Computational Methods for Two-Phase Flow and Particle Transport

The following sections are included:

• Dedication

• Preface

• Contents

The first part of this book describes mathematical formulations and finite difference approximations used to solve two-phase flow equations. Primarily, this code calculates the thermal hydraulic problems related to light water and fast breeder reactors. The physical model also handles the particle and gas flow problems that arise from coal gasification and fluidized beds…

The following sections are included:

• Introduction
  • Governing Equations and Characteristics of the Homogeneous, Equilibrium Model
  • Invariance of Characteristics to Change of Dependent Variable and EOS
  • Eigenvectors and Compatibility Conditions
  • The Ill-Posed Problem

• Mass and Momentum Equations

• The Energy Equation

• The Viscous Stress and Drag Function

• Energy Equation of Enthalpy

• References

The following sections are included:

• Introduction

• The Continuity Equation

• The Momentum Equations

• The Viscous Stresses

• The Internal Energy Equation

• Finite Difference for the Enthalpy Equation

• References

The following sections are included:

• Introduction

• Two-Fluid Model and Constitutive Correlations

• Numerical Solution Procedures

• Derivations of and

• Simulation of Two-Phase Jet Impinged on Vertical Plate

• Discussions

• References

The following sections are included:

• Introduction

• The Mathematical Formulation
  • Governing Equations of the Meso-Scale Meteorology
  • Plume Rise Model
  • Eddy Diffusivity
  • Quality Equations

• A Simple Model for Wind Field Computation from Sparse Data

• Downwind SO₂ Concentration Calculations for the Four Corners Generating Station

• Sulfur Dioxide Concentration Calculations for the Dickerson Power Plant

• Behavior of Massive LNG Spills from Storage Tanks at Prince William Sound, Alaska

• Conclusions

• Appendix 5.A. The derivation of Eqs. (5.11) and (5.12)

• References

The following sections are included:

• Introduction

• The Yield of Fission Fragments

• The Fission Reaction Rate

• Possible Fission Reactions

• Calculations of the Released Energy Q

• References

The following sections are included:

• Introduction

• Inertial Confinement Fusion Problems

• Computational Method for Radiation Hydrodynamics
  • Introduction
  • Finite Difference Equations
  • Boundary Conditions
  • Variable Eddington Factor

• Sample Calculations
  • Introduction
  • Diffusion Wave in a Slab
  • Tests of the Variable Eddington Factors
    • Isothermal Sphere Emission Test
    • Comparison of Variable Eddington Approximation with Transport Theory
  • Compton Scattering Test Problems
    • Maintaining Equilibrium
    • Equilibration at Temperature near 1 keV
    • Equilibration: Temperatures near 10 keV
    • Radiation Energy Diffusion Wave

• References

The following sections are included:

• Introduction

• Basic Equations and Boundary Conditions
  • Formulation of the Problem
  • Derivation of the Density Term
  • Derivation of Governing Equations
  • Boundary Conditions
  • Normalization of the Governing Equations
  • Laplace Operator, Vorticity and Stream Function
  • Non-Dimensional Forms of Governing Equations

• Finite Difference Forms
  • Introduction
  • Taylor Series Expansions
  • Finite Difference Approximations for First and Second Derivatives
  • Alternating-Direction Implicit Method
  • Finite Difference Forms of Vorticity and Energy Equations
  • Finite Difference Forms of Stream Function Equation
  • Finite Difference Forms of Velocity Equations
  • Approximation Forms for those Points Near or on the Boundary
  • Finite Difference Forms of Nusselt Number

• Stability

• Results
  • General
  • Calculating Problems Where the Left Plate Temperature is Equal to One and Right Equal to Zero
  • Calculating Problems Where the Temperatures of both Plates are with Linear Distributions

• Conclusions and Recommendations for Future Work
  • Conclusions
  • Recommendations for Future Work

• Appendix 8.A Formulae for Numerical Differentiation

• References

The following sections are included:

• Appendix A The Two-Phase Flow Computer Code
  • A.1 Definition of the Variables and Symbols Used in the Code
  • A.2 Input Data Descriptions
  • A.3 Sample of the Input Data
  • A.4 Output Data Description
  • A.5 Complete code listing
  • A.6 CD-Rom of the Computer Program
  • References

• Appendix B Photon Transport
  • B.1 Introduction
  • B.2 The Variable Eddington Approximation Method
  • B.3 The Variable Eddington Factor
  • B.4 The Flux-limited Diffusion Description
  • B.5 Sn Radiative Transfer
  • B.6 Monte Carlo Method
  • References

• Appendix C Charge Particle Transport
  • C.1 Introduction
  • C.2 Fokker-Planck-Boltzmann Equation
  • C.3 Application of the Levermore Theory
  • C.4 Spatial Discretization
  • C.5 Time Integration
  • References

• Appendix D Neutron Transport
  • D.1 Introduction
  • D.2 Criticality of the Diffusion Equation
  • D.3 Numerical Method for Solving the Diffusion Equation
  • D.4 The Method of Obtaining k
  • D.5 Solution Method for One-Dimensional, Single Group Diffusion Equations
  • D.6 Computational Method for a Two-Dimensional, Single Group Diffusion Equation
  • References

The following sections are included:

• Appendix A The Two-Phase Flow Computer Code

• Appendix B Photon Transport

• Appendix C Charge Particle Transport

• Appendix D Neutron Transport

• References

• Index