Computational Techniques for Multiphase Flows

Table of Contents

Preface

1. Introduction

1. Classification and Phenomenological Discussion
2. Typical Practical Problems Involving Multiphase Flows
3. Computational Fluid Dynamics as a Research Tool for Multiphase Flows
4. Computational Fluid Dynamics as a Design Tool for Multiphase Flows
5. Impact of Multiphase Flow Study on Computational Fluid Dynamics
6. Scope of This Book

2. Governing Equations and Boundary Conditions

1. Background of Different Approaches
2. Averaging Procedure for Multiphase Flow
3. Equations of Motion for Continuous Phase

1. Conservation of Mass
2. Conservation of Momentum
3. Conservation of Energy
4. Interfacial Transport
5. Effective Conservation Equations

4. Comments and Observations on the Governing Equations for the Two-Fluid Modeling Approach
5. Equations of Motion for Disperse Phase
6. Turbulence in Transport Phenomena

1. Reynolds-Averaged Equations
2. Reynolds-Averaged Closure
3. Some Comments on the k-e Model and Implications of Other Turbulence Models

1. Shear Stress Transport (SST) Model
2. Reynolds Stress Model
3. Near Wall Treatment

4. Comments on Turbulence Modeling of the Disperse Phase

7. Differential and Integral Form of the Transport Equations

1. A Comment on Multi-Fluid Model

8. Boundary Conditions and Their Physical Interpretation

1. Comments on Some Wall Boundary Conditions for Multiphase Problems

9. Summary

3. Solution Methods for Multiphase Flows

1. Introduction

MESH SYSTEMS

2. Consideration for a Range of Multiphase Flow Problems

1. Application of Structured Mesh
2. Application of Body-Fitted Mesh
3. Application of Unstructured Mesh
4. Some Comments on Grid Generation

 

EULERIAN-EULERIAN FRAMEWORK

3. Numerical Algorithms

1. Basic Aspects of Discretisation – Finite Difference Method
2. Basic Aspects of Discretisation – Finite Volume Method
3. Basic Approximation of the Diffusion Term Based Upon the Finite Volume Method
4. Basic Approximation of the Advection Term Based Upon the Finite Volume Method
5. Some Comments on the Need for TVD Schemes
6. Explicit and Implicit Approaches
7. Assembly of Discretised Equations
8. Comments on the Linearization of Source Terms

4. Solution Algorithms

1. The Philosophy Behind the Pressure-Correction Techniques for Multiphase Problems

1. SIMPLE Algorithm for Mixture or Homogeneous Flows
2. A Comment on Other Pressure Correction Methods
3. Evaluation of the Face Velocity in Different Mesh Systems
4. Iterative Procedure Based on the SIMPLE Algorithm
5. Inter-Phase Slip Algorithm (IPSA) for Multiphase Flows
6. Inter-Phase Slip Algorithm-Coupled (IPSA-C) for Multiphase Flows
7. Comments on the Need for Improved Interpolation Methods of Evaluating the Face Velocity in Multiphase Problems

2. Matrix Solvers for the Segregated Approach in Different Mesh Systems
3. Coupled Equation System

EULERIAN-LAGRANGIAN FRAMEWORK

5. Numerical and Solution Algorithms

1. Basic Numerical Techniques
2. Comments on Sampling Particulates for Turbulent Dispersion
3. Some Comments on Attaining Proper Statistical Realizations
4. Evaluation of Source Terms for the Continuous Phase

INTERFACE TRACKING/CAPTURING ALGORITHMS

6. Basic Considerations of Interface Tracking/Capturing Methods

1. Algorithms Based on Surface Methods: With Comments

1. Markers on Interface (Surface Marker Techniques)

2. Algorithms Based on Volume Methods: With Comments

1. Markers in Fluid (MAC Formulation)
2. Volume of Fluid (VOF)
3. Level Set Method
4. Hybrid Methods

3. Computing Surface Tension and Wall Adhesion

7. Summary

4. Gas-Particle Flows

1. Introduction

1. Background
2. Classification of Gas-Particle Flows
3. Particle Loading and Stokes Number
4. Particle Dispersion due to Turbulence

2. Multiphase Models for Gas-Particle Flows

1. Eulerian-Lagrangian Framework
2. Eulerian-Eulerian Framework
3. Turbulence Modeling
4. Particle-Wall Collision Model

3. Worked Examples

1. Dilute Gas-Particle Flow over a Two-Dimensional Backward Facing Step
2. Dilute Gas-Particle Flow over a Three-Dimensional 90^o Bend
3. Dilute Gas-Particle Flow over an Inline Tube Bank

4. Summary

5. Liquid-Particle Flows

1. Introduction

1. Background
2. Some Physical Characteristics of Flow in Sedimentation Tank
3. Some Physical Characteristics of Flow in Slurry Transport

2. Multiphase Models for Liquid-Particle Flows

1. Mixture Model

1. Modeling Source or Sink Terms for Flow in Sedimentation Tank
2. Modeling Source or Sink Terms for Flow in Slurry Transportation

2. Turbulence Modeling

3. Worked Examples

1. Liquid-Particle Flow in Sedimentation Tank
2. Sand-Water Slurry Flow in a Horizontal Straight Pipe

4. Summary

6. Gas-Liquid Flows

1. Introduction

1. Background
2. Categorization of Different Flow Regimes
3. Some Physical Characteristics of Boiling Flow

2. Multiphase Models for Liquid-Particle Flows

1. Multi-Fluid Model

1. Inter-phase Mass Transfer
2. Inter-phase Momentum Transfer
3. Inter-phase Heat Transfer

2. Turbulence Modeling

3. Population Balance Approach

1. Need for Population Balance in Gas-Liquid Flows
2. Population Balance Equation (PBE)
3. Method of Moments (MOM)

1. Quadrature Method of Moments (QMOM)
2. Direct Quadrature Method of Moments (DQMOM)

4. Class Methods (CM)

1. Average Quantities Approach
2. MUltiple SIze Group (MUSIG) Model

4. Bubble Interaction Mechanisms

1. Single Average Scalar Approach for Bubbly Flows
2. Multiple Bubble Size Approach for Bubbly Flows
3. Comments of Other Coalescence and Break-up Kernels
4. Modeling Beyond Bubbly Flows – A Phenomenological Consideration

5. Modeling Subcooled Boiling Flows

1. Review of Current Model Applications
2. Phenomenological Description
3. Nucleation of Bubbles at Heated Walls
4. Condensation of Bubbles in Subcooled Liquid

6. Worked Examples

1. Dispersed Bubbly Flow in a Rectangular Column
2. Bubbly Flow in a Vertical Pipe
3. Subcooled Boiling Flow in a Vertical Annulus

1. Application of MUSIG Boiling Model
2. Application of Improved Wall Heat Partition Model

7. Summary

7. Free Surface Flows

1. Introduction
2. Multiphase Models for Free Surface Flows
3. Relevant Worked Examples

1. Bubble Rising in a Viscous Liquid
2. Single Taylor Bubble
3. Collapse of a Liquid Column (Breaking Dam Problem)
4. Sloshing of Liquid

4. Summary

8. Freezing/Solidification

1. Introduction
2. Mathematical Formulation

1. Governing Equations
2. Solid-Liquid Interface
3. Other Boundary Conditions

3. Numerical Procedure

1. Internal Grid Generation
2. Surface Grid Generation
3. Optimizing Computational Meshes

1. Objective Function
2. Optimization Algorithm
3. Transformation of Governing Equations and Boundary Conditions

4. Worked Examples

1. Freezing of Water on a Vertical Wall in an Enclosed Cavity
2. Freezing of Water in an Open Cubical Cavity

5. Summary

9. Three-Phase Flows

1. Introduction
2. Description of Problem in the Context of Computational Fluid Dynamics
3. Modeling Approaches for Gas-Liquid-Solid Flows

1. Three-Fluid Model
2. Turbulence Modeling

4. Evaluation of Multiphase Models for Gas-Liquid-Solid Flows

1. Three-Phase Modeling of the Air Lift Pump
2. Modeling of Three-Phase Mechanically Agitated Reactor

5. Summary

10. Future Trends in Handling Turbulent Multiphase Flows

1. Introduction
2. Direct Numerical Simulation of Multiphase Flows

1. Model Description

3. Large Eddy Simulation of Multiphase Flows

1. Model Description
2. Basic Sub-Grid Scale Model
3. Dynamic Sub-Grid Scale Model

4. On Modeling Gas-Liquid-Solid Fluidization

1. Governing Equations
2. Interface Tracking/Capturing methods: With Comments
3. Discrete Particle Model
4. Particle-Particle Collision
5. Inter-Phase Couplings
6. Simulation Results

5. Some Concluding Remarks

Appendix A Full Derivation of Conservation Equations

References

Subject Index