Thermo-Fluid Dynamics of Two-Phase Flow
Thermo-Fluid Dynamics of Two-Phase Flow, Second Edition focuses on the fundamental physics of two-phase flow. The authors present the detailed theoretical foundation of multi-phase flow thermo-fluid dynamics as they apply to:Nuclear reactor transient
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Mamoru Ishii • Takashi Hibiki
Thermo-Fluid Dynamics of Two-Phase Flow Second Edition
Mamoru Ishii, Ph.D. School of Nuclear Engineering Purdue University West Lafayette, IN, USA [email protected]
Takashi Hibiki, Ph.D. School of Nuclear Engineering Purdue University West Lafayette, IN, USA [email protected]
ISBN 978-1-4419-7984-1 e-ISBN 978-1-4419-7985-8 DOI 10.1007/978-1-4419-7985-8 Springer New York Dordrecht Heidelberg London © Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer, software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedication
This book is dedicated to our parents and wives.
Table of Contents
Dedication
v
Table of Contents
vii
Preface
xiii
Foreword
xv
Acknowledgments Part I. 1.
xvii
Fundamental of two-phase flow
Introduction 1.1. Relevance of the problem 1.2. Characteristic of multiphase flow 1.3. Classification of two-phase flow 1.4. Outline of the book 2. Local Instant Formulation 1.1. Single-phase flow conservation equations 1.1.1. General balance equations 1.1.2. Conservation equation 1.1.3. Entropy inequality and principle of constitutive law 1.1.4. Constitutive equations 1.2. Interfacial balance and boundary conditions 1.2.1. Interfacial balance (Jump condition)
1 1 3 5 10 11 13 13 15 18 20 24 24
viii
Thermo-Fluid Dynamics of Two-Phase Flow 1.2.2. Boundary conditions at interface 1.2.3. Simplified boundary condition 1.2.4. External boundary conditions and contact angle 1.3. Application of local instant formulation to two-phase flow problems 1.3.1. Drag force acting on a spherical particle in a very slow stream 1.3.2. Kelvin-Helmholtz instability 1.3.3. Rayleigh-Taylor instability
Part II.
32 38 43 46 46 48 52
Two-phase field equations based on time average
3. Various Methods of Averaging 1.1. Purpose of averaging 1.2. Classification of averaging 1.3. Various averaging in connection with two-phase flow analysis 4. Basic Relations in Time Average 1.1. Time domain and definition of functions 1.2. Local time fraction – Local void fraction 1.3. Time average and weighted mean values 1.4. Time average of derivatives 1.5. Concentrations and mixture properties 1.6. Velocity field 1.7. Fundamental identity 5. Time Averaged Balance Equation 1.1. General balance equation 1.2. Two-fluid model field equations 1.3. Diffusion (mi
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