Computational Techniques for Multiphase Flows. Basics and Applications

Copyright......Page 2
Preface......Page 3
Classification and phenomenological discussion......Page 6
Typical Practical Problems Involving Multi-Phase Flows......Page 8
Computational fluid dynamics as a research tool for multi-phase flows......Page 10
Computational fluid dynamics as a design tool for multi-phase flows......Page 16
Impact of multi-phase flow study on computational fluid dynamics......Page 21
Scope of the book......Page 24
Background Of Different Approaches......Page 26
Averaging Procedure For Multi-Phase Flow......Page 27
Conservation of Mass......Page 31
Conservation of Momentum......Page 35
Conservation of Energy......Page 39
Interfacial Transport......Page 45
Effective Conservation Equations......Page 47
Comments And Observations On The Governing Equations For The Two-Fluid modelling Approach......Page 51
Equations Of Motion For Disperse Phase......Page 58
Reynolds-Averaged Equations......Page 61
Reynolds-Averaged Closure......Page 65
Some Comments on the k–ε Model and Implications of Other Turbulence Models......Page 67
Shear Stress Transport (SST) Model......Page 68
Reynolds Stress Model......Page 71
Near-Wall Treatment......Page 76
Some Comments on Turbulence Modelling of the Disperse Phase......Page 80
Differential And Integral Form Of The Transport Equations......Page 81
A Comment on Multi-Fluid Model......Page 89
Boundary Conditions And Their Physical interpretation......Page 90
Comments on Some Wall Boundary Conditions for Multi-Phase Problems......Page 97
Summary......Page 99
Introduction......Page 100
Mesh Systems: Consideration for a Range of Multi-Phase Flow Problems......Page 103
Eulerian–Eulerian Framework: Numerical Algorithms......Page 118
Solution Algorithms......Page 160
Eulerian–Lagrangian Framework: Numerical and Solution Algorithms......Page 197
Interface-Tracking/Capturing Algorithms: Basic Considerations of Interface-tracking/ Capturing Methods......Page 213
Summary......Page 246
Introduction......Page 248
Multi-phase Models for Gas–Particle Flows......Page 254
Worked Examples......Page 283
Summary......Page 315
Background......Page 317
Some Physical Characteristics of Flow in Sedimentation Tank......Page 318
Some Physical Characteristics of Slurry Transport......Page 321
Multi-Phase Models for Liquid–Particle Flows......Page 322
Mixture Model......Page 323
Modelling Source or Sink Terms for Flow in Sedimentation Tank......Page 325
Modelling Source or Sink Terms for Flow in Slurry Transportation......Page 330
Turbulence Modelling......Page 333
Numerical Features......Page 336
Numerical Results......Page 338
Conclusion......Page 343
Sand–Water Slurry Flow in a Horizontal Straight Pipe......Page 344
Numerical Features......Page 345
Numerical Results......Page 348
Conclusion......Page 351
Summary......Page 353
Background......Page 354
Categorization of Different Flow Regimes......Page 356
Some Physical Characteristics of Boiling Flow......Page 358
Multi-phase models for gas–liquid flows......Page 360
Multi-Fluid Model......Page 361
Inter-Phase Mass Transfer......Page 363
Inter-Phase Momentum Transfer......Page 364
Inter-Phase Heat Transfer......Page 369
Turbulence Modelling......Page 370
Need for Population Balance in Gas–Liquid Flows......Page 373
Population Balance Equation (PBE)......Page 376
Method of Moments (MOM)......Page 377
Quadrature Method of Moments (QMOM)......Page 378
Direct Quadrature Method of Moments (DQMOM)......Page 379
Class Methods (CM)......Page 382
Average Quantities Approach......Page 383
Multiple Size Group Model......Page 384
Single Average Scalar Approach for Bubbly Flows......Page 386
Wu et al. (1998) Model......Page 387
Hibiki and Ishii (2002) Model......Page 388
Yao and Morel (2004) Model......Page 389
Multiple Bubble Size Approach for Bubbly Flows......Page 390
DQMOM Model......Page 392
MUSIG Model......Page 393
Comments of Other Coalescence and Break-Up Kernels......Page 395
Modelling Beyond Bubbly Flows – A Phenomenological Consideration......Page 397
Review of Current Model Applications......Page 401
Phenomenological Description......Page 406
Nucleation of Bubbles at Heated Walls......Page 409
Condensation of Bubbles in Sub-Cooled Liquid......Page 416
Dispersed Bubbly Flow in a Rectangular Column......Page 417
Numerical Features......Page 418
Numerical Results......Page 422
Bubbly Flow in a Vertical Pipe......Page 426
Numerical Features......Page 427
Numerical Results......Page 430
Conclusion......Page 438
Sub-Cooled Boiling Flow in a Vertical Annulus......Page 439
Application of MUSIG Boiling Model......Page 440
Application of Improved Wall Heat Partition Model......Page 451
Summary......Page 458
Introduction......Page 460
Multi-Phase Models for Free Surface Flows......Page 461
Bubble Rising in a Viscous Liquid......Page 465
Numerical Features......Page 466
Numerical Results......Page 469
Conclusion......Page 474
Single Taylor Bubble......Page 475
Numerical Features......Page 478
Numerical Results......Page 481
Collapse of a Liquid Column (Breaking Dam Problem)......Page 484
Numerical Features......Page 488
Numerical Results......Page 489
Conclusion......Page 493
Sloshing of Liquid......Page 494
Numerical Features......Page 496
Numerical Results......Page 497
Similar Comparison for the Roll Motion Cases......Page 500
Summary......Page 502
Introduction......Page 504
Governing Equations......Page 505
Solid–Liquid Interface......Page 509
Other Boundary Conditions......Page 511
Surface Grid Generation......Page 512
Objective Function......Page 516
Optimization Algorithm......Page 518
Transformation of Governing Equations and Boundary Conditions......Page 520
Numerical Features......Page 525
Numerical Results......Page 527
Conclusion......Page 530
Freezing of Water in an Open Cubical Cavity......Page 533
Numerical Features......Page 534
Numerical Results......Page 536
Summary......Page 541
Introduction......Page 543
Description of problem in the context of computational fluid dynamics......Page 544
Three-Fluid Model......Page 546
Turbulence Modelling......Page 553
Evaluation of multi-phase models for gas–liquid–solid flows......Page 554
Three-Phase Modelling of the Air-Lift Pump......Page 555
Numerical Features......Page 556
Numerical Results......Page 557
Modelling of Three-Phase Mechanically Agitated Reactor......Page 561
Numerical Features......Page 562
Numerical Results......Page 564
Summary......Page 567
Introduction......Page 569
Model Description......Page 572
Model Description......Page 576
Basic SGS Model......Page 580
Dynamics SGS Model......Page 581
On Modelling Gas–Liquid–Solid Fluidization......Page 585
Governing Equations......Page 586
Interface Tracking/Capturing Methods: with Comments......Page 587
Discrete Particle Model......Page 588
Particle–Particle Collision......Page 592
Inter-Phase Couplings......Page 595
Simulation Results......Page 597
Some Concluding Remarks......Page 603
Full Derivation of Conservation Equations......Page 604
References......Page 608
B......Page 628
C......Page 630
D......Page 631
E......Page 632
F......Page 633
G......Page 634
I......Page 636
M......Page 637
N......Page 638
P......Page 639
S......Page 640
T......Page 642
V......Page 643
Y......Page 644