*Understandable guide to a complex subject
*Important in many industries
*Ideal for potential users of CFD
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 the understanding of fluid mechanics in multiphase reactors, which are widely used in the chemical, petroleum, mining, food, beverage and pharmaceutical industries. Computational Techniques for Multiphase Flows enables scientists and engineers to the undertand the basis and application of CFD in muliphase flow, explains how to use the technique, when to use it and how to interpret the results and apply them to improving aplications in process enginering and other multiphase application areas including the pumping, automotive and energy sectors. Understandable guide to a complex subject Important in many industries Ideal for potential users of CFD
Front Cover 1
Computational Techniques For Multi-Phase Flows 4
Copyright Page 5
Contents 6
Preface 12
Chapter 1. Introduction 16
1.1 CLASSIFICATION AND PHENOMENOLOGICAL DISCUSSION 16
1.2 TYPICAL PRACTICAL PROBLEMS INVOLVING MULTI-PHASE FLOWS 18
1.3 COMPUTATIONAL FLUID DYNAMICS AS A RESEARCH TOOL FOR MULTI-PHASE FLOWS 20
1.4 COMPUTATIONAL FLUID DYNAMICS AS A DESIGN TOOL FOR MULTI-PHASE FLOWS 26
1.5 IMPACT OF MULTI-PHASE FLOW STUDY ON COMPUTATIONAL FLUID DYNAMICS 31
1.6 SCOPE OF THE BOOK 34
Chapter 2. Governing Equations and Boundary Conditions 36
2.1 BACKGROUND OF DIFFERENT APPROACHES 36
2.2 AVERAGING PROCEDURE FOR MULTI-PHASE FLOW 37
2.3 EQUATIONS OF MOTION FOR CONTINUOUS PHASE 41
2.3.1 Conservation of Mass 41
2.3.2 Conservation of Momentum 45
2.3.3 Conservation of Energy 49
2.3.4 Interfacial Transport 55
2.3.5 Effective Conservation Equations 57
2.4 COMMENTS AND OBSERVATIONS ON THE GOVERNING EQUATIONS FOR THE TWO-FLUID MODELLING APPROACH 61
2.5 EQUATIONS OF MOTION FOR DISPERSE PHASE 68
2.6 TURBULENCE IN TRANSPORT PHENOMENA 71
2.6.1 Reynolds-Averaged Equations 71
2.6.2 Reynolds-Averaged Closure 75
2.6.3 Some Comments on the k–& #949
2.6.3.1 Shear Stress Transport (SST) Model 78
2.6.3.2 Reynolds Stress Model 81
2.6.3.3 Near-Wall Treatment 86
2.6.4 Some Comments on Turbulence Modelling of the Disperse Phase 90
2.7 DIFFERENTIAL AND INTEGRAL FORM OF THE TRANSPORT EQUATIONS 91
2.7.1 A Comment on Multi-Fluid Model 99
2.8 BOUNDARY CONDITIONS AND THEIR PHYSICAL INTERPRETATION 100
2.8.1 Comments on Some Wall Boundary Conditions for Multi-Phase Problems 107
2.9 SUMMARY 109
Chapter 3. Solution Methods for Multi-Phase Flows 110
3.1 INTRODUCTION 110
3.2 MESH SYSTEMS: CONSIDERATION FOR A RANGE OF MULTI-PHASE FLOW PROBLEMS 113
3.2.1 Application of Structured Mesh 114
3.2.2 Application of Body-Fitted Mesh 115
3.2.3 Application of Unstructured Mesh 121
3.2.4 Some Comments on Grid Generation 124
3.3 EULERIAN–EULERIAN FRAMEWORK: NUMERICAL ALGORITHMS 128
3.3.1 Basic Aspects of Discretization – Finite Difference Method 129
3.3.2 Basic Aspects of Discretization – Finite-Volume Method 132
3.3.3 Basic Approximation of the Diffusion Term Based upon the Finite-Volume Method 141
3.3.4 Basic Approximation of the Advection Term Based upon the Finite-Volume Method 147
3.3.5 Some Comments on the Need for TVD Schemes 154
3.3.6 Explicit and Implicit Approaches 157
3.3.7 Assembly of Discretized Equations 162
3.3.8 Comments on the Linearization of Source Terms 165
3.4 SOLUTION ALGORITHMS 170
3.4.1 The Philosophy Behind the Pressure-Correction Techniques for Multi-Phase Problems 171
3.4.1.1 SIMPLE Algorithm for Mixture or Homogeneous Flows 171
3.4.1.2 A Comment on Other Pressure-Correction Methods 176
3.4.1.3 Evaluation of the Face Velocity in Different Mesh Systems 177
3.4.1.4 Iterative Procedure Based on the SIMPLE Algorithm 182
3.4.1.5 IPSA for Multi-Phase Flows 183
3.4.1.6 IPSA-C for Multi-Phase Flows 187
3.4.1.7 Comments on the Need for Improved Interpolation Methods of Evaluating the Face Velocity in Multi-Phase Problems 191
3.4.2 Matrix Solvers for the Segregated Approach in Different Mesh Systems 195
3.4.3 Coupled Equation System 205
3.5 EULERIAN–LAGRANGIAN FRAMEWORK: NUMERICAL AND SOLUTION ALGORITHMS 207
3.5.1 Basic Numerical Techniques 208
3.5.2 Comments on Sampling Particulates for Turbulent Dispersion 211
3.5.3 Some Comments on Attaining Proper Statistical Realizations 219
3.5.4 Evaluation of Source Terms for the Continuous Phase 220
3.6 INTERFACE-TRACKING/CAPTURING ALGORITHMS: BASIC CONSIDERATIONS OF INTERFACE-TRACKING/CAPTURING METHODS 223
3.6.1 Algorithms Based on Surface Methods: with Comments 225
3.6.1.1 Markers on Interface (Surface Marker Techniques) 225
3.6.1.2 Surface-Fitted Method 228
3.6.2 Algorithms Based on Volume Methods: with Comments 229
3.6.2.1 Markers in Fluid (MAC Formulation) 229
3.6.2.2 Volume of Fluid (VOF) 230
3.6.2.3 Level Set Method 247
3.6.2.4 Hybrid Methods 251
3.6.3 Computing Surface Tension and Wall Adhesion 252
3.7 SUMMARY 256
Chapter 4. Gas–Particle Flows 258
4.1 INTRODUCTION 258
4.1.1 Background 258
4.1.2 Classification of Gas–Particle Flows 259
4.1.3 Particle Loading and Stokes Number 260
4.1.4 Particle Dispersion Due to Turbulence 262
4.2 MULTI-PHASE MODELS FOR GAS–PARTICLE FLOWS 264
4.2.1 Eulerian–Lagrangian Framework 264
4.2.2 Eulerian–Eulerian Framework 270
4.2.3 Turbulence Modelling 272
4.2.3.1 Gas Phase 273
4.2.3.2 Particle Phase in Lagrangian Reference Frame 276
4.2.3.3 Particle Phase in Eulerian Reference Frame 278
4.2.4 Particle–Wall Collision Model 283
4.2.4.1 Lagrangian Reference Frame 284
4.2.4.2 Eulerian Reference Frame 288
4.3 WORKED EXAMPLES 293
4.3.1 Dilute Gas–Particle Flow over a Two-Dimensional Backwards Facing Step 293
4.3.1.1 Numerical Features 293
4.3.1.2 Numerical Results 296
4.3.1.3 Conclusion 303
4.3.2 Dilute Gas–Particle Flow in a Three-Dimensional 90° Bend 305
4.3.2.1 Numerical Features 306
4.3.2.2 Numerical Results 308
4.3.2.3 Conclusion 313
4.3.3 Dilute Gas–Particle Flow Over an In-Line Tube Bank 314
4.3.3.1 Numerical Features 315
4.3.3.2 Numerical Results 320
4.3.3.3 Conclusion 325
4.4 SUMMARY 325
Chapter 5. Liquid–Particle Flows 328
5.1 INTRODUCTION 328
5.1.1 Background 328
5.1.2 Some Physical Characteristics of Flow in Sedimentation Tank 329
5.1.3 Some Physical Characteristics of Slurry Transport 332
5.2 MULTI-PHASE MODELS FOR LIQUID–PARTICLE FLOWS 333
5.2.1 Mixture Model 334
5.2.1.1 Modelling Source or Sink Terms for Flow in Sedimentation Tank 336
5.2.1.2 Modelling Source or Sink Terms for Flow in Slurry Transportation 341
5.2.2 Turbulence Modelling 344
5.3 WORKED EXAMPLES 347
5.3.1 Liquid–Particle Flows in Sedimentation Tank 347
5.3.1.1 Numerical Features 347
5.3.1.2 Numerical Results 349
5.3.1.3 Conclusion 354
5.3.2 Sand–Water Slurry Flow in a Horizontal Straight Pipe 355
5.3.2.1 Numerical Features 356
5.3.2.2 Numerical Results 359
5.3.2.3 Conclusion 362
5.4 SUMMARY 364
Chapter 6. Gas–Liquid Flows 366
6.1 INTRODUCTION 366
6.1.1 Background 366
6.1.2 Categorization of Different Flow Regimes 368
6.1.3 Some Physical Characteristics of Boiling Flow 370
6.2 MULTI-PHASE MODELS FOR GAS–LIQUID FLOWS 372
6.2.1 Multi-Fluid Model 373
6.2.1.1 Inter-Phase Mass Transfer 375
6.2.1.2 Inter-Phase Momentum Transfer 376
6.2.1.3 Inter-Phase Heat Transfer 381
6.2.2 Turbulence Modelling 382
6.3 POPULATION BALANCE APPROACH 385
6.3.1 Need for Population Balance in Gas–Liquid Flows 385
6.3.2 Population Balance Equation (PBE) 388
6.3.3 Method of Moments (MOM) 389
6.3.3.1 Quadrature Method of Moments (QMOM) 390
6.3.3.2 Direct Quadrature Method of Moments (DQMOM) 391
6.3.4 Class Methods (CM) 394
6.3.4.1 Average Quantities Approach 395
6.3.4.2 Multiple Size Group Model 396
6.4 BUBBLE INTERACTION MECHANISMS 398
6.4.1 Single Average Scalar Approach for Bubbly Flows 398
6.4.1.1 Wu et al. (1998) Model 399
6.4.1.2 Hibiki and Ishii (2002) Model 400
6.4.1.3 Yao and Morel (2004) Model 401
6.4.2 Multiple Bubble Size Approach for Bubbly Flows 402
6.4.2.1 DQMOM Model 404
6.4.2.2 MUSIG Model 405
6.4.3 Comments of Other Coalescence and Break-Up Kernels 407
6.4.4 Modelling Beyond Bubbly Flows – A Phenomenological Consideration 409
6.5 MODELLING SUB-COOLED BOILING FLOWS 413
6.5.1 Review of Current Model Applications 413
6.5.2 Phenomenological Description 418
6.5.3 Nucleation of Bubbles at Heated Walls 421
6.5.4 Condensation of Bubbles in Sub-Cooled Liquid 428
6.6 WORKED EXAMPLES 429
6.6.1 Dispersed Bubbly Flow in a Rectangular Column 429
6.6.1.1 Numerical Features 430
6.6.1.2 Numerical Results 434
6.6.1.3 Conclusion 438
6.6.2 Bubbly Flow in a Vertical Pipe 438
6.6.2.1 Numerical Features 439
6.6.2.2 Numerical Results 442
6.6.2.3 Conclusion 450
6.6.3 Sub-Cooled Boiling Flow in a Vertical Annulus 451
6.6.3.1 Application of MUSIG Boiling Model 452
6.6.3.2 Application of Improved Wall Heat Partition Model 463
6.7 SUMMARY 470
Chapter 7. Free Surface Flows 472
7.1 INTRODUCTION 472
7.2 MULTI-PHASE MODELS FOR FREE SURFACE FLOWS 473
7.3 RELEVANT WORKED EXAMPLES 477
7.3.1 Bubble Rising in a Viscous Liquid 477
7.3.1.1 Numerical Features 478
7.3.1.2 Numerical Results 481
7.3.1.3 Conclusion 486
7.3.2 Single Taylor Bubble 487
7.3.2.1 Numerical Features 490
7.3.2.2 Numerical Results 493
7.3.2.3 Conclusion 496
7.3.3 Collapse of a Liquid Column (Breaking Dam Problem) 496
7.3.3.1 Numerical Features 500
7.3.3.2 Numerical Results 501
7.3.3.3 Conclusion 505
7.3.4 Sloshing of Liquid 506
7.3.4.1 Numerical Features 508
7.3.4.2 Numerical Results 509
7.3.4.3 Similar Comparison for the Roll Motion Cases 512
7.3.4.4 Conclusion 514
7.4 SUMMARY 514
Chapter 8. Freezing/Solidification 516
8.1 INTRODUCTION 516
8.2 MATHEMATICAL FORMULATION 517
8.2.1 Governing Equations 517
8.2.2 Solid–Liquid Interface 521
8.2.3 Other Boundary Conditions 523
8.3 NUMERICAL PROCEDURE 524
8.3.1 Internal Grid Generation 524
8.3.2 Surface Grid Generation 524
8.3.3 Optimizing Computational Meshes 528
8.3.3.1 Objective Function 528
8.3.3.2 Optimization Algorithm 530
8.3.4 Transformation of Governing Equations and Boundary Conditions 532
8.4 WORKED EXAMPLES 537
8.4.1 Freezing of Water on a Vertical Wall in an Enclosed Cubical Cavity 537
8.4.1.1 Numerical Features 537
8.4.1.2 Numerical Results 539
8.4.1.3 Conclusion 542
8.4.2 Freezing of Water in an Open Cubical Cavity 545
8.4.2.1 Numerical Features 546
8.4.2.2 Numerical Results 548
8.4.2.3 Conclusion 553
8.5 SUMMARY 553
Chapter 9. Three-Phase Flows 556
9.1 INTRODUCTION 556
9.2 DESCRIPTION OF PROBLEM IN THE CONTEXT OF COMPUTATIONAL FLUID DYNAMICS 557
9.3 MODELLING APPROACHES FOR GAS–LIQUID–SOLID FLOWS 559
9.3.1 Three-Fluid Model 559
9.3.2 Turbulence Modelling 566
9.4 EVALUATION OF MULTI-PHASE MODELS FOR GAS–LIQUID–SOLID FLOWS 567
9.4.1 Three-Phase Modelling of the Air-Lift Pump 568
9.4.1.1 Numerical Features 569
9.4.1.2 Numerical Results 570
9.4.1.3 Conclusion 574
9.4.2 Modelling of Three-Phase Mechanically Agitated Reactor 574
9.4.2.1 Numerical Features 575
9.4.2.2 Numerical Results 577
9.4.2.3 Conclusion 580
9.5 SUMMARY 580
Chapter 10. Future Trends in Handling Turbulent Multi-Phase Flows 582
10.1 INTRODUCTION 582
10.2 DIRECT NUMERICAL SIMULATION OF MULTI-PHASE FLOWS 585
10.2.1 Model Description 585
10.3 LARGE EDDY SIMULATION OF MULTI-PHASE FLOWS 589
10.3.1 Model Description 589
10.3.1.1 Basic SGS Model 593
10.3.1.2 Dynamics SGS Model 594
10.4 ON MODELLING GAS–LIQUID–SOLID FLUIDIZATION 598
10.4.1 Governing Equations 599
10.4.2 Interface Tracking/Capturing Methods: with Comments 600
10.4.3 Discrete Particle Model 601
10.4.4 Particle–Particle Collision 605
10.4.5 Inter-Phase Couplings 608
10.4.6 Simulation Results 610
10.5 SOME CONCLUDING REMARKS 616
Appendix A. Full Derivation of Conservation Equations 618
References 622
Index 642
A 642
B 642
C 644
D 645
E 646
F 647
G 648
H 650
I 650
J 651
K 651
L 651
M 651
N 652
O 653
P 653
Q 654
R 654
S 654
T 656
U 657
V 657
W 658
Y 658
Introduction
Publisher Summary
This chapter provides an introduction to computational techniques for multiphase flows. In the context of fluid mechanics, multiphase flows can be taken as simply any fluid flow system consisting of two or more distinct phases flowing simultaneously in mixture, having some level of phase separation at a scale well above the molecular level. Multiphase flows can, in general, exist in many different forms. Depending on combinations of phases, two-phase flows can be classified according to the state of the different phases: gas–solid flows or liquid–solid flows or gas–liquid flows. Gas–solid flows, identified as gas–solid or gas–droplet flows, are concerned with the motion of suspended solid or droplet in the gas phase. Depending on the particle number density, such flows can be characterized as either being dilute or dense. Liquid–solid flows consist of the transport of solid particles in liquid flow. More appropriately termed as liquid–particle flows or slurry flows, they can also be categorized as dispersed flows in which the liquid represents the continuous phase. In comparison to gas-particle flows, the liquid and solid phases are mainly driven by and respond largely as one to pressure gradients since the density ratio between phases is normally low and the drag between phases is significantly high in such flows. This chapter also provides an overview of the book, Computational Techniques for Multiphase Flows, which presents the basic concepts and fundamental understanding of multiphase flow formulation using mechanistic modeling and mathematical and theoretical illustrations of computational techniques applicable to multiphase flows. The dominant feature of it is to maintain practicality in understanding the use of computational fluid dynamics techniques in tackling the many different classifications of two-phase flows as well as the many problems associated with two-phase mixtures and three-phase flows.
1.1 Classification and Phenomenological Discussion
In the context of fluid mechanics, multi-phase flows can be taken as simply any fluid flow system consisting of two or more distinct phases flowing simultaneously in mixture, having some level of phase separation at a scale well above the molecular level. Multi-phase flows can, in general, exist in many different forms. Depending on combinations of phases, two-phase flows can be classified according to the state of the different phases: gas–solid flows or liquid–solid flows or gas–liquid flows.
Gas–solid flows, identified as gas–solid or gas–droplet flows, is concerned with the motion of suspended solid or droplet in the gas phase. Depending on the particle number density, such flows can be characterized as either being dilute or dense. When the particle number density is relatively small, the influence of the gas flow is the dominant effect. Such flows are referred to as dilute gas–particle flows which are governed predominantly by the surface and body forces acting on the particles. For the special case of very dilute gas–particle flows, the solid particles act as tracers which do not contribute in altering the gas flow. When the particle number density is taken to be sufficiently large, the motion of solid particles is now controlled by particle–particle interactions. Categorically known as dense gas–particle flows, collisions that exist between the solid particles significantly influence the movement of these particles in the gas phase. In bounded flow domains, the motion of solid particles following impact on the boundary walls, which is different when compared to the free flight of solid particles in air, is affected by the surface characteristics and material properties. Gas–particle flows can be referred to as dispersed flows in which the solid particles constitute the dispersed phase and the gas constitutes the continuous phase.
Liquid–solid flows consist of the transport of solid particles in liquid flow. More appropriately termed as liquid–particle flows or slurry flows, they can also be categorized as dispersed flows in which the liquid represents the continuous phase. In comparison to gas–particle flows, the liquid and solid phases are mainly driven by and respond largely as one to pressure gradients since the density ratio between phases is normally low and the drag between phases is significantly high in such flows. Of significant concern is the sedimentation behaviour of solid particles within the liquid flow, which is strongly governed by the size of particles of the dispersed phase and the flow conditions of the continuous phase.
Gas–liquid flows can, in principle, assume several different configurations. One example is the motion of bubbles in a liquid flow, while another is the motion of liquid droplets in a gas. These two examples can also be categorized as dispersed flows. For the first example, the liquid is taken as the continuous phase and the bubbles are considered as discrete constituents of the dispersed phase. For the second example, the gas, however, is taken as the continuous phase and the droplets are now considered as the finite fluid particles of the dispersed phase. Since bubbles or droplets are permitted to deform freely within the continuous phase, they can take on different geometrical shapes: spherical, elliptical, distorted, toroidal, cap and so on. In addition to dispersed flows, gas–liquid flows often exhibit other complex interfacial structures, namely, separated flows and mixed or transitional flows. Figure 1.1 summarizes the various configurations that can be found for gas–liquid flows (Ishii & Hibiki, 2006). The transitional or mixed flows denote the transition between the dispersed flows and separated flows, which is obviously characterized by the presence of both of these flows. The change of interfacial structures occurs through the presence of bubble–bubble interactions due to coalescence and break-up and any prevailing phase change process.
Free surface flows, which are complicated by the presence of well-defined interfaces, belong to the specific consideration of immiscible liquid flows. Strictly speaking, such flows do not fall into the class of two-phase flows. For practical purposes, they can be treated as two-phase mixtures. In contrast to the above classifications of two-phase flows, free surface flows, which comprise mainly of gas and liquid flows, are usually treated with both phases considered as continuous. Similarly, the process of freezing or solidification may also be judged as another special case of a two-phase mixture. Here, the liquid and solid regions can be treated separately and then coupled through appropriate kinematic and dynamic conditions at the interface.
Of a more sophisticated form, three-phase gas–liquid–solid flows are also encountered in a number of engineering applications of technical relevance. For this particular class of multi-phase flows, we consider the solid particles and gas bubbles as being the discrete constituents of the dispersed phase co-flowing with the continuous liquid phase. The co-existence of three phases considerably complicates the fluid flow due to an array of phenomena associated with particle–particle, bubble–bubble, particle–bubble, particle–fluid and bubble–fluid interactions modifying the flow physics.
1.2 Typical Practical Problems Involving Multi-Phase Flows
Many practical problems involving multi-phase flows are broadly featured in a range of modern technological industries as well as within our body system and in the environment we live in. Examples of multi-phase flows based upon the different classifications are listed below.
Gas–particle flows
• Natural sand storms, volcanoes, avalanches
• Biological aerosols, dust particles, smoke (finely soot particles), rain droplets, mist formation
• Industrial pneumatic conveyers, dust collectors, fluidized beds, solid propellant rockets, pulverized solid particles, spray drying, spray casting
Liquid–solid flows
• Natural sediment transport of sand in rivers and sea, soil erosion, mud slides, debris flows, iceberg formation
• Biological blood flow
• Industrial slurry transportation, flotation, fluidized beds, water jet cutting, sewage treatment plants
Gas–liquid flows
• Natural ocean waves
• Biological blood flow
• Industrial boiling water and pressurized water nuclear reactors, chemical reactor desalination systems, boilers, heat exchangers, internal combustion engines, liquid propellant rockets, fire sprinkler suppression systems
Liquid–liquid flows
• Industrial emulsifiers, fuel-cell...
| Erscheint lt. Verlag | 7.10.2009 |
|---|---|
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik | |
| Technik ► Bauwesen | |
| Technik ► Maschinenbau | |
| ISBN-10 | 0-08-091489-6 / 0080914896 |
| ISBN-13 | 978-0-08-091489-3 / 9780080914893 |
| Haben Sie eine Frage zum Produkt? |
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