Multiphase Flow Dynamics 2: Thermal and Mechanical Interactions , 2nd Edition

Table of Contents......Page 10
1.1 Introduction......Page 20
1.2 Pool flow......Page 22
1.3.1 Channel flow – vertical pipes......Page 25
1.3.2 Channel flow – inclined pipes......Page 29
1.4 Heated channels......Page 37
1.5 Porous media......Page 38
1.6 Particles in film boiling......Page 39
1.7 Rod bundles......Page 40
Nomenclature......Page 42
References......Page 44
2.1 Introduction......Page 46
2.2 Drag coefficient for single bubble......Page 47
2.3 Family of particles in continuum......Page 51
2.4 Droplets-gas......Page 55
2.5.1 Solid particles: free particles regime......Page 57
2.5.2 Solid particles in bubbly flow......Page 59
2.5.3 Solid particles: dense packed regime......Page 63
2.6 Annular flow......Page 68
2.7 Inverted annular flow......Page 74
2.8 Stratified flow in horizontal or inclined rectangular channels......Page 75
2.9 Stratified flow in horizontal or inclined pipes......Page 79
Nomenclature......Page 84
References......Page 87
3.2 Single-phase flow......Page 90
3.3 Two-phase flow......Page 93
3.4 Three-dimensional flow in a porous structure......Page 98
3.5 Heated channels......Page 99
3.6 Three-phase flow......Page 101
Nomenclature......Page 103
References......Page 105
4.1 Introduction......Page 107
4.2.1 Wall force not taken into account......Page 108
4.2.2 Wall forces taken into account......Page 112
4.3.1 Single bubble terminal velocity......Page 113
4.3.2 Single particle terminal velocity......Page 117
4.3.3 Cross section averaged bubble rise velocity in pipes – drift flux models......Page 118
4.3.4 Cross section averaged particle sink velocity in pipes – drift flux models......Page 137
4.4 Slip models......Page 140
4.5 Three velocity fields – annular dispersed flow......Page 142
4.6 Three-phase flow......Page 143
Nomenclature......Page 146
References......Page 148
5.1 Introduction......Page 151
5.2 Some basics......Page 152
5.3 Correlations......Page 153
5.4 Entrainment increase in boiling channels......Page 161
5.5 Size of the entrained droplets......Page 162
Nomenclature......Page 164
References......Page 167
6.2 Analogy between heat and mass transfer......Page 170
6.3 Fluctuation mechanism in the boundary layer......Page 172
6.4 Zaichik's theory......Page 173
6.5 Deposition correlations......Page 174
Nomenclature......Page 178
References......Page 181
7.1 Introduction......Page 183
7.2 General remarks about fragmentation......Page 186
7.3.1 Converging disperse field......Page 187
7.3.2 Analogy to the molecular kinetic theory......Page 188
7.4 Superposition of different droplet coalescence mechanisms......Page 194
7.5 Superposition of different bubble coalescence mechanisms......Page 195
7.6 General remarks about particle size formation in pipes......Page 196
Nomenclature......Page 200
References......Page 202
8.1 Critical Weber number......Page 204
8.2 Fragmentation modes......Page 215
8.3 Relative velocity after fragmentation......Page 218
8.4 Breakup time......Page 222
8.5.2 Bag breakup......Page 229
8.5.4 Sheet stripping and wave crest stripping following by catastrophic breakup......Page 231
8.6 Droplets production due to highly energetic collisions......Page 239
8.7 Acceleration induced bubble fragmentation......Page 241
Nomenclature......Page 245
References......Page 247
9.1 Homogeneous turbulence characteristics......Page 251
9.2 Reaction of a particle to the acceleration of the surrounding continuum......Page 255
9.3 Reaction of particle entrained inside the turbulent vortex – inertial range......Page 257
9.4 Stability criterion for bubbles in continuum......Page 258
9.5 Turbulence energy dissipation due to the wall friction......Page 262
9.6 Turbulence energy dissipation due to the relative motion......Page 264
9.7 Bubble coalescence probability......Page 266
9.8 Coalescence probability of small droplets......Page 271
Nomenclature......Page 272
References......Page 274
10.1 Liquid jet disintegration in pools......Page 276
10.2 Boundary of different fragmentation mechanisms......Page 279
10.3 Size of the ligaments......Page 281
10.4.1 No ambient influence......Page 282
10.4.2 Ambient influence......Page 283
10.4.3 Jets producing film boiling in the ambient liquid......Page 286
10.4.4 An alternative approach......Page 288
10.4.5 Jets penetrating two-phase mixtures......Page 289
10.5. Jet erosion by high velocity gas environment......Page 290
10.6. Jet fragmentation in pipes......Page 292
10.7. Gas jet disintegration in pools......Page 293
Nomenclature......Page 296
References......Page 299
11.1 Introduction......Page 301
11.2 Vapor thickness in film boiling......Page 303
11.3 Amount of melt surrounded by continuous water......Page 305
11.4 Thermo-mechanical fragmentation of liquid metal in water......Page 306
11.4.1 External triggers......Page 307
11.4.2 Experimental observations......Page 312
11.4.3 The mechanism of the thermal fragmentation......Page 318
11.5 Particle production rate during the thermal fragmentation......Page 334
11.6 Tang's thermal fragmentation model......Page 336
11.8 Oxidation......Page 339
11.9.1 Inert gases......Page 340
11.9.3 Surfactants......Page 341
11.9.4 Melt viscosity......Page 342
Nomenclature......Page 343
References......Page 346
12.1 Introduction......Page 352
12.2 Nucleation energy, equation of Kelvin and Laplace......Page 353
12.3 Nucleus capable to grow......Page 355
12.4 Some useful forms of the Clausius-Clapeyron equation, measures of superheating......Page 356
12.5.1 Homogeneous nucleation......Page 359
12.5.2 Heterogeneous nucleation......Page 361
12.6 Maximum superheat......Page 367
12.8 Nucleation in the presence of non-condensable gases......Page 371
12.9 Activated nucleation site density – state of the art......Page 373
12.10 Conclusions and recommendations......Page 379
Nomenclature......Page 380
References......Page 382
13.1 Introduction......Page 385
13.2 The thermally controlled bubble growth......Page 386
13.3 The Mikic solution......Page 389
13.4.1 Non-averaged mass source terms......Page 392
13.4.2 The averaged mass source terms......Page 394
13.5. Superheated steam......Page 395
13.6 Diffusion controlled evaporation into mixture of gases inside the bubble......Page 396
Nomenclature......Page 397
References......Page 400
Appendix 13.1 Radius of a single bubble in a superheated liquid as a function of time......Page 402
14.2 Stagnant bubble......Page 408
14.3 Moving bubble......Page 410
14.4 Non-averaged source terms......Page 415
14.5 Averaged source terms......Page 416
14.6 Change of the bubble number density due to condensation......Page 418
14.7 Pure steam bubble drifting in turbulent continuous liquid......Page 419
14.8.1 Thermally controlled collapse......Page 422
14.8.2 Diffusion controlled collapse......Page 423
Nomenclature......Page 424
References......Page 428
15.1 How accurately can we predict bubble departure diameter for boiling?......Page 430
15.2 Model development......Page 432
15.3 Comparison with experimental data......Page 438
15.4 Significance......Page 441
15.5 Summary and conclusions......Page 442
Nomenclature......Page 443
References......Page 444
16.1 Introduction......Page 447
16.2.1 Basic assumptions......Page 452
16.2.2 Proposed model......Page 454
16.3 Data comparison......Page 456
16.4 Systematic inspection of all the used hypotheses......Page 460
16.6 Conclusions......Page 461
Nomenclature......Page 462
References......Page 464
Appendix 16.1 State of the art of nucleate pool boiling modeling......Page 467
Appendix 16.2 Some empirical correlations for nucleate boiling......Page 473
17.1 Introduction......Page 475
17.2 Bubbles generated due to nucleation at the wall......Page 476
17.3 Bubble growth in the bulk......Page 477
17.4 Bubble fragmentation and coalescence......Page 478
17.5 Film flashing bubble generation in adiabatic pipe flow......Page 479
17.6 Verification of the model......Page 481
17.9 Significance and conclusions......Page 491
Nomenclature......Page 492
References......Page 494
18.2 Initiation of visible boiling on the heated surface......Page 496
18.3.1 Relaxation theory......Page 497
18.3.2 Boundary layer treatment......Page 500
Nomenclature......Page 502
References......Page 504
19.1 Minimum film boiling temperature......Page 505
19.2 Film boiling in horizontal upwards-oriented plates......Page 506
Nomenclature......Page 508
References......Page 510
20.1 Convective boiling of saturated liquid......Page 511
20.2.1 Tubes......Page 513
20.2.2 Annular channel......Page 516
20.2.4 Vertical flow around rod bundles......Page 517
20.3 Transition boiling......Page 518
20.4 Critical heat flux......Page 519
20.4.1 The hydrodynamic stability theory of free convection DNB......Page 520
20.4.2 Forced convection DNB and DO correlations......Page 523
Nomenclature......Page 527
References......Page 529
21.1.1 Introduction......Page 532
21.1.2 State of the art......Page 533
21.1.3 Problem definition......Page 534
21.1.4 Simplifying assumptions......Page 535
21.1.5 Energy balance at the vapor-liquid interface, vapor film thickness, average heat transfer coefficient......Page 538
21.1.6 Energy balance of the liquid boundary layer, layer thickness ratio......Page 542
21.1.7 Averaged heat fluxes......Page 545
21.1.8 Effect of the interfacial disturbances......Page 547
21.1.9 Comparison of the theory with the results of other authors......Page 548
21.1.10 Verification using the experimental data......Page 550
21.1.12 Practical significance......Page 551
21.2.3 Solution method......Page 552
21.2.4 Model......Page 553
21.2.5 Data comparison......Page 562
Nomenclature......Page 566
References......Page 569
Appendix 22.2 Predominant forced convection only at vertical plate......Page 572
22.1 Spontaneous condensation of pure subcooled steam – nucleation......Page 574
22.1.1 Critical nucleation size......Page 575
22.1.2 Nucleation kinetics, homogeneous nucleation......Page 578
22.1.3 Droplet growth......Page 580
22.1.4 Self-condensation stop......Page 582
22.2 Heat transfer across droplet interface without mass transfer......Page 583
22.3 Direct contact condensation of pure steam on subcooled droplet......Page 590
22.4 Spontaneous flashing of superheated droplet......Page 592
22.5 Evaporation of saturated droplets in superheated gas......Page 596
22.6 Droplet evaporation in gas mixture......Page 599
Nomenclature......Page 605
References......Page 606
23.1 Geometrical film-gas characteristics......Page 609
23.2 Convective heat transfer......Page 611
23.2.1 Gas side heat transfer......Page 612
23.2.2 Liquid side heat transfer due to conduction......Page 615
23.2.3 Liquid side heat conduction due to turbulence......Page 617
23.3 Spontaneous flashing of superheated film......Page 625
23.4 Evaporation of saturated film in superheated gas......Page 626
23.5 Condensation of pure steam on subcooled film......Page 627
23.6 Evaporation or condensation in presence of non-condensable gases......Page 628
Nomenclature......Page 630
References......Page 633
24.1.1 Onset of the condensation......Page 635
24.1.2 Condensation from stagnant steam (Nusselt 1916) at laminar liquid film......Page 636
24.1.3 Condensation from stagnant steam at turbulent liquid film (Grigul 1942)......Page 637
24.2.1 Down flow of vapor across horizontal tubes......Page 638
24.2.3 Boyko and Krujilin approach......Page 639
24.3 Steam condensation from mixture containing non-condensing gases......Page 640
24.3.1 Computation of the mass transfer coefficient......Page 642
Nomenclature......Page 644
References......Page 646
25.1.1 Dimensions of the problem......Page 648
25.1.3 The radiation transport equation (RTE)......Page 649
25.2 Discrete ordinate method......Page 650
25.2.1 Discretization of the computational domain for the description of the flow......Page 652
25.2.2 Finite volume representation of the radiation transport equation......Page 653
25.2.3 Boundary conditions......Page 659
25.3.1 Source terms – emission from hot surfaces with known temperature......Page 661
25.3.2 Spectral absorption coefficient of water......Page 662
25.4 Averaged properties for some particular cases occurring in melt-water interaction......Page 666
25.4.1 Spherical cavity of gas inside a molten material......Page 667
25.4.2 Concentric spheres of water droplets, surrounded by vapor, surrounded by molten material......Page 668
25.4.3 Clouds of spherical particles of radiating material surrounded by a layer of vapor surrounded by water –Lanzenberger's solution......Page 672
25.4.4 Chain of infinite number of Wigner cells......Page 688
25.4.5 Application of Lanzenbergers's solution......Page 689
Nomenclature......Page 690
References......Page 692
B......Page 693
D......Page 694
F......Page 695
I......Page 696
N......Page 697
R......Page 698
S......Page 699
W......Page 700
Z......Page 701