Computational Methods for Two-Phase Flow and Particle Transport

465 Pages·2013·5.716 MB·English

by  Wen Ho Lee

Computational Methods for
Two-Phase Flow
Particle Transport
and
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Computational Methods for
Two-Phase Flow
Particle Transport
and
Wen Ho Lee
Department of Hydraulic and Ocean Engineering
National Cheng Kung University
Tainan, Taiwan
and
Department of Aerospace and Systems Engineering
Feng Chia University
Taichung, Taiwan
World Scientific
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
COMPUTATIONAL METHODS FOR TWO-PHASE FLOW AND
PARTICLE TRANSPORT
(With CD-ROM)
Copyright © 2013 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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ISBN 978-981-4460-27-9 (pbk)
Printed in Singapore.
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Dedicated to my wife, Sylvia and the children
Alberta, Kavita Sharma, and Chung
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Preface
The physical and mathematical formulations of two-phase flow problems
has been a controversialtopic over the past 30 years. Since the partial dif-
ferentialequationsoftwo-phaseflowsystemarehyperbolic,manyscientists
attheIdahoNationalEngineeringLaboratoryinsistthatconservationequa-
tions should possess real characteristics to assure the well-posed nature as
aninitial-valueproblem.Ontheotherhand,researchersintheTheoretical-
3 Group of the Los Alamos National Laboratory believe that the problem
will be resolved when one solves the partial differential equations by using
finite difference methods.
In Chapters 2–4, the interfacial momentum transfer, the interfacial en-
ergy transfer and the high order damping mechanism introduced by the
finite difference approximations tend to stabilize the calculations. Chap-
ters 2–4 and Appendix A (which contains complete code listing and the
descriptions of input and output data) can be used for a one semester
graduateor seniorcourse for mechanical, nuclear,or aerospaceengineering
students.
Chapter 5 provides detailed computer modeling of air pollution trans-
port problems which can be used as lecture notes for environmental engi-
neering students. Chapters 6 and 7 describe fission energy and radiation
hydrodynamic calculations. Appendix B discusses the numerical methods
for solving photon transport. Appendix C is for charge particle transport.
Appendix D is a brief description of neutron transport. Therefore, Chap-
ters 6, 7, and appendices B, C, and D can be used for nuclear engineering
or physics students. Chapter 8 deals with natural convection heat trans-
fer modeling. This chapter can also be used for mechanical or aerospace
engineering students.
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viii Computational methods for two-phase flow and particle transport
I would like to express my gratitude to Robert Lyczkowski of Argonne
National Laboratory for his valuable input to the material in Chapter 2.
I would also like to thank Vipin Shah, Hank Domanus, Robert Schmidt
and William Sha, also with Argonne, for developing the early version of
two-phasecodes.Prof.Tzong-HannShiehtaughtmeLATEX.Yong-YiLin,
Min-ChunChen,andYan-LinChen,graduatestudentsItaughtatNational
Cheng Kung University and Feng Chia University, also made significant
contributions to the mathematical formulation of Chapter 2. The author
wanttothankDr.JinH.Huang,DeanofCollegeofEngineering,FengChia
University, for the financial support to finish this book.
SpecialgratitudewillgotoAlbertaLeeforherhelpineditingthisbook.
Wen Ho Lee
Taichung,Taiwan
June 2012
E-mail: [email protected]
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Contents
Preface vii
1. Introduction 1
References 3
2. Differential Equations of the Two-Phase Flow System 5
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Governing Equations and Characteristics of the
Homogeneous, Equilibrium Model . . . . . . . . . 7
2.1.2 Invariance of Characteristics to Change of
Dependent Variable and EOS . . . . . . . . . . . 11
2.1.3 Eigenvectors and Compatibility Conditions . . . . 13
2.1.4 The Ill-Posed Problem . . . . . . . . . . . . . . . 15
2.2 Mass and Momentum Equations . . . . . . . . . . . . . . 17
2.3 The Energy Equation . . . . . . . . . . . . . . . . . . . . 18
2.4 The Viscous Stress and Drag Function . . . . . . . . . . . 19
2.5 Energy Equation of Enthalpy . . . . . . . . . . . . . . . . 22
References 22
3. Finite Differences of the Governing Equations 25
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 The Continuity Equation . . . . . . . . . . . . . . . . . . 27
3.3 The Momentum Equations . . . . . . . . . . . . . . . . . 37
3.4 The Viscous Stresses . . . . . . . . . . . . . . . . . . . . . 45
ix