Preface i Nomenclature iii Introduction v
1. Some Fundamentals of Dispersed Multiphase Flows 1
1.1ParticleSpray Basic Properties 1
1.1.1ParticleDroplet Size and Its Distribution 1
1.1.2Apparent Density and Volume Fraction 2
1.2Particle Drag, Heat, and Mass Transfer 2
1.3Single-Particle Dynamics 3
1.3.1
1.3.2
1.3.3
1.3.4
1.3.5
1.3.6
References
Single-Particle Motion Equation 3 Motion of a Single Particle in a Uniform Flow Field 4 Particle Gravitational Deposition 4 Forces Acting on Particles in Nonuniform Flow Field 5
1.3.4.1Magnus Force 5
1.3.4.2 Saffman Force5
1.3.4.3Particle Thermophoresis, Electrophoresis, and Photophoresis 5 Generalized Particle Motion Equation 6 Recent Studies on Particle Dynamics 6 7
Further Reading8
2. Basic Concepts and Description of Turbulence 9
2.1Introduction 9
2.2Time Averaging 9
2.3Probability Density Function 10
2.4 Correlations, Length, and Time Scales 12 References 13
3. Fundamentals of Combustion Theory15
3.1Combustion and Flame 15
3.2Basic Equations of Laminar Multicomponent Reacting Flows and Combustion 16
3.2.1Thermodynamic Relationships of Multicomponent Gases 16
xiii
3.2.2Molecular Transport Laws of Multicomponent Reacting Gases 18
3.2.3Basic Relationships of Chemical Kinetics 19
3.2.4The Reynolds Transport Theorem 20
3.2.5Continuity and Diffusion Equations 21
3.2.6Momentum Equation 22
3.2.7Energy Equation 23
3.2.8Boundary Conditions at the Interface and Stefan Flux 26
3.3 Ignition and Extinction30
3.3.1Basic Concept 30
3.3.2Dimensional Analysis 30
3.3.3Ignition in an Enclosed VesselSimonovs Unsteady Model 31
3.3.4Ignition Lag Induction Period 34
3.3.5Ignition by a Hot PlateKhitrin-Goldenberg Model 35
3.3.6Ignition and ExtinctionVulis Model 37
3.4 Laminar Premixed and Diffusion Combustion41
3.4.1Background 41
3.4.2Basic Equations and Their Properties 41
3.4.3Two-Zone Approximate Solution 43
3.4.4Laminar Diffusion Flame 46
3.5 Droplet Evaporation and Combustion47
3.5.1Background 47
3.5.2Droplet Evaporation in Stagnant Air 48
3.5.3Basic Equations for Droplet Evaporation and Combustion 48
3.5.4Droplet Evaporation With and Without Combustion 49
3.5.5Droplet Evaporation and Combustion under Forced Convection 50
3.5.6The d2 Law 52
3.5.7Experimental Results 52
3.5.8Droplet Ignition and Extinction 54
3.6 Solid-Fuel： Coal-Particle Combustion54
3.6.1Background 54
3.6.2Coal Pyrolyzation Devolatilization 55
3.6.3Carbon Oxidation 56
3.6.4Carbon OxidationBasic Equations 56
3.6.5Carbon OxidationSingle-Flame-Surface Model-Only Reaction 1 or 2 at the Surface 57
3.6.6Carbon OxidationTwo-Flame-Surface Model 60
3.6.7Coal-Particle Combustion 62
3.7 Turbulent Combustion and Flame Stabilization64
3.7.1Background 64
3.7.2Turbulent Jet Diffusion Flame 64
3.7.3Turbulent Premixed FlameDamkohler-Shelkins Wrinkled-Flame Model 66
Contents xY
3.7.4Turbulent Premixed FlameSummerfield-Shetinkovs Volume Combustion Model 67
3.7.5Flame Stabilization 67
3.8 Conclusion on Combustion Fundamentals 69 References 69
4.Basic Equations of Multiphase Turbulent Reacting Flows 71
4.1The Control Volume in a Multiphase-Flow System 71
4.2The Concept of Volume Averaging 72
4.3Microscopic Conservation Equations Inside Each Phase 73
4.4The Volume-Averaged Conservation Equations for LaminarInstantaneous Multiphase Flows 73
4.5The Reynolds-Averaged Equations for Dilute Multiphase Turbulent Reacting Flows 78
4.6The PDF Equations for Turbulent Two-Phase Flows and Statistically Averaged Equations 80
4.7The Two-Phase Reynolds Stress and Scalar Transport Equations 83 References 87
5.Modeling of Single-Phase Turbulence 89
5.1Introduction 89
5.2The Closure of Single-Phase Turbulent Kinetic Energy Equation 90
5.3The k- Two-Equation Model and Its Application 92
5.4The Second-Order Moment Closure of Single-Phase Turbulence 96
5.5The Closed Model of Reynolds Stresses and Heat Fluxes 99
5.6The Algebraic Stress and Flux ModelsExtended k- Model 101
5.7The Application of DSM and ASM Models and Their Comparison with Other Models 103
5.8Large-Eddy Simulation 112
5.8.1Filtration 112
5.8.2SGS Stress Models 113
5.8.3LES of Swirling Gas Flows 114
5.9 Direct Numerical Simulation 116 References 119
6.Modeling of Dispersed Multiphase Turbulent Flows 121
6.1Introduction 121
6.2The Hinze-Tchens Algebraic Model of Particle Turbulence 124
6.3The Unified Second-Order Moment Two-Phase Turbulence Model 124
6.4The k 2 2 kp and k 2 2 Ap Two-Phase Turbulence Model 128
6.5The Application and Validation of USM, k 2 2 kp -kpg and k 2 2 Ap Models 129
6.6An Improved Second-Order Moment Two-Phase Turbulence Model 134
6.7The Mass-Weighted Averaged USM Two-Phase Turbulence Model 136
6.8The DSM-PDF and k 2 -PDF Two-Phase Turbulence Models 141
6.9An SOM-MC Model of Swirling Gas-Particle Flows 144
6.10The Nonlinear k 2 2 kp Two-Phase Turbulence Model 146
6.11The Kinetic Theory Modeling of Dense Particle Granular Flows 150
6.12Two-Phase Turbulence Models for Dense Gas-Particle Flows 153
6.13The Eulerian-Lagrangian Simulation of Gas-Particle Flows 155
6.13.1Governing Equations for the Deterministic Trajectory Model 156
6.13.2Modification for Particle Turbulent Diffusion 157
6.13.3The Stochastic Trajectory Model 159
6.13.4The DEM Simulation of Dense Gas-Particle Flows 161
6.14The Large-Eddy Simulation of Turbulent Gas-Particle Flows 163
6.14.1Eulerian-Lagrangian LES of Swirling Gas-Particle Flows 165
6.14.2Eulerian-Lagrangian LES of Bubble-Liquid Flows 166
6.14.3Two-Fluid LES of Swirling Gas-Particle Flows 167
6.14.4Application of LES in Engineering Gas-Particle Flows 170
6.15The Direct Numerical Simulation of Dispersed Multiphase Flows 172 References 177
7.Modeling of Turbulent Combustion 183
7.1Introduction 183
7.2The Time-Averaged Reaction Rate 183
7.3The Eddy-Break-Up EBU ModelEddy Dissipation Model EDM 184
7.4The Presumed PDF Models 186
7.4.1The Probability Density Distribution Function 186
7.4.2The Simplified PDF-Local Instantaneous Nonpremixed Fast-Chemistry Model 187
7.4.3The Simplified PDF-Local Instantaneous Equilibrium Model 191
7.4.4The Simplified-PDF Finite-Rate Model 194
7.5The PDF Transport Equation Model 198
7.6The Bray-Moss-Libby BML Model 200
7.7The Conditional Moment Closure CMC Model 201
7.8The Laminar-Flamelet Model 202
Contents xYii
7.9The Second-Order Moment Combustion Model 204
7.9.1 The Early Developed Second-Order Moment Model 204
7.9.2 An Updated Second-Order Moment SOM Model 207
7.9.3 Application of the SOM Model in RANS Modeling 208
7.9.4 Validation of the SOM Model by DNS212
7.10Modeling of Turbulent Two-Phase Combustion 215
7.10.1Two-Fluid Modeling of Turbulent Two-Phase Combustion 216
7.10.2Two-Fluid-Simulation of Coal Combustion in a Combustor with High-Velocity Jets 218
7.10.3Two-Fluid Modeling of Coal Combustion and NO Formation in a Swirl Combustor 221
7.10.4Eulerian-Lagrangian Modeling of Two-Phase Combustion 223
7.11Large-Eddy Simulation of Turbulent Combustion 224
7.11.1LES Equations and Closure Models for Simulating Gas Turbulent Combustion 224
7.11.2LES of Swirling Diffusion Combustion, Jet Diffusion Combustion, and Bluff-Body Premixed Combustion 226
7.11.3LES of Ethanol-Air Spray Combustion 232
7.11.4LES of Swirling Coal Combustion 235
7.12 Direct Numerical Simulation of Turbulent Combustion 242 References 249
8.The Solution Procedure for Modeling Multiphase Turbulent Reacting Flows 253
8.1The PSIC Algorithm for Eulerian-Lagrangian Models 253
8.2The LEAGAP Algorithm for E-E-L Modeling 256
8.3The PERT Algorithm for Eulerian-Eulerian Modeling 257
8.4The GENMIX-2P and IPSA Algorithms for Eulerian-Eulerian Modeling 257 References 260
Multiphase, turbulent, and reacting flows are widely encountered in engi-neering and the natural environment. The basic theory, phenomena, mathe-matical models, numerical simulations, and applications of multiphase gas or liquid flows with particlesdroplets or bubbles, turbulent reacting flows are presented in this book. The special feature of this book is in combining the multiphase fluid dynamics with the turbulence modeling theory and reacting fluid dynamics combustion theory. There are nine chapters in this book, namely： Fundamentals of Dispersed Multiphase Flows; Basic Concepts and Description of Turbulence; Fundamentals of Combustion Theory; Basic Equations of Multiphase Turbulent Reacting Flows; Modeling of Single-Phase Turbulent Flows; Modeling of Dispersed Multiphase Turbulent Flows; Modeling of Turbulent Combustion; The Solution Procedure for Modeling Multiphase Turbulent Reacting Flows; and Simulation of Flows and Combustion in Practical Fluid Machines, Combustors and Furnaces. The main difference between this book and pre-vious books written by the author is that more much better descriptions of basic equations and closure models of multiphase turbulent reacting flows are introduced, and recent advances made by the author and other investiga-tors between 1994 and 2016 are included.This book serves as a reference book for teaching, research, and engi-neering design for faculty members, students, and research engineers in the fields of fluid dynamics, thermal science and engineering, aeronautical, astronautical, chemical, metallurgical, petroleum, nuclear, and hydraulic engineering.The author wishes to thank Prof. F.G. Zhuang, H.X. Zhang, and C.K. Wu for their valuable comments and suggestions. Thanks also go to colleagues and former students： Prof. W.Y. Lin, R.X. Li, X.L. Wang, J. Zhang, B. Zhou, Y.C. Guo, H.Q. Zhang, L.Y. Hu, Y. Yu, F. Wang, Z.X. Zeng, K. Li,Y. Zhang; Drs. Gene X.Q. Huang, T. Hong, C.M. Liao, W.W. Luo, K.M. Sun, Y. Li, T. Chen, Y. Xu, G. Luo, M. Yang, L. Li, H.X. Gu, X.L. Chen,X. Zhang, and Y. Liu. Their research results under the direction and coopera-tion of the author contributed to the context of this book.Finally, the authors gratitude is given to the editors from Elsevier and the Executive Editor, Dr. Qiang Li from the Tsinghua University Press for their hard work in the final editing and publishing of this book.Any comments and suggestions from the experts and readers would be highly appreciated.Lixing ZhouTsinghua University, Beijing, ChinaFebruary, 2017
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