Computational Techniques for Multiphase Flows, Second Edition, provides the latest research and theories covering the most popular multiphase flows The book begins with an overview of the state-of-the-art techniques for multiple numerical methods in handling multiphase flow, compares them, and finally highlights their strengths and weaknesses. In addition, it covers more straightforward, conventional theories and governing equations in early chapters, moving on to the more modern and complex computational models and tools later in the book. It is therefore accessible to those who may be new to the subject while also featuring topics of interest to the more experienced researcher.
Mixed or multiphase flows of solid/liquid or solid/gas are commonly found in many industrial fields, and their behavior is complex and difficult to predict in many cases. The use of computational fluid dynamics (CFD) has emerged as a powerful tool for understanding fluid mechanics in multiphase reactors, which are widely used in the chemical, petroleum, mining, food, automotive, energy, aerospace and pharmaceutical industries. This revised edition is an ideal reference for scientists, MSc students and chemical and mechanical engineers in these areas.
Author(s): Guan Heng, Yeoh Jiyuan Tu
Edition: 2
Publisher: Butterworth-Heinemann
Year: 2019
Language: English
Pages: 633
Cover......Page 1
Computational Techniques for Multiphase Flows......Page 2
Copyright......Page 3
Preface to the Second Edition......Page 4
Preface to the First Edition......Page 5
1.1 Classification and Phenomenological Discussion......Page 7
1.2 Typical Practical Problems Involving Multiphase Flows......Page 9
1.3 Computational Fluid Dynamics as a Research Tool for Multiphase Flows......Page 10
1.4 Computational Fluid Dynamics as a Design Tool for Multiphase Flows......Page 16
1.5 Impact of Mulitiphase Flow Study on Computational Fluid Dynamics......Page 19
1.6 Scope of the Book......Page 23
10. Future Trends in Handling Turbulent Multiphase Flows......Page 25
2.2 Background of Different Approaches......Page 26
2.3 Averaging Procedure for Multiphase Flow......Page 27
2.4.1 Conservation of Mass......Page 30
2.4.2 Conservation of Momentum......Page 34
2.4.3 Conservation of Energy......Page 37
2.4.4 Interfacial Transport......Page 43
2.4.5 Effective Conservation Equations......Page 45
2.5 Comments and Observations on the Governing Equations for the Two-Fluidling Approach......Page 48
2.6 Equations of Motion for Disperse Phase......Page 54
2.7.1 Reynolds-Averaged Equations......Page 55
2.7.1.1 Mixture Model......Page 57
2.7.1.2 Two-Fluid Model......Page 58
2.7.2 Reynolds-Averaged Closure......Page 59
2.7.3 Some Comments on the k-ε Model and Implications of Other Turbulence Models......Page 60
2.7.3.1 Shear Stress Transport (SST) Model......Page 61
2.7.3.2 Reynolds Stress Model......Page 64
2.7.3.3 Near-Wall Treatment......Page 68
2.7.4 Some Comments on Turbulence Modelling of the Disperse Phase......Page 71
2.8.1 Mixture Model......Page 73
2.8.2 Two-Fluid Model......Page 74
2.8.3 A Comment on Multifluid Model......Page 80
2.9 Boundary Conditions and Their Physical Intrepretation......Page 81
2.9.1 Comments on Some Wall Boundary Conditions for Multiphase Problems......Page 86
2.10 Summary......Page 88
3.1 Introduction......Page 90
3.2 Consideration for a Range of Multiphase Flow Problems......Page 92
3.2.1 Application of Structured Mesh......Page 93
3.2.2 Application of Body-Fitted Mesh......Page 95
3.2.3 Application of Unstructured Mesh......Page 100
3.2.4 Some Comments on Grid Generation......Page 102
3.3 Numerical Algorithms......Page 106
3.3.1 Basic Aspects of Discretisation - Finite Difference Method......Page 107
3.3.2 Basic Aspects of Discretisation - Finite Volume Method......Page 109
3.3.3 Basic Approximation of the Diffusion Term Based Upon the Finite Volume Method......Page 118
3.3.4 Basic Approximation of the Advection Term Based Upon the Finite Volume Method......Page 122
3.3.5 Some Comments on the Need for TVD Schemes......Page 129
3.3.6 Explicit and Implicit Approaches......Page 133
3.3.7 Assembly of Discretised Equations......Page 137
3.3.8 Comments on the Linearisation of Source Terms......Page 140
3.4 Solution Algorithms......Page 144
3.4.1.1 SIMPLE Algorithm for Mixture or Homogeneous Flows......Page 145
3.4.1.3 Evaluation of the Face Velocity in Different Mesh Systems......Page 150
3.4.1.5 Inter-Phase Slip Algorithm (IPSA) for Multiphase Flows......Page 155
3.4.1.6 Inter-phase Slip Algorithm-Coupled (IPSA-C) for Multiphase Flows......Page 159
3.4.1.7 Comments on the Need for Improved Interpolation Methods of Evaluating the Face Velocity in Multiphase Problems......Page 163
3.4.2 Matrix Solvers for the Segregated Approach in Different Mesh Systems......Page 167
3.4.3 Coupled Equation System......Page 175
3.5 Numerical and Solution Algorithms......Page 176
3.5.1 Fluid-Particle Interaction (Forces Related to Fluid Acting on Particle – One-Way, Two-Way Coupling)......Page 177
3.5.2.1 Hard-Sphere Model......Page 180
3.5.2.2 Soft-Sphere Model......Page 183
3.5.3 Basic Numerical Techniques......Page 185
3.5.4 Comments on Sampling Particles for Turbulent Dispersion......Page 187
3.5.5.1 Evaluation of Source Terms for the Continuous Phase......Page 195
3.6.1.1 Surface Marker Approaches......Page 198
3.6.1.2 Front Tracking Method......Page 201
3.6.1.3 Intersection Marker Method......Page 203
3.6.2.1 Markers in Fluid (MAC Formulation)......Page 206
3.6.2.2 Volume of Fluid (VOF)......Page 207
3.6.2.2.1 Donor-Acceptor Formulation......Page 208
3.6.2.2.2 Line Techniques (Geometric Reconstruction)......Page 215
3.6.2.3 Level Set Method......Page 222
3.6.2.4 Hybrid Methods......Page 225
3.6.3 Computing Surface Tension and Wall Adhesion......Page 226
3.7 Summary......Page 230
4.1.1.1 Gas-Particle Flows......Page 232
Liquid-Particle Flows......Page 233
4.1.2 Classification of Gas-Particle Flows......Page 234
4.1.3 Particle Loading and Stokes Number......Page 235
6.3.4 Sloshing of Liquid......Page 449
4.1.5 Some Physical Characteristics of Flow in Sedimentation Tank......Page 238
4.1.6 Some Physical Characteristics of Slurry Transport......Page 240
4.2 Multiphase Models for Gas-Particle Flows......Page 241
4.2.1 Eulerian-Lagrangian Framework......Page 242
7.4.2 Liquid Bridging......Page 246
4.2.3 Turbulence Modelling......Page 248
Gas Phase......Page 249
Particle Phase in Lagrangian Reference Frame......Page 252
Particle Phase in Eulerian Reference Frame......Page 253
4.2.4 Particle-Wall Collision Model......Page 258
Lagrangian Reference Frame......Page 259
Eulerian Reference Frame......Page 262
4.3.1 Mixture Model......Page 266
Buoyancy due to Density Difference......Page 268
Settling Velocity of Particle Phase......Page 269
Flocculation Modelling......Page 270
Rheology of the Mixture......Page 271
4.3.1.2 Modelling Source or Sink Terms for Flow in Slurry Transportation......Page 273
4.3.2 Turbulence Modelling......Page 276
4.4.1 Dilute Gas-Particle Flow over a Two-Dimensional Backward Facing Step......Page 278
4.4.2 Dilute Gas-Particle Flow in a Three-Dimensional 90° Bend......Page 288
4.4.3 Dilute Gas-Particle Flow over an Inline Tube Bank......Page 297
4.4.4 Liquid-Particle Flows in Sedimentation Tank......Page 308
4.4.5 Sand-Water Slurry Flow in a Horizontal Straight Pipe......Page 315
4.5 Summary......Page 323
5.1.1 Background......Page 325
5.1.2 Categorisation of Different Flow Regimes......Page 326
5.1.3 Some Physical Characteristics of Boiling Flow......Page 328
5.2 Multiphase Models for Gas–Liquid Flows......Page 330
5.2.1 Multif luid Model......Page 331
5.2.1.1 Inter-Phase Mass Transfer......Page 332
5.2.1.2 Inter-Phase Momentum Transfer......Page 334
5.2.1.3 Interphase Heat Transfer......Page 338
5.2.2 Turbulence Modelling......Page 339
5.3.1 Need for Population Balance in Gas-Liquid Flows......Page 342
5.3.2 Population Balance Equation (PBE)......Page 344
5.3.3 Method of Moments (MOM)......Page 345
10.4.5.2 Coupling Between Particle and Liquid Phases......Page 346
5.3.3.2 Direct Quadrature Method of Moments (DQMOM)......Page 347
5.3.4 Class Methods (CM)......Page 349
5.3.4.1 Average Quantities Approach......Page 350
5.3.4.2 Multiple Size Group Model......Page 351
5.4.1 Single Average Scalar Approach for Bubbly Flows......Page 353
5.4.1.1 Wu et al. (1998) Model......Page 354
5.4.1.2 Hibiki and Ishii (2002) Model......Page 355
5.4.2 Multiple Bubble Size Approach for Bubbly Flows......Page 356
5.4.2.1 DQMOM Model......Page 358
5.4.2.2 MUSIG Model......Page 359
5.4.3 Comments of Other Coalescence and Break-Up Kernels......Page 361
5.4.4 Modeling Beyond Bubbly Flows–A Phenomenological Consideration......Page 363
5.5.1 Review of Current Model Applications......Page 366
5.5.2 Phenomenological Description......Page 371
5.5.3 Nucleation of Bubbles at Heated Walls......Page 373
5.5.4 Condensation of Bubbles in Subcooled Liquid......Page 379
7.6 Summary......Page 381
5.6.2 Bubbly Flow in a Vertical Pipe......Page 389
5.6.2.1 Experimental Data of Liu and Bankoff (1993a,b)......Page 393
5.6.2.2 Experimental Data of Hibiki et al. (2001)......Page 395
5.6.3 Subcooled Boiling Flow in a Vertical Annulus......Page 401
5.6.3.1 Application of MUSIG Boiling Model......Page 402
5.6.3.2 Application of Improved Wall Heat Partition Model......Page 412
5.7 Summary......Page 418
6. Free Surface Flows......Page 419
8.1 Introduction......Page 513
6.2 Multiphase Models for Free Surface Flows......Page 420
6.3.1 Bubble Rising in a Viscous Liquid......Page 423
6.3.2 Single Taylor Bubble......Page 432
6.3.3 Collapse of a Liquid Column (Breaking Dam Problem)......Page 440
6.3.5 Slug Bubbles in Microchannel Flow......Page 458
6.4 Summary......Page 466
7. Granular Flows......Page 467
B......Page 622
9.2 Description of Problem in the Context of Computational Fluid Dynamics......Page 548
7.3 Particle-Particle Interaction Without Adhesion......Page 469
7.3.1 Normal Force Due to Continuous Potential......Page 470
7.3.2 Normal Force Due to Linear Viscoelastic......Page 472
7.3.3 Normal Force Due to Nonlinear Viscoelastic......Page 473
7.3.4 Normal Force Due to Hysteretic......Page 474
7.3.5 Tangential Force......Page 476
7.3.6 Sliding, Twisting and Rolling Resistance......Page 478
10.4 On Modelling Gas-Liquid-Solid Fluidisation......Page 585
7.4.1 DVLO, JKR and DMT Theories......Page 481
7.4.3 Interfacial Attractive......Page 484
7.4.4 Other Types of Field-Particle Interaction......Page 486
7.5.1 Abrasive Jet Particles......Page 489
7.5.2 Magnetic Nanoparticles in Fluids......Page 501
7.5.3 Fluidised Bed......Page 506
8.2.1 Governing Equations......Page 514
8.2.2 Solid-Liquid Interface......Page 517
C......Page 519
8.3.2 Surface Grid Generation......Page 520
8.3.3 Optimizing Computational Meshes......Page 523
8.3.3.1 Objective Function......Page 524
8.3.3.2 Optimisation Algorithm......Page 525
8.3.4 Transformation of Governing Equations and Boundary Conditions......Page 526
8.4.1 Freezing of Water on a Vertical Wall in an Enclosed Cubical Cavity......Page 531
8.4.2 Freezing of Water in an Open Cubical Cavity......Page 538
9.5 Summary......Page 568
9.1 Introduction......Page 547
9.3.1 Three-Fluid Model......Page 550
10.3.1 Model Description......Page 576
9.4.1 Three-phase Modelling of the Air-Lift Pump......Page 557
9.4.2 Modelling of Three-Phase Mechanically Agitated Reactor......Page 563
10.1 Introduction......Page 570
10.2.1 Model Description......Page 572
10.3.1.1 Basic Subgrid-Scale Model......Page 580
10.3.1.2 Dynamics Subgrid-Scale Model......Page 581
10.4.1 Governing Equations......Page 586
10.4.3 Discrete Particle Model......Page 587
10.4.5.1 Coupling Between Gas and Liquid Phases......Page 591
10.4.6 Simulation Results......Page 593
10.5 Some Concluding Remarks......Page 599
References......Page 600
Further Reading......Page 620
E......Page 623
F......Page 624
G......Page 625
I......Page 626
M......Page 627
P......Page 628
S......Page 629
T......Page 630
W......Page 632
Back Cover......Page 633
