1 Introduction 1
1.1 Industrial applications 4
1.1.1 Spray drying 4
1.1.2 Pollution control 5
1.1.3 Transport systems 6
1.1.4 Fluidized beds 10
1.1.5 Manufacturing and material processing 11
1.2 Energy conversion and propulsion 14
1.2.1 Pulverized-coal-fired furnaces 14
1.2.2 Solid propellant rocket 14
1.3 Fire suppression and control 15
1.4 Summary 15
2 Properties of Dispersed Phase Flows 17
2.1 Concept of a continuum 17
2.2 Density and volume fraction 19
2.3 Particle or droplet spacing 21
2.4 Response times 24
2.5 Stokes number 25
2.6 Dilute versus dense Flows 26
2.7 Phase coupling 29
2.7.1 Mass coupling 30
2.7.2 Momentum coupling 33
2.7.3 Energy coupling 34
2.8 Properties of an equilibrium mixture 35
2.9 Summary 36
2.10 Exercises 36
3 Size Distribution 39
3.1 Discrete size distributions 39
3.2 Continuous size distributions 41
3.3 Statistical parameters 42
3.3.1 Mode 43
3.3.2 Mean 43
3.3.3 Variance 43
3.3.4 Median 43
3.3.5 Sauter mean diameter 44
3.4 Frequently used size distributions 44
3.4.1 Log-normal distribution 44
3.4.2 Rosin-Rammler distribution 47
3.4.3 Log-hyperbolic distribution 49
3.5 Summary 51
3.6 Exercises 51
4 Particle-Fluid Interaction 57
4.1 Single-particle equations 57
4.1.1 Continuity equation 58
4.1.2 Translational momentum equation 59
4.1.3 Angular momentum equation 59
4.1.4 Energy equation 60
4.2 Mass coupling 60
4.2.1 Evaporation or condensation 60
4.2.2 Mass transfer from slurry droplets 63
4.2.3 Combustion 65
4.3 Linear momentum coupling 67
4.3.1 Particle drag forces 67
4.3.2 Particle lift forces 96
4.3.3 Equation summary 100
4.3.4 Body forces 100
4.3.5 Rotational momentum coupling 102
4.4 Energy coupling 103
4.4.1 Convective heat transfer 104
4.4.2 Transient term 107
4.4.3 Radiative heat transfer 108
4.4.4 Dielectric heating 110
4.5 Summary 110
4.6 Exercises 110
5 Particle-Particle Interaction 119
5.1 Particle-particle interaction 119
5.1.1 Hard sphere model 120
5.1.2 Soft sphere model （DSEM） 124
5.1.3 Hard sphere simulation of a soft sphere model 132
5.1.4 Cohesive force 133
5.1.5 van der Waals forces 135
5.1.6 Solid particle agglomeration 137
5.1.7 Fluid forces on approaching particles 137
5.2 Particle-wall interaction 139
5.2.1 Momentum and energy exchange at walls 140
5.2.2 Irregular bouncing 149
5.2.3 Erosion 151
5.3 Summary 152
5.4 Exercises 153
6 Continuous Phase Equations 157
6.1 Averaging procedures 158
6.1.1 Time averaging 158
6.1.2 Volume averaging 160
6.1.3 Ensemble averaging 162
6.2 Volume averaging 163
6.3 Property flux through a particle cloud 167
6.4 Volume-averaged conservation equations 169
6.4.1 Quasi-one-dimensional flow 169
6.4.2 Continuity equation 169
6.4.3 Momentum equation 173
6.4.4 Energy equation 181
6.5 Equation summary 191
6.6 Summary 191
6.7 Exercises 192
7 Turbulence 199
7.1 Review of turbulence in single-phase flow 199
7.1.1 General features of turbulence 199
7.1.2 Modeling single-phase turbulence 201
7.2 Turbulence modulation by particles 202
7.3 Review of modulation models 207
7.3.1 Empirical Models 208
7.3.2 Turbulence models with dusty-gas equations 209
7.3.3 Point particle models 211
7.3.4 Models based on volume averaging 211
7.4 Basic test case for turbulence models 212
7.5 Volume-averaged turbulence models 214
7.5.1 Defining volume-averaged turbulence 215
7.5.2 Turbulence kinetic energy equation 216
7.5.3 Turbulence dissipation equation 217
7.5.4 Turbulence Reynolds stress equation 222
7.6 Application to experimental results 226
7.7 Summary 230
7.8 Exercises 232
8 Droplet-Particle Cloud Equations 235
8.1 Discrete Element Method （DEM） 238
8.2 Discrete Parcel Method （DPM） 239
8.2.1 Non-dense flows 240
8.2.2 Dense flows 253
8.3 Two-fluid model 254
8.4 PDF models 257
8.5 Summary 258
9 Numerical Modeling 259
9.1 Complete Numerical Simulation 260
9.2 DNS models 261
9.2.1 Model formulation and solution procedure 261
9.2.2 Application to particle-laden flows 262
9.2.3 Current status 264
9.3 LES models 264
9.3.1 Model formulation 264
9.3.2 Application to particle-laden flows 265
9.4 VANS numerical models 267
9.4.1 Boundary conditions 276
9.4.2 Numerical solution procedures 276
9.4.3 Application examples 285
9.5 Summary 290
10 Experimental Methods 291
10.1 Sampling methods 294
10.1.1 Imaging methods，microscopy 295
10.1.2 Sieving analysis 296
10.1.3 Sedimentation methods 299
10.1.4 Electrical sensing zone method （Coulter principle） 306
10.1.5 Optical analysis 308
10.2 Integral methods 308
10.2.1 Light attenuation 309
10.2.2 Laser-diffraction method 310
10.2.3 Cross-correlation techniques 314
10.3 Local measurement techniques 317
10.3.1 Isokinetic sampling 318
10.3.2 Optical fiber probes 322
10.3.3 Scattering intensity measurements 324
10.3.4 Laser-Doppler anemometry 335
10.3.5 Phase-Doppler anemometry 347
10.3.6 Imaging techniques 367
10.4 Summary 377
10.5 Exercises 378
A Single-Particle Equations 381
A.1 Reynolds transport theorem 381
A.2 Mass conservation 386
A.3 Momentum conservation 387
A.3.1 Linear momentum 387
A.3.2 Moment of momentum 391
A.4 Energy conservation 393
A.4.1 Heat transfer to particle 396
A.4.2 Work rate of particles on surroundings 396
B Volume Averaging 401
B.1 Volume average of the gradient operation 402
B.2 Volume averaging of the time derivative 406
C Volume-Averaged Equations 409
C.1 Continuity equation 409
C.2 Momentum equation 411
C.3 Energy equation 414
C.3.1 Thermal energy equation 415
C.3.2 Mechanical energy equation 419
C.3.3 Total energy equation 424
D Turbulence Equations 425
D.1 Turbulence energy 426
D.1.1 Continuity and momentum equations 427
D.1.2 Mechanical energy equation 427
D.1.3 Turbulence energy equation 432
D.2 Turbulence dissipation 435
D.2.1 Volume averaging 436
D.2.2 The dissipation transport equation 443
D.3 Reynolds stress 446
D.3.1 Volume-averaged momentum equations 446
D.3.2 Volume average for the Reynolds stress 447
D.3.3 Reynolds stress equation 451
E Brownian Motion 455
References 461
Nomenclature 483
Index 489