1 Introduction to Multiphase Flow 1
1.1 Introduction 1
1.1.1 Scope 1
1.1.2 Multiphase Flow Models 2
1.1.3 Multiphase Flow Notation 3
1.1.4 Size Distribution Functions 6
1.2 Equations of Motion 8
1.2.1 Averaging 8
1.2.2 Continuum Equations for Conservation of Mass 9
1.2.3 Disperse Phase Number Continuity 10
1.2.4 Fick’s Law 11
1.2.5 Continuum Equations for Conservation of Momentum 12
1.2.6 Disperse Phase Momentum Equation 14
1.2.7 Comments on Disperse Phase Interaction 15
1.2.8 Equations for Conservation of Energy 16
1.2.9 Heat Transfer between Separated Phases 19
1.3 Interaction with Turbulence 21
1.3.1 Particles and Turbulence 21
1.3.2 Effect on Turbulence Stability 24
1.4 Comments on the Equations of Motion 25
1.4.1 Averaging 25
1.4.2 Averaging Contributions to the Mean Motion 26
1.4.3 Averaging in Pipe Flows 27
1.4.4 Modeling with the Combined Phase Equations 28
1.4.5 Mass，Force，and Energy Interaction Terms 28
2 Single-Particle Motion 30
2.1 Introduction 30
2.2 Flows Around a Sphere 31
2.2.1 At High Reynolds Number 31
2.2.2 At Low Reynolds Number 32
2.2.3 Molecular Effects 37
2.3 Unsteady Effects 38
2.3.1 Unsteady Particle Motions 38
2.3.2 Effect of Concentration on Added Mass 41
2.3.3 Unsteady Potential Flow 41
2.3.4 Unsteady Stokes Flow 44
2.4 Particle Equation of Motion 48
2.4.1 Equations of Motion 48
2.4.2 Magnitude of Relative Motion 52
2.4.3 Effect of Concentration on Particle Equation of Motion 53
2.4.4 Effect of Concentration on Particle Drag 55
3 Bubble or Droplet Translation 60
3.1 Introduction 60
3.2 Deformation Due to Translation 60
3.2.1 Dimensional analysis 60
3.2.2 Bubble shapes and terminal velocities 61
3.3 Marangoni Effects 66
3.4 Bjerknes Forces 68
3.5 Growing or Collapsing Bubbles 69
4 Bubble Growth and Collapse 73
4.1 Introduction 73
4.2 Bubble Growth and Collapse 73
4.2.1 Rayleigh-Plesset Equation 73
4.2.2 Bubble Contents 75
4.2.3 In the Absence of Thermal Effects； Bubble Growth 78
4.2.4 In the Absence of Thermal Effects； Bubble Collapse 81
4.2.5 Stability of Vapor/Gas Bubbles 82
4.3 Thermal Effects 84
4.3.1 Thermal Effects on Growth 84
4.3.2 Thermally Controlled Growth 85
4.3.3 Cavitation and Boiling 89
4.3.4 Bubble Growth by Mass Diffusion 89
4.4 Oscillating Bubbles 91
4.4.1 Bubble Natural Frequencies 91
4.4.2 Nonlinear Effects 93
4.4.3 Rectified Mass Diffusion 95
5 Cavitation 97
5.1 Introduction 97
5.2 Key Features of Bubble Cavitation 97
5.2.1 Cavitation Inception 97
5.2.2 Cavitation Bubble Collapse 99
5.2.3 Shape Distortion during Bubble Collapse 101
5.2.4 Cavitation Damage 104
5.3 Cavitation Bubbles 106
5.3.1 Observations of Cavitating Bubbles 106
5.3.2 Cavitation Noise 109
5.3.3 Cavitation Luminescence 115
6 Boiling and Condensation 116
6.1 Introduction 116
6.2 Horizontal Surfaces 117
6.2.1 Pool Boiling 117
6.2.2 Nucleate Boiling 119
6.2.3 Film Boiling 120
6.2.4 Leidenfrost Effect 121
6.3 Vertical Surfaces 122
6.3.1 Film Boiling 122
6.4 Condensation 125
6.4.1 Film Condensation 125
7 Flow Patterns 127
7.1 Introduction 127
7.2 Topologies of Multiphase Flow 127
7.2.1 Multiphase Flow Patterns 127
7.2.2 Examples of Flow Regime Maps 129
7.2.3 Slurry Flow Regimes 131
7.2.4 Vertical Pipe Flow 132
7.2.5 Flow Pattern Classifications 134
7.3 Limits of Disperse Flow Regimes 136
7.3.1 Disperse Phase Separation and Dispersion 136
7.3.2 Example：Horizontal Pipe Flow 138
7.3.3 Particle Size and Particle Fission 140
7.3.4 Examples of Flow-Determined Bubble Size 141
7.3.5 Bubbly or Mist Flow Limits 142
7.3.6 Other Bubbly Flow Limits 143
7.3.7 Other Particle Size Effects 144
7.4 Inhomogeneity Instability 144
7.4.1 Stability of Disperse Mixtures 145
7.4.2 Inhomogeneity Instability in Vertical Flows 148
7.5 Limits on Separated Flow 151
7.5.1 Kelvin-Helmoltz Instability 151
7.5.2 Stratified Flow Instability 153
7.5.3 Annular Flow Instability 154
8 Internal Flow Energy Conversion 155
8.1 Introduction 155
8.2 Frictional Loss in Disperse Flow 155
8.2.1 Horizontal Flow 155
8.2.2 Homogeneous Flow Friction 157
8.2.3 Heterogeneous Flow Friction 159
8.2.4 Vertical Flow 161
8.3 Frictional Loss in Separated Flow 163
8.3.1 Two-Component Flow 163
8.3.2 Flow with Phase Change 168
8.4 Energy Conversion in Pumps and Turbines 172
8.4.1 Multiphase Flows in Pumps 172
9 Homogeneous Flows 176
9.1 Introduction 176
9.2 Equations of Homogeneous Flow 176
9.3 Sonic Speed 177
9.3.1 Basic Analysis 177
9.3.2 Sonic Speeds at Higher Frequencies 181
9.3.3 Sonic Speed with Change of Phase 182
9.4 Barotropic Relations 186
9.5 Nozzle Flows 187
9.5.1 One-Dimensional Analysis 187
9.5.2 Vapor/Liquid Nozzle Flow 192
9.5.3 Condensation Shocks 195
10 Flows with Bubble Dynamics 199
10.1 Introduction 199
10.2 Basic Equations 200
10.3 Acoustics of Bubbly Mixtures 200
10.3.1 Analysis 200
10.3.2 Comparison with Experiments 203
10.4 Shock Waves in Bubbly Flows 205
10.4.1 Shock-wave Analysis 205
10.4.2 Shock-wave Structure 208
10.5 Finite Bubble Clouds 210
10.5.1 Natural Modes of a Spherical Cloud of Bubbles 210
10.5.2 Response of a Spherical Bubble Cloud 214
11 Flows with Gas Dynamics 217
11.1 Introduction 217
11.2 Equations for a Dusty Gas 217
11.2.1 Basic Equations 217
11.2.2 Homogeneous Flow with Gas Dynamics 219
11.2.3 Velocity and Temperature Relaxation 220
11.3 Normal Shock Wave 221
11.4 Acoustic Damping 224
11.5 Other Linear Perturbation Analyses 227
11.5.1 Stability of Laminar Flow 227
11.5.2 Flow over a Wavy Wall 228
11.6 Small Slip Perturbation 229
12 Sprays 232
12.1 Introduction 232
12.2 Types of Spray Formation 232
12.3 Ocean Spray 233
12.4 Spray Formation 234
12.4.1 Spray Formation by Bubbling 234
12.4.2 Spray Formation by Wind Shear 235
12.4.3 Spray Formation by Initially Laminar Jets 237
12.4.4 Spray Formation by Turbulent Jets 239
12.5 Single-Droplet Mechanics 243
12.5.1 Single-Droplet Evaporation 243
12.5.2 Single-Droplet Combustion 245
12.6 Spray Combustion 249
13 Granular Flows 252
13.1 Introduction 252
13.2 Particle Interaction Models 253
13.2.1 Computer Simulations 255
13.3 Flow Regimes 255
13.3.1 Dimensional Analysis 255
13.3.2 Flow Regime Rheologies 256
13.3.3 Flow Regime Boundaries 259
13.4 Slow Granular Flow 259
13.4.1 Equations of Motion 259
13.4.2 Mohr-Coulomb Models 260
13.4.3 Hopper Flows 261
13.5 Rapid Granular Flow 263
13.5.1 Introduction 263
13.5.2 Example of Rapid Flow Equations 264
13.5.3 Boundary Conditions 267
13.5.4 Computer Simulations 267
13.6 Effect of Interstitial Fluid 268
13.6.1 Introduction 268
13.6.2 Particle Collisions 268
13.6.3 Classes of Interstitial Fluid Effects 270
14 Drift Flux Models 272
14.1 Introduction 272
14.2 Drift Flux Method 273
14.3 Examples of Drift Flux Analyses 274
14.3.1 Vertical Pipe Flow 274
14.3.2 Fluidized Bed 276
14.3.3 Pool Boiling Crisis 278
14.4 Corrections for Pipe Flows 282
15 System Instabilities 284
15.1 Introduction 284
15.2 System Structure 284
15.3 Quasistatic Stability 286
15.4 Quasistatic Instability Examples 288
15.4.1 Turbomachine Surge 288
15.4.2 Ledinegg Instability 288
15.4.3 Geyser Instability 289
15.5 Concentration Waves 290
15.6 Dynamic Multiphase Flow Instabilities 292
15.6.1 Dynamic Instabilities 292
15.6.2 Cavitation Surge in Cavitating Pumps 292
15.6.3 Chugging and Condensation Oscillations 293
15.7 Transfer Functions 297
15.7.1 Unsteady Internal Flow Methods 297
15.7.2 Transfer Functions 298
15.7.3 Uniform Homogeneous Flow 300
16 Kinematic Waves 302
16.1 Introduction 302
16.2 Two-Component Kinematic Waves 303
16.2.1 Basic Analysis 303
16.2.2 Kinematic Wave Speed at Flooding 304
16.2.3 Kinematic Waves in Steady Flows 305
16.3 Two-Component Kinematic Shocks 306
16.3.1 Kinematic Shock Relations 306
16.3.2 Kinematic Shock Stability 308
16.3.3 Compressibility and Phase-Change Effects 309
16.4 Examples of Kinematic Wave Analyses 311
16.4.1 Batch Sedimentation 311
16.4.2 Dynamics of Cavitating Pumps 313
16.5 Two-Dimensional Kinematic Waves 318
Bibliography 321
Index 341