Computational Techniques for Multiphase Flows - 2nd Edition - ISBN: 9780081024539

Computational Techniques for Multiphase Flows

2nd Edition

Authors: Guan Heng Yeoh Jiyuan Tu
Paperback ISBN: 9780081024539
Imprint: Butterworth-Heinemann
Published Date: 11th March 2019
Page Count: 640
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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 newer 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.

Key Features

  • Includes updated chapters in addition to a brand-new section on Granular Flows
  • Features novel solution methods for multiphase flow, along with recent case studies
  • Explains how and when to use the featured technique, and how to interpret the results and apply them to improving applications


Chemical and mechanical engineers, especially in filtration, separation, gas/ liquid pumping, aerospace, automotive and energy industries. MSc students and researchers in chemical and mechanical engineering.

Table of Contents

1. Introduction 1.1 Classification and Phenomenological Discussion 1.2 Typical Practical Problems Involving Multiphase Flows 1.3 Computational Fluid Dynamics as a Research Tool for Multiphase Flows 1.4 Computational Fluid Dynamics as a Design Tool for Multiphase Flows 1.5 Impact of Multiphase Flow Study on Computational Fluid Dynamics 1.6 Scope of This Book

2. Governing Equations and Boundary Conditions 2.1 Basic concepts of Fluid Mechanics 2.2 Background of Different Approaches 2.3 Averaging Procedure for Multiphase Flow 2.4 Equations of Motion for Continuous Phase 2.4.1 Conservation of Mass 2.4.2 Conservation of Momentum 2.4.3 Conservation of Energy 2.4.4 Interfacial Transport 2.4.5 Effective Conservation Equations 2.5 Comments and Observations on the Governing Equations for the Two-Fluid Modeling Approach 2.6 Equations of Motion for Disperse Phase 2.7 Turbulence in Transport Phenomena 2.7.1 Reynolds-Averaged Equations 2.7.2 Reynolds-Averaged Closure 2.7.3 Some Comments on the k- Model and Implications of Other Turbulence Models Shear Stress Transport (SST) Model Reynolds Stress Model Near Wall Treatment 2.7.4 Comments on Turbulence Modeling of the Disperse Phase 2.8 Differential and Integral Form of the Transport Equations 2.8.1 A Comment on Multi-Fluid Model 2.9 Boundary Conditions and Their Physical Interpretation 2.9.1 Comments on Some Wall Boundary Conditions for Multiphase Problems 2.10 Summary

3. Solution Methods for Multiphase Flows 3.1 Introduction MESH SYSTEMS 3.2 Consideration for a Range of Multiphase Flow Problems 3.2.1 Application of Structured Mesh 3.2.2 Application of Body-Fitted Mesh 3.2.3 Application of Unstructured Mesh 3.2.4 Some Comments on Grid Generation EULERIAN-EULERIAN FRAMEWORK 3.3 Numerical Algorithms 3.3.1 Basic Aspects of Discretisation – Finite Difference Method 3.3.2 Basic Aspects of Discretisation – Finite Volume Method 3.3.3 Basic Approximation of the Diffusion Term Based Upon the Finite Volume Method 3.3.4 Basic Approximation of the Advection Term Based Upon the Finite Volume Method 3.3.5 Some Comments on the Need for TVD Schemes 3.3.6 Explicit and Implicit Approaches 3.3.7 Assembly of Discretised Equations 3.3.8 Comments on the Linearization of Source Terms 3.4 Solution Algorithms 3.4.1 The Philosophy Behind the Pressure-Correction Techniques for Multiphase Problems SIMPLE Algorithm for Mixture or Homogeneous Flows A Comment on Other Pressure Correction Methods Evaluation of the Face Velocity in Different Mesh Systems Iterative Procedure Based on the SIMPLE Algorithm Inter-Phase Slip Algorithm (IPSA) for Multiphase Flows Inter-Phase Slip Algorithm-Coupled (IPSA-C) for Multiphase Flows Comments on the Need for Improved Interpolation Methods of Evaluating the Face Velocity in Multiphase Problems 3.4.2 Matrix Solvers for the Segregated Approach in Different Mesh Systems 3.4.3 Coupled Equation System EULERIAN-LAGRANGIAN FRAMEWORK 3.5 Numerical and Solution Algorithms 3.5.1 Basic Numerical Techniques 3.5.2 Fluid-Particle Interaction (Forces related to fluid acting on particle – one-way , two-way coupling) 3.5.3 Particle-Particle Interaction (Four-way coupling concept – collisions and turbulent dispersion of particles) Hard Sphere Model Soft Sphere Model 3.5.4 Comments on Sampling Particulates for Turbulent Dispersion 3.5.5 Some Comments on Attaining Proper Statistical Realizations 3.5.6 Evaluation of Source Terms for the Continuous Phase INTERFACE TRACKING/CAPTURING ALGORITHMS 3.6 Basic Considerations of Interface Tracking/Capturing Methods 3.6.1 Algorithms Based on Surface Methods: With Comments Surface Marker Approaches Front Tracking Method Intersection Marker Method 3.6.2 Algorithms Based on Volume Methods: With Comments Markers in Fluid (MAC Formulation) Volume of Fluid (VOF) Level Set Method Hybrid Methods 3.6.3 Computing Surface Tension and Wall Adhesion 3.7 Summary

4. Gas-Particle and Liquid-Particles Flows 4.1 Introduction 4.1.1 Background 4.1.2 Classification of Gas-Particle and Liquid-Particle Flows 4.1.3 Particle Loading and Stokes Number 4.1.4 Particle Dispersion due to Turbulence 4.1.5 Some Physical Characteristics of Flow in Sedimentation Tank 4.1.6 Some Physical Characteristics of Flow in Slurry Transport 4.2 Multiphase Models for Gas-Particle Flows 4.2.1 Eulerian-Lagrangian Framework 4.2.2 Eulerian-Eulerian Framework 4.2.3 Turbulence Modeling 4.2.4 Particle-Wall Collision Model 4.3 Multiphase Models for Liquid-Particle Flows 4.3.1 Mixture Model Modeling Source or Sink Terms for Flow in Sedimentation Tank Modeling Source or Sink Terms for Flow in Slurry Transportation 4.3.2 Turbulence Modeling 4.4 Worked Examples 4.4.1 Dilute Gas-Particle Flow over a Two-Dimensional Backward Facing Step 4.4.2 Dilute Gas-Particle Flow over a Three-Dimensional 90o Bend 4.4.3 Dilute Gas-Particle Flow over an Inline Tube Bank 4.4.4 Liquid-Particle Flow in Sedimentation Tank 4.4.5 Sand-Water Slurry Flow in a Horizontal Straight Pipe 4.5 Summary

5. Gas-Liquid Flows 5.1 Introduction 5.1.1 Background 5.1.2 Categorization of Different Flow Regimes 5.1.3 Some Physical Characteristics of Boiling Flow 5.2 Multiphase Models for Liquid-Particle Flows 5.2.1 Multi-Fluid Model Inter-phase Mass Transfer Inter-phase Momentum Transfer Inter-phase Heat Transfer 5.2.2 Turbulence Modeling 5.3 Population Balance Approach 5.3.1 Need for Population Balance in Gas-Liquid Flows 5.3.2 Population Balance Equation (PBE) 5.3.3 Method of Moments (MOM) Quadrature Method of Moments (QMOM) Direct Quadrature Method of Moments (DQMOM) 5.3.4 Class Methods (CM) Average Quantities Approach MUltiple SIze Group (MUSIG) Model 5.4 Bubble Interaction Mechanisms 5.4.1 Single Average Scalar Approach for Bubbly Flows 5.4.2 Multiple Bubble Size Approach for Bubbly Flows 5.4.3 Comments of Other Coalescence and Break-up Kernels 5.4.4 Modeling Beyond Bubbly Flows – A Phenomenological Consideration 5.5 Modeling Subcooled Boiling Flows 5.5.1 Review of Current Model Applications 5.5.2 Phenomenological Description 5.5.3 Nucleation of Bubbles at Heated Walls 5.5.4 Condensation of Bubbles in Subcooled Liquid 5.6 Worked Examples 5.6.1 Dispersed Bubbly Flow in a Rectangular Column 5.6.2 Bubbly Flow in a Vertical Pipe 5.6.3 Subcooled Boiling Flow in a Vertical Annulus Application of MUSIG Boiling Model Application of Improved Wall Heat Partition Model 5.7 Summary

6. Free Surface Flows 6.1 Introduction 6.2 Multiphase Models for Free Surface Flows 6.3 Relevant Worked Examples 6.3.1 Bubble Rising in a Viscous Liquid 6.3.2 Single Taylor Bubble 6.3.3 Collapse of a Liquid Column (Breaking Dam Problem) 6.3.4 Sloshing of Liquid 6.3.5 Slug Bubbles in Microchannel Flow 6.4 Summary

7. Granular Flows 7.1 Introduction 7.2 Multiphase Models for Granular Flows 7.3 Particle-Particle Interaction Without Adhesion 7.3.1 Normal Force due to Continuous Potential 7.3.2 Normal Force due to Linear Viscoelastic 7.3.3 Normal Force due to Non-Linear Viscoelastic 7.3.4 Normal Force due to Hysteretic 7.3.5 Tangential Force 7.3.6 Sliding, Twisting and Rolling Resistance 7.4 Particle-Particle Interaction With Adhesion 7.4.1 DVLO and JKR Theories 7.4.2 Liquid Bridging 7.4.3 Interfacial Attractive 7.4.4 Other Types of Field-Particle Interaction 7.5 Worked Examples 7.5.1 Magnetic Nanoparticles in Fluids 7.5.2 Abrasive Jet Particles 7.5.3 Fluidized Bed 7.6 Summary

8. Freezing/Solidification 8.1 Introduction 8.2 Mathematical Formulation 8.2.1 Governing Equations 8.2.2 Solid-Liquid Interface 8.2.3 Other Boundary Conditions 8.3 Numerical Procedure 8.3.1 Internal Grid Generation 8.3.2 Surface Grid Generation 8.3.3 Optimizing Computational Meshes Objective Function Optimization Algorithm Transformation of Governing Equations and Boundary Conditions 8.4 Worked Examples 8.4.1 Freezing of Water on a Vertical Wall in an Enclosed Cavity 8.4.2 Freezing of Water in an Open Cubical Cavity 8.5 Summary

9. Three-Phase Flows 9.1 Introduction 9.2 Description of Problem in the Context of Computational Fluid Dynamics 9.3 Modeling Approaches for Gas-Liquid-Solid Flows 9.3.1 Three-Fluid Model 9.3.2 Turbulence Modeling 9.4 Evaluation of Multiphase Models for Gas-Liquid-Solid Flows 9.4.1 Three-Phase Modeling of the Air Lift Pump 9.4.2 Modeling of Three-Phase Mechanically Agitated Reactor 9.5 Summary

10. Future Trends in Handling Turbulent Multiphase Flows 10.1 Introduction 10.2 Direct Numerical Simulation of Multiphase Flows 10.2.1 Model Description 10.3 Large Eddy Simulation of Multiphase Flows 10.3.1 Model Description 10.3.2 Basic Sub-Grid Scale Model 10.3.3 Dynamic Sub-Grid Scale Model 10.4 On Modeling Gas-Liquid-Solid Fluidization 10.4.1 Governing Equations 10.4.2 Interface Tracking/Capturing methods: With Comments 10.4.3 Discrete Particle Model 10.4.4 Particle-Particle Collision 10.4.5 Inter-Phase Couplings 10.4.6 Simulation Results 10.5 Some Concluding Remarks Appendix A Full Derivation of Conservation Equations


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About the Author

Guan Heng Yeoh

Guan Heng Yeoh is an Associate Professor at the School of Mechanical and Manufacturing Engineering, UNSW, and a Senior Research Scientist at ANSTO. He is the founder and Editor of the Journal of Computational Multiphase Flows and the Group Leader of Computational Thermal-Hydraulics of OPAL Research Reactor, ANSTO. He has approximately 180 publications including 7 books, 10 book chapters, 83 journal articles, and 80 conference papers with an H-index 16 and over 800 citations. His research interests are computational fluid dynamics (CFD); numerical heat and mass transfer; turbulence modelling using Reynolds averaging and large eddy simulation; combustion, radiation heat transfer, soot formation and oxidation, and solid pyrolysis in fire engineering; fundamental studies in multiphase flows: free surface, gas-particle, liquid-solid (blood flow and nanoparticles), and gas-liquid (bubbly, slug/cap, churn-turbulent, and subcooled nucleate boiling flows); computational modelling of industrial systems of single-phase and multiphase flows.

Affiliations and Expertise

Mechanical Engineering (CFD), University of New South Wales, Sydney, Australian Nuclear Science and Technology Organisation, University of New South Wales, Australia

Jiyuan Tu

Jiyuan Tu has 33 years of industry experience in this field. He is an author on 9 book publications, is an editor on 6 journals, has over 300 journal articles published and is in service of expert committee members to the United Nations (UN) and International Atomic Energy Agency (IAEA). In the last 10 years he has won 6 awards for excellence in research and teaching. His areas of research and consulting expertise are: Computational fluid dynamics (CFD) and numerical heat transfer (NHT); computational and experimental modelling of multiphase flows; fluid-structure interaction; biomedical engineering: optimal design of drug delivery devices; prediction of aerosol deposition in human airways and nasal cavity; and simulation of blood flow in arteries.

Affiliations and Expertise

Professor, School of Engineering, RMIT University, Australia; and Distinguished Professor, Tsinghua University, China

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