Fundamentals of turbulent and multiphase combustion

897 Pages·2012·6.07 MB·English

by  Kenneth K Kuo

FUNDAMENTALS
OF TURBULENT
AND MULTIPHASE
COMBUSTION
Fundamentals of Turbulent and Multiphase Combustion Kenneth K. Kuo and Ragini Acharya
Copyright © 2012 John Wiley & Sons, Inc.
FUNDAMENTALS
OF TURBULENT
AND MULTIPHASE
COMBUSTION
KENNETH K. KUO
RAGINI ACHARYA
JOHN WILEY & SONS, INC.
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LibraryofCongressCataloging-in-PublicationData:
Kuo,KennethK.
KuFundamentalsofturbulentandmultiphasecombustion/KennethK.Kuo,
RaginiAcharya.—1sted.
Raginip.cm.
RaIncludesbibliographicalreferencesandindex.
RagiISBN978-0-470-22622-3(hardback);978-111-8-09929-2(ebk.);978-111-8-09931-5(ebk.);
978-111-8-09932-2(ebk.);978-111-8-10767-6(ebk.);978-111-8-10768-3(ebk.);
978-111-8-10770-6(ebk.)
R1.Combustionengineering.2.Turbulence.3.Combustion—Mathematicalmodels.I.Acharya,
Ragini.II.Acharya,Ragini.III.Title.
RaQD516.K8582012
Ra541(cid:2).361—dc23
2011024787
ISBN:978-0-470-22622-3
PrintedintheUnitedStatesofAmerica
10987654321
KenKuo would like to dedicate this book to his wife, Olivia (Jeon-lin), and their
daughters, Phyllis and Angela, for their love, understanding, patience, and
support, and to his mother, Mrs. Wen-Chen Kuo, for her love and
encouragement.
Ragini Acharya would like to dedicate this book to her parents, Meenakshi and
KrishnamaAcharya,fortheirlove,patience,andsupportandforhavingendless
faith in her.
CONTENTS
Preface xix
1 Introduction and Conservation Equations 1
1.1 Why Is Turbulent and Multiphase Combustion
Important?, 3
1.2 Different Applications for Turbulent and Multiphase
Combustion, 3
1.2.1 Applications in High Rates of Combustion of
Materials for Propulsion Systems, 5
1.2.2 Applications in Power Generation, 7
1.2.3 Applications in Process Industry, 7
1.2.4 Applications in Household and Industrial Heating, 7
1.2.5 Applications in Safety Protections for Unwanted
Combustion, 7
1.2.6 Applications in Ignition of Various Combustible
Materials, 8
1.2.7 Applications in Emission Control of Combustion
Products, 8
1.2.8 Applications in Active Control of Combustion
Processes, 8
1.3 Objectives of Combustion Modeling, 8
1.4 Combustion-Related Constituent Disciplines, 9
1.5 General Approach for Solving Combustion Problems, 9
vii
viii CONTENTS
1.6 Governing Equations for Combustion Models, 11
1.6.1 Conservation Equations, 11
1.6.2 Transport Equations, 11
1.6.3 Common Assumptions Made in Combustion
Models, 11
1.6.4 Equation of State, 12
1.6.4.1 High-Pressure Correction, 13
1.7 Definitions of Concentrations, 14
1.8 Definitions of Energy and Enthalpy Forms, 16
1.9 Velocities of Chemical Species, 19
1.9.1 Definitions of Absolute and Relative Mass and
Molar Fluxes, 20
1.10 Dimensionless Numbers, 23
1.11 Derivation of Species Mass Conservation Equation and
Continuity Equation for Multicomponent Mixtures, 23
1.12 Momentum Conservation Equation for Mixture, 29
1.13 Energy Conservation Equation for Multicomponent
Mixture, 33
1.14 Total Unknowns versus Governing Equations, 40
Homework Problems, 41
2 Laminar Premixed Flames 43
2.1 Basic Structure of One-Dimensional Premixed Laminar
Flames, 46
2.2 Conservation Equations for One-Dimensional Premixed
Laminar Flames, 47
2.2.1 Various Models for Diffusion Velocities, 49
2.2.1.1 Multicomponent Diffusion Velocities
(First-Order Approximation), 49
2.2.1.2 Various Models for Describing Source
Terms due to Chemical Reactions, 54
2.2.2 Sensitivity Analysis, 66
2.3 Analytical Relationships for Premixed Laminar Flames
with a Global Reaction, 68
2.3.1 Three Analysis Procedures for Premixed Laminar
Flames, 77
2.3.2 Generalized Expression for Laminar Flame
Speeds, 80
2.3.2.1 Reduced Reaction Mechanism for HC-Air
Flame, 81
CONTENTS ix
2.3.3 Dependency of Laminar Flame Speed on
Temperature and Pressure, 82
2.3.4 Premixed Laminar Flame Thickness, 84
2.4 Effect of Flame Stretch on Laminar Flame Speed, 86
2.4.1 Definitions of Stretch Factor and Karlovitz
Number, 86
2.4.2 Governing Equation for Premixed Laminar Flame
Surface Area, 94
2.4.3 Determination of Unstretched Premixed Laminar
Flame Speeds and Markstein Lengths, 95
2.5 Modeling of Soot Formation in Laminar Premixed
Flames, 103
2.5.1 Reaction Mechanisms for Soot Formation and
Oxidation, 104
2.5.1.1 Empirical Models for Soot
Formation, 106
2.5.1.2 Detailed Models for Soot Formation and
Oxidation, 108
2.5.1.3 Formation of Aromatics, 109
2.5.1.4 Growth of Aromatics, 110
2.5.1.5 Migration Reactions, 112
2.5.1.6 Oxidation of Aromatics, 113
2.5.2 Mathematical Formulation of Soot Formation
Model, 114
Homework Problems, 124
3 Laminar Non-Premixed Flames 125
3.1 Basic Structure of Non-Premixed Laminar Flames, 128
3.2 Flame Sheet Model, 129
3.3 Mixture Fraction Definition and Examples, 130
3.3.1 Balance Equations for Element Mass Fractions, 134
3.3.2 Temperature-Mixture Fraction Relationship, 138
3.4 Flamelet Structure of a Diffusion Flame, 142
3.4.1 Physical Significance of the Instantaneous Scalar
Dissipation Rate, 145
3.4.2 Steady-State Combustion and Critical Scalar
Dissipation Rate, 147
3.5 Time and Length Scales in Diffusion Flames, 151
3.6 Examples of Laminar Diffusion Flames, 153
3.6.1 Unsteady Mixing Layer, 153
x CONTENTS
3.6.2 Counterflow Diffusion Flames, 155
3.6.3 Coflow Diffusion Flame or Jet Flames, 165
3.7 Soot Formation in Laminar Diffusion Flames, 172
3.7.1 Soot Formation Model, 173
3.7.1.1 Particle Inception, 174
3.7.1.2 Surface Growth and Oxidation, 174
3.7.2 Appearance of Soot, 175
3.7.3 Experimental Studies by Using Coflow
Burners, 176
3.7.3.1 Sooting Zone, 178
3.7.3.2 Effect of Fuel Structure, 182
3.7.3.3 Influence of Additives, 183
3.7.3.4 Coflow Ethylene/Air Laminar Diffusion
Flames, 186
3.7.3.5 Modeling of Soot Formation, 191
Homework Problems, 204
4 Background in Turbulent Flows 206
4.1 Characteristics of Turbulent Flows, 210
4.1.1 Some Pictures, 212
4.2 Statistical Understanding of Turbulence, 213
4.2.1 Ensemble Averaging, 214
4.2.2 Time Averaging, 215
4.2.3 Spatial Averaging, 215
4.2.4 Statistical Moments, 215
4.2.5 Homogeneous Turbulence, 216
4.2.6 Isotropic Turbulence, 217
4.3 Conventional Averaging Methods, 217
4.3.1 Reynolds Averaging, 218
4.3.1.1 Correlation Functions, 222
4.3.2 Favre Averaging, 225
4.3.3 Relation between Time Averaged-Quantities and
Mass-Weighted Averaged Quantities, 227
4.3.4 Mass-Weighted Conservation and Transport
Equations, 228
4.3.4.1 Continuity and Momentum
Equations, 228
4.3.4.2 Energy Equation, 230
4.3.4.3 Mean Kinetic Energy Equation, 231
CONTENTS xi
4.3.4.4 Reynolds-Stress Transport Equations, 232
4.3.4.5 Turbulence-Kinetic-Energy Equation, 234
4.3.4.6 Turbulent Dissipation Rate Equation, 236
4.3.4.7 Species Mass Conservation
Equation, 242
4.3.5 Vorticity Equation, 243
4.3.6 Relationship between Enstrophy and the Turbulent
Dissipation Rate, 246
4.4 Turbulence Models, 247
4.5 Probability Density Function, 249
4.5.1 Distribution Function, 250
4.5.2 Joint Probability Density Function, 252
4.5.3 Bayes’ Theorem, 254
4.6 Turbulent Scales, 256
4.6.1 Comment on Kolmogorov Hypotheses, 260
4.7 Large Eddy Simulation, 266
4.7.1 Filtering, 268
4.7.2 Filtered Momentum Equations and Subgrid Scale
Stresses, 270
4.7.3 Modeling of Subgrid-Scale Stress Tensors, 274
4.8 Direct Numerical Simulation, 279
Homework Problems, 280
5 Turbulent Premixed Flames 283
5.1 Physical Interpretation, 289
5.2 Some Early Studies in Correlation Development, 291
5.2.1 Damko¨hler’s Analysis (1940), 292
5.2.2 Schelkin’s Analysis (1943), 295
5.2.3 Karlovitz, Denniston, and Wells’s Analysis
(1951), 296
5.2.4 Summerfield’s Analysis (1955), 297
5.2.5 Kovasznay’s Characteristic Time Approach
(1956), 298
5.2.6 Limitations of the Preceding Approaches, 299
5.3 Characteristic Scale of Wrinkles in Turbulent Premixed
Flames, 304
5.3.1 Schlieren Photographs, 305
5.3.2 Observations on the Structure of Wrinkled Laminar
Flames, 305
xii CONTENTS
5.3.3 Measurements of Scales of Unburned and Burned
Gas Lumps, 307
5.3.4 Length Scale of Wrinkles, 310
5.4 Development of Borghi Diagram for Premixed Turbulent
Flames, 310
5.4.1 Physical Interpretation of Various Regimes in
Borghi’s Diagram, 311
5.4.1.1 Wrinkled Flame Regime, 311
5.4.1.2 Wrinkled Flame with Pockets Regime
(also Called Corrugated Flame
Regime), 311
5.4.1.3 Thickened Wrinkled Flames, 313
5.4.1.4 Thickened Flames with Possible
Extinctions/Thick Flames, 314
5.4.2 Klimov-Williams Criterion, 314
5.4.3 Construction of Borghi Diagram, 316
5.4.3.1 Thick Flames (or Distributed Reaction
Zone or Well-Stirred Reaction Zone), 318
5.4.4 Wrinkled Flames, 318
5.4.4.1 Wrinkled Flamelets (Weak
Turbulence), 320
5.4.4.2 Corrugated Flamelets (Strong
Turbulence), 322
5.5 Measurements in Premixed Turbulent Flames, 324
5.6 Eddy-Break-up Model, 324
5.6.1 Spalding’s EBU Model, 335
5.6.2 Magnussen and Hjertager’s EBU Model, 336
5.7 Intermittency, 337
5.8 Flame-Turbulence Interaction, 339
5.8.1 Effects of Flame on Turbulence, 341
5.9 Bray-Moss-Libby Model, 342
5.9.1 Governing Equations, 349
5.9.2 Gradient Transport, 353
5.9.3 Countergradient Transport, 354
5.9.4 Closure of Transport Terms, 357
5.9.4.1 Gradient Closure, 357
5.9.4.2 BML Closure, 358
5.9.5 Effect of Pressure Fluctuations Gradients, 361
5.9.6 Summary of DNS Results, 364
5.10 Turbulent Combustion Modeling Approaches, 368