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 Annroach for Solvine Combustion Problems ........ 9
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
Flump ................................... 81
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
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
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 Damköhler'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
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
5.11 Geometrical Description of Turbulent Premixed Flames
and G-Equation ............................................. 368
5.11.1 Level Set Approach for the Corrugated
Flamelets Regime ............................... 371
5.11.2 Level Set Approach for the Thin Reaction Zone
Regime ......................................... 374
5.12 Scales in Turbulent Combustion ........................ 376
5.13 Closure of Chemical Reaction Source Term .............. 380
5.14 Probability Density Function Approach to Turbulent
Combustion ............................................ 381
5.14.1 Derivation of the Transport Equation for
Probability Density Function ................... 386
5.14.2 Moment Equations and PDF Equations ............. 391
5.14.3 Lagrangian Equations for Fluid Particles ....... 392
5.14.4 Gradient Transport Model in Composition PDF
Method ......................................... 395
5.14.5 Determination of Overall Reaction Rate ......... 397
5.14.6 Lagrangian Monte Carlo Particle Methods ........ 398
5.14.7 Filtered Density Function Approach ............. 398
5.14.8 Prospect of PDF Methods ........................ 399
Homework Problems .......................................... 400
Project No. 1, 400 Project No. 2 ........................... 401
6 Non-premixed Turbulent Flames .............................. 402
6.1 Major Issues in Non-premixed Turbulent Flames ......... 404
6.2 Turbulent Damköhler number ............................ 406
6.3 Turbulent Reynolds Number ............................. 407
6.4 Scales in Non-premixed Turbulent Flames ............... 407
6.4.1 Direct Numerical Simulation and Scales .......... 411
6.5 Turbulent Non-premixed Combustion Regime Diagram ...... 414
6.6 Turbulent Non-premixed Target Flames .................. 418
6.6.1 Simple Jet Flames .............................. 419
6.6.1.1 CH4/H2/N2 Jet Flame ................... 420
6.6.1.2 Effect of Jet Velocity ................ 430
6.6.2 Piloted Jet Flames ............................. 432
6.6.2.1 Comparison of Simple Jet Flame and
Sandia Flames D and F .................. 448
6.6.3 Bluff Body Flames .............................. 452
6.6.4 Swirl Stabilized Flames ........................ 455
6.7 Turbulence-Chemistry Interaction ...................... 456
6.7.1 Infinite Chemistry Assumption .................. 456
6.7.1.1 Unity Lewis Number .................... 457
6.7.1.2 Nonunity Lewis Number ................. 458
6.7.2 Finite-Rate Chemistry .......................... 458
6.8 Probability Density Approach for Turbulent
Non-premixed Combustion ............................... 462
6.8.1 Physical Models ................................ 465
6.8.2 Turbulent Transport in Velocity-Composition
Pdf Methods .................................... 466
6.8.2.1 Stochastic Mixing Model ............... 467
6.8.2.2 Stochastic Reorientation Model ........ 468
6.8.3 Molecular Transport and Scalar Mixing Models ... 469
6.8.3.1 Interaction by Exchange with the
Mean Model ............................ 471
6.8.3.2 Modified Curl Mixing Model ............ 471
6.8.3.3 Euclidean Minimum Spanning Tree
Model ................................. 472
6.9 Flamelet Models ....................................... 476
6.9.1 Laminar Flamelet Assumption .................... 477
6.9.2 Unsteady Flamelet Modeling ..................... 478
6.9.3 Flamelet Models and PDF ........................ 479
6.10 Interactions of Flame and Vortices .................... 480
6.10.1 Flame Rolled Up in a Single Vortex ............. 482
6.10.2 Flame in a Shear Layer ......................... 483
6.10.3 Jet Flames ..................................... 483
6.10.4 Kármán Vortex Street/V-Shaped Flame
Interaction .................................... 484
6.10.5 Burning Vortex Ring ............................ 484
6.10.6 Head-on Flame/Vortex Interaction ............... 485
6.10.7 Experimental Setups for Flame/Vortex
Interaction Studies ............................ 486
6.10.7.1 Reaction Front/Vortex Interaction in
Liquids ............................... 486
6.10.7.2 Jet Flames ............................ 487
6.10.7.3 Counterflow Diffusion Flames .......... 488
6.11 Generation and Dissipation of Vorticity Effects ....... 492
6.12 Non-premixed Flame-Vortex Interaction Combustion
Diagram ............................................... 493
6.13 Flame Instability in Non-premixed Turbulent Flames .... 496
6.14 Partially Premixed Flames or Edge Flames .............. 500
6.14.1 Formation of Edge Flames ....................... 501
6.14.2 Triple Flame Stabilization of Lifted
Diffusion Flame ................................ 502
6.14.3 Analysis of Edge Flames ........................ 503
Homework Problems .......................................... 506
Project No. 6.1 ............................................ 506
Project No. 6.2 ............................................ 507
Project No. 6.3 ........................................... 507
7 Background in Multiphase flows with Reactions .............. 509
7.1 Classification of Multiphase Flow Systems ............. 512
7.2 Practical Problems Involving Multiphase Systems ....... 514
7.3 Homogeneous versus Multi-component/Multiphase
Mixtures .............................................. 515
7.4 CFD and Multiphase Simulation ......................... 516
7.5 Averaging Methods ..................................... 520
7.5.1 Eulerian Average - Eulerian Mean Values ........ 522
7.5.2 Lagrangian Average - Lagrangian Mean Values .... 523
7.5.3 Boltzmann Statistical Average .................. 524
7.5.4 Anderson and Jackson's Averaging for Dense
Fluidized Beds ................................. 525
7.6 Local Instant Formulation ............................. 533
7.7 Eulerian-Eulerian Modeling ............................ 536
7.7.1 Fluid-Fluid Modeling ........................... 536
7.7.1.1 Closure Models ......................... 538
7.7.2 Fluid-Solid Modeling ........................... 540
7.7.2.1 Closure Models ........................ 541
7.7.2.2 Dense Particle Flows .................. 547
7.7.2.3 Dilute Particle Flows ................. 549
7.8 Eulerian-Lagrangian Modeling .......................... 550
7.8.1 Fluid-Solid Modeling ............................ 551
7.8.1.1 Fluid Phase ........................... 551
7.8.1.2 Solid Phase ........................... 552
7.9 Interfacial Transport (Jump Conditions) ............... 555
7.10 Interface-Tracking/Capturing .......................... 561
7.10.1 Interface Tracking ............................. 563
7.10.1.1 Markers on Interface (Surface Marker
Techniques) ........................... 564
7.10.1.2 Surface-Fitted Method ................. 567
7.10.2 Interface Capturing ............................ 568
7.10.2.1 Markers in Fluid (MAC Formulation) .... 568
7.10.2.2 Volume of Fluid Method ................ 569
7.11 Discrete Particle Methods ............................. 573
Homework Problems .......................................... 575
8 Spray Atomization and Combustion ........................... 576
8.1 Introduction to Spray Combustion ...................... 578
8.2 Spray-Combustion Systems .............................. 580
8.3 Fuel Atomization ...................................... 582
8.3.1 Injector Types ................................. 582
8.3.2 Atomization Characteristics .................... 584
8.4 Spray Statistics ...................................... 584
8.4.1 Particle Characterization ...................... 584
8.4.2 Distribution Function .......................... 585
8.4.2.1 Logarithmic Probability Distribution
Function .............................. 588
8.4.2.2 Rosin-Rammler Distribution Function ... 588
8.4.2.3 Nukiyama-Tanasawa Distribution
Function .............................. 589
8.4.2.4 Upper-Limit Distribution Function of
Mugele and Evans ...................... 589
8.4.3 Transport Equation of the Distribution
Function ....................................... 590
8.4.4 Simplified Spray Combustion Model for Liquid-
Fuel Rocket Engines ............................ 591
8.5 Spray Combustion Characteristics ...................... 594
8.6 Classification of Models Developed for Spray
Combustion Processes .................................. 602
8.6.1 Simple Correlations ............................ 602
8.6.2 Droplet Ballistic Models ....................... 603
8.6.3 One-Dimensional Models ......................... 603
8.6.4 Stirred-Reactor Models ......................... 604
8.6.5 Locally Homogeneous-How Models ................. 605
8.6.6 Two-Phase-Flow (Dispersed-Flow) Models ......... 605
8.7 Locally Homogeneous Flow Models ....................... 605
8.7.1 Classification of LHF Models ................... 606
8.7.2 Mathematical Formulation of LHF Models ......... 609
8.7.2.1 Basic Assumptions ..................... 609
8.7.2.2 Equation of State ..................... 609
8.7.2.3 Conservation Equations ................ 615
8.7.2.4 Turbulent Transport Equations ......... 619
8.7.2.5 Boundary Conditions ................... 620
8.7.2.6 Solution Procedures ................... 620
8.7.2.7 Comparison of LHF-Model Predictions
with Experimental Data ................ 626
8.8 Two-Phase-Flow (Dispersed-Flow) Models ................ 634
8.8.1 Particle-Source-in-Cell Model (Discrete-
Droplet Model) ................................. 637
8.8.1.1 Models for Single Drop Behavior ........ 639
8.8.2 Drop Breakup Process and Mechanism ............. 654
8.8.2.1 Drop Breakup Process .................. 654
8.8.2.2 Multi-component Droplet Breakup by
Microexplosion ........................ 659
8.8.3 Deterministic Discrete Droplet Models .......... 662
8.8.3.1 Gas-Phase Treatment in DDDMs .......... 664
8.8.3.2 Liquid-Phase Treatment in DDDMs ....... 666
8.8.3.3 Results of DDDMs ...................... 667
8.8.4 Stochastic Discrete Droplet Models ............. 669
8.8.5 Comparison of Results between DDDMs and SDDMs .. 671
8.8.6 Dense Sprays ................................... 682
8.8.6.1 Introduction .......................... 682
8.8.6.2 Background ............................ 684
8.8.6.3 Jet Breakup Models .................... 690
8.8.6.4 Impinging Jet Atomization ............. 699
8.9 Group-Combustion Models of Chiu ....................... 700
8.9.1 Group-Combustion Numbers ....................... 701
8.9.2 Modes of Group Burning in Spray Flames ......... 703
8.10 Droplet Collison ...................................... 706
8.10.1 Droplet-Droplet Collisions ..................... 707
8.10.2 Droplet-Wall Collision ......................... 708
8.10.3 Interacting Droplet in a Many-Droplet System ... 710
8.11 Optical Techniques for Particle Size Measurements ..... 710
8.11.1 Types of Optical Particle Sizing Methods ....... 711
8.11.2 Single Particle Counting Methods ............... 711
8.11.2.1 Scattering Ratio Technique ............ 712
8.11.2.2 Intensity Deconvolution Method ........ 713
8.11.2.3 Interferometric Method (Phase-Shift
Method) ............................... 713
8.11.2.4 Visibility Method Using a Laser
Doppler Velocimeter LDV ............... 713
8.11.2.5 Phase Doppler Sizing Anemometer ....... 713
8.11.3 Ensemble Particle Sizing Techniques ............ 714
8.11.3.1 Extinction Measurement Techniques ..... 714
8.11.3.2 Multiple Angle Scattering Technique ... 714
8.11.3.3 Fraunhofer Diffraction Particle
Analyzer .............................. 715
8.11.3.4 Integral Transform Solutions for
Near-Forward Scattering ............... 716
8.12 Effect of Droplet Spacing on Spray Combustion ......... 717
8.12.1 Evaporation and Combustion of Droplet
Arrays ......................................... 717
Homework Problems .......................................... 720
Appendix A: Useful Vector and Tensor Operations ............... 723
Appendix B: Constants and Conversion Factors Often Used in
Combustion ........................................ 751
Appendix C: Naming of Hydrocarbons ............................ 755
Appendix D: Detailed Gas-Phase Reaction Mechanism for
Aromatics Formation ............................... 759
Appendix E: Particle Size-U.S. Sieve Size and Tyler Screen
Mesh Equivalents .................................. 795
Bibliography .................................................. 799
Index ......................................................... 869
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