, which are summarized in Table 3.2. The first model is the H 2 /CO sub-model of USC Mech II [8]. This model will be referred to as Model I hereafter. Model II is the H 2 /CO sub-model of Li et al. [7]. Model III is a recently updated H 2 /O 2 model by Burke et al. [12]. Model Ia is the model by Davis et al. [10]. Model Ia is identical to Model I with the exception of the reaction rate parameter for the chain termination reaction, HO 2 +OH=H 2 O+O 2 . Mechanism Model I USC Mech II [8] Model Ia Davis et al. [10] Model II Li et al. [7] Model III Burke et al. [12] Table 3.2. Kinetic models used to simulated present data. The diffusion coefficients for Models I, Ia, and III were implemented in the simulations using updated H and H 2 diffusion coefficients for several key pairs based on a re-evaluated set of Lennard Johns parameters by Wang and coworkers [7,8]. The elementary reactions common to all four models in Table 3.2 are listed in a consistent manner in Table 3.3 to facilitate proceeding analysis and discussion. 57 Reaction (H 2 /O 2 system) Uncertainty factor (Model I) (R1) H + O 2 O + OH 1.2 (R2) H + O 2 +M HO 2 + M 1.3 (R3) O + H 2 OH + H 1.3 (R4) H 2 + OH H 2 O + H 2.0 (R5) HO 2 + H OH + OH 2.0 (R6) HO 2 + OH H 2 O + O 2 2.0 (R7) HO 2 + O O 2 + OH 2.0 (R8) HO 2 + H H 2 + O 2 1.3 (R9) O +H 2 O OH + OH 1.3 (R10) H + OH +M H 2 O + M 2.0 (R11) H + H + M H 2 + M 2.0 Table 3.3. List of reactions and associated uncertainties. The elementary reactions of the H 2 /O 2 oxidation system discussed in this chapter and the uncertainty factors associated with the Arrhenius pre-factors of each rate parameter were listed Table 3.3. The uncertainty factors were determined in Ref. [33]. 58 3.4 . Laminar flame speeds of H 2 /oxidizer mixtures Figure 3.3 depicts literature experimental results [14-20,29] and numerical calculations for ’s of H 2 /air mixtures at P = 1 atm and T u = 298 K. Calculations were performed using Models I, II, and III. Between 0.5 ≤ ≤ 1.2, Fig. 3.3a, there is relatively good agreement between all eight sets of experimental data. Differences between experimental measurements appear at richer ’s, Fig. 3.3b. For example, at = 2.6, there is a 55 cm/s spread in the measured of a H 2 /air flame. There is closer agreement between the numerical calculations of in both Figs. 3.3a and 3.3b relative to experimental results. For H 2 /air flames, predictions by Models I and II are nearly identical. For ≤ 1.2 Model III’s predictions are in close agreement with those by Models I and II. At richer ’s, Model III consistently predicts higher ’s. For all three models, the at which peaks is nearly identical, ≈ 1.75. This value coincides with experimental observations for the at which ’s of H 2 /air peak. The literature results in Fig. 3.3 were all determined using the spherically expanding flame technique except for the measurements performed by Egolfopoulos and Law [29], which were determined using the counterflow configuration. It should be noted that it is difficult to perform meaningful comparisons between existing literature results, depicted in Fig. 3.3, as there is a distinct lack of meaningful quantification of experimental uncertainties for these measurements. Nevertheless, from Figs. 3.3a and b, it can be observed that the present calculations lie well within the range of experimental results. A new set of experimental measurements, with carefully quantified experimental uncertainties of ’s of H 2 /(9.5%O 2 +90.5%N 2 ) mixtures were determined. The S u o S u o S u o S u o S u o S u o S u o S u o 59 percentage of diluent, N 2 , was determined in order to maintain a maximum S u,ref below 90 cm/s. Reducing the stretched flame speed resulted in a lower propensity for the mixture to flash back. Additionally, the overall Re of the flow at the burner exit was reduced, reducing flow induced instabilities. Figure 3.3. Comparison of experimental and numerical ’s for H 2 /air mixture with literature experimental data [14,15,16,17,18,19,20,29] at T u = 298 K, and P = 1 atm. Numerical simulations using Model I ( ), Model II ( ), and Model III ( ). Huang et al. (2006) Hu et al. (2009) Dowdy et al. (1990) Tse et al. (2000) Tang et al. (2008) Aung et al. (1997) Egolfopoulos and Law (1990) Lamoureux et al. (2003) (a) (b) S u o 60 Figure 3.4a compares literature results [29,30] and numerical calculations for ’s of H 2 /(7.7%O 2 +92.3%N 2 ) mixtures at T u = 298 K, and P = 1 atm. Experimental results by Hermanns et al. [30] were determined using the heat flux burner technique. There is closer agreement between the two literature data sets over a wide range of ’s compared to the experimental data sets compared in Fig. 3.3. For ≥ 2.0, the results from Egolfopoulos and Law [29] are generally higher than those from Ref. [30]. Figure 3.4b compares present experimental results and numerical calculations for H 2 /(9.5%O 2 +90.5%N 2 ) mixtures. S u o 61 Figure 3.4. Comparison of experimental and numerical ’s of (a) H 2 /(9.5%O 2 +90.5%N 2 ) and (b) H 2 /(7.7%O 2 +92.3%N 2 ) taken from Refs. 18 and 32. T u = 298 K, and P = 1 atm. Numerical simulations using Model I ( ), Model II ( ), and Model III ( ). H 2 /(7.7%O 2 +92.3%N 2 ) Hermanns et al. (2007) Egolfopoulos and Law (1990) H 2 /(9.5%O 2 +90.5%N 2 ) Present results S u o 62 Comparing model calculations of ’s for the two H 2 /O 2 /N 2 mixtures in Figs. 3.4a and 3.4b, some clear differences emerge relative to Fig. 3.3. Namely, there are now observable differences between predictions using all three modes. Detailed analysis that will be presented later in this section illustrates that this difference is kinetic in nature and stems from the varying treatment of the 3 rd body collision efficiency of N 2 . From Fig. 3.4b, it can be seen that for ≤ 2.0 Model III calculations agree best with the new measurements. At larger ’s, calculations from Model II reproduce present experimental results. Overall, with increasing diluent fraction in the oxidizer stream, all three models tend to underpredict the measured ’s. Detailed analysis of the computed flame structures was performed and the results are shown in Figs. 3.3 and 3.4 to better understand the kinetic differences and similarities between H 2 /air and diluted H 2 /O 2 /N 2 flames. The latter mixtures have a reduced adiabatic flame temperature. The normalized logarithmic sensitivity coefficients of to reaction rate coefficients for H 2 /air (left two panels) and H 2 /(9.5%O 2 +90.5%N 2 ) (right two panels) flames at = 1.1 (upper two panels), and = 1.75 (lower two panels) are shown in Fig. 3.5. The logarithmic sensitivity coefficients are normalized by the value of the sensitivity coefficient of the main branching reaction (R1) H+O 2 →OH+O. Comparing sensitivity coefficients of H 2 /air and H 2 /(9.5%O 2 +90.5%N 2 ) flames reveals that overall, these two sets of mixtures appear to be similar. There is notable sensitivity to the chain branching (R1 and R3), propagating (R4 and R5), and termination (R10) reactions for all three models apparent in Fig. 3.5. The key difference in the sensitivity analysis results between these two flames is in their sensitivity to R2. For H 2 /air flames, increasing the rate of R2 has a positive effect on reactivity, whereas for S u o S u o S u o 63 H 2 /(9.5%O 2 +90.5%N 2 ) flames, increasing the rate of R2 will have a negative effect on reactivity. Figure 3.5. Normalized logarithmic sensitivity coefficients of to reaction rate coefficients at = 1.1 and 1.75, for H 2 /air flames and H 2 /(9.5%O 2 +90.5%N 2 ) flames computed using Model I, II, and III for T exit = 298 K, and P = 1 atm. -1.0 -0.5 0.0 0.5 1.0 1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -1.0 -0.5 0.0 0.5 1.0 1.5 (R4) OH+H 2 → H+H 2 O (R1) H+O 2 → O+OH (R5) HO 2 +H → OH+OH (R6) HO 2 +OH → H 2 O+O 2 (R3) O+H 2 → H+OH (R8) HO 2 +H → H 2 +O 2 (R10) H+OH+M → H 2 O+M (R2) H+O 2 +M → HO 2 +M (R11) H+H+M → H 2 +M (b) = 1.1 H 2 /(9.5%O 2 +90.5%N 2 ) (R4) OH+H 2 → H+H 2 O (R1) H+O 2 → O+OH (R5) HO 2 +H → OH+OH (R6) HO 2 +OH → H 2 O+O 2 (R3) O+H 2 → H+OH (R8) HO 2 +H → H 2 +O 2 (R10) H+OH+M → H 2 O+M (R2) H+O 2 +M → HO 2 +M (R11) H+H+M → H 2 +M (d) = 1.75 H 2 /(9.5%O 2 +90.5%N 2 ) (c) = 1.75 H 2 /air Normalized Logarithmic Sensitivity Coefficient Normalized Logarithmic Sensitivity Coefficient (R4) OH+H 2 → H+H 2 O (R1) H+O 2 → O+OH (R5) HO 2 +H → OH+OH (R6) HO 2 +OH → H 2 O+O 2 (R3) O+H 2 → H+OH (R8) HO 2 +H → H 2 +O 2 (R10) H+OH+M → H 2 O+M (R2) H+O 2 +M → HO 2 +M (a) = 1.1 H 2 /air Model I Model II Model III (R11) H+H+M → H 2 +M (R4) OH+H 2 → H+H 2 O (R1) H+O 2 → O+OH (R5) HO 2 +H → OH+OH (R6) HO 2 +OH → H 2 O+O 2 (R3) O+H 2 → H+OH (R8) HO 2 +H → H 2 +O 2 (R10) H+OH+M → H 2 O+M (R2) H+O 2 +M → HO 2 +M (R11) H+H+M → H 2 +M S u o 64 Figure 3.6 depicts the concentrations of major radicals H, OH, HO 2 , and O (left two panels) and the reaction rates for R1, R2, and R5 (right two panels) for H 2 /air and H 2 /(9.5%O 2 +90.5%N 2 ) flames at = 1.1. Figure 3.6 clearly demonstrates some of the key differences between these two flames caused by increasing diluent ratio in the oxidizer stream. Firstly, the ratios of HO 2 :H, HO 2 :OH, and HO 2 :O are clearly larger in the H 2 /(9.5%O 2 +90.5%N 2 ) flame. Secondly, there is a change in the ratio between the main branching and main termination reaction. For the H 2 /air flame, R1/R2 > 1, whereas for the H 2 /(9.5%O 2 +90.5%N 2 ) flame R1/R2 < 1. Finally, R5 is an order of magnitude lower in the H 2 /(9.5%O 2 +90.5%N 2 ) flame relative to the H 2 /air flame. The differences in the characteristics of the radical pools and elementary reaction rates between these two flames factor into the observed differences in sensitivity of to R2 observed in Fig. 3.5. For H 2 /air flames approximately 70% of HO 2 , a large majority of which is produced via R2, is consumed through R5 resulting in the more reactive OH. The percentage of HO 2 consumed via R5 is greatly reduced in the H 2 /(9.5%O 2 +90.5%N 2 ) flame. S u o 65 Figure 3.6. Comparison of species mass fraction and reaction rate for H 2 /air and H 2 /(9.5%O 2 +90.5%N 2 ) flames at = 1.1, T u = 298 K, and P = 1 atm computed using Model III. 3.4.1 A brief consideration of numerical uncertainties Although there has been tremendous progress in the understanding of chemical kinetic reaction mechanism for the oxidation of the H 2 /O 2 system since the pioneering work of Dixon-Lewis [31,32], there remains an important role for experimental results with carefully quantified experimental uncertainties. Inherent in all kinetic models of the oxidation of H 2 are uncertainties in their elementary reaction rate parameters. As discussed in Chapters 1 and 2, uncertainties in elementary rate parameters, when propagated into numerical predictions of combustion phenomena manifest themselves as numerical uncertainties in predictions. Figure 3.7 depicts the probability density function and 2 uncertainty (95% confidence interval) band for the predicted ’s of H 2 /(9.5%O 2 +90.5%N 2 ) flames using Model I. From Fig. 3.7 it can be seen that the 0.00E+00 2.00E-03 4.00E-03 6.00E-03 8.00E-03 1.00E-02 1.20E-02 0.00E+00 4.00E-04 8.00E-04 1.20E-03 1.60E-03 2.00E-03 2.40E-03 0 0.02 0.04 0.06 0.08 0.1 0 400 800 1200 1600 2000 2400 0.0E+00 1.0E-02 2.0E-02 3.0E-02 4.0E-02 5.0E-02 6.0E-02 0 0.02 0.04 0.06 0.08 0 400 800 1200 1600 2000 2400 0.0E+00 5.0E-04 1.0E-03 1.5E-03 2.0E-03 2.5E-03 3.0E-03 0.02 0.04 0.06 0.08 0.1 0.12 0.0E+00 2.0E-04 4.0E-04 6.0E-04 8.0E-04 1.0E-03 1.2E-03 0.0E+00 6.0E-05 1.2E-04 1.8E-04 2.4E-04 3.0E-04 3.6E-04 0 0.05 0.1 0.15 0.2 H, HO 2 Mass Fraction OH H HO 2 O, OH Mass Fraction OH H HO 2 Spatial Coordinate, x, cm O O (b) H 2 /O 2 /N 2 (a) H 2 /air Reaction Rate, R, mol cm -3 s -1 Flame Temperature, T f , K R1 R1 R2 R2 R5 R5 (b) H 2 /O 2 /N 2 (a) H 2 /air Spatial Coordinate, x, cm T f T f S u o 66 combined uncertainties in the individual rate parameters results in a 5-10 cm/s uncertainty in calculated results. Figure 3.7. Probability density function and 2 uncertainty band of the predicted ’s of H 2 /(9.5%O 2 +90.5%N 2 ) flames using Model I. As mentioned earlier in Sec 3.3, the elementary reactions of the H 2 /O 2 oxidation system discussed in this chapter and the uncertainty factors associated with the Arrhenius pre-factors of each rate parameter were listed Table 3.3. For the calculation depicted in Fig. 3.7, the collision efficiency of H 2 O was considered separately from the general third body, M, of R2. The reaction, H + O 2 + H 2 O HO 2 + H 2 O, was assigned an uncertainty factor of 2.5. The eventual goal of H 2 oxidation reaction model development will be to constrain this uncertainty which will require the experimental results provided in this section. This process is discussed in depth in Chapter 7. 0.01 0.02 0.03 0.04 0.05 S u o 67 3.5. Experimental results and kinetic modeling of stretched flames Throughout this thesis there is an overarching discussion with regards to the value of modeling laminar flame speeds vs. modeling the raw, un-extrapolated, or directly measured, stretched flame speed results. Figures 3.8a and 3.8b compare linear vs. non- linear extrapolation techniques for H 2 /air and H 2 /(9.5%O 2 +90.5%N 2 ) flames over a wide range of ’s. Clearly at the conditions depicted in Fig. 3.8b there is little discrepancy between ’s determined using either technique. For the leaner mixtures depicted in Fig. 3.8a, there can be as large as a 10 cm/s difference between ’s determined using linear vs. non-linear extrapolations. In this section S u,ref vs. K data is directly modeled using the opposed jet code given our confidence in its underlying physical model. S u o S u o 68 Figure 3.8. Comparison of non-linear and linear extrapolation techniques for H 2 /air and H 2 /(9.5%O 2 +90.5%N 2 ). It was explained in the introduction to this chapter that H 2 /oxidizer flames are prone to developing cellular instabilities. These instabilities are suppressed in positively stretch counterflow H 2 /oxidizer flames. Figure 3.9 depicts S u,ref vs. K results for a H 2 /air flame at = 0.28. Clearly at K < 140 s -1 such instabilities are still manifested in the counterflow configuration as the large scatter in S u,ref values at a fixed strain rate. Increasing K, = 1.1 = 0.45, H 2 /air Non-linear extrapolation Linear extrapolation = 0.32, H 2 /air H 2 /(9.5%O 2 +90.5%N 2 ) = 1.75 = 2.4 Non-linear extrapolation Linear extrapolation H 2 /(9.5%O 2 +90.5%N 2 ) (a) (b) 69 reduces this scatter. That is, for K > 150 s -1 these instabilities are suppressed and the scatter in S u,ref at a fixed strain rate is greatly reduced. Care needs to be taken even for counterflow H 2 /oxidizer flames that K is sufficiently large enough to avoid such instabilities. Figure 3.9. Sample case for cellular flame observed from counterflow configuration at lower strain rate for H 2 /air flame at = 0.28, T u = 298 K, and P = 1 atm. Figures 3.10a to 10f depict a subset of the experimental results for H 2 /air and H 2 /(9.5%O 2 +90.5%N 2 ) flames at = 0.35, 0.45, 1.10, 1.75, 2.10, and 2.40 respectively. For the fuel lean cases depicted in Figs. 3.10a, 3.10b, and 3.10c, there is a notably large gradient (i.e., large Markstein Length) in the S u,ref vs. K data. At very fuel rich ’s, the results of Figs. 3.10e and 3.10f show that there is a much weaker dependence of S u,ref to K relative to the two aforementioned fuel ultra-lean cases, i.e., smaller Markstein Lengths. This is to be expected as the latter are more vigorously burning flames that are Cellular instability #1 Cellular instability #2 Cellular instability #3 70 less sensitive to stretch than the weaker burning fuel lean flames. Additionally, as mentioned in the introduction, fuel lean H 2 /air flames have a sub-unity Le, i.e., molecular diffusivity is larger than the thermal diffusivity of the bulk mixture; hence their stretched flame speeds have a strong positive dependence on stretch. As K is increased, there is a greater net flux of H 2 into the reaction zone than heat loss from the reaction zone. Figures 3.10a to 3.10f also compare numerical calculations using Models I to III against present experimental data. At all ’s considered, the present models reproduce to a very high degree the slope or gradient in the experimentally determined S u,ref vs. K data. This is as expected since it has been demonstrated repeatedly (e.g., [34,35]) that the balance of momentum and heat, upstream of the preheat zone where S u,ref is determined, should not depend to the first order on kinetics or transport of the chemical kinetic model. This agreement also provides confidence in the underlying physical numerical simulations of the opposed jet. Comparing numerical predictions against experimental results, Model I consistently underpredicts measured S u,ref . At very fuel lean ( = 0.35) and very fuel rich ( = 2.4) conditions, Model II is in good agreement with present experimental data. Between 0.35 < < 2.1, calculations using Model II underpredict experimentally measured S u,ref . Calculations using Model III underpredict the experimental data for the fuel lean cases considered, = 0.32, 0.35 and 0.45. Model III predicts a much stronger effect of increasing on the reactivity of H 2 /oxidizer mixtures compared with Models I and II. Therefore, calculated S u,ref ’s using Model III go from underpredicting experimental results for the leanest case (Fig. 3.10a) to overpredicting experimental results for the richest case (Fig. 3.10f). 71 Figure 3.10. Comparison of experimental raw data and numerical predictions for stretched flame speeds for H 2 /air at = 0.32, 0.35 and 0.45, and H 2 /(9.5%O 2 +90.5%N 2 ) mixtures at = 1.1, 1.75, and 2.4, for T u = 298 K and P = 1 atm. Numerical simulation by Model I( ), Model II( ), Model III ( ). It is reassuring to observe that the relative trends between the models in Fig. 3.4b for are consistent with the trends observed between the models for the computed S u,ref vs. (b) Model I Model II Model III (a) (d) (c) (f) (e) S u o 72 K. It is also observed that the magnitude of the differences between numerically calculated and experimentally determined ’s is also mirrored in a similar comparison of model calculations and experimental results for S u,ref .vs. K’s lending further confidence to the non-linear extrapolation methodology. 3.6 . Extinction limits of premixed and non-premixed flames In this section the chemical kinetics governing the near limit phenomena for premixed and non-premixed H 2 flames is further investigated. The differences and similarities to the previously studied flame phenomena, flame propagation, are discussed. 3.6.1 Extinction limits of premixed H 2 /air flames Figure 3.11 compares the experimentally determined and numerically computed K ext for premixed H 2 /air flames between 0.28 ≤ ≤ 0.35. There is excellent agreement between the experimental and computed results using Model II for 0.28 ≤ ≤ 0.35. Predicted K ext ’s by Models I and III are identical and 20 to 55 % lower than the predictions by Model II. The largest differences ~50 % are at the leanest ’s considered. S u o 73 Figure 3.11. K ext ’s of premixed H 2 /air flames at T exit = 298 K and P = 1 atm. Numerical simulation by Model I( ), Model II( ), Model III ( ). The overall trends between experimental results and numerical calculations of K ext ’s of premixed H 2 /air flames are identical to the trends observed in Figs. 3.10a ( = 0.32) and 3.10b (at = 0.35). That is, Model II reproduces experimental results and predictions made using Models I and III are identical but notably underpredict experimental results. This observation is somewhat different to trend seen in Fig. 3.3a. That is, for ’s of H 2 /air flames, Model III has the strongest reactivity, and calculations by Models I and II are identical and lower than Model III. Figure 3.12 depicts the normalized logarithmic sensitivity coefficients of K ext to reaction rate coefficients computed by using Models I, II and III for H 2 /air flames at = 0.28. S u o 74 Figure 3.12. Normalized Logarithmic sensitivity coefficients of K ext to reaction rate coefficients for premixed H 2 /air flames at = 0.28, T u = 298 K, and P = 1 atm using Model I, Model II, and Model III. Comparing Fig. 3.5 which shows the sensitivity of ’s to rate parameters with Fig. 3.12, there are a number of key differences between these two sets of flame phenomena and the kinetics sensitized. In Fig. 3.12, there is notable sensitivity to the chain propagating, terminating, and branching reactions for all three models; OH + H 2 → H + H 2 O (R4) H + O 2 + M → HO 2 + M (R2) H + O 2 → OH + O . (R1) Additionally, there is a large sensitivity to chain branching reactions O + H 2 → H + OH (R3) HO 2 + H → OH + OH. (R5) -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 (R4) OH+H 2 → H+H 2 O (R1) H+O 2 → O+OH (R5) HO 2 +H → OH+OH (R6) HO 2 +OH → H 2 O+O 2 (R3) O+H 2 → H+OH (R8) HO 2 +H → H 2 +O 2 (R7) HO 2 +O → OH+O 2 (R2) H+O 2 +M → HO 2 +M H 2 /air = 0.28 Normalized Logarithmic Sensitivity Coefficient Model I Model II Model III S u o 75 Compared to ’s, K ext ’s are not sensitive to R10 and R11, chain termination reactions involving H. There is instead increased sensitivity to reactions involving HO 2 , such as HO 2 consumption by O, R7. The largest difference between the kinetics of these two phenomena is the large negative sensitivity of K ext ’s to R2. In Fig. 3.5a there is a small positive sensitivity of ’s to R2, but for extinction phenomena this sensitivity is strongly negative. To better understand the differences observed between the numerical calculations depicted in Figs. 3.3, 3.10, and 3.11, it is important to look closer at the choices of rate parameters for the elementary reactions used in the three models considered in this study. R1 is well parameterized. Most recently, Hong et al. [36] proposed a new rate coefficient for R1 with improved uncertainty bounds, this rate is used in Model III. Although all three models have selected slightly different values for the rate parameters the resulting net reaction rate is within 7 % for all three models between 1000-1400 K and within 15 % between 1400-2500 K. Since the vast majority of studies in this chapter are within the former range, discrepancies observed in predictions using these three models is unlikely due to choice of rate coefficient of R1. From Fig. 3.12 it is clear that for numerical calculations of K ext ’s of ultra-lean H 2 /air flames, the ratio of R2 to R1 will play a prominent role in dictating the overall reactivity. Figure 3.13 plots the branching ratio between R2 and R1 for all three models over a wide range of temperatures and at 1 and 7 atm. Clearly Model II has the lower ratio of R2:R1 resulting in increased overall reactivity for calculations of fuel lean flames. For Models I and III this ratio is identical. The ranking of R1:R2 between all three models is consistent with observations in Fig. 3.11. S u o S u o 76 Figure 3.13. Branching ratio between R2 and R1. Compared to R1, there exist notable uncertainty in the rate parameter for R2. This is especially the case for the 3 rd body collisional efficiency of H 2 O. Models II and III use the same value for the low pressure limit rate coefficient for R2 proposed by Michael et al [37] but have changed the centering factor and 3 rd body efficiency of H 2 O [2]. Between Models II and III, the centering factor was changed from 0.8 to 0.5 and the collisional efficiency of water was updated. The collisional efficiency of H 2 O relative to N 2 in R2 has been assigned a value of 11.89, 11.0, and 14 for Models I, II, and III respectively. The result of this analysis is that although Model I uses a different rate constant for R2 [10,38] compared with Models II and III, the resulting overall reaction rate for R2 between Models I and III are nearly identical. This explains the identical predictions between Models I and III depicted in Fig. 3.11. Models I and III adopt the high pressure limit rate coefficient expression of R2 proposed by Troe [38]. Model I then 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 700 1000 1300 1600 1900 2200 2500 1 atm 7 atm T emperature, K Branching ratio, R2/R1 Model I Model II Model III 77 optimized the pre-exponential Arrhenius factor by 1.1. In Model II the high pressure limit rate parameter is from Ref. [39]. 3.6.2 Non-premixed extinction limits of H 2 /N 2 -air flames Figure 3.14 depicts the experimental and computed K ext ’s for non-premixed H 2 flames. As stated in the experimental methodology section, previous, a H 2 /N 2 jet was co- flowed against an air jet. Experimental results are presented as K ext ’s as a function of H 2 mole fraction in the fuel stream, i.e., . ) ( 2 2 2 2 N H H H n n n x Experimental conditions were T u = 298 K and P = 1, 4, and 7 atm. Numerical calculations were performed using Models I, II, and III in addition to a Model Ia (Davis et al., [10]). As stated earlier, Model Ia is nearly identical to Model I except in its representation of the reaction rate parameter of the chain terminating reaction, HO 2 + OH O 2 + H 2 O. (R6) At 1 atm, there is good agreement between the current experimental data and predictions using all three models. Calculated K ext ’s using models II, III, and Ia are identical at 1 atm. For all three conditions, P = 1, 4, and 7 atm, Model II predicts the largest K ext ’s for these non-premixed flames. Calculations by Model II overpredict experimental results at 4 and 7 atm by a factor of two. It is apparent from these results that Model II is unable to capture the pressure dependence in the chemical kinetics of non-premixed flames. There are little observable differences between calculations of K ext ’s from 78 Models I and III at all pressures considered. There is good agreement between calculated (Models I and II) and measured K ext ’s at P = 1 and 4 atm. At P = 7 atm, calculations overpredict experimental results. For all ambient pressures considered in Fig. 3.14, Model Ia is able to reproduce, with excellent agreement, experimental results for K ext ’s of non-premixed H 2 flames. Clearly, the pressure dependence of the kinetics of non- premixed H 2 flames has been better represented modeled in Model Ia relative to the other three models considered. 79 Figure 3.14. K ext ’s of non-premixed H 2 /N 2 -air flames at T exit = 298 K, and P = 1, 4, and 7 atm. Lines: Model I ( ), Model II ( ), Model III ( ), and Model Ia( ). Present data (7atm) P = 7 atm T u = 298 K Model Ia Model I Model II Model III Present data (1atm) P = 1 atm T u = 298 K P = 4 atm T u = 298 K Present data (4atm) 80 Again, the difference between Models I and Ia is in the expression of the rate parameter of R6 which is known to increase in importance with pressure. The rate constant for R6 in Model Ia was expressed by the combination of two Arrhenius forms: ) / 17330 exp( 10 0 . 1 ) / 500 exp( 10 375 . 2 0 16 0 13 6 RT T RT T k R . The first term in the above rate expression is from Keyser [40] with the original pre- exponential factor optimized by 0.82. This portion of the rate, the first term, determined by Keyser [40], represents the low temperature portion of the rate constant. The second term in the above rate expression of R6 is from Hippler et al. [41] for the intermediate and high temperature regimes. Model I used a combination of four Arrhenius forms developed by Sivaramakrishnan et al. [42], ). / 34800 exp( 10 0 . 1 ) 40000 exp( 10 51 . 2 ) / 32900 exp( 10 37 . 5 ) / 26900 exp( 10 12 . 1 ) / 60 exp( 10 41 . 1 40 136 2 12 72 . 16 70 3 . 22 85 76 . 1 18 6 RT T T RT T RT T RT T k R Models II and III use only the singular rate constant expression developed by Keyser [40]. ) / 497 exp( 10 89 . 2 0 13 6 RT T k R . Although replacing R6 in Model I with the expression from Model Ia improves its predictions of non-premixed H 2 flames at elevated pressures, this is not the case for Models II and III. Each elementary reaction in a H 2 -O 2 system is tightly coupled with significant sensitivities for predictions of global properties. Difficulties of determining the R6 rate expression are caused from the lack of consistent experimental determinations and its unusual apparent temperature dependence (e.g., [43,44]). To parameterize 81 correctly the non-Arrhenius expression for R6 accurately, and over a wide range of conditions, additional experimental data will be needed. 82 3.7 . Sensitizing three-body reactions in H 2 flames 3.7.1 ‘Wet’ H 2 /air flames Figure 3.15 shows the effect of water addition to a premixed H 2 /air flame on extinction limits. Similar with dry H 2 /air experiments, a H 2 /air jet is co-flowed against a N 2 jet with the addition of H 2 O, in the vapor phase, added to the H 2 /air jet. Experiments in Fig. 3.15 were performed at = 0.38, P =1 atm, and T u = 343 K. The percentages noted on the x-axis are the mole fraction of H 2 O in the fuel/air/H 2 O mixture. The agreements between the experimental data and numerical predictions are consistent with 1 atm results for premixed ultra fuel lean H 2 /air flame extinction limits as shown in Fig. 3.11. That is, Model II is in good agreement with the current experimental data and computation results by models I and III consistently underpredicts measurements. Figure 3.15. K ext ’s of premixed H 2 /H 2 O/air flames at = 0.38, T exit = 343 K, and P = 1 atm. Numerical simulations by Model I: ( ), Model II ( ), Model III: ( ). P = 1 atm T u = 343 K = 0 3 8 Model I Model II Model III 83 To understand better the effect of H 2 O as a third body molecule, the main termination reaction was separated into R2 and R2a, H + O 2 + M HO 2 + M (M ≠ H 2 O) (R2) H + O 2 + H 2 O HO 2 + H 2 O. (R2a) The normalized logarithmic sensitivity coefficients of K ext of wet H 2 /air flames to reaction rate coefficients computed using Model I is shown in Fig. 3.16. Figure 3.16 demonstrates that at a X H2O = 17%, K ext sensitivity to R2a is larger than sensitivity to the main branching reaction. This demonstrates that such experimental results might be effective in constraining the uncertainty associated with the collisional efficiency of the water molecule. Figure 3.16. Normalized Logarithmic sensitivity coefficients of S u o with respect to reaction rate coefficients for premixed H 2 /air/H 2 O flames computed using Model I at = 0.38, T exit = 343 K, and P = 1 atm using Model I. -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 X H 2 O = 0% X H 2 O = 10% X H 2 O = 17% (R4) OH+H 2 → H+H 2 O (R1) H+O 2 → O+OH (R5) HO 2 +H → OH+OH (R6) HO 2 +OH → H 2 O+O 2 (R3) O+H 2 → H+OH (R2a) H+O 2 +H 2 O → HO 2 +H 2 O (R9) H 2 O+O → OH+OH (R2) H+O 2 +M → HO 2 +M H 2 /air/H 2 O = 0.38 Normalized Logarithmic Sensitivity Coefficient 84 3.7.2 ‘Wet’ non-premixed H 2 flames Figure 3.17 depicts the experimental and computed K ext ’s for a non-premixed H 2 flames with H 2 O added to the oxidizer stream. In Fig. 3.17a, H 2 mole fraction of the (H 2 +N 2 ) mixture, X F is 0.17, T u = 353 K, and P = 1 atm. In Fig. 3.17b, X H2 = 0.15, P = 4 atm, and T u = 393 K. The percentages noted on the x-axis are the mole fraction of H 2 O in the oxidizer stream. The unburned mixture temperature for non-premixed flame at 1 atm was chosen as 353 K. For 4 atm experiments, a higher T u was used since the boiling point of water at 4 atm is 417 K. The agreements between the experimental results and numerical predictions at 1 atm are consistent with Figs. 3.11, 3.14a, and 3.15. That is, predictions obtained using Model II shows good agreement with current experimental data at 1 atm but notably overpredicts the data at 4 atm. Models I and III slightly underpredict the data at 1 atm but give good agreement at 4 atm. Model Ia underpredicts experimental results to a larger degree compared to Models I and III at elevated pressures. 85 Figure 3.17. K ext ’s of non-premixed H 2 /N 2 flames with water added to the oxidizer jet at (a) T exit = 353 K, P = 1 atm, and X F =0.17, and (b) T exit = 393 K, P = 4 atm, and X F = 0.15. Numerical simulations by Model I ( ), Model II ( ), Model III ( ) and Model Ia ( ). X F = 0.17 P = 1 atm T u = 353 K Present data Model Ia Model I Model II Model III (a) X F = 0.15 P = 4 atm T u = 393 K (b) 86 3.8. Concluding remarks Although the oxidation of hydrogen has been extensively studied, there exist notable discrepancies between existing experimental data sets and kinetic model predictions for propagation and extinction of hydrogen flames. Additionally, there remain significant uncertainties in the individual rate expressions in H 2 kinetic models. New experimental flame results with well-quantified uncertainties are needed to constrain these uncertainties. To this end this chapter addresses this issue by providing a wide range of fundamental flame data for premixed and non-premixed hydrogen flames will carefully quantified uncertainties. The first part of this study focused on premixed H 2 /oxidizer flames. It was observed that there exists a large variation in existing literature laminar flame speeds of H 2 /air flames. To resolve this issue better, the laminar flame speeds of diluted H 2 /oxidizer flames, with a lower maximum stretched flame speed, were measured in the counterflow configuration. Although this data is useful for model validation, there are differences in the detailed flame structure between diluted H 2 /O 2 /N 2 flames and H 2 /air flames. To alleviate any ambiguities caused by extrapolation methodologies to zero stretch, a comprehensive set of stretched flame speed results, as a function of stretch, were presented for H 2 /O 2 /N 2 flames over a range of equivalence ratios. Comparisons between model predictions and experimental results were consistent for both sets of experimental results for flame propagation. To probe the kinetics of ultra-lean H 2 flames, the extinction limits of premixed H 2 /air flames were experimentally determined. The ratio of the main branching to main termination reaction dictated the ability of the kinetic model to reproduce experimental 87 results. To supplement these results, the extinction limits of non-premixed H 2 flames were measured at atmospheric and elevated pressures. The difficulty in capturing the pressure dependent kinetics of non-premixed H 2 flames was demonstrated. Finally, flame type experiments were designed specifically to sensitize three-body reactions involving water as the 3 rd body. Such data are needed to constrain the large uncertainty in the main termination reaction involving water. To this end, extinction limits for both premixed H 2 /air flames with water dilution, and non-premixed H 2 flames with water added to the oxidizer stream were measured. It was demonstrated through comprehensive sensitivity analysis that these flames were successful in heavily sensitizing the target three-body reactions. 88 3.9. References [1] M. Chaos, F.L. Dryer, Combustion Science and Technology, 180 (2008) 1053- 1096. [2] M. P. Burke, M. Chaos, F.L. Dryer, Y. Ju, Combust. Flame, 157 (2010) 618-631. [3] J.M. 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Inst. 34 (2013) 565-571. 91 Chapter 4 Combustion Characteristics of Alternative Gaseous Fuels 4.1. Introduction Current trends in fuel prices, world politics, and environmental regulations have renewed interest in alternative sources of energy. Renewable and short carbon-cycle fuels such as gasified coal, waste- and biomass-derived gas, and byproduct gases from coke manufacturing are among the viable alternatives. Such fuels are typically mixtures of hydrogen (H 2 ), carbon monoxide (CO), and C 1 -C 4 hydrocarbons, and frequently notable quantities of carbon dioxide (CO 2 ), which is a highly efficient chaperon molecule in three-body radical recombination reactions. The hierarchical significance of the chemistry of the H 2 - CO-CH 4 -C 2 H 6 -C 3 H 8 system in the oxidation of fuels containing carbon and hydrogen has resulted in its extensive study. For example, early shock-tube investigations of CO-H 2 oxidation sought to determine the oxidation rates of CO-O 2 with minimal H 2 addition (e.g., [1-4]). Subsequent studies have extended the mixture and shock conditions to even wider ranges (e.g., [5-8]). The flame properties of mixtures of CO and H 2 with air have been extensively studied, experimentally and numerically. Previous flame studies have concentrated on laminar flame speeds and extinction limits (e.g., [9-11]). On more than one occasion, the auto-ignition of CO-H 2 mixtures has been studied also in rapid 92 compression machines at high pressures [12,13]. Flame properties of the neat fuels for C 1 -C 4 hydrocarbons have been studied extensively both experimentally (e.g. [14-18]) and numerically (e.g. [19-24]). Additionally, several kinetic models have been published for H 2 , CO, and C 1 -C 4 hydrocarbons (e.g. [25-28]) and have been validated largely against experiments involving neat components (e.g. [10,16, 29,30]) or H 2 /CO mixtures (e.g. [10,31]). Potential kinetic couplings stemming from fuel blending have been assessed to lesser extent, with the main exception being the addition of H 2 to hydrocarbons (e.g. [32- 33]) especially to CH 4 (e.g. [34-36]). However, kinetic interactions between H 2 and CO with CH 4 , as well as fuel blends involving propane (C 3 H 8 ) or n-butane (n-C 4 H 10 ) have not been studied systematically. Previous work involving flame properties of binary fuels includes work performed by Wang and coworkers [37]. Wang and coworkers [37] developed a semi-empirical mixing rule requiring only the knowledge of ’s and flame temperatures, T f , of the individual fuel components in order to estimate ’s of binary mixtures. They successfully tested their methodology for determining ’s of mixtures of air with Ethylene/n-butane, ethylene/toluene, and n-butane/toluene. Ji and Egolfopoulos [38] extended this work in order to estimate ’s for binary liquid fuel mixtures of n-dodecane/toluene. Their mixing rule for determining the ’s of binary mixtures in air is, ). / ~ exp( , / ln / ~ ~ 2 1 , , 2 1 , fm am o um i m o i u i f i i i m i a i i am T T S n S T n x n T n x T (4.1) S u o S u o S u o S u o S u o 93 The total moles of combustion products and diluent are 2 1 i i i m n x n . Figure 4.1 compares experimentally determined ’s of methane/ethane fuel blends with those estimated using the mixing rule from Ref. [37]. There is excellent agreement between measurements and estimated results. Figure 4.1. Comparison of measured and estimated ’s using the mixing rule proposed by Ref. [37] as a function of equivalence ratio for methane-ethane binary fuel mixtures with air flames. Opened symbols: experimental data by author; Closed symbols: predictions by the mixing rule. Dirrenberger et al. [39] proposed an empirical correlation for binary mixtures of methane/ethane, methane/propane, and methane/hydrogen. In this study it was reported that the methane/hydrogen correlation is only able reproduce experimental results for a H 2 content less than 40 % of the total binary mixture. The correlation in Ref. [39] is based on the properties of CH 4 /air flames, when the H 2 content in the mixture exceeds S u o Experiment (90%CH 4 +10%C 2 H 6 )/air Experiment (10%CH 4 +90%C 2 H 6 )/air Prediction (90%CH 4 +10%C 2 H 6 )/air Prediction (10%CH 4 +90%C 2 H 6 )/air S u o 94 40 %, the properties of the flame do not follow the correlation. The flame characteristics of H 2 are unique and different from hydrocarbons hence its kinetic coupling will vary significantly compared to the aforementioned hydrocarbon compounds. Leiuwen et al. [40] discussed the importance of understanding flame propagation of syngas mixtures due to their high H 2 content. They stated that such properties are related directly to the stability characteristics of premixed gas turbine combustors operating on lean syngas mixtures. Based on those considerations, the goal of this study was to provide archival experimental flame data for blends of H 2 , CO, CH 4 , C 3 H 8 , and n-C 4 H 10 and to provide insight into the underlying kinetic couplings. The study was conducted for premixed flames in the counterflow configuration, and the combustion characteristics in focus were ’s and K ext . 4.2. Experimental and numerical approach The majority of the measurements were performed for fuel lean mixtures due to their relevance to lean-burning applications. The propagation and extinction studies were performed in a variable-pressure chamber for pressures ranging from P = 1 to 4 atm and for unburned mixture temperature T u = 298 K. The burner diameters were 9 and 14 mm. The fuel blends tested in this study are outlined in Table 4.1. Fuels-1 and -2 simulate products of the destructive distillation of coal, otherwise referred to as by-product coke oven gas and contain large amounts of H 2 [41]. Fuels-3 and -4 represent synthesis gas, which is produced via steam reforming coal or other condense-phase hydrocarbon fuels, and it contains largely CO and H 2 , two particularly clean-burning fuels [42]. Fuels-5 and S u o 95 -6 are surrogate mixtures that simulate digester and landfill gas, a fuel produced by the biological reduction of organic solids and they consist primarily of methane and carbon dioxide [43,44]. USC Mech II [41] was used in simulations without modification. Fuel Blended Fuel Composition 1 60% H 2 + 10% CO + 30% CH 4 1a 60% H 2 + 10% CO + 30% C 3 H 8 1b 60% H 2 + 10% CO + 30% n-C 4 H 10 2 95% H 2 + 5% CH 4 2a 95% H 2 + 5% C 3 H 8 2b 95% H 2 + 5% n-C 4 H 10 3 32% H 2 + 58% CO + 10% CH 4 3a 32% H 2 + 58% CO + 10% C 3 H 8 4 54% H 2 + 11% CO + 25% CH 4 + 10% CO 2 5 55% CH 4 + 45% CO 2 6 75% CH 4 + 25% CO 2 Table 4.1. Composition of fuel blends on molar basis. 96 4.3. Results and discussion Figure 4.2a depicts experimental and computed ’s of flames of Fuel-1 (60% H 2 + 10% CO + 30% CH 4 ) and Fuel-3 (32% H 2 + 58% CO + 10% CH 4 ) at P = 1 atm, T u = 298 K, and < 1.0. While the computed ’s of Fuel-3/air flames are in good agreement with the experimental ones, ’s of Fuel-1/air flames are underpredicted by the simulations. Over the -range considered, Fuel-1/air and Fuel-3/air flames have similar ’s even though Fuel-1 contains approximately twice the amount of H 2 compared to Fuel-3. This is primarily due to the fact that the adiabatic flame temperature, T ad , of Fuel-3/air flames is approximately 100 K higher than T ad , of Fuel- 1/air flames. Additionally, there is less than half the amount of CH 4 in Fuel-3/air flames compared to Fuel-1/air flames. The experimental and computed ’s of flames of Fuel-1 and Fuel-4 (54% H 2 + 11% CO + 25% CH 4 + 10% CO 2 ) at P = 1 atm, T u = 298 K, and < 1.0 are compared in Fig. 4.2b. The composition of Fuel-4 is similar to Fuel-1 with the exception of the addition of CO 2 to Fuel-4 and as a result ’s of Fuel-4/air flames are lower. The computed ’s of Fuel-4/air flames are in agreement with the experimental data. Figure 4.3 depicts the experimental and computed K ext ’s of Fuel-1/air and Fuel-3/air flames at P = 1 atm, T u = 298 K, and < 1.0. Similarly to , the experimental K ext ’s of Fuel-1/air and Fuel-3/air flames are very close to each other. On the other hand, the model underpredicts the experimental data for both Fuel-1/air and Fuel-3/air flames as increases. S u o S u o S u o S u o S u o S u o S u o S u o 97 Figure 4.2. Experimental and computed ’s of (a) Fuel-1/air and Fuel-3/air flames and (b) Fuel-1/air and Fuel-4/air flames at P = 1 atm, T u = 298 K, and < 1.0. Symbols: experimental data; Lines: numerical results. The error bars indicate 2 standard deviations. (a) (b) Laminar Flame Speed, S u , cm/s Laminar Flame Speed, S u , cm/s S u o 98 Figure 4.3. Experimental and computed K ext ’s of (a) Fuel-1/air and Fuel-3/air flames at P = 1 atm, T u = 298 K, and < 1.0. Symbols: experimental data; Lines: numerical results. The error bars indicate 2 standard deviations. In Fig. 4.4, the experimental and computed K ext ’s of H 2 /air and Fuel-2 (95% H 2 + 5% CH 4 )/air flames at p = 1 atm, T u = 298 K, and < 1.0 are compared. As expected, the addition of trace amounts of CH 4 to H 2 /air flames reduces K ext . The model predicts closely both sets of experimental data. 99 Figure 4.4. Experimental and computed K ext ’s of H 2 /air and Fuel-2/air flames at P = 1 atm, T u = 298 K, and < 1.0. Symbols: experimental data; Lines: numerical results. The error bars indicate 2 standard deviations. Additional experiments were carried out, by substituting CH 4 in Fuel-1 with equal amounts C 3 H 8 (Fuel-1a) and n-C 4 H 10 (Fuel-1b) on molar basis, while the H 2 and CO mole fractions were kept equal to that in Fuel-1. Both experimental and computed ’s of Fuel-1a/air and Fuel-1b/air flames are lower compared to Fuel-1/air at P = 1 atm, T u = 298 K, and < 1.0, as depicted in Fig. 3.5a. Similarly, the 5% CH 4 in Fuel-2 was substituted with 5% C 3 H 8 (Fuel-2a). In Fig. 4.5b, ’s of Fuel-2 and Fuel-2a at P = 1 atm, T u = 298 K, and < 1.0 are shown. Consistent with observations in Fig. 4.5a, the substitution of CH 4 with C 3 H 8 results in a reduction of . Since the numerical simulations captured the effect of substituting CH 4 by a heavier fuel compound, the computed flame structures were used to provide insight into the controlling mechanisms. Additionally, it was determined that the substitution of CH 4 by C 3 H 8 or n-C 4 H 10 , affects S u o S u o S u o 100 adiabatic flame temperature, T ad at most by 10 K for Fuel-1 and by negligible amounts for Fuel-2, given that in both cases the hydrocarbons are additives. Thus, the observed effect is not of thermal but rather of kinetic nature. Figure 4.5. Experimental and computed ’s of (a) Fuel-1/air, Fuel-1a/air, and Fuel-1b/air flames and (b) Fuel-2/air, Fuel-2a/air, and Fuel-2b/air flames at P = 1 atm, T u = 298 K, and < 1.0. Symbols: experimental data; Lines: numerical results. The error bars indicate 2 standard deviations. (a) (b) S u o 101 Figure 4.6 depicts a pseudo-Arrhenius plot [45] which shows the variation of the computed mass burning rate, o u u S for Fuel-2/air and Fuel-2a/air mixtures at = 0.65 as a function of 1/T ad . u is the unburned mixture density and variation of T ad was achieved by substituting N 2 with Argon (Ar). The pseudo-activation energy, E a [46,47] can be derived as, ) / 1 ( / ) ln( 2 ad o u u a T S R E (4.1) where R is the ideal gas constant. It was shown that E a is 30 kcal/mol over a wide range of T ad for both Fuel-2/air and Fuel- 2a/air mixtures at = 0.65. Therefore, differences of ’s between Fuel-2 and Fuel-2a are independent of the flame temperature. S u o 102 Figure 4.6. Pseudo-Arrhenius plot of mass flux computed for Fuel-2/air and Fuel-2a/air mixtures = 0.65, P = 1 atm, and T u = 298 K. The lowest temperature results correspond to a fuel-air mixture without Ar substitution; the variation of the adiabatic flame temperature is accomplished through N 2 substitution by Ar. Figure 4.7a depicts the species profiles of methyl (CH 3 ) and hydrogen (H) radicals for = 0.6 Fuel-1/air, Fuel-1a/air, and Fuel-1b/air flames at P = 1 atm and T u = 298 K. Similar species profiles for = 0.6 Fuel-2/air, Fuel-2a/air, and Fuel-2b/air flames are shown in Fig. 4.7b. For both Fuel-1 and Fuel-2, substituting CH 4 by either C 3 H 8 or n- C 4 H 10 , results in a notable increase of CH 3 concentration and a corresponding decrease of H concentration. ) / 1 ( ) ln( 2 ad o u u a T S R E E a = 30 kcal/mol 6 103 Figure 4.7. Computed CH 3 and H mole fraction profiles for = 0.6 (a) Fuel-1/air, Fuel-1a/air, and Fuel-1b/air flames and (b) Fuel-2/air, Fuel-2a/air, and Fuel-2b/air flames at P = 1 atm and T u = 298 K. In Fuel-1a/air and Fuel-2a/air flames, ethylene (C 2 H 4 ) forms from the thermal decomposition of n-propyl (n-C 3 H 7 ) H (Fuel-2) H (Fuel-2a) H (Fuel-2b) CH 3 _Fuel-2 CH 3 _Fuel-2a CH 3 _Fuel-2b (b) H (Fuel-1) H (Fuel-1a) H (Fuel-1b) CH 3 _Fuel-1 CH 3 _Fuel-1a CH 3 _Fuel-1b (a) 104 n-C 3 H 7 → C 2 H 4 + CH 3 . (R1) Subsequently, C 2 H 4 reacts with H to form CH 3 via the following sequence C 2 H 4 + H + M → C 2 H 5 + M, (R2) C 2 H 5 + H → CH 3 + CH 3 . (R3) In Fuel-1b/air and Fuel-2b/air flames, C 2 H 5 forms from the thermal decomposition of p- butyl (p-C 4 H 9 ) p-C 4 H 9 → C 2 H 4 + C 2 H 5 (R4) and CH 3 is produced via R3. Reaction path analysis of Fuel-2a/air flames reveals that CH 3 is additionally produced from acetaldehyde (CH 3 CHO) via i-C 3 H 7 + O → CH 3 CHO + CH 3 . (R5) CH 3 CHO + X → CH 3 CO + XH (R6) CH 3 CO → CH 3 + CO (R7) where X denotes H, O, or OH. CH 3 then scavenges H through CH 3 + H + M → CH 4 + M. (R8) When CH 4 is substituted by n-C 4 H 10 (Fuel-1b and Fuel-2b), notable amounts of CH 3 CHO are produced from reactions of C 2 H 5 and s-butyl (s-C 4 H 9 ) C 2 H 5 + O → CH 3 CHO + H (R9) s-C 4 H 9 + HO 2 → CH 3 CHO + C 2 H 5 + OH (R10) and from 2-butene (2-C 4 H 8 ) via 2-C 4 H 8 + O → CH 3 CHO + C 2 H 4 (R11) 105 resulting again in higher concentrations of CH 3 via the R6-R7 sequence. In summary, adding small amounts of C 3 H 8 or n-C 4 H 10 to H 2 /air flames results in increased consumption of H through reactions with C 2 H 4 and C 2 H 5 , and increased concentrations of CH 3 that in turn consumes H, lowering thus the rate of the main branching reaction H + O 2 → O + OH (R12) and the attendant values of and K ext . Reaction path analyses are shown in Fig. 4.8a for C 3 H 8 substitution and Fig. 4.8b for C 4 H 10 substitution cases. S u o 106 Figure 4.8. Reaction path analysis of (a) Fuel-2a/air and (b) Fuel-2b/air flames at T u = 298 K, P = 1 atm, and = 0.6 using USC Mech II. The numbers indicate the conversion percentage. C 3 H 8 n-C 3 H 7 i-C 3 H 7 C 2 H 4 + CH 3 C 2 H 5 CH 3 CHO C 3 H 6 a-C 3 H 5 CH 2 CO 48.6% 51.4% 72 % +H +H 29% CH 3 CO +H, O, OH 80 % 37 % 13% +O +M + CH 3 CH 3 , CO 2CH 3 +O CH 3 , HCO +M +H +H CH 3 , CO 74% 10% +H, O, HO 2 +H 30% +O, OH C 2 H 3 22% 10 % +O 72% +O +H, OH, O 2 99% 91.5% (a) Fuel-2a (95% H 2 + 5% C 3 H 8 ) C 4 H 10 p-C 4 H 9 s-C 4 H 9 C 2 H 4 + CH 3 C 2 H 5 CH 3 CHO C 3 H 6 a-C 3 H 5 CH 2 CO 35% 65% 67 % +H +H 14% CH 3 CO +H, O, OH 78 % 33 % 12% +O +M + C 2 H 4 CH 3 , CO 2CH 3 +O CH 3 , HCO +M +H +H CH 3 , CO 74% +H 34% +O, OH C 2 H 3 26% 68% +O +M 99% 91.5% 1-C 4 H 8 23% + CH 3 2-C 4 H 8 30 % +O 2 , OH +O 31% + C 2 H 5 +O 2 , OH (b) Fuel-2a (95% H 2 + 5% C 4 H 10 ) 107 The effect of CO 2 on flame propagation and extinction was assessed, and Figs. 4.9 and 4.10 depict the experimental and computed ’s and K ext ’s respectively for CH 4 /air, Fuel-5 (55% CH 4 + 45% CO 2 )/air, and Fuel-6 (75% CH 4 + 25% CO 2 )/air flames at P = 1 atm and T u = 298 K. As expected, Fuel-5/air flames have the lowest ’s and K ext ’s. In addition, the peak of shifts closer to = 1.0 as the CO 2 concentration in the fuel increases because T ad is lower and product dissociation is suppressed. The simulations capture the effect of CO 2 accurately. Figure 4.9. Experimental and computed ’s of CH 4 /air, Fuel-5/air, and Fuel-6/air flames at P = 1 atm and T u = 298 K. The error bars indicate 2 standard deviations. S u o S u o S u o S u o 108 Figure 4.10. Experimental and computed K ext ’s of CH 4 /air, Fuel-5/air, and Fuel-6/air flames at P = 1 atm and T u = 298 K. The error bars indicate 2 standard deviations. The pressure effect on was assessed also for CH 4 /air and Fuel-5/air flames, by performing experiments at P = 1, 2, and 4 atm and T u = 298 K, and the results are shown in Figs. 4.11a and 4.11b. As expected, is reduced with pressure for all ’s as ~ p n/2-1 , and the overall reaction order, n, is less than 2 (e.g., [47]). The computed ’s are in good agreement with the current experimental data over all ’s considered and for the pressure range of 1 to 4 atm. Previously published CH 4 /air data can be found in Refs. [14] and [48]. S u o S u o S u o S u o S u o 109 Figure 4.11. Experimental and computed ’s of (a) CH 4 /air flames (b) Fuel-5/air flames at T u = 298 K and P = 1, 2, and 4 atm. (a) (b) S u o 110 4.4. Concluding remarks Laminar flame speeds and extinction limits of mixtures of hydrogen, carbon monoxide, and C 1 -C 4 saturated hydrocarbons with air were studied experimentally and numerically in the counterflow configuration. The fuel mixtures were chosen to simulate alternative gaseous fuels. Laminar flame speeds were determined at ambient unburned gas temperature and pressures ranging from one to four atmospheres, while extinction limits were determined at ambient unburned gas temperature and pressure. The experimental flame data of these mixtures are of practical important and they also provide information that can be used to assess the effects of kinetic couplings during the oxidation of fuel mixtures involving hydrogen, carbon monoxide, methane, propane, and n-butane. The experiments were modeled using detailed descriptions of chemical kinetics and molecular transport. The experimental results revealed that the substitution of methane in a fuel mixture with either propane or n-butane results in the reduction of the mixture’s reactivity under vigorous burning conditions. The numerical simulations reproduced closely the experimental laminar flame speeds and extinction strain rates over all experimental conditions. 111 4.5. References [1] K.G.P. Sulzmann, B. F. Myers, E. R. Bartle, J. Chem. Phys. 42 (1965) 3969-3979. [2] B. F. Myers, K. G. P. Sulzmann, E. R. Bartle, J. Chem. Phys. 43 (1965) 1220-1228. [3] T. A. Brabbs, F. E. Belles, R. S. Brokaw, Proc. Combust. 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Santavicca, ASME Paper No. GT2006- GT90770 (2006) [41] Steam, Its Generation and Use, Babcock & Wilcox Company, 35 th Ed. [42] E. Monteiro, M. Bellenoue. J. Sotton, N.A. Moreira, S. Malheiro, Proc. European Combust. Meeting (2009). [43] W. Qin, F.N. Egolfopoulos, T.T. Tsotsis, Chem. Eng. J. 3773 (2001) 1-16. [44] B. Eklund, E. Anderson, B. Walker, D. Burrows, Environ. Sci. Technol. (32) (1998) 2233-2237. [45] C.Ji, E. Dames, B. Sirjean, H. Wang, F.N. Egolfopoulos, Proc. Combust. Inst. 33 (2011) 971-978. [46] C.K. Law, Combustion Physics, Cambridge University Press, Cambridge, 2006 [47] F.N. Egolfopoulos, C.K. Law, Combust. Flame 80 (1990) 7-16. [48] C. Vagelopoulos, F.N.Egolfopoulos, Proc. Combust. Inst. 27 (1998) 513-519. 114 Chapter 5 Studies of C 2 Hydrocarbons 5.1. Introduction In the present study, the propagation of C 2 -hydrocarbon flames is revisited. The hierarchical nature of combustion kinetics has resulted in the extensive study of the oxidation of C 2 hydrocarbons (e.g., [1-6]). Recent studies in the combustion literature have consistently demonstrated that uncertainties in C 1 -C 3 kinetics can notably affect the predictions made by detailed models for large molecular weight alcohols or hydrocarbons (e.g., [7,8]). C 2 H 6 has been investigated to a lesser extent among the C 1 -C 3 hydrocarbons, but it has begun to attract additional attention as a fuel given recent technological developments in recovering natural gas in shale formations. The composition of this type of natural gas is typically a blend of CH 4 and C 2 H 6 (e.g., [9,10]). In this study, it will be shown that there is a large degree of variation in measured and computed, using recent kinetic models, ’s of fuel rich C 2 -hydrocarbon flames. The oxidation kinetics of fuel rich flames of C 2 hydrocarbons are of direct relevance to the kinetics of soot formation (e.g., [11,12]). Hence it is important to present a possible resolution to these differences presently. S u o 115 ’s of C 2 H 6 /air, C 2 H 4 /air, and C 2 H 2 /air flames have been determined previously in a number of experimental configurations, using, for example, stagnation flames (e.g. [1,2,5]), spherically expanding flames (e.g. [3,4]), and the heat flux method (e.g., [9,13]). In developing kinetic models, the reported rate constants are characterized by inherent uncertainty factors (UF) even for “well-validated” reactions [14]. Thus, for every rate coefficient the k 0 /UF ~ UF*k 0 range is equally probable, where k 0 is the nominal rate coefficient (e.g., [15]). For example, UF’s of C 2 H 4 + H + M = C 2 H 5 + M and CH 3 + CH 3 = H + C 2 H 5 , two reactions that will be discussed later, are reported as 3 and 5 respectively in USC Mech II [16]. It has been shown recently [15], that uncertainties in model predictions can be reduced notably by using more experimental data as constraints and by accounting also for the attendant data uncertainty. In this study, ’s and K ext ’s of C 2 -hydrocarbon flames were measured in the counterflow configuration with well-quantified uncertainties. The data were modeled using three recently developed kinetic models, with the goal being their further validation and the identification of rate constants that need to be improved. S u o S u o 116 5.2 . Experimental and numerical approach All measurements were carried out in the counterflow configuration at P = 1 atm pressure and unburned reactant temperature T u = 298 K. The burner diameters and separation distance was 14 mm. The experimental results in the present study were simulated using three kinetic models, namely USC Mech II [16], Galway Mech [10,17], and San Diego Mech [18] that are describing the high-temperature kinetics of H 2 /CO and C 1 -C 4 hydrocarbons. The Galway Mech consists of 293 species and 1593 reactions, and San Diego Mech consists of 46 species and 235 reactions. 117 5.3. Results and discussion The experimental and computed ’s of C 2 H 6 /air mixtures are shown in Fig. 5.1. The present data obtained in stagnation flames, are compared in Fig. 5.1a against those obtained using the transition from Bunsen to stagnation flame technique [2], spherical expanding flames [3,19], and the heat flux technique [9,20]. Although all four approaches result in very similar measured ’s for < 1.0, large discrepancies persist for > 1.0. The discrepancy between the present data and those by Dirrenberger et al. [9] increases as increases, e.g. ’s differ by approximately 2.5 cm/s (5%) at = 1.2 and 7 cm/s (50%) at = 1.4. uncertainties in this study were determined by the 2 standard deviations (95.45% confidence) of S u,ref ’s based on sampling errors in S u,ref , and have been quantified systematically in detail by the authors [21]. Dirrenberger et al. [9] reported uncertainties of ±1.5% whose primary source was from the mass flow controller and a 97.5% confidence level from three measurements; in Refs. 2 and 3 uncertainties in ’s were unreported. S u o S u o S u o S u o S u o 118 Figure 5.1. ’s of C 2 H 6 /air mixtures at T u = 298 K and P = 1 atm. (a) Comparison with literature experimental data; (b) Comparison with simulations. In Fig. 1b, the experimental data and numerically computed ’s of C 2 H 6 /air mixtures are compared. USC Mech II and San Diego Mech slightly overpredict data by an average of 2 cm/s for all ’s. Galway Mech predictions are in good agreement for < 1.0, but notably overpredicts data for > 1.0, by as much as 7 cm/s at = 1.4. The USC Mech II Galway Mech San Diego Mech Present data (b) Dirrenberger et al. (2011) Present data Vagelopoulos & Egolfopoulos (1998) Jomaas et al. (2005) Bosschaart and de Goey (2004) Lowry et al. (2011) (a) S u o S u o S u o 119 peak of C 2 H 6 /air flames occurs between 1.05 and 1.1 in experimental results and numerical computations using USC Mech II and San Diego Mech. However, Galway Mech predicts the peak to occur at 1.15. In general peak corresponds to the location of the maximum adiabatic flame temperature, T ad . The computed peak T ad using all three models for C 2 H 6 /air mixtures occurs at = 1.05. This suggests that the differences between the models in predicting the location of peak are a result of kinetic differences between these three models. In order to remove ambiguities that could potentially result from extrapolations to zero stretch, Fig. 5.2 depicts the directly measured and computed S u,ref .vs. K for = 0.8 and = 1.4 C 2 H 6 /air mixtures. The raw experimental data are predicted closely by Galway Mech for = 0.8, but they are overpredicted for = 1.4 by approximately 6 cm/s. USC Mech II and San Diego Mech overpredicts the raw data by approximately 3.5 cm/s and 2 cm/s at = 0.8 and 1.4 respectively. These differences are very consistent with the results shown in Fig. 5.1b, providing confidence in the non-linear extrapolations that were used. Thus, kinetic models can be validated against these raw experimental data that are characterized by a minimum possible uncertainty S u o S u o S u o S u o 120 Figure 5.2. Variation of S u,ref against K for C 2 H 6 /air mixtures at (a) = 0.8 (b) = 1.4. Sensitivity analysis of to reaction rate parameters was performed for C 2 H 6 /air flames at = 1.0 using USC Mech II and representative results are shown in Fig. 5.3. It can be seen that exhibits notable sensitivities to reactions R1 and R2 involving C 2 H 5 , (a) USC Mech II Galway Mech San Diego Mech Present data (b) USC Mech II Galway Mech San Diego Mech Present data S u o S u o 121 a fuel specific radical, which is not typically observed for the sensitivity analysis of most C 1 -C 4 saturated hydrocarbon flames. C 2 H 5 + M → C 2 H 4 + H + M (R1) H + C 2 H 5 → CH 3 + CH 3 (R2) The bond energies for C 2 H 5 are relatively weak [22], and thus C 2 H 5 tends to dissociate rapidly in flames, enhancing thus the main branching H + O 2 → OH + O reaction through the H production. R2 results in weak chain-termination by consuming H and C 2 H 5 to form the relatively stable (or un-reactive) CH 3 . Figure 5.3. Ranked logarithmic sensitivity coefficients of with respect to kinetics for C 2 H 6 /air flames at = 1.0, computed using USC Mech II. -0.10 0.00 0.10 0.20 0.30 CO + OH → CO 2 + H H + O 2 → O + OH CH 3 + OH → CH 2 (s) + H 2 O H + O 2 + M → HO 2 + M CH 3 + H +M → CH 4 + M HCO + H → CO + H 2 C 2 H 5 + H → CH 3 + CH 3 C 2 H 5 + M → C 2 H 4 + H +M H + OH +M → H 2 O+ M HO 2 +H → OH + OH A i : Pre-exponential factor i u u i A S S A 0 0 C 2 H 3 + M → C 2 H 2 + H + M C 2 H 3 + H → C 2 H 2 + H 2 S u o 122 The experimental and computed ’s of C 2 H 4 /air mixtures are shown in Fig. 5.4. The present data are compared in Fig. 5.4a against those obtained in counterflow [5] and spherically expanding flames [3,4,23]. Present ’s are very similar to those obtained in spherically expanding flames [3,4,23], but lower, by as much as 6 cm/s, when compared to ’s by Kumar et al. [5]. Data from Ref. 5 were determined using linear extrapolations but this alone cannot account for the observed differences given the near- unity Le of C 2 H 4 /air mixtures [7]. Figure 5.4b depicts the experimental and computed ’s for C 2 H 4 /air mixtures. The predicted ’s using USC Mech II and San Diego Mech, are in good agreement with the present data. Similarly to comparisons made for C 2 H 6 /air flames, Galway Mech predictions are in good agreement with experimental data for ≤ 1.0, but the data are over-predicted for > 1.0. S u o S u o S u o S u o S u o 123 Figure 5.4. ’s of C 2 H 4 /air mixtures at T u = 298 K and P = 1 atm. (a) Comparison with literature experimental data; (b) Comparison with simulations. Literature experimental results [1,3] for ’s of C 2 H 2 /air flames and numerical calculations using present kinetic models are presented in Fig. 5.5. Experimental data for ’s of C 2 H 2 /air flames by Egolfopoulos et al. [1] and Jomaas et al. [3] are in good P = 1 atm T u = 298 K Jomaas et al. (2005) Hassan et al. (1998) Kumar et al. (2008) Liu et al. (2010) Present data P = 1 atm T u = 298 K USC Mech II Galway Mech San Diego Mech Present data (b) (a) S u o S u o S u o 124 agreement for fuel lean conditions but the former results are notably higher for > 1.0 as shown in Fig. 5.5. For example, at = 1.4 there is a 26 cm/s (20%) difference between these two data sets. Instead of considering C 2 H 2 /air flames, this study experimentally determined ’s of less vigorously burning, C 2 H 2 /(13%O 2 +87%N 2 ) flames. The rationale for studying these diluted mixtures is the same as discussed in depth in Chapter 3 for studying diluted H 2 /oxidizer flames. These mixtures have previously been considered by Egolfopoulos et al. [1] and both present and existing experimental results are depicted in the Fig. 5.6. Although the previous data were determined in counterflow flames using linear extrapolations [1], it is of interest to note that they are very close to the present data that were obtained through non-linear extrapolations. This is reasonable as similarly to C 2 H 4 /air, C 2 H 2 /air mixtures have also near-unity Le (e.g., [7]). Predicted ’s using USC Mech II are in good agreement with both sets of experimental data, while the predictions using San Diego Mech agree with the data in general but overpredict the data by 6-18% for 1.2 1.5. Again, Galway Mech calculations are in good agreement with data for < 0.9 and notably overpredicts results for > 0.9, by as much as 20 cm/s at = 1.5. Experimental results and numerical calculations using USC Mech II predict a peak at = 1.20, whereas peaks at 's of 1.25 and 1.3 in calculations made using San Diego Mech and Galway Mech respectively. S u o S u o S u o S u o 125 Figure 5.5. Experimental and computed ’s of C 2 H 2 /air mixtures at T u = 298 K and P = 1 atm. Figure 5.6. Experimental and computed ’s of C 2 H 2 /O 2 /N 2 mixtures at T u = 298 K and P = 1 atm. USC Mech II Galway UCSD Egolfopoulos et al. (1990) Jomaas et al. (2005) C 2 H 2 /air S u o USC Galway UCSD Present work Egolfopoulos et al. (1990) P = 1 atm T u = 298 K C 2 H 2 /O 2 /N 2 (X O 2 + X N 2 ) X O 2 = 13% S u o 126 The kinetics reasons behind the notable overpredict of ’s of C 2 H 2 /O 2 /N 2 mixtures using Galway Mech are presently further assessed. Sensitivity analysis of to rate parameters was performed using all three models for a = 1.4 C 2 H 2 /O 2 /N 2 flame, and the results are shown in Fig. 5.7. The two main fuel consumption reactions are C 2 H 2 + O → HCCO + H (R3) C 2 H 2 + O → CH 2 + CO. (R4) Notable differences can be observed between all three models. More specifically, using Galway Mech, exhibits no sensitivity to R3 and notable sensitivity to R4, and the opposite is true for USC Mech II and San Diego Mech, suggesting that the R3 : R4 branching ratios are different in these three reaction models. Figure 5.7. Ranked logarithmic sensitivity coefficients of with respect to kinetics for a = 1.4 C 2 H 2 /O 2 /N 2 flames. S u o S u o S u o -0.2 0.0 0.2 0.4 0.6 Galway Mech San Diego Mech USC Mech II H + O 2 → O + OH CO + OH → CO 2 + H CH 3 + H +M → CH 4 + M CH 3 + O → CH 2 O + H CH 3 + OH → CH 2 (s) + H 2 O HCO + M → CO + H + M HCO + H → CO + H 2 HCCO + H → CH 2 (s) + CO HCCO + O 2 → OH + CO + CO C 2 H 2 + O → HCCO + H C 2 H 2 + O → CH 2 + CO C 2 H 2 + OH → CH 2 CO + H C 2 H 2 + H + M → C 2 H 3 + M C 2 H 3 + O 2 → CH 2 CHO + O C 2 H 3 + H → C 2 H 2 + H 2 CH 2 + O 2 → CO 2 + H + H A i : Pre-exponential factor i u u i A S S A 0 0 S u o 127 The importance of C 2 H 2 + O → products reactions in C 2 H 2 combustion is established. A wide variation of R3 : R4 branching ratios has been reported, and in recent studies it has been shown that R3 is indeed the dominant fuel consumption path (e.g., [24,25]). In USC Mech II, R3 : R4 = 0.8 : 0.2 and these rates are based on the work of Michael and Wagner [24]. In the Galway Mech R3 : R4 = 0.42 : 0.58. Although R3 tends to enhance the overall reactivity by producing H, the resulting ketenyl radicals (HCCO) consume on the other hand H via, HCCO + H → CH 2 (s) + CO. (R5) Using Galway Mech, does not exhibit any measurable sensitivity on R5 contrary to USC Mech II and San Diego Mech. When R3 and R4 rate constants in the Galway Mech were replaced by those from USC Mech II, and it was determined that the computed ’s of C 2 H 2 /O 2 /N 2 mixtures were notably reduced, by as much as 5 cm/s for 1.0. This further indicates the importance of the R3 : R4 branching ratio in predicting properties of C 2 H 2 /air flames. The R3 : R4 branching ratio can also affect the rate of production of singlet methylene (CH 2 (s)) via R5. S u o S u o 128 5.4. Concluding remarks Laminar flame speeds of mixtures of ethane/air, ethylene/air, and acetylene/O 2 /N 2 mixtures were measured in the counterflow configuration. Experimental data were simulated using three different kinetic models and detailed description of molecular transport. Although using these kinetic models resulted, in general, in good agreement against present and literature experimental data for fuel lean conditions, there is a large spread in predictions for fuel rich conditions. The computed laminar flame speeds and extinction strain rates using USC Mech II and San Diego Mech showed in good agreement with present experimental data for all C 2 hydrocarbon/air mixtures. Using USC Mech II the data of ethylene and acetylene flames were predicted accurately. On the other hand, while the computed laminar flame speeds using Galway Mech are in good agreement with experimental results at fuel lean conditions, they overpredict experimental results at fuel rich ethane/air mixtures. For acetylene/air flames, discrepancies were identified between the models with regarding to the branching ratio involving fuel consumption reactions by atomic oxygen, and it was found that the values of the branching ratio could have a large impact on the computed laminar flame speeds especially for rich mixtures. For flames of C 2 hydrocarbons, uncertainties remain in major fuel specific reaction rates that are significant and the choice of the attendant rate constants will notably impact predictions of laminar flame speeds and other global combustion phenomena. 129 5.5. References [1] F.N. Egolfopoulos, D.L. Zhu, C.K. Law, Proc. Combust. Inst. 23 (1990) 471-478. [2] C.M. Vagelopoulos, F.N. Egolfopoulos, Proc. Combust. Inst. 27 (1998) 513-519. [3] G. Jomaas, X.L. Zheng, D.L.Zhu, C.K. Law, Proc. Combust. Inst. 30 (2005) 193- 200. [4] M.I. Hassan, K.T. Aung, O.C. Kwon, G.M. Faeth, J. Propul. Power 14 (4) (1998) 479-488. [5] K. Kumar, G. Mittal, C.-J. Sung, C.K. Law, Combust. Flame 153 (2008) 343-354. [6] J. de Vries, J. M. Hall, S.L. Simmons, M. J.A. Rickard, D.M. Kalitan, E.L. Petersen, Combust. Flame 150 (2007) 137-150. [7] C. Ji, E. Dames, Y.L. Wang, H. Wang, F.N. Egolfopoulos, Combust. Flame 157 (2010) 277-287. [8] P.S. Veloo, F.N. Egolfopoulos, Combust. Flame 158 (2011) 501-510. [9] P. Dirrenberger, H. Le Gall, R. Bounaceur, O. Herbinet, P.-A. Glaude, A. Konnov, and F. Battin-Leclerc, Energy Fuel 25 (2011) 3875-3884. [10] D. Healy, N.S. Donato, C.J. Aul, E.L. Petersen, C.M. Zinner, G. Bourque, H.J. Curran, Combust. Flame 157 (2010) 1540-1551. [11] A.D. Abid, E.D. Tolmachoff, D.H. Phares, H. Wang, Y. Liu, A. Laskin, Proc. Combust.Inst. 32 (2009) 681-688. [12] A.D. Abid, J. Camacho, D.A. Sheen, H. Wang, Combust. Flame 156 (2009) 1862- 1870. [13] K.J. Bosschaart, L.P.H. de Goey, Combust. Flame 136 (2004) 261–269. 130 [14] M. Frenklach, H. Wang, M.J. Rabinowitz, Prog. Energy Combust. Sci. 18 (1992) 47-73. [15] D.A. Sheen, X. You, H. Wang, T. Løvås, Proc. Combust. Inst. 32 (2009) 535-542. [16] H. Wang, X. You, A.V. Joshi, S. G. Davis, A. Laskin, F. Egolfopoulos, C.K. Law, USC Mech Version II. High Temperature combustion Reaction Model of H 2 /CO/C 1 -C 4 Compound, http://ignis.usc.edu/USC_Mech_II.htm (2007). [17] D. Healy, D.M. Kalitan, C.J. Aul, E. L.Petersen, G. Bourque, H.J. Curran, Energy and Fuel, 24 (2010) 1521-1528. [18] Chemical-Kinetic Mechanisms for Combustion Applications", San Diego Mechanism web page, Mechanical and Aerospace Engineering (Combustion Research), University of California at San Diego (http://combustion.ucsd.edu), (2009). [19] W. Lowry, J. de Vries, M. Krejci, E. Petersen, Z. Serinyel, W. Metcalfe, H. Curran, G. Bourque, J. Eng. Gas Turbine Power 133 (2011) ASME Paper No. 091501. [20] K.J. Bosschaart, L.P.H. de Goey, Combustion and Flame 136 (2004) 261–269. [21] C. Ji, Y.L. Wang, F.N. Egolfopoulos, J. Propul. Power 27 (2011) 856-863. [22] W. Liu, A.P. Kelley, C.K. Law, Combust. Flame 157 (2010) 1027-1036. [23] J.A. Miller, S.J. Klippenstein, Phys. Chem. Chem. Phys. 6 (2004) 1192-1202. [24] J.V. Michael, A.F. Wagner J. Phys. Chem. 94 (1990) 2453-2464. [25] J. Peeters, M. Schaekers, C. Vinckier, J. Phys. Chem. 90 (1986) 6552-6557. 131 Flame Propagation of C 3 and C 4 hydrocarbons with air mixtures 6.1 . Introduction The hierarchical nature of the combustion kinetics of hydrocarbons means that the high-temperature reaction kinetics of C 1 -C 4 hydrocarbons are the foundation to accurate descriptions of the combustion kinetics of higher or large molecular weight hydrocarbons (and oxygenated compounds). It is for this reason that the combustion chemistry of C 1 - C 4 hydrocarbon have been subject to intensive studies over the last several decades, both experimentally and numerically (see, e.g., [1-5]). C 1 -C 4 hydrocarbons include saturated and unsaturated, branched and straight chain, hydrocarbons. They are usually formed as critical stable intermediates during the oxidation of higher hydrocarbons. In recent years, the chemical kinetics of straight and branched-chain C 3 -C 4 alkenes have received particular attention. These compounds are key stable intermediates produced in the oxidation of larger hydrocarbons (e.g., [6,7]) and bio-derived alcohols (e.g., [8,9,10]). The oxidation of these alkene intermediates is usually the rate limiting steps towards the overall oxidation rate of the larger, parent hydrocarbons. To effectively isolate the uncertainties in the fuel specific kinetics of large hydrocarbons and oxygenated fuels, it is essential to first minimize the contribution of Chapter 6 132 uncertainties derived from the foundational C 0 -C 4 model. Within this foundational fuel model, the oxidation kinetics of unsaturated hydrocarbons has been studied to a far lesser degree than straight chain n-alkanes. It has been demonstrated (e.g., [6,7]) that the uncertainties in the oxidation chemistry of key intermediates produced during the high-temperature oxidation of the primary reference fuel iso-octane, including iso-butene (i-C 4 H 8 ) and propene (C 3 H 6 ), are responsible for difficulties in the model predictions of high-temperature iso-octane combustion phenomena. Alkenes are produced also readily during the oxidation of alcohols (e.g. [8,10,11,12]). For example, molecular dehydration is a significant pathway for the consumption of iso- and tert-butanol resulting in large quantities of i-C 4 H 8 (e.g., [9,13]). It was shown that errors in model predictions of the combustion phenomena of large molecular weight alcohols stem largely from uncertainties in the pyrolysis and oxidation kinetics of their unsaturated intermediates. Previous studies of the oxidation of C 4 alkenes include work performed in a jet stirred reactor (JSR) [14]. A detailed chemical kinetic reaction model for the oxidation of C 4 alkenes was developed in Ref. 15 and was validated using ignition delay times in a shock tube and species profiles in a JSR. Recently, Qi and coworkers [16] performed a systematic study on the pyrolysis of three butene isomers 1-C 4 H 8 , 2-C 4 H 8 , and i-C 4 H 8 in a flow reactor at low pressures focusing on the fuel decomposition and recombination reactions. Although several kinetic studies have been reported for i-C 4 H 8 , few data exist. Several experimental studies have been reported for the high-temperature oxidation of 1,3-butadiene (1,3-C 4 H 6 ) in shock tubes [17], flow reactors (e.g. [18,19]), and jet-stirred reactors (e.g., [20]). The flame propagation of a wide set of unsaturated, S u o 133 straight chain and branched C 1 -C 4 hydrocarbons have been studied by Davis and Law [2] and Farrell et al. [21]. As mentioned in previous chapters, existing experimental results have little to no systematic quantification of experimental uncertainties limiting their value to model uncertainty minimization. The primary goal of this chapter is to experimentally determine ’s of mixtures of air with saturated and unsaturated C 3 and C 4 hydrocarbons. C 3 hydrocarbons studied were propane (C 3 H 8 ) and propene (C 3 H 6 ). C 4 saturated hydrocarbons are iso-butane (i- C 4 H 10 ) and n-butane (n-C 4 H 10 ). Unsaturated C 4 hydrocarbons included 1-butene (1- C 4 H 8 ), 2-butene (2-C 4 H 8 ), iso-butene (i-C 4 H 8 ), and 1,3-butadiene (1,3-C 4 H 6 ). This systematically determined set of experimental measurements was then compared against existing literature experimental data for ’s of flames of these compounds. The relative reactivities of flames of the fuels is discussed. A comprehensive comparison between present measurements and literature data for ’s of mixtures of these fuels is discussed in depth. The predictions of recently developed foundational fuel (H 2 , CO, and C 1 -C 4 ) chemical kinetic reaction models are compared against present and literature experimental results. S u o S u o S u o 134 6.2 . Experimental and numerical approach All measurements were carried out in the counterflow configuration at P = 1 atm pressure and unburned reactant temperature T u = 298 K. The burner diameters and separation distance was 14 mm. The purities of all C 3 - and C 4 -hydrocarbons considered in this study are 99.0 %. To measure ’s of 2-butene/air mixtures, a mixture of 70% cis-2-butene and 30 % trans-2-butene was used with a purity of 99%. With the exception of C 4 hydrocarbons, sonic nozzles were used to meter the mass flow rates of gases. C 4 hydrocarbon fuels were metered with Teledyne Hastings mass flow controllers. Nominal model prediction using different kinetic models were also compared along with USC Mech II [23]. The Galway Mech, C 1 -C 5 model of Curran and coworkers [5,24], and the four butanol isomers model by Battin-Leclerc and coworkers (Nancy model) [8]. The Nancy model consists of 158 species and 1250 reactions. S u o 135 6.3. Results and discussion As a consequence of the energetic double bond in the C 3 H 6 molecule, it is expected that C 3 H 6 /air mixtures will be more reactive than C 3 H 8 /air mixtures, and will therefore have higher measured . Current experimental results are compared with literature measurements in Fig. 6.1 [3]. The current experimental results clearly reproduce the expected trend. There is, however, no difference in the measured ’s of C 3 H 8 /air and C 3 H 6 /air flames from Ref. [3]. As such, experimental results from Ref. [3] should be used with caution for model validation. S u o S u o 136 Figure 6.1. Experimentally determined ’s of C 3 H 6 /air and C 3 H 8 /air mixtures, T u = 298 K and P = 1 atm. (a) Present experimental results and (b) Experimental results from Ref. [3]. Present and literature results for C 3 H 8 /air and C 3 H 6 /air flames are compared with the nominal predictions of USC Mech II in Fig. 6.2. Overall, there is good agreement between present experimental results and calculations. The experimental measurements from Davis and Law [2] are consistently 5 to 10 cm/s higher at fuel rich conditions (a) present data Laminar Flame Speed, S u , cm/s C 3 H 6 /air C 3 H 8 /air Equivalence Ratio, (b) Jomaas et al. (2005) C 3 H 6 /air C 3 H 8 /air Equivalence Ratio, Laminar Flame Speed, S u , cm/s S u o 137 compared to both present experimental results and calculations. This trend, data from Ref. [2] being significantly higher at fuel rich conditions, will be observed throughout the remainder of this chapter. Figure 6.2. Literature data and present measurements for ’s of (a) C 3 H 8 /air and (b) C 3 H 6 /air flames compared to computed results. Lines: simulation results using USC Mech II. (a) C 3 H 8 /air Laminar Flame Speed, S u , cm/s Equivalence Ratio, Vagelopoulos & Egolfopoulos (1998) Jomaas et al. (2005) Bosschaart and de Goey (2004) Present data (b) C 3 H 6 /air Equivalence Ratio, Davis and Law (1998) Jomaas et al. (2005) Present data Laminar Flame Speed, S u , cm/s S u o 138 Experimental determination of ’s requires the measurement of S u,ref at a finite K and extrapolating to K = 0. In order to demonstrate the validity of the extrapolation technique, direct experimental measurements and numerical calculations of S u,ref vs. K are presented in Fig. 6.3 for C 3 H 8 /air mixtures and Fig. 6.4 for C 3 H 6 /air mixtures. In other words, if a model is able to reproduce , it should also accurately reproduce the non- extrapolated, raw experimental data. This is clearly the case demonstrated in Fig. 6.3. In Fig. 6.4, it is shown that the magnitude of the differences between numerically calculated and experimentally determined ’s is also mirrored in a similar comparison of model and experimental S u,ref vs. K variation. S u o S u o S u o 139 Figure 6.3. Variation of S u,ref vs. K for C 3 H 8 /air mixtures. Lines: simulation results using USC Mech II. = 1.2 = 1.3 = 1.1 = 1.4 (b) Strain rate, K, s -1 = 0.8 = 0.9 = 1.0 (a) Reference Flame Speed, S u,ref , cm/s Reference Flame Speed, S u,ref , cm/s 140 Figure 6.4. Variation of S u,ref vs. K for C 3 H 6 /air mixtures. Lines: simulation results using USC Mech II. The present experimental results are compared against available literature data for ’s of C 4 alkane/air mixtures in Fig. 6.5. At fuel lean conditions there is very good agreement between all three sets of experimental data. For fuel-rich flames, the data reported in Refs. [2] and [25] are significantly higher than present experimental results, = 0.8 = 0.9 = 1.0 (a) Reference Flame Speed, S u,ref , cm/s Strain rate, K, s -1 = 0.7 = 1.2 = 1.3 = 1.1 = 1.4 (b) Strain rate, K, s -1 Reference Flame Speed, S u,ref , cm/s (a) S u o 141 consistent with previous observations made for C 3 H 8 /air and C 3 H 6 /air flames in Fig. 6.2 The present measurements are compared with nominal predictions using USC Mech II in Fig. 6.6. Model predictions are higher than experimental results for n-C 4 H 10 /air mixtures. There is good agreement between calculations and data for i-C 4 H 10 /air mixtures. Figure 6.5. Experimentally determined ’s of C 4 -alkanes with air mixtures, T u = 298 K and P = 1 atm. (a) n-C 4 H 10 /air Kelley (2011) Davis and Law (1998) Bosschaart and de Goey (2004) Dirrenberger et al. (2011) Present data Laminar Flame Speed, S u , cm/s Equivalence Ratio, (b) i-C 4 H 10 /air Kelley(2011) Davis and Law (1998) Bosschaart and de Goey (2004) Present data Equivalence Ratio, Laminar Flame Speed, S u , cm/s S u o 142 Figure 6.6. Experimentally determined and numerical calculations for ’s of C 4 -alkanes with air mixtures (T u = 298 K and P = 1 atm). Lines: simulation results using USC Mech II. The experimental ’s of flames of C 4 H 8 isomers are compared in Fig 6.7a. 2-C 4 H 8 exists as two stereoisomers cis-2-butene and trans-2-butene. Both isomers have very similar heat of formation and behave similarly. In present study, mixed 2-butene, 70% (a) n-C 4 H 10 /air Laminar Flame Speed, S u , cm/s Equivalence Ratio, (b) i-C 4 H 10 /air Equivalence Ratio, Laminar Flame Speed, S u , cm/s S u o S u o 143 cis-2-butene and 30% trans-2-butene were used as mentioned earlier. Comparing the relative reactivity of 1-C 4 H 8 and 2-C 4 H 8 , 1-C 4 H 8 /air flames propagate faster than 2- C 4 H 8 /air. 2-C 4 H 8 is thermodynamically more stable than 1-C 4 H 8 due to the hyper- conjugation effect. 1-C 4 H 8 has a mono-alkyl-substituted double bond, since it has one methyl group attached to the double bond. In contrast, 2-C 4 H 8 has two methyl groups attached to the double bond. As a result, 2-C 4 H 8 is more stable than 1-C 4 H 8 , which is consistent with present experimental observations. In Fig. 6.7b, the variation of S u,ref vs. K is shown for all three butene isomer/air flames at = 1.0, in order to provide an additional comparison using the direct experimental measurements in addition to the extrapolated values of . S u o 144 Figure 6.7. Experimentally determined (a) ’s of butene isomers with air mixtures (b) S u,ref vs. K of butene isomer/air mixtures at = 1.0 (T u = 298 K and P = 1 atm). (a) S u Laminar Flame Speed, S u , cm/s Equivalence Ratio, 2-C 4 H 8 /air 1-C 4 H 8 /air i-C 4 H 8 /air (b) S u, ref , = 1.0 Strain rate, K, s -1 2-C 4 H 8 /air 1-C 4 H 8 /air i-C 4 H 8 /air Reference Flame Speed, S u,ref , cm/s S u o 145 The computed relative reactivity of butene isomers using USC Mech II, the Galway model, the Nancy model, and the Ranzi model [26] are compared in Fig. 6.8. Both USC Mech II and the Nancy model predict that ’s of 2-C 4 H 8 are greater than those of 1- C 4 H 8. The Ranzi model does not contain a sub-model for the oxidation of 2-C 4 H 8 . Only the Galway predicted the correct order for the reactivities of the three C 4 alkenes although its predictions are significantly greater than present experimental results as will be shown later in this paper. Figure 6.8. Computationally determined ’s of butene isomers with air mixtures using (a) USC Mech II [23], (b) Galway model [5], (c) Nancy model [8], (d) Ranzi model [26] (T u = 298 K and P = 1 atm). S u o (a) (b) (c) (d) Equivalence Ratio, Equivalence Ratio, Laminar Flame Speed, S u , cm/s Laminar Flame Speed, S u , cm/s 1-C 4 H 8 /air i-C 4 H 8 /air 2-C 4 H 8 /air 1-C 4 H 8 /air i-C 4 H 8 /air 2-C 4 H 8 /air 1-C 4 H 8 /air i-C 4 H 8 /air 2-C 4 H 8 /air 1-C 4 H 8 /air i-C 4 H 8 /air S u o 146 Comparisons of the predicted reaction pathways for the three C 4 H 8 isomers using USC Mech II revealed that 1- and 2-C 4 H 8 can undergo decomposition forming 1,3-C 4 H 6 and H, while i-C 4 H 8 does not. i-C 4 H 8 is instead consumed through H abstraction reactions, followed by -scission forming allene (a-C 3 H 4 ) and methyl (CH 3 ). Recent molecular beam mass spectrometry of low-pressure burner-stabilized i-C 4 H 8 flames revealed notable concentrations of 1,3-C 4 H 6 [16,27]. This indicates that USC Mech II is missing reaction pathways for the decomposition of i-C 4 H 8 through 1,3-C 4 H 6 . Experimental results and numerical calculations of 1-C 4 H 8 /air and 2-C 4 H 8 /air flames are compared in Fig 6.9. There is good agreement between nominal predictions and present experimental results for 1-C 4 H 8 /air flames. Model predictions are consistently higher than experimental results for 2-C 4 H 8 /air flames. 147 Figure 6.9. Experimentally determined ’s of 1-C 4 H 8 /air and 2-C 4 H 8 /air mixtures compared to computed results (T u = 298 K and P = 1 atm). Lines: simulation results using USC Mech II. Experimental results and calculations for ’s of i-C 4 H 8 /air mixtures are compared in Fig. 6.10. Present experimental data and computed ’s are in good agreement for i- (a) 1-C 4 H 8 /air Laminar Flame Speed, S u , cm/s Equivalence Ratio, Kelley (2011) Davis and Law (1998) Present data Kelley (2011) Present data (b) 2-C 4 H 8 /air Equivalence Ratio, Laminar Flame Speed, S u , cm/s S u o S u o S u o 148 C 4 H 8 /air mixtures. Although possibly missing key pathways for the decomposition of i- C 4 H 8 , USC Mech II is still able to reproduce present experimental data. Consistent with previous observations, at fuel rich conditions, experimental results from Ref. [2] are notably higher than present experimental results. Figure 6.10. Experimentally determined ’s of i-C 4 H 8 /air mixtures compared to computed results (T u = 298 K and P = 1 atm). Lines: simulation results using USC Mech II. Measurements of ’s of 1,3-C 4 H 6 /air mixtures are compared with the nominal predictions of USC Mech II in Fig. 6.11. Computed ’s are in good agreement with measurements of Davis and Law [2], but overpredict the present data for fuel rich conditions. Davis and Law (1998) Present data i-C 4 H 8 /air Laminar Flame Speed, S u , cm/s Equivalence Ratio, S u o S u o S u o 149 Figure 6.11. Experimentally determined ’s of 1,3-C 4 H 6 /air mixtures compared to computed results (T u = 298 K and P = 1 atm). Lines: simulation results using USC Mech II. It has been consistently demonstrated that for fuel rich conditions, ’s for C 3 and C 4 hydrocarbon/air mixtures are notably higher in Ref. [2] compared to present experimental results. ’s experimentally determined by Davis and Law [2] were extrapolated from their raw stretched flame speed data linearly to zero stretch. To address the argument that all these differences simply stem from the choice of extrapolation methodology, Fig. 6.12 presents the present determination of for 1-C 4 H 8 /air flames using linear and non- linear extrapolation and compares these results with literature measurements [2]. For the fuel lean flame, there is no difference between the linear and non-linear extrapolated . At = 1.4 if linear extrapolation was utilized for present S u,ref vs. K data, the final result would still be 6 cm/s lower than the result from Ref. [2]. This is the case for all fuels which exhibit this discrepancy. There is some fundamental problem with the fuel rich Davis and Law (1998) Present data 1,3-C 4 H 6 /air Laminar Flame Speed, S u , cm/s Equivalence Ratio, S u o S u o S u o S u o S u o 150 flame data from Ref. [2] and as such it should be utilized with extreme caution for validating chemical kinetic reaction models. All present experimental results are in close agreement with new spherically expanding flame data for these C 4 isomers determined by Kelley [28]. Figure 6.12. Nonlinear and linear extrapolation of present data and Davis and Law [2]. = 1.4 = 0.8 = 1.2 Davis and Law (1998), = 1.2 Davis and Law (1998), = 1.4 Davis and Law (1998), = 0.8 Non-linear, = 1.2 Non-linear, = 0.8 Non-linear, = 1.4 Linear extrapolation Present raw data, = 1.2 Present raw data, = 0.8 Present raw data, = 1.4 S u o S u o S u o S u,ref S u,ref S u,ref Strain rate, K, s -1 Reference Flame Speed, S u,ref , cm/s 1-C 4 H 8 /air 151 6.4. Concluding remarks A comprehensive set of laminar flame speed measurements was performed for mixtures of C 3 and C 4 saturated and unsaturated hydrocarbons with air. These compounds included propane, propene, n-butane, iso-butane, 1-butene, 2-butene, iso- butene, and 1,3-butadiene. The present experimental results were determined using the computationally assisted non-linear extrapolation technique with carefully quantified uncertainties, and were compared against literature data wherever possible. It was observed that present and literature data were found to be in very close agreement at fuel lean to stoichiometric conditions. Under fuel-rich conditions, there was an up to 10 cm/s spread between literature and present experimental results for the laminar flame speeds of the fuels considered. This comprehensive data set was useful to perform systematic comparisons between the relative reactivities of flames of mixtures of air with these compounds. Comparing laminar flame speeds for propane/air and propene/air flames, the double bond in propene resulted in an increased reactivity. As a result it was observed that propene/air flame propagate faster than propane/air flames. n-Butane/air flames propagate faster than iso- butane/air flames. The branching in iso-butane promotes the production of resonant stable radicals. Resonant stabilized radicals actively consume the reactive H radical reducing overall reactivity, and as a consequence, the overall flame speeds of the mixture. From observations of experimental results for flames of C 4 H 8 /air isomers, 1- butene/air flames had the highest reactivity, and iso-butene/air flames, the lowest. The laminar flame speeds for 2-butene/air flames lay between the other two flames. 2- Butene/air flames have a lower reactivity compared to 1-butene/air flames due to the 152 location of the double bond. The two carbon groups adjacent to the two carbons in the double bond of 2-butene are methyl groups. For 1-butene, there is only one methyl group. The larger methyl radical pool in 2-butene/air flames actively consumes H reducing its overall reactivity. Predictions using four recently developed kinetic models were compared with experimental results and it was observed that only one model was able to reproduce the observed relative reactivity of the C 4 H 8 isomers. Typically, these models predicted that flames of 2-butene/air mixtures propagate faster than flames of 1-butene/air mixtures. Finally it was demonstrated that the present computationally assisted non-linear extrapolation methodology for extrapolating stretched flame speed data to zero stretch does not explain the variation between present results and literature data for laminar flame speeds of fuel/air mixtures at fuel-rich conditions. 153 6.5. References [1] F.N. Egolfopoulos, D.L. Zhu, C.K. Law, Proc. Combust. Inst. 23 (1990) 471-478. [2] S.G. Davis, C.K. Law, Combust. Sci. Technol. 140 (1998) 427-449. [3] G. Jomaas, X.L. Zheng, D.L. Zhu, C.K. Law, Proc. Combust. Inst. 30 (2005) 193- 200. [4] C.K. Westbrook, Combust. Sci. Technol. 20 (1979) 5-17. [5] D. Healy, D.M. Kalitan, C.J. Aul, E.L. Petersen, G. Bourque, H.J. Curran, Energy Fuels 24 (2010) 1521-1528. [6] F.L. Dryer, K. Brezinsky, Combust. Sci. Technol. 45 (1986) 199-212. [7] S.G. Davis, C.K. Law, Proc. Combust. Inst. 27 (1998) 521-527. [8] J.T. Moss, A.M. Berkowitz, M.A. Oehlschlaeger, J. Biet, V. Warth, P. Glaude, F. Battin-Leclerc, J. Phys. Chem. A 112 (2008) 10843-10855. [9] P.S. Veloo, F.N. Egolfopoulos, Proc. Combust. Inst. 33 (2011) 987-993. [10] P.S. Veloo, F.N. Egolfopoulos, Combust. Flame 158 (2011) 501-510. [11] C. Beatrice, C. Bertoli, N.D. Giacomo, Combust. Sci. Techonol. 137 (1998) 31-50. [12] T.S. Norton, F.L. Dryer, Proc. Combust. Inst. 23 (1990) 179-185. [13] J.K. Lefkowitz, J.S. Heyne, S.H. Won, S. Dooley, H.H. Kim, F.M. Haas, S. Jahangirian, F.L. Dryer, Y. Ju, Combust. Flame 159 (2012) 968-978. [14] A. Chakir, M. Cathonnet, J.C. Boettner, F. Gaillard, Proc. Combust. Inst. 22 (1989) 873-881. [15] B. Heyberger, N. Belmekki, V. Conraud, P.A. Glaude, R. Fournet, F. Battin- Leclerc, Int. J. Chem. Kinet. 34 (2002) 666-677. [16] Y, Zhang, J. Cai, L.Zhao, J. Yang, H. Jin, Z. Cheng, Y. Li, L. Zhang, F. Qi, Combust. Flame 159 (2012) 905-917. 154 [17] R. Fournet, J.C. Baugé, F. Battin-Leclerc, Int. J. Chem. Kinet. 31 (1999) 361-379. [18] K. Brezinsky, E.J. Burke, I. Glassman, Proc. Combust. Inst. 20 (1984) 613-622. [19] M.S. Skjøth-Rasmussen, P. Glarborg, M. Ostberg, M.B. Larsen, S.W. Sorensen, J.E. Johnsson, A.D. Jensen, T.S. Christensen, Proc. Combust. Inst. 29 (2002) 1329- 1336. [20] P. Dagaut, M. Cathonnet, Combust. Flame 113, (1998) 620-623. [21] J.T. Farrell, R.J. Johnston, I.P. Androulakis, SAE Paper No. 2004-01-2936, 2004. [22] C. Ji, Y.L. Wang, F.N. Egolfopoulos, J. Propul. Power 27 (2011) 856-863. [23] H. Wang, X. You, A.V. Joshi, S.G. Davis, A. Laskin, F.N. Egolfopoulos, C.K. Law, USC Mech Version II. High-Temperature Combustion Reaction Model of H 2 /CO/C 1 -C 4 Compounds, 2007. <http://ignis.usc.edu/Mechanisms/USC- Mech%20II/USC_Mech%20II.htm>. [24] D. Healy, N.S. Donato, C.J. Aul, E.L. Petersen, C.M. Zinner, G. Bourque, H.J. Curran, Combust. Flame 157 (2010) 1540-1551. [25] K.J. Bosschaart, L.P.H. de Goey, Combust. Flame 136 (2004) 261–269. [26] E. Ranzi, A. Frassoldati, R. Grana, A. Cuoci, T. Faravelli, A.P. Kelley, C.K. Law, Prog. Energy Combust. Sci. 38 (2012) 468-501. [27] V. Dias, J. Vandooren, Fuel 89 (2010) 2633-2639. [28] A.P. Kelley, Dynamics of Expanding Flames, Ph.D. Dissertation, Princeton University, 2011. 155 Chapter 7 Chemical Kinetic Model Uncertainty Minimization through Laminar Flame Speed Measurements 7.1 . Introduction A chemical kinetic reaction model is developed through compiling a set of critically evaluated elementary reaction rate parameters. These rate parameters are determined either through reaction rate theory (quantum chemistry calculations), experimental techniques, or estimation from analogous reactions. It is well established that there is an uncertainty associated with each elementary rate parameter present within a chemical kinetic reaction model [1]. The uncertainties in these rate parameters manifest as uncertainties in model predictions of combustion phenomena. Validation of a chemical kinetic reaction model typically consists of comparison of model predictions of a number of fundamental combustion experiments such as ’s, ignition delay times, extinction strain rates, and multispecies time history data. It is typical that a model will undergo tuning, adjustment of rate parameters within their uncertainties, as part of the validation step in order to better reproduce the combustion data considered [2]. A large number of chemical kinetic reaction models for H 2 /CO/C 1 -C 4 have been proposed and there exist large discrepancies in model predictions for combustion properties (see, e.g. [3]) although theoretical and experimental studies of H 2 /CO/C 1 -C 4 S u o 156 hydrocarbons have been performed and validated for decades. For a number of these foundation fuels such as methane or propane, there is no major fundamental difference with respect to the elementary reaction rates and reaction pathways among the published kinetic models. It is an interpretation that the proliferation of chemical kinetic reaction models within the combustion literature is nothing more than a statistical sampling of the respective rate parameters within their uncertainty space [2]. There are a number of methodologies that have been developed to quantify and propagate the uncertainty associated with elementary reaction rate parameters within a chemical model. Warnatz introduced the use of local sensitivity analysis combined with published uncertainties to determine the reactions with the most significant contribution to prediction uncertainties [4]. This method was expanded by Turanyi and coworkers [5] and later combined with a Monte Carlo approach to estimate the parametric uncertainty (e.g., [6,7,8]). A recent study by Nagy and Turanyi addressed importance of temperature dependence of the Arrhenius parameters in determination of the uncertainty domain [9] and proposed an analytical expression approach using the covariance matrix of the Arrhenius parameters and the joint uncertainty of the Arrhenius parameters. However, this technique is limited to a system, which has sufficient data to constrain rate constants over the full range of temperature, pressure and bath gas conditions. Tomlin and coworkers developed the global sensitivity and uncertainty method in conjunction with the high-dimensional model representation (HDMR) [10,11,12]. Klippestein et al. combined global uncertainty screening and ab initio theoretical kinetics to study methanol oxidation mechanisms [13,14]. Frenklach and coworkers [1,15] developed the response surface optimization method by solution mapping using factorial 157 design. This technique was applied to optimize GRI-Mech (e.g., [16]), propane chemistry by Wang and coworkers [17] and H 2 /CO subset [18] of USC Mech II [19]. This study uses the uncertainty minimization methodology, referred to as the method of uncertainty minimization using polynomial chaos expansions (MUM-PCE) [20]. The comprehensive mathematical background for this methodology was presented in Ref. [2]. MUM-PCE combines the response surface and optimization methodology with the spectral uncertainty expansion method of polynomial chaos expansion introduced by Najm, Ghanem, and coworkers [21,22,23]. This methodology addresses the impact of uncertainties in the model predictions of combustion properties and provides additional constraints to rate coefficients and their uncertainties by using experimental targets. Using experimental data with well-quantified experimental uncertainties, it is possible to constrain the uncertainties in the reaction model and as a result reduce the overall prediction uncertainties. For this reason, precise quantification of the uncertainty associated with experimental data is essential. A simplified version of this MUM-PCE was tested against the combustion model of ethylene [20] and more recently, MUM-PCE has been demonstrated for its ability to utilize multispecies time histories from shock tubes within the framework of MUM-PCE to constrain kinetic uncertainties [24]. In that study, it was concluded that accurate measurements of global combustion properties, like , are still necessary for constraining the kinetic model. It is the intent of this chapter to better understand the role of measurements in model uncertainty minimization. In particular, MUM-PCE was employed to demonstrate how systematically determined ’s with well-defined measurement uncertainties can be utilized to constrain the model uncertainty, using USC Mech II [19] as a case study. For S u o S u o S u o 158 this purpose the comprehensive set of ’s of C 1 -C 4 hydrocarbon flames determined in the previous chapters are utilized. With this data set, several questions critical to a better utilization of were explored. For example, the accuracy required from measurements was assessed. The ability of flame measurements to detect missing reaction pathways was explored also. 7.2 . Reaction model The chemical kinetic model used here is based on USC Mech II [19], which consists of 111 species and 784 elementary reactions. USC Mech II has been developed to describe the high temperature oxidation kinetics of H 2 /CO and C 1 -C 4 hydrocarbons and has been validated against ignition delay times in shock tubes, ’s, and speciation measurements made in flow reactors, shock tubes, and burner stabilized flames. Although a comprehensive optimization study was conducted for the H 2 /CO kinetic subset [18], USC Mech II as a whole is un-tuned. For the current optimization study, the rate parameters of the H 2 /CO subset were restored to their nominal values listed in Ref. [20]. Additionally, the rate parameter for the OH + HO 2 → H 2 O + O 2 reaction was revised using the expression of Baulch et al. [25], which was shown to represent more accurately the recent measurements by Hanson and coworkers [26] and Michael and co- workers [27]. For the reaction H + O 2 + M = HO 2 + M, the collision efficiency of H 2 O is taken as an adjustable parameter in the optimization study. The reaction model described above is referred to as the unconstrained or prior model. Further details of this unconstrained model can be found Ref. [24]. Uncertainties for the Arrhenius pre-factors in USC Mech II are provided in the supplementary materials S u o S u o S u o S u o 159 of Ref. [20]. These factors were taken either in consultation with literature compilations (e.g., [25,28]) or through evaluation [20,24]. The uncertainty in the activation energy and the pressure fall-off parameters was not considered in the present work. Nominal model predictions using different kinetic models were compared also along with USC Mech II [19]. The Galway Mech, C 1 -C 5 model of Curran and coworkers [29,30], San Diego Mech [31] for C 1 -C 3 hydrocarbons, and the four butanol isomers model by Battin-Leclerc and coworkers (Nancy Model) [32]. The Galway Mech consists of 293 species and 1593 reactions, the San Diego Mech consists of 46 species and 235 reactions, the Nancy Model consists of 158 species and 1250 reactions. Table 1 lists the experimental targets for uncertainty minimization. 160 Series mixtures equivalence ratio 1 CH 4 /air = 0.7, 1.0, 1.3 2 C 2 H 4 /air = 0.7, 0.8, 1.0, 1.2, 1.4 3 C 2 H 6 /air = 0.7, 0.8, 1.0, 1.2, 1.4 4 C 2 H 2 /O 2 /N 2 = 0.7, 0.8, 1.0, 1.2, 1.4,1.6 5 C 3 H 6 /air = 0.7, 0.8, 1.0, 1.2, 1.4 6 C 3 H 8 /air = 0.7, 0.8, 1.0, 1.2, 1.4 7 n-C 4 H 10 /air = 0.7, 0.8, 1.0, 1.2, 1.4 8 iso-C 4 H 10 /air = 0.7, 0.8, 1.0, 1.2, 1.4 9 1-C 4 H 8 /air = 0.7, 0.8, 1.0, 1.2, 1.4 10 2-C 4 H 8 /air = 0.7, 0.8, 1.0, 1.2, 1.4 11 iso-C 4 H 8 /air = 0.7, 0.8, 1.0, 1.2, 1.4 12 1,3-C 4 H 6 /air = 0.7, 0.8, 1.0, 1.2, 1.4 Table 7.1. Experimental data set considered for optimization. 161 7.3 . Active rate parameters Active rate parameters for the optimization were chosen based on sensitivity information for all C 1 -C 4 hydrocarbon fuels studied. Sensitivity coefficients of to reaction A-factors for fuel/O 2 /N 2 mixtures are presented in Figs. 7.1-7.3. The high temperature oxidation of hydrocarbon/air mixtures is dominated by the reaction kinetics of H, CO, HCO and CH x reactions. The reactions H + O 2 O + OH (R1) CH 3 + OH CH 2 (s) + H 2 O (R95) are ranked for most of fuel/air mixtures. The uncertainty factor of R1 is 1.2 (20%) and the logarithmic sensitivity coefficient of a calculated to this reaction is typically about 0.3, for a total uncertainty of about 5%. The uncertainty factor of R95 is 5.0 [20], and with a logarithmic sensitivity coefficient typically around 0.03 the total uncertainty is also about 5%. Although R95 is on the sensitivity list for all fuel/air mixtures and its associated uncertainty is large, its sensitivity is fairly low. Therefore, R95 does not significantly contribute to the predicted . Calculated values for mixtures of C 2 H 2 , C 2 H 6 , C 3 H 6 , i-C 4 H 8 , 1-C 4 H 8 and 1,3-C 4 H 6 with air also show strong sensitivity to reactions involving primary intermediates of fuel breakdown reactions, e.g. 2- C 4 H 9 products. S u o S u o S u o S u o 162 Figure 7.1. Logarithmic sensitivity coefficients of with respect to kinetic rate parameters, computed for flames of CH 4 /air. Figure 7.2 depicts ranked logarithmic sensitivity coefficients of to rate constants for mixtures of C 2 -C 4 normal alkanes with air and C 4 branched alkanes with air at = 1.0. R108 and R252 are highly sensitive for C 2 H 6 /air mixtures and their uncertainty factors are 5.0 and 3.0 respectively as shown in Table 7.2, which are fairly large value of uncertainties. Logarithmic sensitivity coefficient S u o S u o 163 Figure 7.2. Logarithmic sensitivity coefficients of with respect to kinetic rate parameters, computed for flames of C 2 -C 4 alkanes and branched alkanes with air. Logarithmic sensitivity coefficient Logarithmic sensitivity coefficient S u o 164 Reactions span a 1 H + O 2 ↔ O + OH 1.2 95 CH 3 + OH ↔ CH 2 (s) + H 2 O 5.0 108 CH 3 + CH 3 ↔ C 2 H 5 + H 5.0 150 HCCO + H ↔ CH 2 (s) + CO 2.0 152 HCCO + O 2 ↔ OH + 2CO 5.0 156 HCCO + OH ↔ C 2 O + H 2 O 3.0 161 C 2 H 2 + O ↔ HCCO + H 1.5 191 C 2 H 3 + H ↔ C 2 H 2 + H 2 3.0 197 C 2 H 3 + O 2 ↔ CH 2 CHO + O 4.0 252 C 2 H 4 + H + M ↔ C 2 H 5 + M 3.0 254 C 2 H 4 + O ↔ C 2 H 3 + OH 3.0 257 C 2 H 4 + OH ↔ C 2 H 3 + H 2 O 2.0 328 a-C 3 H 5 + H + M ↔ C 3 H 6 + M 3.0 363 C 3 H 6 +H ↔ a-C 3 H 5 + H 2 2.0 372 C 3 H 6 + OH ↔ a-C 3 H 5 + H 2 O 2.0 483 C 4 H 6 + H ↔ i-C 4 H 5 + H 2 5.0 484 C 4 H 6 + H ↔ C 2 H 4 + C 2 H 3 2.0 491 C 4 H 6 + OH ↔ n-C 4 H 5 + H 2 O 3.0 492 C 4 H 6 + OH ↔ i-C 4 H 5 + H 2 O 5.0 555 1-C 4 H 8 + H ↔ C 2 H 4 + C 2 H 5 3.0 556 1-C 4 H 8 + H ↔ C 3 H 6 + CH 3 5.0 557 1-C 4 H 8 + H ↔ C 4 H 7 + H 2 5.0 a uncertainty factor Table 7.2. Selected active reactions discussed in the sensitivity analysis section and their uncertainty factors [20]. Figure 7.3 depicts ranked logarithmic sensitivity coefficients of to rate constants for mixtures of C 2 -C 3 unsaturated hydrocarbons with air at = 1.0. R257 is highly sensitive for C 2 H 4 /air mixtures. R191 and R197 were also shown in the sensitivity list for both C 2 H 6 and C 2 H 4 with air flames. USC Mech II includes R254 C 2 H 4 + O C 2 H 3 + OH, while other models (e.g., [29,31]) chose reaction pathways of C 2 H 4 + O CH 2 CHO + H instead. Although the dominant reaction channel is R255 C 2 H 4 + O CH 3 + HCO, sensitivity coefficients of R254 is slightly larger than R255 in fuel lean and stoichiometry condition. However, R255 has larger sensitivity at fuel rich S u o 165 condition. Introducing or replacing the latter to the USC Mech II does not affect the prediction of ’s of C 2 H 4 /air mixtures. ’s of C 3 H 6 /air mixtures are also sensitive to the fuel specific reactions R328, R363, and R372. Figure 7.3. Logarithmic sensitivity coefficients of with respect to kinetic rate parameters, computed for flams of C 2 H 4 /air and C 3 H 6 /air mixtures. S u o S u o Logarithmic sensitivity coefficient Logarithmic sensitivity coefficient S u o 166 Figure 7.4 depicts ranked logarithmic sensitivity coefficients of to rate constants for C 2 H 2 /O 2 /N 2 mixtures at = 1.0. Active parameters are different from CH 4 /air mixtures compared to other hydrocarbons. Predicted ’s of C 2 H 2 /O 2 /N 2 mixtures showed notable sensitivities to R150, R152, and R161. Figure 7.4. Logarithmic sensitivity coefficients of with respect to kinetic rate parameters, computed for flames of C 2 H 2 /O 2 /N 2 mixtures. Figure 7.5 depicts ranked logarithmic sensitivity coefficients of to rate constants for mixtures of unsaturated C 4 - hydrocarbons with air mixtures at = 1.0. For 1- C 4 H 8 /air mixtures, 1-C4H8 and C 3 H 6 oxidation reactions are dominantly sensitive. Not much strong sensitivities of fuel specific reactions are observed from 2-C 4 H 8 /air mixtures compare to other C 4 unsaturated hydrocarbons. In 1,3-C 4 H 6 /air mixtures, R484 is dominantly sensitive for overall ’s and R492 is more sensitive for fuel lean conditions. Uncertainties associated with selected active parameters in this sensitivity analysis section were listed in the table 7.2. S u o S u o Logarithmic sensitivity coefficient S u o S u o 167 Figure 7.5. Logarithmic sensitivity coefficients of with respect to kinetic rate parameters, computed for flames of C 4 unsaturated hydrocarbons with air. Logarithmic sensitivity coefficient Logarithmic sensitivity coefficient S u o 168 7.4 . Uncertainty propagation The response surface methodology maps the solutions of differential equations in the form of an algebraic expansion, whose variables of this expansion are simply the factorial representation of the rate parameters, and the coefficients of expansion are basically sensitivity coefficients. We measure the quality of the response surface by comparing the predicted using the PREMIX flame code against the polynomial predictions of , which is depicted in Fig. 7.6. The 45-degree line demonstrates that the response surface has a mean error less than 0.5 %, well below the experimental uncertainty. Figure 7.6. 45 ○ Diagonal plot of response surface predictions versus directly computed laminar flame speeds for the flames of C 1 -C 4 hydrocarbons. Figures 7.7 to 7.12 compare the experimental results and nominal predictions of various kinetic models. The 2 uncertainty (95% confidence level) band of the prior model (base model of USC Mech II) is superimposed onto these figures. It was assumed S u o S u o Computed prediction of S u , cm/s Polynomial prediction of S u , cm/s 45 degree line 169 that the rate parameters were log-normally distributed. The underlying uncertainty in the individual rate coefficients results in an uncertainty in the model predictions, which are far larger than the scatter in experimental data. There are larger 2 uncertainties for stoichiometric flame and fuel rich flames compared to fuel lean flames. For CH 4 /air flames, shown in Fig. 7.7, the 2 uncertainty is ±5 cm/s at = 0.7, ±7 cm/s at = 1.0, and ±8 cm/s at = 1.3. For 1,3-C 4 H 6 /air flames, shown in Fig. 7.12, the 2 uncertainty is ±6 cm/s at = 0.7 increasing to ±10 cm/s at = 1.2. The growing width of the 2 uncertainty bands at richer conditions, is caused by the larger number of active rate parameters impacting the predictions. For hydrocarbon/air mixtures, the predicted ’s is mostly sensitive to R1, R9, R34, R38, R42 R43, and R95, as shown in Figs. 7.1 through 7.5. As a result, the 2 uncertainty bands of prior model for flames of these mixtures are very similar. ’s of flames of C 2 H 2 , C 2 H 6 , C 3 H 6 , i-C 4 H 8 , 1-C 4 H 8 and 1,3-C 4 H 6 with air mixtures have large sensitivities to reactions involving the fuel and primary intermediates following initial fuel decomposition. As a result the 2 uncertainty bands of these fuels are larger than other fuels in this study, since the rate parameters of such reactions have large associated uncertainties. Three different kinetic models; USC Mech II (USC) [19], Galway Mech (Galway) [29,30], and San Diego Mech (UCSD) [31], predicted ’s of CH 4 /air mixtures within 2 uncertainty band of the prior model along with experimental measurements [33,34], shown in Fig. 7.7. There are no major fundamental differences in the reaction pathways among these kinetic models regarding the high temperature CH 4 oxidation chemistry. S u o S u o S u o 170 Figure 7.7. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of CH 4 /air mixtures using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), and UCSD (San Diego Mech, [31]); The shaded bands indicate the 2 model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. Comparing the prior model predictions for C 2 H 6 with that for C 3 H 8 , shown in Fig 7.8, it is observed that the 2 uncertainty band for C 2 H 6 /air flames are larger. From Fig 2a, ’s of C 2 H 6 /air flames are sensitive to a number of reactions involving C 2 H 5 , (R108) and (R252). These reactions have large uncertainties associated with their rate parameters. Although predictions of ’s using the Galway model are better agreement with measurements of Bosschaart and de Goey [33] for C 2 H 6 /air and C 3 H 8 /air as well as CH 4 /air mixtures, notable discrepancies are observed comparing with present data and other kinetic models in fuel rich conditions, for instance, the Nancy model [32]. 2 uncertainty band Galway USC UCSD Bosschaart and de Goey (2004) Park et al. (2011) CH 4 /air 0.14 0.12 0.10 0.08 0.06 0.04 0.02 S u o S u o S u o 171 Figure 7.8. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of C 2 H 6 /air and C 3 H 8 /air mixtures using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), Nancy (Nancy model [32]) and UCSD (San Diego Mech, [31]); The shaded bands indicate the 2 model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. Galway USC UCSD Bosschaart and de Goey (2004) Park et al. (2012) (a) C 2 H 6 /air 0.16 0.14 0.12 0.10 0.06 0.04 0.02 0.08 0.16 0.14 0.12 0.10 0.06 0.04 0.02 0.08 Galway USC UCSD Bosschaart and de Goey (2004) Present data (b) C 3 H 8 /air Nancy S u o 172 Figure 7.9 depicts the 2 uncertainty band of prior model predictions for n-C 4 H 10 /air and i-C 4 H 10 /air mixtures. For i-C 4 H 10 /air mixtures, data from Davis and Law [35] and Bosschaart and de Goey [33] lie outside of 2 uncertainty band. Although data by Bosschaart and de Goey showed discrepancies with present data and prior model predictions for fuel rich condition, they remained inside of 2 uncertainty bands for C 1 - C 3 alkanes and n-C 4 H 10 . In the next section we will discuss in detail the validity of these data sets. Typically, model predictions for unsaturated hydrocarbon mixtures have larger uncertainties than their saturated counterparts. The 2 uncertainty is ±8 cm/s for C 2 H 6 /air flames at = 1.2 (Fig. 7.8a), ±11 cm/s for C 2 H 4 /air flames at = 1.2 (Fig. 7.10a), and ±12 cm/s for C 2 H 2 /O 2 /N 2 flames at = 1.2 (Fig. 7.10b). ’s of flames of unsaturated hydrocarbons are sensitive to fuel specific reactions and these rates parameters have large inherent uncertainties. S u o 173 Figure 7.9. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of n-C 4 H 10 /air and i-C 4 H 10 /air mixtures using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), and Nancy (Nancy Model, [32]); The shaded bands indicate the 2- model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. Galway USC Davis and Law (1998) Bosschaart and de Goey (2004) Present data (a) n-C 4 H 10 /air Nancy 0.16 0.14 0.12 0.10 0.06 0.04 0.02 0.08 0.18 Galway USC (b) i-C 4 H 10 /air Davis and Law (1998) Bosschaart and de Goey (2004) Present data 0.16 0.14 0.12 0.10 0.06 0.04 0.02 0.08 0.18 0.20 S u o 174 Figure 7.10. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of C 2 H 4 /air and C 2 H 2 /(13%O 2 +87%N 2 ) mixtures using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), and UCSD (San Diego Mech, [31]); The shaded bands indicate the 2- model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. Galway USC Park et al. (2012) (a) C 2 H 4 /air UCSD 0.08 0.07 0.06 0.05 0.03 0.02 0.01 0.04 0.09 0.10 0.11 Galway USC (b) C 2 H 2 /(13%O 2 +87%N 2 ) 0.16 0.14 0.12 0.10 0.06 0.04 0.02 0.08 Park et al. (2012) UCSD S u o 175 For ’s of C 2 H 2 /(13%O 2 +87%N 2 ) mixtures, nominal predictions using the Galway model lie outside the 2 uncertainty band of the prior model for ≥ 1.2. This indicates that there must be fundamental differences in the reaction pathways between Galway model and our prior model. As discussed in Ref. [3], the Galway model has different branching ratios for the two main fuel consumption reactions C 2 H 2 + O CH 2 + CO (R160) C 2 H 2 + O HCCO + H (R161) The C 2 H 2 oxidation mechanism affects also predictions of fuel rich C 2 H 4 /air flames. The probability density function and the 2 uncertainty of ’s of C 3 H 6 /air mixtures predicted for the prior model are shown in Fig. 7.11. Similar to C 2 unsaturated hydrocarbons, nominal predictions of ’s of C 3 H 6 /air from Galway model are outside the 2 uncertainty bands of the prior model at fuel rich conditions. In the initial fuel consumption pathway, C 3 H 6 is primarily consumed through pathways forming both a- C 3 H 5 and C 2 H 4 . In the Galway model, a larger fraction of C 3 H 6 passes through C 2 H 4 compared with USC Mech II via C 3 H 6 + H C 2 H 4 + CH 3 (R362) As a result, the C 2 H 4 sub-mechanisms are important to predict accurately the oxidation of C 3 H 6 /air flames. Large 2 uncertainty bands are computed for ’s of C 3 H 6 /air mixtures, which are ±7.5 cm/s and ±5 cm/s for = 1.0 and = 1.2 respectively. Experimental data by Davis and Law [35] is also outside of 2 uncertainty band for C 3 H 6 /air mixtures for > 1.2. S u o S u o S u o S u o 176 Figure 7.11. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of C 3 H 6 /air mixtures using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), and Nancy (Nancy model, [32]); The shaded bands indicate the 2- model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. The 2 uncertainty bands of ’s of C 4 -hydrocarbon/air mixtures in prior model was showed in Fig. 7.12. Nominal predictions by the Nancy model were also used for C 4 hydrocarbons as well as USC Mech II and Galway model. Computed ’s of C 4 - hydrocarbons with air mixtures using Galway model stays consistently outside of predicted 2 uncertainty band of prior model for fuel rich conditions especially for mixtures of 1-C 4 H 8 /air and i-C 4 H 8 /air. Experimental data by Davis and Law [35] are also notably outside of 2 -uncertainty band of the prior model for i-C 4 H 8 /air mixtures at ≥ 1.0. 2 uncertainty band Galway USC Nancy Davis and Law (1998) Present data C 3 H 6 /air 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.16 S u o S u o S u o 177 Figure 7.12. The 2 model prediction uncertainty band of prior model comparing with experimental and computed ’s of C 4 - hydrocarbon with air using various kinetic models of USC (USC Mech II, [19]), Galway (Galway Mech, [29,30]), and Nancy (Nancy model, [32]); The shaded bands indicate the 2- model prediction uncertainty; the actual ±2 curves are indicated by the dashed lines. 2 uncertainty band Galway (b) 2-C 4 H 8 /air Present data 0.14 0.12 0.10 0.06 0.04 0.02 0.08 0.16 0.14 0.12 0.10 0.06 0.04 0.02 0.08 USC Nancy 0.14 0.12 0.10 0.06 0.04 0.02 0.08 0.18 0.16 2 uncertainty band Galway USC Davis and Law (1998) Present data (a) 1-C 4 H 8 /air Nancy (c) i-C 4 H 8 /air Davis and Law (1998) Present data Nancy Galway USC 2 uncertainty band (d) 1,3-C 4 H 6 /air USC 2 uncertainty band Davis and Law (1998) Present data Galway 0.09 0.08 0.07 0.06 0.04 0.03 0.02 0.05 0.12 0.11 0.10 Laminar flame speed, S u , cm/s Laminar flame speed, S u , cm/s S u o 178 7.5 . Uncertainty minimization Figures 7.13 through 7.18 depict the probability density function of ’s predicted for C 2 -C 4 hydrocarbon/air mixtures using both the unconstrained, prior model (top panel) and the posterior model (bottom panel, henceforth Model I), which is optimized and constrained by the experimental data by the current authors only. As shown in Figs. 7.13 through 7.18, Model I gives notably improved predictions, both for the nominal values and reduced uncertainty bands. Additional work is being conducted to understand better the utility of the current set of data and to formulate rational strategies for model optimization and uncertainty minimization. Target values for Model I are shown in Table 7.3. The experimental uncertainties of listed in Table 7.3 are much smaller than the prior model uncertainty. This means that each target will have a large contribution to model uncertainty minimization. There is a preferred model within the uncertainty space and therefore the experiments not only can be used for constraining the kinetic model but also will have taught us something. These observations underscore the purpose and utility for model constraining. S u o S u o S u o S u o 179 No Mixture (exp) No Fuel/air (exp) 1 CH 4 /air [34] 0.7 0.8 1.0 1.2 1.3 18.2±1.3 25.4±1.5 35.9±1.0 31.2±1.3 20.8±1.4 7 C 4 H 6 /air 0.7 0.8 1.0 1.2 1.4 30.0±0.9 41.0±1.0 51.0±1.1 52.0±1.5 38.0±1.5 2 C 2 H 2 /O 2 /N 2 [3] 0.7 0.8 1.0 1.2 1.4 1.6 19.7±1.0 29.3±1.0 44.4±1.3 50.3±1.6 39.8±1.3 23.0±0.8 8 1-C 4 H 8 /air 0.7 0.8 1.0 1.2 1.4 25.2±1.2 31.8±1.3 41.5±1.2 40.0±1.5 25.5±1.5 3 C 2 H 4 /air [3] 0.7 0.8 1.0 1.2 1.4 36.9±1.5 47.0±1.2 64.6±1.2 66.5±1.4 51.6±1.7 9 2-C 4 H 8 /air 0.7 0.8 1.0 1.2 1.4 22.2±1.3 30.7±1.3 39.5±1.6 36.1±1.5 21.2±1.5 4 C 2 H 6 /air [3] 0.7 0.8 1.0 1.2 1.4 20.0±1.6 29.1±1.2 39.1±1.2 37.5±1.9 22.8±1.5 10 i-C 4 H 8 /air 0.7 0.8 1.0 1.2 1.4 17.3±1.0 25.8±1.0 35.0±1.6 32.5±1.1 17.8±1.5 5 C 3 H 6 /air 0.7 0.8 1.0 1.2 1.4 24.4±0.8 32.5±0.8 42.0±1.0 40.5±1.2 25.5±1.3 11 n-C 4 H 10 /air 0.7 0.8 1.0 1.2 1.4 21.1±1.1 28.2±1.0 36.9±1.3 34.3±1.1 18.5±1.5 6 C 3 H 8 /air 0.7 0.8 1.0 1.2 1.4 22.5±1.0 30.0±1.0 38.3±1.0 36.0±1.2 18.7±1.2 12 i-C 4 H 10 /air 0.7 0.8 1.0 1.2 1.4 19.7±1.1 25.8±1.0 33.4±1.0 30.3±1.0 16.8±1.3 Table 7.3. Optimization targets and their associated uncertainties for posterior Model I. S u o S u o 180 Figure 7.13. Comparison of prediction uncertainties of the prior model (top panel) and those of the posterior model I (bottom panel) for CH 4 /air mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are the experimental data [34]. CH 4 /air 0 181 Figure 7.14. Comparison of prediction uncertainties of the prior model (top panel) and those of the posterior model I (bottom panel) for (a) C 2 H 6 /air and (b) C 3 H 8 /air mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are the experimental data for (a) C 2 H 6 /air by Ref. [3] and for (b) C 3 H 8 /air by present data. Figure 7.15. Comparison of prediction uncertainties of the prior model (top) and those of the posterior model I for (a) n-C 4 H 10 /air and (b) i-C 4 H 10 /air mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are present experimental data. (a) C 2 H 6 /air (b) C 3 H 8 /air 0.15 0.10 0.05 0.6 0.4 0.2 0.8 0.15 0.10 0.05 0.3 0.2 0.1 0.4 0.5 (a) n-C 4 H 10 /air (b) i-C 4 H 10 /air 0.15 0.10 0.05 0.6 0.4 0.2 0.8 0.15 0.10 0.05 0.6 0.4 0.2 0.8 0.20 1.0 182 Figure 7.16. Comparison of prediction uncertainties of the prior model (top panel) and those of the posterior model I (bottom panel) for (a) C 2 H 4 /air and (b) C 2 H 2 /(13%O 2 +87%N 2 ) mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are the experimental data [3]. Figure 7.17. Comparison of prediction uncertainties of the prior model (top panel) and those of the posterior model I (bottom panel) for C 3 H 6 /air mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are present experimental data. (a) C 2 H 4 /air (b) C 2 H 2 /O 2 /N 2 0.15 0.10 0.05 0.3 0.2 0.1 0.4 0.08 0.04 0.02 0.3 0.2 0.1 0.4 0.5 0.06 0.10 0.6 C 3 H 6 /air 0.15 0.10 0.05 0.6 0.4 0.2 0.8 183 Figure 7.18. Comparison of prediction uncertainties of the prior model (top) and those of the posterior model for C 4 unsaturated hydrocarbon/air mixtures. The shaded bands represent the model uncertainties and the dashed lines represent the ±2 uncertainty bounds. Grey intensity indicates the normalized probability density function. Symbols are present experimental data. 184 7.6 . Consistency analysis for data set In the previous section, Figs. 7.13 to 7.18 demonstrated that the optimized model was in excellent agreement with present data sets. What about the case when the constrained model predictions, ) ( * o r x , do not agree with experimental observations, obs r ? This disagreement can be caused by a number of factors, namely; the uncertainties of the experimental results or rate parameters have been under-estimated or the chemical kinetic reaction model is incomplete, i.e., missing kinetic pathways. To address these questions, we employ a data-consistency analysis algorithm that was described in [2] and Chapter 2. Constraining the uncertainty of a kinetic model is a two- stage process. Firstly, the model is constrained by minimizing the least-squares difference between the model prediction and the experimental measurements, weighted by the experimental uncertainty, obs r . For Model I, none of the target experimental data were removed as an optimization target. Therefore, it can be concluded that the experimental data used to constrain Model I form a self-consistent target set. In addition to using experimental data by authors, multiple target data sets were considered for optimization including all other literature data discussed earlier for C 1 -C 4 hydrocarbons in addition to present experimental data as optimization targets (Model II). Flames of C 2 H 2 /air data by both Jomaas et al. [36] and Egolfopoulos et al. [37] were included for optimization targets of Model II. The posterior Model III included as experimental targets only the measurements of Davis and Law [35], which consists of ’s of C 3 H 6 /air, n-C 4 H 10 /air, i-C 4 H 10 /air, 1-C 4 H 8 , i-C 4 H 8 , and 1,3-C 4 H 6 /air flames. Finally, the posterior Model IV included experimental data for all C 1 -C 4 hydrocarbons literature S u o 185 data in addition to present experimental data as multiple targets but excluded C 3 and C 4 data by Ref. [35] and C 2 H 4 /air by Ref. [38]. Also, C 2 H 2 /air data were excluded from Model IV as well. Optimization targets for three posterior models are listed in Table 7.4. Experimental uncertainties for all literature data were assumed as ±2 cm/s except data by Ref. [33], and uncertainties of present data are shown in Table 7.3 with 2 of sampling error from these measurements. Data by Bosschaart and de Goey [33] have uncertainties, stated by the authors, of ±1 cm/s. If the standard deviation of the target experiment ) ( obs r is small, it will provide strong constraint to the posterior model so it will have a large contribution to the optimized value. Model I Model II Model III Model IV CH 4 /air [34] [41], [34], [33], [42] [41], [34], [33], [42] C 2 H 2 /O 2 /N 2 [3] [37], [3] [37], [3] C 2 H 2 /air N/A [37], [36] C 2 H 4 /air [3] [36], [3], [39], [43],[38] [36], [3], [39], [43] C 2 H 6 /air [3] [36], [41], [33], [3] [36], [41], [33], [3] C 3 H 8 /air Present data Present data, [36], [41], [33] Present data, [36], [41], [33] C 3 H 6 /air Present data Present data, [35], [36] [35] Present data, [36] n-C 4 H 10 /air Present data Present data, [35], [33] [35] Present data,[33] i-C 4 H 10 /air Present data Present data, [35], [33] [35] Present data,[33] 1-C 4 H 8 /air Present data Present data, [35] [35] Present data 2-C 4 H 8 /air Present data Present data Present data i-C 4 H 8 /air Present data Present data, [35] [35] Present data 1,3-C 4 H 6 /air Present data Present data, [35] [35] Present data Table 7.4. List of optimization targets. The results from the posterior Model II indicated that the multiple experimental data sets for ’s of CH 4 /air, C 2 H 2 /O 2 /N 2 , and C 2 H 6 /air flames over all ’s considered were equally-good targets, i.e., no targets were removed. The targets removed through optimization from Model II are depicted in Fig. 7.19. data from Ref. [35], for fuel rich flames of C 3 and C 4 hydrocarbons were removed from the experimental data target S u o S u o 186 set because they yield a larger F r value than other data. A target may be removed either because multiple measurements for a particular experimental condition did not agree with each other or the experimental measurement cannot be reconciled with the other targets within the uncertainty bounds of the prior model. The data from Ref. [39] for of a C 2 H 4 /air flame at = 1.4 was removed from the Model II. All data points except = 1.3 from Ref. [38] for of a C 2 H 4 /air flame were also removed from the Model II. From Fig. 7.19a, it can be seen that this point is inconsistent with other experimental measurements. For C 3 H 8 /air mixtures at = 1.4, data from Ref. [36] was also removed as an optimization target. S u o S u o 187 Figure 7.19. Consistency analyses for (a) posterior Model II (b) posterior Model II (C 2 H 2 ). CH 4 /air, =0.7 CH 4 /air, =0.8 CH 4 /air, =1.0 CH 4 /air, =1.2 CH 4 /air, =1.3 CH 4 /air, =1.3 C 2 H 6 /air, =1.2 C 2 H 4 /air, =0.7 C 2 H 4 /air, =0.8 C 2 H 4 /air, =1.0 C 2 H 4 /air, =1.2 C 2 H 4 /air, =1.4 C 2 H 4 /air, =1.4 C 2 H 2 /air, =0.7 C 2 H 2 /air, =1.6 C 3 H 8 /air, =1.4 C 3 H 8 /air, =1.4 C 3 H 6 /air, =1.4 1-C 4 H 8 /air, =1.2 1-C 4 H 8 /air, =1.4 2-C 4 H 8 /air, =1.2 2-C 4 H 8 /air, =1.4 i-C 4 H 8 /air, =1.2 1,3-C 4 H 6 /air, =1.4 n-C 4 H 10 /air, =1.4 n-C 4 H 10 /air, =1.4 i-C 4 H 10 /air, =1.2 i-C 4 H 10 /air, =1.4 i-C 4 H 10 /air, =1.4 [34] [34] [34] [34] [34] [33] [3] [38] [38] [38] [38] [38] [39] [36] [36] [36] present [35] [35] [35] present present [35] [35] [33] [35] [33] [35] [33] F r (a) 0 1 2 3 4 5 6 fls_24f fls_24e fls_24d fls_24c fls_24b fls_24f fls_24e fls_24d fls_24c fls_24b fls_24a fls_23f fls_23e fls_23d fls_23c fls_23b fls_23a fls_23f fls_23e fls_23d fls_23c fls_23b fls_23a C 2 H 2 /O 2 /N 2 , =0.7 present data =0.8 =1.0 =1.2 =1.4 =1.6 C 2 H 2 /O 2 /N 2 , =0.7 [37] =0.8 =1.0 =1.2 =1.4 =1.6 C 2 H 2 /air, =0.7 [36] =0.8 =1.0 =1.2 =1.4 =1.6 C 2 H 2 /air, =0.8 [37] =1.0 =1.2 =1.4 =1.6 F r (b) 188 Although ’s of C 2 H 2 /O 2 /N 2 flames by Egolfopoulos et al. [37] was considered as consistent targets in Model II optimization, their C 2 H 2 /air data set from the same study [37] was removed as a results of optimization. From Fig.7 18 it can be clearly observed that data from Ref. [37] is significantly higher than newer results by Jomaas et al. [36] and nominal predictions by USC Mech II. Figure 7.19 depicts selected F r test results of the posterior Model II. From the consistency test, all data from Ref. [37] for C 2 H 2 /air flames were removed and two data points from Ref. [36] at = 0.7 and = 1.6 were also removed as shown in Fig. 7.19b. The rejection of a target may not imply that the particular measurement is wrong, but it indicates that the available data in that region of condition space should be critically evaluated [2]. Many of experimental targets for flames of C 4 hydrocarbons including both present experimental data and those from Ref. [35] were removed from the optimization targets in Model II. It could be assumed from earlier observations that there are notable discrepancies between present data and Ref. [35] and some targets remained out of 2 bands of prior model. ’s of mixtures of C 3 H 6 /air at = 1.4, 1-C 4 H 8 /air at = 1.2 and 1.4, i-C 4 H 8 /air at = 1.2, 1,3-C 4 H 6 /air at = 1.2 and 1.4, n-C 4 H 10 /air at = 1.4, and i- C 4 H 10 /air at = 1.4 from Ref. [35] were removed from posterior Model II as depicted in Fig. 7.19a. Targets for i-C 4 H 10 /air mixtures at = 1.4 by Bosschaart and de Goey [33] were found to be inconsistent with their CH 4 /air, C 2 H 6 /air, and C 3 H 8 /air, and n-C 4 H 10 /air flame results considering only experimental targets with Ref. [33] only for a consistency analysis. From the Model II, targets for CH 4 /air at = 1.3, n-C 4 H 10 /air at = 1.4 and i- C 4 H 10 /air at = 1.2 and 1.4 from Ref. [33] were removed. Although target of i-C 4 H 10 /air at = 1.2 from Ref. [35] showed slightly larger discrepancies with prior model S u o S u o 189 predictions and present data comparing to that of Ref. [33], target from Ref. [33] was removed in Model II. Experimental uncertainty for the target from Ref. [33] is ±1 cm/s and uncertainty for the same target from Ref. [35] is ±2 cm/s. The smaller the uncertainty of the target set yields a larger F r which means that it has the stronger effect on the posterior model, and a greater chance of inconsistency. The present data for mixtures of 2-C 4 H 8 /air at = 1.2 and 1.4, C 3 H 8 /air at = 1.4 were also removed from Model II. The target of C 2 H 6 /air mixtures at = 1.2 from Ref. [3] was also removed at the final iteration stage, even though they were consistent in Model I. The larger spread of experimental target sets in fuel rich conditions between existing literature data and present data results in removing lots of data from the final target set and it indicates that the available data in those region of condition must be more carefully re-evaluated. Finally we consider only experimental targets with Davis and Law [35] only for a consistency analysis, which consists of ’s of C 3 H 6 /air, n-C 4 H 10 /air, i-C 4 H 10 /air, 1- C 4 H 8 , i-C 4 H 8 , and 1,3-C 4 H 6 /air flames (Posterior Model III). From the F and W tests as shown in Fig. 7.20, only the C 3 H 6 /air at = 1.4 and i-C 4 H 10 /air = 1.4 are removed as optimization targets. Figure 7.21 depicts the posterior Model III with 2 uncertainty band for C 3 H 6 /air and 1-C 4 H 8 /air flames. Although predictions by Galway Mech are notably higher than both model predictions and experimental data, Model III brought base model of USC Mech II towards closer to the Galway Mech predictions, which showed notably fast reactivity under fuel-rich conditions. Predictions by this posterior Model III showed agreement with recently published kinetic model by Ranzi, Law and S u o 190 co-workers [40], which used a large amount of experimental ’s of hydrocarbon and oxygenated fuels with air mixtures. For the posterior Model IV, targets of CH 4 /air at = 1.2 and 1.4 from Ref. [33], C 2 H 4 /air at = 1.4 from Ref. [39], C 3 H 8 /air at = 1.4 from Ref. [36], 2-C 4 H 8 /air at = 1.2 from the present experimental data, and i-C 4 H 10 /air at = 1.2 and 1.4 from Ref. [33] were removed. Figure 7.20. Consistency analysis for posterior Model III using Davis and Law [35]. S u o 0 0.2 0.4 0.6 0.8 1 1.2 fls*46e fls_46d fls_46c fls_46b fls_46a fls_45e fls_45d fls_45c fls_45b fls_45a fls_44e fls_44d fls_44c fls_44b fls_44a fls_43e fls_43d fls_43c fls_43b fls_43a fls_41e fls_41d fls_41c fls_41b fls_41a fls_32e fls_32d fls_32c fls_32b fls_32a C 3 H 6 /air, =0.7 =0.8 =1.0 =1.2 =1.4 1-C 4 H 8 /air, =0.7 =0.8 =1.0 =1.2 =1.4 i-C 4 H 8 /air, =0.7 =0.8 =1.0 =1.2 =1.4 1,3-C 4 H 6 /air, =0.7 =0.8 =1.0 =1.2 =1.4 n-C 4 H 10 /air, =0.7 =0.8 =1.0 =1.2 =1.4 i-C 4 H 10 /air, =0.7 =0.8 =1.0 =1.2 =1.4 F r 191 Figure 7.21. Posterior Model III using optimization target only by Davis and Law [35]. Galway USC (a) C 3 H 6 /air Ranzi Davis and Law (1998) Present data USC (b)1-C 4 H 8 /air Ranzi Davis and Law (1998) Present data Galway 192 7.7 . Uncertainty minimization on reaction rate parameters In order to determine the coupling between rate parameters, MUM-PCE [2] interprets the objective function by using a joint probability density function (PDF) for x, p x (x), for uncertainty minimization. ) x ( 2 1 exp ) x ( A p x , where A is a normalization constant. The constrained (posterior model) factorial variable, M i i i x x 1 * * 0 * , follows a multivariate normal distribution with mean * 0 x and covariance matrix * * T . α * , the uncertainty space of a posterior (constrained) model. α * can be found by linearizing the response surface in the neighborhood of * 0 x . * 0 x and α * form a posterior model which most closely approximates the observed experimental uncertainty. The uncertainties in the posterior model’s rate parameters should be significantly reduced and the parameters become tightly coupled to each other. If the uncertainty of a particular reaction is not well constrained by the experimental data, the a priori assumption of i = 1/2 will be preferred. This implies that the experimental targets do not impose a constraint on the uncertainty space of the reaction rates. This covariance matrix, , indicates the degree of coupling among rate coefficients in relation to the constraining experimental targets. The covariance matrix computed for Model I is divided to three areas shown in Fig. 7.22-7.25 to focus on where strong reaction couplings were observed from a huge covariance matrix. The covariance is 193 presented here as ij ij K . This transformation allows us to compare covariance to standard deviation, which is the squared root of the diagonal elements shown in the figures. The off-diagonal elements of the covariance matrix are fairly large. Consequently, the reduction in the uncertainty in the model comes primarily from inter- parameter coupling, i.e., large covariance between rate parameters, rather than a reduction in the variance of particular parameters. As shown in Fig. 7.22, the covariance matrix is sparse but certain clusters of rate coefficient coupling jump out as being particularly interesting. For example, the coupling of methyl reactions, CH 3 + H + M ↔ CH 4 + M (R91) CH 3 + O ↔ CH 2 O + H (R92) CH 3 + OH ↔ CH 2 (s) + H 2 O (R95) CH 3 + HO 2 ↔ CH 3 O + OH (R99) As shown in Fig. 7.22, R95 is coupled to many other reactions. Coupling of this reaction includes reactions which would impact H 2 O concentration, H + O 2 + H 2 O ↔ HO 2 + H 2 O (R17) HCO + H 2 O ↔ CO + H + H 2 O (R43) Coupling to R34 for OH consumption and R76 regarding to single methylene (CH 2 (s)). R95 more strongly coupled to methyl (CH 3 ) reactions such as R91 and R99. CH 3 + H + M ↔ CH 4 (R91) CH 3 + HO 2 ↔ CH 3 O + OH (R99) 194 These couplings underscore the limitation of the rate constraining method [2]. Many of the couplings are similar to what would happen in individual rate coefficient measurements under a degree of chemical isolation (e.g., R91 and R99). Figure 7.22. Covariance matrix of Model I reactions involving H 2 /CO/C 1 -hydrocarbon species. Table 7.5 lists the ratio of factorial optimized-to-unoptimized rate coefficients of the H 2 /CO subset of reactions. No significant (|x opt | > 0.5) offset factors from optimized rate parameters were observed. Table 7.6 lists the same ratio for a selection of rate coefficients from the C 1 -C 4 subset of active reactions. Several rate coefficients are changed by large amounts (|x opt | > 0.5), and three are pushed to the 2 σ limit. 0.20 0.10 0.05 0.15 0.25 0.45 0.35 0.30 0.40 CH 4 +OH CH 3 +H 2 O (R128) H+O 2 O+OH (R1) O+H 2 H+OH (R2) OH+H 2 H+H 2 O (R3) H+OH+M H 2 O+M (R9) O+H+M OH+M (R10) H+O 2 +M HO 2 +M (R12) H+O 2 +H 2 O HO 2 +H 2 O (R17) H 2 +O 2 HO 2 +H (R20) HO 2 +H 2OH (R23) OH+HO 2 H 2 O+O 2 (R27) CO+OH CO 2 +H (R34) CO+OH CO 2 +H (R35) HCO+O 2 CO+HO 2 (R44) CH+H C+H 2 (R48) CH+H 2 CH 2 +H (R51) CH+O 2 HCO+O (R53) CH 2 +O 2 HCO+OH (R62) CH 2 +O 2 CO 2 +2H (R63) CH 2 (s)+N 2 CH 2 +N 2 (R69) CH 3 +O CH 2 O+H (R92) CH 3 +OH+M CH 3 OH+M (R93) CH 3 +OH CH 2 (s)+H 2 O (R95) CH 3 +HO 2 CH 3 O+OH (R99) 2CH 3 H+C 2 H 5 (R108) CH 3 +HCCO C 2 H 4 +CO (R109) CH 4 +H CH 3 +H 2 (R126) CH 4 +O CH 3 +OH (R127) HCO+H CO+H 2 (R38) HCO+OH CO+H 2 O (R41) HCO+M CO+H+M (R42) HCO+H 2 O CO+H+H 2 O (R43) CH 2 (s)+O 2 H+OH+CO (R76) CH 3 +H+M CH 4 +M (R91) (R128) (R1) (R2) (R3) (R9) (R10) (R12) (R17) (R20) (R23) (R27) (R34) (R35) (R44) (R48) (R51) (R53) (R62) (R63) (R69) (R92) (R93) (R95) (R99) (R108) (R109) (R126) (R127) (R38) (R41) (R42) (R43) (R76) (R91) 195 No Reactions Model I Model IV span a x opt k/k o x opt k/k o 1 H + O 2 ↔ O + OH 1.2 -0.34 0.94 0.13 1.02 12 H + O 2 + M ↔ HO 2 + M 1.2 0.27 1.05 0.32 1.06 17 H + O 2 + H 2 O ↔ HO 2 + H 2 O 1.2 0.17 1.03 0.24 1.04 34 CO + OH ↔ CO 2 + H duplicate 1.2 -0.43 0.92 -0.32 0.94 35 CO + OH ↔ CO 2 + H duplicate 1.2 -0.20 0.96 -0.26 0.95 38 HCO + H ↔ CO + H 2 2.0 -0.10 0.94 -0.49 0.71 41 HCO + OH ↔ CO + H 2 O 3.0 -0.18 0.82 -0.12 0.88 42 HCO + M ↔ CO + H + M 4.0 0.25 1.42 0.31 1.54 43 HCO + H 2 O ↔ CO + H + H 2 O 2.0 0.28 1.21 0.10 1.07 a uncertainty factor Table 7.5. Selected rate parameter values for H 2 /CO subset reactions for posterior Model I and Model IV. By comparing rate parameter values for posterior Models I and IV, in general, there are few significant differences in the offset values of the rate parameter. However, reactions involving HCO (e.g., R38 and R43) and CH 3 (e.g., R92, R95, R99, and R108) showed some differences. The differences between two models are small and the discrepancies in the model predictions of ’s by these two posterior models effect only on the fuel rich conditions less than 2 cm/s. Therefore, the tendency to improve the model prediction and their reaction parameter uncertainties are similar. It was previously stated that is sensitive to R95 for most hydrocarbon/air flames and its associated uncertainty in the base model is relatively large as shown in Table 7.6. The total rate for the reaction system CH 3 + OH Products is important in the hydrocarbon combustion system in determining the further oxidation pathways of CH 3 and the rate of heat release. Uncertainties in the rate coefficients of the reactions in this S u o S u o 196 system represent the uncertainties in the product branching ratios.. It proceeds through a chemically activated, highly energized methanol intermediate (CH 3 OH) * . The collisionally stabilized reaction CH 3 + OH ↔ (CH 3 OH) * CH 3 OH (a, R93) competes with re-dissociation back to reactants or dissociation into several possible bimolecular product channels [40]. CH 3 + OH ↔ (CH 3 OH) * CH 2 (s) + H 2 O (b, R95) CH 3 + OH ↔ (CH 3 OH) * CH 3 O + H (c, R114) CH 3 + OH ↔ (CH 3 OH) * CH 2 OH + H (d, R121) CH 3 + OH ↔ (CH 3 OH) * CH 2 + H 2 O (e, R94) CH 3 + OH ↔ (CH 3 OH) * HCOH + H 2 (f) CH 3 + OH ↔ (CH 3 OH) * H 2 CO + H 2 (g) In the posterior model, R108 and R252 were found to have been offset by a significant fraction from their original rate parameters as listed in Table 7.6. These two reactions represent significant steps in the oxidation of C 2 H 6 in flames and have been discussed in length by the authors recently in Ref. 3. The covariance matrix focusing on C 2 species, Fig. 23, also showed that R108 is strongly coupled with R252. Flames of C 2 H 6 /air mixtures are highly sensitive to both these reactions. CH 3 + CH 3 ↔ C 2 H 5 + H (R108) C 2 H 4 + H+ M ↔ C 2 H 5 + M (R252) 197 R152, a major pathway in the oxidation of C 2 H 2 oxidation, also has a notable offset from its base rate following the optimization process. HCCO + O 2 ↔ OH + 2CO (R152) The rate coefficient of this reaction was adopted originally from GRI 1.2 [44]. From the covariance matrix shown in Fig. 7.23, R152 is coupled to not only HCCO related reactions such as R150 and R156, but also to reactions involving C 2 H 2 (e.g., R161) and vinyl (C 2 H 3 ) oxidation reaction (e.g., R197). R161 is the major channel to produce HCCO. In addition, CH 2 CHO produced via R197 can decompose to CH 2 CO and H and subsequently CH 2 CO reacts with O or OH by producing HCCO. HCCO + H ↔ CH 2 (s) + CO (R150) HCCO + OH ↔ C 2 H + H 2 O (R156) C 2 H 2 + O ↔ HCCO +H (R161) 198 Model I Model IV Reactions span a x opt k/k o x opt k/k o 53 CH + O 2 ↔ HCO + O 10.0 0.57 3.75 0.35 2.26 91 CH 3 + H +M ↔ CH 4 + M 2.0 0.16 1.11 -0.10 0.93 92 CH 3 + O ↔ CH 2 O + H 2.0 -0.49 0.71 0.23 1.18 93 CH 3 + OH + M ↔ CH 3 OH + M 5.0 -0.17 0.76 -0.05 0.92 95 CH 3 + OH ↔ CH 2 (s) + H 2 O 5.0 0.25 1.50 -0.46 0.47 99 CH 3 + HO 2 ↔ CH 3 O + OH 3.0 0.06 1.07 -0.33 0.70 108 CH 3 + CH 3 ↔ C 2 H 5 + H 5.0 0.55 2.44 0.13 1.24 152 HCCO + O 2 ↔ OH + 2CO 5.0 -0.65 0.35 -0.77 0.29 197 C 2 H 3 + O 2 ↔ CH 2 CHO + O 4.0 0.32 1.56 0.20 1.32 198 C 2 H 3 + O 2 ↔ HCO + CH 2 O 4.0 -0.27 0.69 -0.33 0.63 252 C 2 H 4 + H + M ↔ C 2 H 5 + M 3.0 -0.68 0.47 -0.98 0.34 268 C 2 H 4 + C 2 H 3 ↔ C 4 H 7 2.0 -0.53 0.69 -0.34 0.79 328 a-C 3 H 5 + H + M ↔ C 3 H 6 + M 3.0 -0.37 0.66 -0.47 0.59 337 a-C 3 H 5 + HO 2 ↔ OH+C 2 H 3 + CH 2 O 3.0 0.36 1.48 0.23 1.28 442 i-C 4 H 3 + H ↔ C 4 H 2 + H 2 10.0 0.15 1.42 0.25 1.80 483 C 4 H 6 + H ↔ i-C 4 H 5 + H 2 5.0 1.0 5.0 0.87 4.07 484 C 4 H 6 + H ↔ C 2 H 4 + C 2 H 3 2.0 -0.32 0.80 -0.27 0.83 490 C 4 H 6 + O ↔ C 2 H 4 + C 2 H 3 3.0 -0.30 0.72 -0.19 0.81 491 C 4 H 6 + OH ↔ n-C 4 H 5 + H 2 O 3.0 0.42 1.59 0.39 1.53 492 C 4 H 6 + OH ↔ i-C 4 H 5 + H 2 O 5.0 -0.48 0.46 -0.49 0.45 549 i-C 4 H 7 + H +M ↔ i-C 4 H 8 + M 2.0 -0.30 0.81 -0.45 0.73 565 2-C 4 H 8 + H + M ↔ s-C 4 H 9 + M 3.0 0.50 1.73 0.04 1.05 566 2-C 4 H 8 + H ↔ C 4 H 7 + H 2 3.0 -1.0 0.33 -0.73 0.45 567 2-C 4 H 8 + O ↔ C 2 H 4 + CH 3 CHO 3.0 1.0 3.0 0.96 2.86 573 i-C 4 H 8 + H ↔ i-C 4 H 7 + H 2 3.0 -0.25 0.76 -0.28 0.73 578 i-C 4 H 8 + OH ↔ i-C 4 H 7 + H 2 O 3.0 -0.17 0.83 -0.26 0.75 592 C 3 H 6 + CH 3 +M ↔ s-C 4 H 9 + M 2.0 0.38 1.30 0.45 1.37 634 C 4 H 10 + H +M ↔ s-C 4 H 9 + H 2 3.0 0.24 1.30 0.43 1.61 a uncertainty factor Table 7.6. Selected rate parameter values for C 1 -C 4 chemistry of the posterior Model I and Movel IV. 199 Figure 7.23. Covariance matrix of Model I reactions involving C 1 - and C 2 -hydrocarbon species. The reaction of C 2 H 3 and O 2 strongly influences the combustion characteristics of C 2 H 4 and 1,3-C 4 H 6 . There are several theoretical studies for reaction products and branching ratios (e.g., [45,46]) and USC Mech II adopted the rate coefficients by Mebel et al. [46] and assigned three relevant reaction channels. C 2 H 3 + O 2 ↔ C 2 H 2 + HO 2 (R196) C 2 H 3 + O 2 ↔ CH 2 CHO + O (R197) C 2 H 3 + O 2 ↔ CH 2 O + HCO (R198) Uncertainty minimization resulted in significant offset values for R198, listed in Table 7.6. Lean C 2 H 6 /air flames have a notable sensitivity to R198. Both R197 and R198 required notable amounts of change in the posterior model, which is highly sensitive 2CH 3 H+C 2 H 5 (R108) CH 3 +HCCO C 2 H 4 +CO (R109) CH 4 +H CH 3 +H 2 (R126) CH 4 +O CH 3 +OH (R127) C 2 H 4 +C 2 H 3 C 4 H 7 (R268) C 2 H 6 +OH C 2 H 5 +H 2 O (R284) CH 4 +OH CH 3 +H 2 O (R128) C 2 H+O 2 HCO+CO (R144) HCCO+H CH 2 (s)+CO (R150) HCCO+O 2 OH+2CO (R152) HCCO+OH C 2 O+H 2 O (R156) C 2 H 3 +M C 2 H 2 +H+M (R158) C 2 H 2 +O CH 2 +CO (R160) C 2 H 2 +O HCCO+H (R161) C 2 H 2 +OH C 2 H+H 2 O (R164) C 2 H 2 +CH 2 C 3 H 3 +H (R167) C 2 H 2 +CH 2 (s) C 3 H 3 +H (R168) C 2 H 2 +C 2 H C 4 H 2 +H (R169) C 2 H 2 +CH 3 p-C 3 H 4 +H (R173) CH 2 CO+H CH 3 +CO (R185) C 2 H 3 +H C 2 H 2 +H 2 (R191) C 2 H 3 +H H 2 CC+H 2 (R192) C 2 H 3 +O 2 CH 2 CHO+O (R197) C 2 H 3 +O 2 HCO+CH 2 O (R198) C 2 H 3 +CH 3 +M C 3 H 6 +M (R204) C 2 H 3 +CH 3 aC 3 H 5 +H (R205) C 2 H 4 +H+M C 2 H 5 +M (R252) C 2 H 4 +H C 2 H 3 +H 2 (R253) C 2 H 4 +O C 2 H 3 +OH (R254) C 2 H 4 +O CH 3 +HCO (R255) C 2 H 4 +OH C 2 H 3 +H 2 O (R257) 0.20 0.10 0.05 0.15 0.25 0.45 0.35 0.30 0.40 CH 3 +O CH 2 O+H (R92) CH 3 +OH+M CH 3 OH+M (R93) CH 3 +OH CH 2 (s)+H 2 O (R95) CH 3 +HO 2 CH 3 O+O (R99) (R268) (R284) (R108) (R109) (R126) (R127) (R128) (R144) (R150) (R152) (R156) (R158) (R160) (R161) (R164) (R167) (R168) (R169) (R173) (R185) (R191) (R192) (R197) (R198) (R204) (R205) (R252) (R253) (R254) (R255) (R257) (R92) (R93) (R95) (R99) 200 reaction for C 2 H 2 /air, C 2 H 4 /air and 1,3-C 4 H 6 /air flames. R196 was not included as active parameters in the uncertainty minimization. From the covariance matrix, R198 is coupled to R152, R191, R192, and R197. C 2 H 3 + H ↔ C 2 H 2 + H 2 (R191) C 2 H 3 + H ↔ H 2 CC + H 2 (R192) R483, R566, and R567 required the maximum offset in the posterior model as listed in Table 7.6. ’s of fuel rich 1,3-C 4 H 6 /air mixtures are very sensitive to R483, R484, R491, and R492. R566 and R567 are major fuel consumption pathways of 2–C 4 H 8 /air mixtures. The prior model significantly overpredicted the experimental results for these particular flames. Detailed kinetics of 1,3-C 4 H 6 oxidation at high temperatures used in USC Mech II is discussed in Ref. [47,48]. The model was validated for 1,3-C 4 H 6 high temperature kinetics against flow reactor [47,49], shock tube ignition [50], pyrolysis study from shock tube [51], and ’s [35]. As shown earlier in Fig 7.12d and Chapter 5, ’s of 1,3-C 4 H 6 /air mixtures from literature were notably higher than present experimental data at fuel rich conditions. Strong reaction couplings regarding C 3 -C 4 hydrocarbon species are shown in Fig. 7.24 and 7.25. S u o S u o S u o 201 Figure 7.24. Covariance matrix of Model I reactions involving C 2 - and C 3 - hydrocarbon species. Figure 7.25. Covariance matrix of Model I reactions involving C 3 - and C 4 -hydrocarbon species. C 2 H 4 +C 2 H 3 C 4 H 7 (R268) C 2 H 6 +OH C 2 H 5 +H 2 O (R284) HCCO+H CH 2 (s)+CO (R150) HCCO+O 2 OH+2CO (R152) HCCO+OH C 2 O+H 2 O (R156) C 2 H 3 +M C 2 H 2 +H+M (R158) C 2 H 2 +O CH 2 +CO (R160) C 2 H 2 +O HCCO+H (R161) C 2 H 2 +OH C 2 H+H 2 O (R164) C 2 H 2 +CH 2 C 3 H 3 +H (R167) C 2 H 2 +CH 2 (s) C 3 H 3 +H (R168) C 2 H 2 +C 2 H C 4 H 2 +H (R169) C 2 H 2 +CH 3 p-C 3 H 4 +H (R173) CH 2 CO+H CH 3 +CO (R185) C 2 H 3 +H C 2 H 2 +H 2 (R191) C 2 H 3 +H H 2 CC+H 2 (R192) C 2 H 3 +O 2 CH 2 CHO+O (R197) C 2 H 3 +O 2 HCO+CH 2 O (R198) C 2 H 3 +CH 3 +M C 3 H 6 +M (R204) C 2 H 3 +CH 3 aC 3 H 5 +H (R205) C 2 H 4 +H+M C 2 H 5 +M (R252) C 2 H 4 +H C 2 H 3 +H 2 (R253) C 2 H 4 +O C 2 H 3 +OH (R254) C 2 H 4 +O CH 3 +HCO (R255) C 2 H 4 +OH C 2 H 3 +H 2 O (R257) 0.20 0.10 0.05 0.15 0.25 0.45 0.35 0.30 0.40 a-C 3 H 4 +H a-C 3 H 5 (R308) a-C 3 H 4 +CH 3 i-C 4 H 7 (R312) a-C 3 H 5 +H+M C 3 H 6 +M (R328) C 3 H 6 +H C 2 H 4 +CH 3 (R362) C 3 H 6 +H a-C 3 H 5 +H 2 (R363) C 3 H 6 +H CH 3 CHCH+H 2 (R365) C 3 H 6 +O C2H 3 CHO+2H (R367) C 3 H 6 +OH a-C 3 H 5 +H 2 O (R372) C 3 H 6 +OH CH 3 CHCH+H 2 O (R374) a-C 3 H 5 +O C 2 H 3 CHO+H (R330) a-C 3 H 5 +HO 2 OH+C 2 H 3 +CH2O (R337) C 3 H 6 +O C 2 H 5 +HCO (R368) C 3 H 6 +O a-C 3 H 5 +OH (R369) C 4 H 2 +H i-C 4 H 3 (R425) C 4 H 2 +OH H 2 C 4 O+H (R426) C 3 H 8 +H H 2 +n-C 3 H 7 (R412) C 3 H 8 +H H 2 +i-C 3 H 7 (R413) i-C 4 H 3 +H C 4 H 2 +H 2 (R442) (R268) (R284) (R150) (R152) (R156) (R158) (R160) (R161) (R164) (R167) (R168) (R169) (R173) (R185) (R191) (R192) (R197) (R198) (R204) (R205) (R252) (R253) (R254) (R255) (R257) (R308) (R312) (R328) (R362) (R363) (R365) (R367) (R372) (R374) (R330) (R337) (R368) (R369) (R425) (R426) (R412) (R413) (R442) i-C 4 H 8 +H i-C 4 H 7 +H 2 (R573) i-C 4 H 8 +OH i-C 4 H 7 +H 2 O (R578) C 3 H 6 +CH 3 (+M) s-C 4 H 9 +M (R592) a-C 3 H 4 +H a-C 3 H 5 (R308) a-C 3 H 4 +CH 3 i-C 4 H 7 (R312) a-C 3 H 5 +H+M C 3 H 6 +M (R328) C 3 H 6 +H C 2 H 4 +CH 3 (R362) C 3 H 6 +H a-C 3 H 5 +H 2 (R363) C 3 H 6 +H CH 3 CHCH+H 2 (R365) C 3 H 6 +O C2H 3 CHO+2H (R367) C 3 H 6 +OH a-C 3 H 5 +H 2 O (R372) C 3 H 6 +OH CH 3 CHCH+H 2 O (R374) 2-C 4 H 6 H+2-C 4 H 5 (R519) i-C 4 H 7 +H+M i-C 4 H 8 +M (R549) 1-C 4 H 8 +H C 4 H 7 +H 2 (R557) 2-C 4 H 8 +H+M s-C 4 H 9 +M (R565) 2-C 4 H 8 +H C 4 H 7 +H 2 (R566) 2-C 4 H 8 +O C 2 H 4 +CH 3 CHO (R567) C 4 H 10 +H p-C 4 H 9 +H 2 (R633) C 4 H 10 +H s-C 4 H 9 +H 2 (R634) i-C 3 H 7 +CH 3 +M i-C 4 H 10 +M (R645) i-C 4 H 10 +H i-C 4 H 9 +H 2 (R646) a-C 3 H 5 +O C 2 H 3 CHO+H (R330) a-C 3 H 5 +HO 2 OH+C 2 H 3 +CH2O (R337) C 3 H 6 +O C 2 H 5 +HCO (R368) C 3 H 6 +O a-C 3 H 5 +OH (R369) C 4 H 2 +H i-C 4 H 3 (R425) C 4 H 2 +OH H 2 C 4 O+H (R426) C 3 H 8 +H H 2 +n-C 3 H 7 (R412) C 3 H 8 +H H 2 +i-C 3 H 7 (R413) i-C 4 H 3 +H C 4 H 2 +H 2 (R442) C 4 H 4 +H i-C 4 H 5 (R446) C 4 H 6 +H i-C 4 H 5 +H 2 (R483) C 4 H 6 +H C 2 H 4 +C 2 H 3 (R484) C 4 H 6 +O CH 3 CHCHCO+H (R489) C 4 H 6 +O CH 2 CHCHCHO+H (R490) C 4 H 6 +OH n-C 4 H 5 +H 2 O (R491) C 4 H 6 +OH i-C 4 H 5 +H 2 O (R492) i-C 4 H 7 +H CH 3 CCH 2 +CH 3 (R550) 1-C 4 H 8 +H C 2 H 4 +C 2 H 5 (R555) 1-C 4 H 8 +H C 3 H 6 +CH 3 (R556) (R573) (R578) (R592) (R308) (R312) (R328) (R362) (R363) (R365) (R367) (R372) (R374) (R519) (R549) (R557) (R565) (R566) (R567) (R633) (R634) (R645) (R646) (R330) (R337) (R368) (R369) (R425) (R426) (R412) (R413) (R442) (R446) (R483) (R484) (R489) (R490) (R491) (R492) (R550) (R555) (R556) 0.20 0.10 0.05 0.15 0.25 0.45 0.35 0.30 0.40 202 (R566) and (R567) are important pathways for the oxidation of 2-C 4 H 8 /air mixtures whose reaction rate coefficients were estimated from analogous reactions of C 3 H 6 . USC Mech II was not validated originally for 2-C 4 H 8 oxidation, and there is strong likelihood it is missing reaction pathways with regards to the oxidation of 2-C 4 H 8 . R566 and R567 are major fuel consumption pathways for ’s of 2-C 4 H 8 /air mixtures. 2-C 4 H 8 + H ↔ C 4 H 7 + H 2 (R566) 2-C 4 H 8 + O ↔ C 2 H 4 + CH 3 CHO (R567) Although R567 is also one of major consumption pathway for 2-C 4 H 8 , it was not included as active parameter for optimization because it was not as sensitivity as in the computed ’s of 2-C 4 H 8 /air mixtures using prior model. 2-C 4 H 8 + OH ↔ C 4 H 7 + H 2 O (R567) Reactions involving C 4 H 7 are important for both 1-C 4 H 8 and 2-C 4 H 8 . C 4 H 7 ( 2 2 2 CHCH CH CH ) in USC Mech II is as lumped species and the reaction involving this radical are global reactions. Both Galway and Nancy models included both 2 2 2 CHCH CH CH and 2 3 CHCH CH CH . 2-C 4 H 8 would produce greater concentration of 2 3 CHCH CH CH , which is resonantly stabilized radical. This can effect that USC Mech II overpredicts experimental ’s of 2-C 4 H 8 /air mixtures. S u o S u o S u o 203 7.8 . Prediction uncertainties for laminar flame speed If it is desirable to reduce the uncertainty of model predictions for ’s of a particular hydrocarbon/air flame, it is interesting to know which subset of targets impacts this uncertainty reduction to the largest extent. For example, if we want to reduce the 2 band for n-C 4 H 10 /air model predictions, is it necessary to include all experimental targets of flames of C 1 to C 4 hydrocarbons or is there an optimal subset with the largest impact? Additionally, we would like to explore the question of what precision is needed in experimental measurements of to sufficiently constrain a model. Table 7.7 lists various models considered in this section for predictions of uncertainties. The purpose of the various models is to compare how the predictions of ’s of the various fuels are improved as data for larger and larger hydrocarbons are added to the constraining data set. Model Ia is constrained only by ’s of CH 4 /air mixtures as its optimization targets. Model Ib is constrained by experimental ’s of both CH 4 /air and all C 2 - hydrocarbons with air targets. Model Ic* represents a posterior model constrained by a single fuel only; there is a Model Ic* for each pure fuel, and the purpose of this model is to compare the uncertainty in the predictions for a particular fuel, as constrained by measurements using that fuel only, with the uncertainty in the predictions for that fuel as constrained by the smaller hydrocarbon flame measurements. Model Id is constrained by ’s of all C 1 - to C 3 - hydrocarbons with air mixtures as optimization targets. Model I is constrained by using all C 1 - to C 4 - hydrocarbons with air data presented in this study by authors. Finally, Model V is constrained by ’s of S u o S u o S u o S u o S u o S u o S u o S u o S u o S u o 204 butanol isomers with air mixtures in addition to Model I (all C 1 - to C 4 - hydrocarbons with air mixtures) as optimization targets. Model Constraints Model Ia CH 4 /air Model Ib All C 1 - to C 2 - hydrocarbons with air Model Ic* Single fuel only with air (see text) Model Id All C 1 - to C 3 - hydrocarbons with air Model I All C 1 - to C 4 - hydrocarbons with air Model V Model I + butanol isomers with air Table 7.7. List of various models. For C 3 H 6 /air mixtures, the uncertainty remains largely unconstrained without ’s of C 3 H 6 /air flames as optimization targets, as shown in Fig. 7.26. The computed prediction uncertainties r are r 4 cm/s for the prior model and for Models Ia and Ib. Only when the experimental ’s of C 3 H 6 /air mixtures are introduced as targets does the r become strongly constrained. C 3 H 8 /air predictions, on the other hand, can be largely constrained without using ’s of C 3 H 8 /air flames explicitly as targets, as shown in Fig. 7.26. The r values for ’s of C 3 H 8 /air mixture were reduced from r 4 cm/s (Prior Model) to r 2 cm/s (Model Ia) at =1.2. When ’s of C 3 H 8 /air mixture itself is considered as target, the prediction uncertainty r is ~1 cm/s =1.2. The 2 uncertainties of the experimentally measured ’s of C 3 H 8 /air mixtures are 1.0~1.2, which can have large contribution to minimize prediction uncertainty of ’s. Table 7.8 shows experimental target uncertainty effect on uncertainties in the posterior model for the case of C 3 H 8 /air. S u o S u o S u o S u o S u o S u o S u o 205 Figure 7.26. Predicted uncertainties for ’s of (a) C 3 H 8 /air and (b) C 3 H 6 /air mixtures at T u = 298 K and p = 1 atm for the prior model and posterior Models Ia-1d. (a) C 3 H 8 /air (b) C 3 H 6 /air S u o 206 obs r (prior) (posterior Model I) r 2.5 3.72 1.56 2.0 3.72 1.34 1.0 3.72 0.87 0.5 3.72 0.63 Table 7.8. Experimental target uncertainty effect on prediction uncertainty in the model, C 3 H 8 /air, =1.2. From Figs. 7.27a and 7.27b, it can be observed that the predicted uncertainties of the constrained models for ’s of flames of n-C 4 H 10 and i-C 4 H 10 follow a similar trend observed for C 3 H 8 /air flames. That is, the model predictions of ’s of n-C 4 H 10 and i- C 4 H 10 flames are largely constrained in Models Ia and Ib, without using ’s targets of these two fuels explicitly. Using only CH 4 /air data as a target, Model Ia reduces model uncertainty notably. Additionally, only using C 3 H 8 /air data the model uncertainty can be reduced to 0.8 ≤ r ≤ 1.2. In the case of Model Id, using all C 1 -C 3 hydrocarbon data reduces this uncertainty to between 0.65 ≤ r ≤ 0.9. S u o S u o S u o 207 Figure 7.27. Predicted uncertainties for ’s of (a) n-C 4 H 10 /air and (b) i-C 4 H 10 /air mixtures at T u = 298 K and p = 1 atm for the prior model and posterior Models Ia through Ic. The uncertainty in the model predictions for flames of unsaturated C 4 hydrocarbons, e.g., 1-C 4 H 8 /air and 1,3-C 4 H 6 /air flames depicted in Fig. 7.28, remains largely unconstrained without including the specific fuels in the experimental target data set. (a) n-C 4 H 10 /air (b) i-C 4 H 10 /air S u o 208 Using all C 1 -C 3 data as experimental targets, the posterior model uncertainty for these two cases is still large especially at fuel rich conditions. Figure 7.28. Predicted uncertainties for ’s of (a) 1-C 4 H 8 /air and (b) 1,3-C 4 H 6 /air mixtures at T u = 298 K and P = 1 atm. (a) 1-C 4 H 8 /air (b) 1,3-C 4 H 6 /air S u o 209 Finally, a prior model was developed by combining USC Mech II with the butanol chemistry of Ref. [32]. The purpose of this model was to explore how uncertainties in the predictions for oxygenated fuels, in this case the C 4 alcohols, can be constrained using alkane and alkene flame data as optimization targets. An uncertainty span of 2.5 was assigned to all butanol related reactions. The predicted model uncertainties for ’s of the various butanol/air mixtures are shown in Fig. 7.29. For n-butanol/air flames, the highest value of prior model uncertainty of ’s of is at = 1.0, whereas the model prediction uncertainties for both i- and t- C 4 H 9 OH/air flames are fairly uniform with respect to stoichiometry. The r of ’s of n-butanol/air flames in the prior model is ~5 cm/s near stoichiometry, compared to ~4 cm/s lean and rich conditions. This uncertainty was constrained notably in Model I to ~3 cm/s at = 1.0, and ~1 cm/s at = 0.8 and 1.4. For i-C 4 H 9 OH/air flames the prior model uncertainty is ~5.5 cm/s at = 1.4, compared to Model I, which is ~1 cm/s. For t-C 4 H 9 OH/air flames, the model uncertainty was constrained to an even larger extent with r < 1 cm/s at = 0.8, 1.0, and 1.2. Adding constraints from experimental ’s, has only small effect on r for all cases of C 4 H 9 OH isomers with air flames. This exercise demonstrates that experimental measurements of ’s of a particular saturated oxygenated fuel/air flame may not be needed to constrain the uncertainty of model predictions of said flame. What is needed is accurate and consistent set of experimental flame measurements of the major hydrocarbon intermediates formed during the oxidation of this fuel. S u o S u o S u o S u o S u o 210 Figure 7.29. Predicted uncertainties for ’s of (a) n-C 4 H 9 OH/air, (b) i-C 4 H 9 OH/air, and (c) t- C 4 H 9 OH mixtures at T u = 298 K and P = 1 atm. (a) n-C 4 H 9 OH/air (b) i-C 4 H 9 OH/air (c) t-C 4 H 9 OH/air S u o 211 7.9 . Uncertainty propagation into application Perfectly stirred reactor (PSR) simulations can provide a test of how the posterior model better constrains uncertainty in predictions compared to the prior model when simulating combustion problems outside the range of the target set. The PSR simulates a canonical, idealized combustion problem in which a steady flow of fuel and oxidizer enter a reactor and are assumed to be spatially uniform through high-intensity turbulent mixing. Therefore, the rate of conversion of reactants to products is controlled by chemistry, not mixing. Figure 7.30 shows OH (a, b) and H 2 O (c, d) mole fractions with respect to residence time for a steady state, constant-temperature of 1500 K, constant- pressure of 1 atm, and = 1.0 n-C 4 H 10 /air PSR along with associated uncertainties predicted by the prior (a, c) and the posterior (b, d) Model IV. Two distinct branches in concentration as a function of residence time for the oxidation of n-C 4 H 10 /air are observed in the PSR predictions. At the short residence times, unburned fuel leaves the reactor as fast as it enters. This indicates weakly reactive cold states (lower branch) where chemistry is largely frozen. As the resident time is increased, a critical point is reached where the mixture in the reactor suddenly ignites, as evidenced by the hysteresis in OH mole fraction. When the residence time becomes sufficiently long the mixture is effectively at its chemical equilibrium state. This upper branch represents strong or vigorously reacting states. In this region, the uncertainty in OH or H 2 O mole fraction is very small because the equilibrium concentration does not depend strongly on the residence time or rate parameters. Figure 7.30 demonstrates that the posterior Model IV reduced the uncertainty in the calculated model fractions of OH and H 2 O overall from a 212 factor of 3-4 (prior model) to a factor of 2. The uncertainty in model predictions reaches a maximum near the ignition point. Figure 7.30. Variations of OH (a, b) and H 2 O (c, d) mole fraction with mean residence time in a simulated PSR in which n-C 4 H 10 is oxidized in stoichiometric air at a constant temperature of 1500 K and 1 atm pressure. The predictions for (a, c) the prior model and (b, d) the posterior model IV. Lines are model calculation and symbols are the uncertainty calculated using Monte Carlo sampling of the uncertainty space. Figure 7.31 shows variations of OH (a, b) and H 2 O (c, d) mole fraction with as a function of residence time in a simulated PSR in which a stoichiometric CH 4 /air mixture is oxidized a constant temperature of 1600 K and pressure of 1 atm. The predictions for the prior model (a, c) are compared with the posterior Model IV (b, d). There is no observable change in the uncertainties of the prior and posterior Model IV predictions for OH mole fraction 10 -5 10 -4 10 -3 10 -2 (a) 1.2 (x10 -3 ) 1.4 1.6 1.8 2.0 2.2 2.4 2.6 0.5 1.0 1.5 2.0 (x10 -3 ) 10 -5 10 -4 10 -3 10 -2 (b) 1.2 (x10 -3 ) 1.4 1.6 1.8 2.0 2.2 2.4 2.6 0.5 1.0 1.5 2.0 (x10 -3 ) Residence time, (s) 10 -5 10 -4 10 -3 10 -2 10 -1 H 2 O mole fraction 10 -4 10 -3 10 -2 10 -1 (c) 10 -0 10 -5 10 -4 10 -3 10 -2 10 -1 Residence time, (s) 10 -4 10 -3 10 -2 10 -1 (d) 10 -0 213 oxidation of the CH 4 /air mixture over the range of the cold branch. Nevertheless, there is a significant reduction in the prediction uncertainty near extinction between the prior and posterior Model IV near extinction. The first order sensitivity coefficients of OH mole fraction with respect to rate parameters at a residence time of = 226 s, near ignition is shown in Fig. 7.32. The reactions sensitized at these conditions are different compared to the reactions to which ’s are sensitive to (Fig. 7.1). Magnitudes of sensitivity coefficients are large for reactions R107, R96, R84, and R118, reactions that were not included as active parameters for the model optimization. Figure 7.31. Variations of OH (a, b) and H 2 O (c, d) mole fraction with mean residence time in a simulated PSR in which CH 4 is oxidized in stoichiometric air at a constant temperature of 1600 K and 1 atm pressure. The predictions for the prior model (a, c) are compared with the posterior Model IV (b, d). Lines are model calculation and symbols are the uncertainty calculated using Monte Carlo sampling of the uncertainty space. S u o 10 -5 10 -4 10 -3 10 -2 H 2 O mole fraction Residence time, (s) 10 -4 10 -3 10 -2 10 -1 (c) 10 -5 10 -1 10 -5 10 -4 10 -3 10 -2 10 -1 Residence time, (s) (d) 10 -4 10 -3 10 -2 10 -1 10 -5 OH mole fraction 10 -6 10 -5 10 -4 10 -3 10 -2 (a) 1.0 (x10 -3 ) 2.0 3.0 4.0 5.0 0.5 1.0 1.5 2.0 (x10 -3 ) 2.5 3.0 (b) 10 -6 10 -5 10 -4 10 -3 10 -2 1.0 (x10 -3 ) 2.0 3.0 4.0 5.0 0.5 1.0 1.5 2.0 (x10 -3 ) 2.5 3.0 214 Figure 7.32. First order sensitivity coefficients of OH concentration with respect to reaction rate coefficients for CH 4 /air mixtures PSR at constant temperature of 1600 K and 1 atm pressure at = 1.0 using Model IV. (At residence time = 226 s) Figure 7.33 illustrates the PSR predictions of C 2 H 4 /air mixtures for OH (a, b) and H 2 O (c, d) mole fractions with respect to residence time for a steady state, constant- temperature of 1400 K, constant-pressure of 1 atm, and = 1.0 along with associated uncertainties predicted by the prior (a,c) model and the posterior Model IV (b, d). Compared with the previous two sets of PSR simulations, Figs. 7.30 and 7.31, for n- C 4 H 10 and CH 4 respectively, the oxidation characteristics of a C 2 H 4 /air mixture are distinct, Fig. 7.33. In Fig. 7.33 there are three distinct regions, lower weakly reacting branch, middle branch, and upper or vigorously reacting branch at equilibrium. Figure 7.34 illustrates the first order sensitivity coefficients of OH concentrations with respect to rate parameters at 7.28 s (lower branch near first ignition) and 380 s (middle branch near the second ignition point). At the lower branch near ignition point, Fig 7.34a, -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Sensitivity coefficients of OH mole fraction (R96) CH 3 +O 2 O+CH 3 O (R126) CH 4 +H CH 3 +H 2 (R1) H+O 2 O+OH (R99) CH 3 +HO 2 CH 3 O+OH (R118) CH 3 O+O 2 CH 2 O+HO 2 (R107) CH 3 +CH 3 +M C 2 H 6 +M (R128) CH 4 +OH CH 3 +H 2 O (R108) CH 3 +CH 3 H + C 2 H 5 (R44) HCO+O 2 CO+HO 2 (R27) OH+HO 2 H 2 O+O 2 (R92) CH 3 +O CH 2 O+H (R127) CH 4 +O CH 3 +OH (R91) CH 3 +H+M CH 4 +M (R20) H 2 +O 2 HO 2 +H (R42) HCO+M CO+H+M (R84) CH 2 O+H+M CH 3 O+M CH 4 /air = 1.0 = 226 s 215 reactions involving C 2 H 4 oxidation dominate the sensitivity spectrum. At this residence time, OH production is largely dependent on the fuel consumption reaction R254. However, the sensitivity analysis at a residence time of 380 s, Fig 7.34b, (middle branch at ignition) shows that the OH radical pool becomes large enough and ignition can take place. Similar to other fuels, uncertainties of the calculated mole fractions are notably reduced in the posterior Model IV. The maximum uncertainties are near the first or cold ignition, almost negligible uncertainties for the vigorously reacting branch. Figure 7.33. Variations of OH (a, b) and H 2 O (c, d) mole fraction with mean residence time in a simulated PSR in which C 2 H 4 is oxidized in stoichiometric air at a constant temperature of 1400 K and 1 atm pressure. The predictions for the prior model (a, c) are compared with the posterior Model IV (b, d). Lines are model calculation and symbols are the uncertainty calculated using Monte Carlo sampling of the uncertainty space. Residence time, (s) 10 -5 10 -3 10 -6 10 -5 10 -4 10 -3 (d) 10 -7 10 -9 10 -1 10 -6 10 -5 10 -3 10 -5 10 -3 (c) 10 -7 10 -9 10 -1 H 2 O mole fraction Residence time, (s) 10 -4 10 -6 10 -5 10 -4 10 -3 10 -2 (b) 10 -7 10 -8 10 -9 0.2 (x10 -3 ) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.0 2.0 (x10 -3 ) 3.0 4.0 OH mole fraction 10 -6 10 -5 10 -4 10 -3 10 -2 10 -7 10 -8 10 -9 (a) 0.2 (x10 -3 ) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.0 2.0 (x10 -3 ) 3.0 4.0 216 Figure 7.34. First order sensitivity coefficients of OH concentration with respect to reaction rate coefficients for C 2 H 4 /air mixtures PSR using Model IV for constant temperature of 1400 K and 1 atm pressure at = 1.0 at residence time (a) 7.28 s (lower branch near ignition point) and (b) 380 s (middle branch near ignition point). Figure 7.35 shows OH mole fractions with respect to residence time for the oxidation of a n-C 4 H 9 OH/air mixture at a constant-temperature of 1500 K, constant-pressure of 1 atm, and = 1.0 in a PSR along with associated uncertainties predicted by the prior model (a), the posterior (b) Model IV, and (c) Model VI which includes butanol isomers -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 (R99) CH 3 +HO 2 CH 3 O+OH (R255) C 2 H 4 +O CH 3 +HCO (R1) H+O 2 O+OH (R42) HCO+M CO+H+M (R197) C 2 H 3 +O 2 CH 2 CHO+O (R254) C 2 H 4 +O C 2 H 3 +OH (R27) OH+HO 2 H 2 O+O 2 (R23) HO 2 +H OH+OH (R20) H 2 +O 2 HO 2 +H (R108) CH 3 +CH 3 H+C 2 H 5 (R213) CH 2 CHO CH 3 +CO (R44) HCO+O 2 CO+HO 2 (R38) HCO+H CO+H 2 (R95) CH 3 +OH CH 2 (s)+H 2 O (R91) CH 3 +H+M CH 4 +M (R43) HCO+H 2 O CO+H+H 2 O (R158) C 2 H 3 +M C 2 H 2 +H+M Sensitivity coefficients of OH (b) C 2 H 4 /air = 1.0 = 380 s -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 (R254) C 2 H 4 +O C 2 H 3 +OH (R1) H+O 2 O+OH (R42) HCO+M CO+H+M (R251) C 2 H 4 +M H 2 +H 2 CC+M (R253) C 2 H 4 +H C 2 H 3 +H 2 (R255) C 2 H 4 +O CH 3 +HCO (R44) HCO+O 2 CO+HO 2 (R197) C 2 H 3 +O 2 CH 2 CHO+O (R198) C 2 H 3 +O 2 HCO+CH 2 O (R257) C 2 H 4 +OH C 2 H 3 +H 2 O (R258) C 2 H 4 +HCO C 2 H 5 +CO (R264) C 2 H 4 +CH 3 C 2 H 3 +CH 4 (R213) CH 2 CHO CH 3 +CO (R158) C 2 H 3 +M C 2 H 2 +H+M (R183) CH 2 CO+H+M CH 2 CHO+M (R196) C 2 H 3 +O 2 C 2 H 2 +HO 2 (a) C 2 H 4 /air = 1.0 = 7.28 s (R269) C 2 H 4 +HO 2 CH 2 OCH 2 +OH 217 target sets in addition to Model IV. If we consider the magnitude of the model uncertainty, similar results are shown for n-C 4 H 9 OH/air PSR comparing Model IV (Fig. 7.35b) and Model VI (Fig. 7.35c). Both Models IV and VI reduced uncertainty of OH model fraction of n-C 4 H 9 OH/air PSR as compared to the prior model. However, there are insignificant differences in uncertainties of the posterior Models IV and VI. Similar to ’s of n-C 4 H 9 OH/air mixtures, adding constraints from experimental ’s of n- C 4 H 9 OH/air flames has no effect on uncertainties for n-C 4 H 9 OH/air PSR predictions. S u o S u o 218 Figure 7.35. Variations of OH mole fraction with mean residence time in a simulated PSR in which n-butanol is oxidized in stoichiometric air at a constant temperature of 1500 K and 1 atm pressure. The predictions for (a) the prior model are compared with (b) the posterior Model IV and (c) Model VI. Lines are model calculation and symbols are the uncertainty calculated using Monte Carlo sampling of the uncertainty space. OH mole fraction 10 -6 10 -5 10 -4 10 -3 10 -2 (b) OH mole fraction 10 -6 10 -5 10 -4 10 -3 10 -2 (a) 10 -6 10 -5 10 -4 10 -3 10 -2 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 Residence time, (s) OH mole fraction (c) 219 In conclusion, there is strong evidence that the posterior model presents a significant reduction in its prediction uncertainty compared to the prior model for all fuel/air cases. Overall the uncertainty in predicted OH or H 2 O concentration is reduced from a factor of 3-4 to about a factor of 2 when the model is constrained. Therefore it can be concluded that MUM-PCE is able to characterize the reactor behavior much more reliably than compiling a model from the literature (essentially a prior model) consistent with prior work by the senior authors, Ref. 2. However, it has also been demonstrated that flame measurements for a specific fuel are not necessary. ’s of n-C 4 H 9 OH/air flames did not further constrain model uncertainty. Utilizing precise flame measurements of its major hydrocarbon intermediates constrained the model to a much larger extent. Finally, this study demonstrated that the application of MUM-PCE to a reaction model within a narrow range of constraint conditions could lead to improvements of the accuracy of the model outside the conditions in which the model is constrained. S u o 220 7.10. Concluding remarks A large set of laminar flame speeds data for mixtures of C 1 -C 4 hydrocarbons with air were collected in addition to these newly determined C 3 -C 4 hydrocarbons/air mixtures. The method of uncertainty minimization using polynomial chaos expansions (MUM- PCE) and this large set of laminar flame speed data with systematically quantified uncertainties were utilized to examine the underlying uncertainty of USC Mech II laminar flame speed predictions. It is shown that the reaction model accuracy and precision can be greatly improved through uncertainty minimization against this flame speed dataset. The consistency test of experimental targets allows us to obtain an optimized model based on a self-consistent experimental data set. There exist notable discrepancies in the existing literature data for laminar flame speeds at fuel rich conditions. Therefore it can be concluded that a number of experimental targets are unsuitable for kinetic model optimization and accurate kinetic model development. The final portion of this study quantified the value, in a hierarchical manner, of laminar flame speed data in a multi-parameter kinetic model optimization problem. 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Inst. 20 (1984) 613-622. [50] R. Fournet, J.C. Baugé, F. Battin-Leclerc, Int. J. Chem. Kinet. 31 (1999) 361-379. [51] Y. Hidaka, T. Higashihara, N. Ninomiya, H. Masaoka, T. Nakamura, H. Kawano, J. Phys Chem 28 (1996) 137-151. 226 Chapter 8 Concluding Remarks and Recommendations 8.1 . Concluding remarks Flame propagation and extinction limits of flames of hydrogen, carbon monoxide, and C 1 -C 4 hydrocarbons were studied experimentally and numerically in the counterflow configuration. Additionally, an in-depth study was performed to investigate the ability of the laminar flame speed results, determined in this thesis, to constrain the uncertainty present in chemical kinetic reaction models. 8.1.1 Hydrogen It was established that there exists a large variation in existing literature laminar flame speed measurement for H 2 /air flames at atmospheric pressure. Therefore, in the first part of this study laminar flame speeds of H 2 /oxidizer flames were experimentally determined. For present measurements, an oxidizer with a higher diluent concentration relative to air was utilized in order to lower the maximum stretched flame speed, thus lowering overall uncertainties in flow field measurements. To remove ambiguities caused by the present non-linear extrapolation methodology to zero stretch, stretched flame speed results for H 2 /oxidizer flames were modeled directly. Comparisons between 227 model predictions and experimental results were consistent for both stretched and laminar flame speed data. The extinction limits of premixed H 2 /air flames were measured to probe the kinetics of ultra-lean H 2 flames. The rate limiting kinetics of extinction limits differed from the rate limiting kinetics for laminar flame speeds. The ratio of the main branching to main termination reaction dictated the ability of the kinetic model to reproduce experimental results. To validate the pressure dependent kinetics of H 2 flames, the extinction limits of non-premixed H 2 flames were measured at atmospheric and elevated pressures. Finally, to constrain the large uncertainty in the main termination reaction involving water, flame type experiments were formulated specifically to sensitize three body reactions involving water as the 3 rd body. Extinction limits for both premixed H 2 /air flames with water dilution, and non-premixed H 2 flames with water added to the oxidizer stream were measured. 8.1.2 Fuel mixtures Laminar flame speeds and extinction limits of fuel mixtures of hydrogen, carbon monoxide, and C 1 -C 4 saturated hydrocarbons with air, which simulate various alternative gaseous fuels, were experimentally and numerically investigated in the counterflow configuration. Experimental flame results for these mixtures are of practical importance and are useful to assess the effects of kinetic couplings during the oxidation of fuel mixtures involving hydrogen, carbon monoxide, methane, propane, and n-butane. 228 8.1.3 C 2 hydrocarbons Laminar flame speeds of mixtures of ethane/air, ethylene/air, and acetylene/O 2 /N 2 mixtures were determined experimentally. Experimental data were simulated using three different, recently developed, kinetic models. Although using these kinetic models resulted, in general, in good agreement against present and literature experimental data for fuel lean conditions, there is a large degree of variation in predictions for fuel rich conditions. For flames of C 2 hydrocarbons, remaining notable uncertainties in branching ratios for major fuel specific reactions. The choice of the attendant rate constants for fuel specific reactions has a first order impact on global combustion properties especially in the case of acetylene/oxidizer flames. 8.1.4 C 3 -C 4 hydrocarbons A comprehensive set of laminar flame speed measurements was performed for mixtures of C 3 and C 4 saturated and unsaturated hydrocarbons with air. These compounds included propane, propene, n-butane, iso-butane, 1-butene, 2-butene, iso- butene, and 1,3-butadiene. The present results are compared against literature data wherever possible. This comprehensive data set was useful to perform systematic comparisons between the relative reactivities of flames of mixtures of air with these compounds. From observations of experimental results for flames of C 4 H 8 /air isomers, 1- butene/air flames had the highest reactivity, and iso-butene/air flames, the lowest. The laminar flame speeds for 2-butene/air flames lay between the other two flames. 2- Butene/air flames have a lower reactivity compared to 1-butene/air flames due to the location of the double bond. The larger methyl radical pool in 2-butene/air flames 229 actively consumes H reducing overall reactivity. Predictions using four recently developed kinetic models were compared with experimental results and it was observed that only one model was able to reproduce the observed relative reactivity of the C 4 H 8 isomers. Nevertheless, this same model was unable to reproduce experimental results for laminar flame speed measurements. It was demonstrated that the present computationally assisted non-linear extrapolation methodology for extrapolating stretched flame speed data to zero stretch does not explain the variation between the present results and literature data for flame speeds of fuel/air mixtures at fuel rich conditions. 8.1.5 Chemical kinetic model uncertainty minimization The method of uncertainty minimization using polynomial chaos expansions (MUM- PCE) and a large set of laminar flame speed data with systematically quantified uncertainties were utilized to examine the underlying uncertainty of USC Mech II laminar flame speed predictions. It was illustrated that reaction model accuracy and precision can be greatly improved through uncertainty minimization against this flame speed dataset. From the consistency test of experimental targets, it was concluded that a number of experimental targets from existing literature of laminar flame speeds are unsuitable for kinetic model optimization and kinetic model validation, especially at fuel rich conditions. A quantitative analysis was performed to determine how laminar flame speed experimental data could be used to constrain quantitatively a kinetic model. Laminar 230 flame speeds, as expected, appear to constrain more strongly the heat release and chain branching reactions. It was demonstrated that a model constrained only by the laminar flame speeds of methane/air flames, reduces notably the uncertainty in the predictions of the laminar flame speeds of C 3 and C 4 n-alkanes with air mixtures. The uncertainty in the model predictions for flames of unsaturated C 3 -C 4 hydrocarbons with air flames however remains largely unconstrained without including fuel specific laminar flames speeds in the experimental target data set. The constraint provided by the laminar flame speeds of C 3 -C 4 unsaturated hydrocarbons fuels with air mixtures could reduce notably the uncertainties in the predictions of laminar flame speeds of C 4 alcohols/air mixtures. 8.2 . Recommendations This thesis presents a large number of experimental datasets with precisely quantified experimental uncertainties. Furthermore quantitative analysis utilizes these data for chemical kinetic model validation and optimization. There is significant scope to further improve and refine the work contained in this thesis. Experimental uncertainties for laminar flame speeds results in this thesis indicated 2 standard deviation of DPIV associated sampling uncertainties from reference flame speed measurements. It is apparent that uncertainties in reference flame speed measurements are strongly a function of seeding particle choice (e.g., solid versus liquid particles), density of seeding, DPIV post processing methodology (e.g., search radius and search area), and laser pulse timing. A parametric study needs be performed to better understand each of these variables impact on measurement uncertainties. Such a study needs to be performed for both flames 231 of liquid and gaseous fuels to eliminate uncertainties due to vaporization methodology. Throughout this thesis it was observed that there exist notable discrepancies between experimentally determined laminar flame speeds especially at fuel rich conditions between various experimental methodologies. Where possible, as done for counterflow flames throughout this thesis, the direct numerical simulations of spherically expanding flames and flames established using the heat flux method should be performed to understand these differences. Such a degree of variation between experimental results prevents the minimization and optimization of kinetic models using flame data at fuel rich conditions. To improve the kinetic modeling of the H 2 -O 2 system, it will be useful to integrate into kinetic model optimization for the H 2 -O 2 reaction model, extinction limit data. Presently only laminar flame speed results are utilized in the optimization of reaction models through MUM-PCE, it has been demonstrated that both premixed and non-premixed hydrogen flame sensitize and important set of kinetics unique to extinction limits. Additionally, since the models for the oxidation of hydrogen are relatively small this will be a good test case to observe the utility of extinction limits in the optimization target set to constrain rate parameter uncertainties. In the present thesis, experiments for flames of C 3 and C 4 hydrocarbons were conducted at atmospheric pressure. 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Abstract (if available)
Abstract
Developing reliable chemical kinetic models is a key ingredient in current and future efforts to develop science-based predictive tools, which will be used for the design of more efficient, less polluting, and flexible-fuel combustion systems. While a variety of combustion properties are needed for the comprehensive validation of detailed kinetic models, a minimum requirement for a model’s validity is the prediction of fundamental mixture properties including the laminar flame speed that is a measure of the heat release rate, and thus the driving force of dilatation that leads to power production. ❧ In this study, the combustion characteristics of hydrogen/carbon monoxide/C₁-C₄ hydrocarbons were investigated both experimentally and numerically in laminar premixed and non-premixed flames. These characteristics included laminar flame speeds and extinction limits. Experimentally, flames were established in the counterflow configuration and flow velocity measurements were made using the particle image and laser Doppler velocimetry. Numerically, laminar flame speeds and extinction limits were simulated using quasi-one-dimensional codes, which integrated the conservation equations with detailed descriptions of molecular transport and chemical kinetics. ❧ Although the hierarchical importance of hydrogen chemistry to the modeling of combustion kinetics has long been recognized, there exist notable discrepancies between experimental and computed fundamental combustion properties especially in flames. Hydrogen/air mixtures are flammable for a wide range of equivalence ratios, with reactivity that ranges quite notably from near-limit to near-stoichiometric conditions. Among others, the extent of reactivity is manifested by the laminar flame speed that could vary from several cm/s to few m/s under atmospheric conditions. Additionally, due to the very low molecular weight of hydrogen, its lean mixtures with nitrogen containing oxidizers are thermo-diffusionally unstable due to the sub-unity Lewis numbers. In the present investigation, accurate experimental data were determined for hydrogen/oxygen/nitrogen flames and compared against computed results. The novelty of this investigation is that reference flame speeds that are raw experimental data obtained in positively stretched flames were compared against computed results, which eliminates issues related to cellular flames and linear or non-linear extrapolations. ❧ In addition, uncertainties still exist in modeling of important three-body recombination reactions, such as for example the H-terminating H + Ο₂ + M → HΟ₂ + M. The collision efficiency of the water molecule is known to be large, and as a result its presence at conditions of high density can have a notable effect on various combustion phenomena. The influence of water vapor addition on the extinction of premixed and non-premixed H₂/air flames was investigated experimentally and numerically in low temperature flames. ❧ One of the critical elements towards accurate predictions of combusting flows is to characterize and minimize the uncertainties associated with predictions of fundamental flame properties. In this work, a large set of laminar flame speed data, systematically collected for C₁-C₄ hydrocarbons with well-defined uncertainties, were used to demonstrate how well-characterized laminar flame speed data can be utilized to explore and reduce the remaining uncertainties in a reaction model for small hydrocarbons. The USC Mech II kinetic model was used as a case study. The method of uncertainty minimization using polynomial chaos expansions (MUM-PCE) was employed to constrain the model uncertainty in laminar flame speed prediction. In addition, the types of hydrocarbon fuels with the greatest impact on model uncertainty reduction are identified along with the attendant accuracy that is needed in flame measurements to facilitate better reaction model development. Results demonstrate that a reaction model constrained only by laminar flame speeds of methane/air flames reduces notably the uncertainty in the predictions of the laminar flame speeds of C₃ and C₄ alkanes, because the key chemical pathways of all of these flames are similar to each other. However, the uncertainty in the model predictions for flames of unsaturated C₃-C₄ hydrocarbons remains significant without considering their laminar flames speeds in the constraining target data set, because the secondary rate controlling reaction steps are different from those in methane flames.
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Park, Okjoo
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Experimental and kinetic modeling studies of flames of H₂, CO, and C₁-C₄ hydrocarbons
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Viterbi School of Engineering
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Doctor of Philosophy
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Aerospace Engineering
Publication Date
10/01/2013
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07/22/2013
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combustion,hydrocarbon,hydrogen,laminar flame,OAI-PMH Harvest,synthesis gas,uncertainty minimization
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Egolfopoulos, Fokion N. (
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), Ronney, Paul D. (
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), Shing, Katherine (
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okjoo.park@gmail.com
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Tags
combustion
hydrocarbon
hydrogen
laminar flame
synthesis gas
uncertainty minimization