Thermo-Fluid Dynamics of Two-Phase Flow (eBook)

Dedication 5
Table of Contents 6
Preface 12
Foreword 14
Acknowledgments 16
Chapter 1 INTRODUCTION 17
1.1 Relevance of the problem 17
1.2 Characteristic of multiphase flow 19
1.3 Classification of two-phase flow 21
1.4 Outline of the book 26
Chapter 2 LOCAL INSTANT FORMULATION 27
1.1 Single-phase flow conservation equations 29
1.1.1 General balance equations 29
1.1.2 Conservation equation 31
1.1.3 Entropy inequality and principle of constitutive law 34
1.1.4 Constitutive equation 36
1.2 Interfacial balance and boundary condition 40
1.2.1 Interfacial balance (Jump condition) 40
1.2.2 Boundary conditions at interface 48
1.2.3 Simplified boundary condition 54
1.2.4 External boundary condition and contact angle 59
1.3 Application of local instant formulation to two-phase flow problems 62
1.3.1 Drag force acting on a spherical particle in a very slow stream 62
1.3.2 Kelvin-Helmholtz instability 64
1.3.3 Rayleigh-Taylor instability 68
Chapter 3 VARIOUS METHODS OF AVERAGING 70
1.1 Purpose of averaging 70
1.2 Classification of averaging 73
1.3 Various Averaging in Connection with Two-Phase Flow Analysis 76
Chapter 4 BASIC RELATIONS IN TIME AVERAGING 82
1.1 Time domain and definition of functions 83
1.2 Local time fraction - Local void fraction 87
1.3 Time average and weighted mean values 88
1.4 Time average of derivatives 93
1.5 Concentrations and mixture properties 97
1.6 Velocity field 101
1.7 Fundamental identity 104
Chapter 5 TIME AVERAGED BALANCE EQUATION 108
1.1 General balance equation 108
1.2 Two-fluid model field equations 113
1.3 Diffusion (mixture) model field equations 118
1.4 Singular case of vni=0 (quasi-stationary interface) 123
1.5 Macroscopic jump conditions 125
1.6 Summary of macroscopic field equations and jump conditions 128
1.7 Alternative form of turbulent heat flux 129
Chapter 6 CONNECTION TO OTHER STATISTICAL AVERAGES 133
1.1 Eulerian statistical average (ensemble average) 133
1.2 Boltzmann statistical average 134
Chapter 7 KINEMATICS OF AVERAGED FIELDS 143
1.1 Convective coordinates and convective derivatives 143
1.2 Streamline 146
1.3 Conservation of mass 147
1.4 Dilatation 154
Chapter 8 INTERFACIAL TRANSPORT 156
1.1 Interfacial mass transfer 156
1.2 Interfacial momentum transfer 158
1.3 Interfacial energy transfer 162
Chapter 9 TWO-FLUID MODEL 168
1.1 Two-fluid model field equations 169
1.2 Two-fluid model constitutive laws 182
1.2.1 Entropy inequality 182
1.2.2 Equation of state 185
1.2.3 Determinism 190
1.2.4 Average molecular diffusion fluxes 192
1.2.5 Turbulent fluxes 194
1.2.6 Interfacial transfer constitutive laws 199
1.3 Two-fluid model formulation 211
1.4 Various special cases 218
Chapter 10 INTERFACIAL AREA TRANSPORT 230
1.1 Three-dimensional interfacial area transport equation 231
1.1.1 Number transport equation 232
1.1.2 Volume transport equation 233
1.1.3 Interfacial area transport equation 235
1.2 One-group interfacial area transport equation 240
1.3 Two-group interfacial area transport equation 241
1.3.1 Two-group particle number transport equation 242
1.3.2 Two-group void fraction transport equation 243
1.3.3 Two-group interfacial area transport equation 247
1.3.4 Constitutive relations 253
Chapter 11 CONSTITUTIVE MODELING OF INTERFACIAL AREA TRANSPORT 256
1.1 Modified two-fluid model for the two-group interfacial area transport equation 258
1.1.1 Conventional two-fluid model 258
1.1.2 Two-group void fraction and interfacial area transport equations 259
1.1.3 Modified two-fluid model 261
1.1.4 Modeling of two gas velocity fields 266
1.2 Modeling of source and sink terms in one-group interfacial area transport equation 270
1.2.1 Source and sink terms modeled by Wu et al. (1998) 272
1.2.2 Source and sink terms modeled by Hibiki and Ishii (2000a) 280
1.2.3 Source and sink terms modeled by Hibiki et al. (2001b) 288
1.3 Modeling of source and sink terms in two-group interfacial area transport equation 289
1.3.1 Source and sink terms modeled by Hibiki and Ishii (2000b) 290
1.3.2 Source and sink terms modeled by Fu and Ishii (2002a) 294
1.3.3 Source and sink terms modeled by Sun et al. (2004a) 303
1.4 Modeling of phase change terms in interfacial area transport equation 312
1.4.1 Active nucleation site density modeled by Kocamustafaogullari and Ishii (1983) and Hibiki and Ishii (2003b) 313
1.4.2 Bubble departure size modeled by Situ et al. (2008) 318
1.4.3 Bubble departure frequency modeled by Euh et al. (2010) 320
1.4.4 Sink term due to condensation modeled by Park et al. (2007) 320
Chapter 12 HYDRODYNAMIC CONSTITUTIVE RELATIONSFOR INTERFACIAL TRANSFER 327
1.1 Transient forces in multiparticle system 329
1.2 Drag force in multiparticle system 335
1.2.1 Single-particle drag coefficient 336
1.2.2 Drag coefficient for dispersed two-phase flow 342
1.3 Other forces 358
1.3.1 Lift force 358
1.3.2 Wall-lift (wall-lubrication) force 363
1.3.3 Turbulent dispersion force 364
1.4 Turbulence in multiparticle system 366
Chapter 13 DRIFT-FLUX MODEL 373
1.1 Drift-flux model field equations 374
1.2 Drift-flux (or mixture) model constitutive laws 383
1.3 Drift-flux (or mixture) model formulation 400
1.3.1 Drift-flux model 400
1.3.2 Scaling parameters 401
1.3.3 Homogeneous flow model 405
1.3.4 Density propagation model 406
Chapter 14 ONE-DIMENSIONAL DRIFT-FLUX MODEL 408
1.1 Area average of three-dimensional drift-flux model 409
1.2 One-dimensional drift velocity 414
1.2.1 Dispersed two-phase flow 414
1.2.2 Annular two-phase flow 425
1.2.3 Annular mist flow 430
1.3 Covariance of convective flux 433
1.4 One-dimensional drift-flux correlations for various flow conditions 438
1.4.1 Constitutive equations for upward bubbly flow 439
1.4.2 Constitutive equations for upward adiabatic annulus and internally heated annulus 439
1.4.3 Constitutive equations for downward two-phase flow 440
1.4.4 Constitutive equations for bubbling or boiling pool systems 440
1.4.5 Constitutive equations for large diameter pipe systems 441
1.4.6 Constitutive equations at reduced gravity conditions 442
1.4.7 Constitutive equations for rod bundle geometry 445
1.4.8 Constitutive equations for pool rod bundle geometry 447
Chapter 15 ONE-DIMENSIONAL TWO-FLUID MODEL 448
1.1 Area average of three-dimensional two-fluid model 449
1.2 Special consideration for one-dimensional constitutive relations 452
1.2.1 Covariance effect in field equations 452
1.2.2 Effect of phase distribution on constitutive relations 455
1.2.3 Interfacial shear term 457
Chapter 16 TWO-FLUID MODEL CONSIDERING STRUCTURAL MATERIALS IN A CONTROL VOLUME 460
1.1 Time-averaged two-fluid model 462
1.2 Local volume averaging operations 464
1.2.1 Definitions of parameters and averaged quantities 464
1.2.2 Some important theorems 466
1.3 Time-volume averaged two-fluid model formulation 467
1.3.1 Formulation with volume porosity only 467
1.3.2 Formulation with volume and surface porosities 472
1.4 Special consideration for time-volume averaged constitutive relations 477
1.4.1 Covariance effect in field equations 477
1.4.2 Effects of phase distribution on constitutive relations 478
1.4.3 Interfacial shear term 481
1.4.4 Relationship between surface and volume averaged quantities 482
1.5 Appendix 483
Chapter 17 ONE-DIMENSIONAL INTERFACIAL AREA TRANSPORT EQUATION IN SUBCOOLED BOILING FLOW 485
1.1 Formulation of interfacial area transport equation in subcooled boiling flow 486
1.2 Development of bubble layer thickness model 489
References 492
Nomenclature 504
Index 522