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MULTIPHASE SCIENCE AND TECHNOLOGY
Editorial Advisory Board
D. AZIZ Department of Chemical Engineering The Universit'y of Calgary Calgary T2N 1 N4, Canada
S. BANERJEE Chemical and Nuclear Engineering Departinent University of California Santa Barbara, California 93106, USA
H. BRAUER Technische Universität Berlin Institut für Chemieingenieurtechnik 1 Berlin 10, RFA
J. C. CHARPENT1ER CPIC/ENSIC 54042 Nancy Cedex, France
J.G.COLLIER Central Electricity Generating Board Generation and Construction Division Barnwood, Gloucester GL4 7RS, England
M. CUMO Comitato per I'Energia Nucleare Centro Studi Nucleari della Casaccia Departimento Reattori Termici Rome, Italy
M. GIOT Departement Thermodynamique et Turbomachines B-1348 Louvain la Neuve, Belgium
D.HASSON Technion Department of Chemical Engineering Haifa, Israel
M. HIRATA University of Tokyo Department of Mechanical Engineering Bunkyo-Ku Tokyo 113, Japan
A. KONORSKI Instytut Maszyn Przeplywowych 80 - 952 Gdansk, Poland
S. S. KUTATELADZE Institute of Thermophysics Novosibirsk 63 0090, USSR
K. R. LAWTHER A.A.E.C. Research Establishment Privatemail bag, Sutherland 2232 NSW Australia
F. MARBLE Jet Propulsion Center California Institute of Technology Pasadena, CA 91125, USA
F. MAYINGER Lehrstule A. für Thermodynamik Technische Universitat München 8000 München 2 Arcistrasse 21 München, FRG
G.OOMS Sheil Research B.V. Badhuisweg 3 Postbus 3003 1003AA Amsterdam, The Netherlands
F. RESCH Institut de Mecanique Statistique de la Turbulence 13003 Marseille, France
L. E. SCRIVEN Department of Chemical Engineering and Materials Science University of Minnesota Minneapolis, MN 55455, USA
G. V. TSIKLAURI Institute of High Temperature Krasnokas Armenaya Moscow, USSR
M. WICKS Shell Oil Company P. O. Box 3105 Houston, TX 77001, USA
MULTIPHASE SCIENCE AND TECHNOLOGY Volume 2 Edited by
G. F. Hewitt Thermal Hydraulics Division U.K. Atomic Energy Authoritv Harwell Laboratory, England and Department of Chemicai Engineering and Chemical Technology Imperial College of Science and Technology London, England
J. M. Delhaye Centre d'Etudes Nucleaires de Grenoble Service des Transferts Thermiques Grenoble, France
N. Zuber Division of Reactor Safety Research U.S. Nuclear Regulatory Commission Washington, D.C., U.S.A.
Springer-Verlag Berlin Heidelberg GmbH
MULTIPHASE SCIENCE AND TECHNOLOGY, Volume 2
Copyright © 1986 by Springer-Verlag Berlin Heidelberg All rights reserved.
Originally published by Springer-Verlag in 1986
Except as permitted under the United States Copyright Act of 1976, no part of this publkation may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher.
1234567890 BCBC 89876
Library of Congress Cataloging in Publication Data
(Revised tor volume 2)
Main entry under title:
Multiphase science and technology.
Includes bibliographies and indexes. 1. Vapor-liquid equilibrium-Addresses, essays,
lectures. 2. Ebullition-Addresses, essays, lectures. 3. eooling -Addresses, essays, lectures. I. Hewitt, G. F. (Geoffrey Frederick) 11. Delhaye, J. M. date. 111. Zuber, N. TP156.E65M84 660.2'96 81-4527
ISBN 978-3-662-01659-6 ISBN 978-3-662-01657-2 (eBook) DOI 10.1007/978-3-662-01657-2
Contents
Preface xiii
Contents of Volume 1 xv
Chapter 1 Flow Pattern Transitions in Gas-liquid Systems: Measurement and Modeling A. E. Dukler and Y. Taitel 1
1 Introduction 1 2 Classification of Flow Patterns 3
2.1 Horizontal Pipes: Fig. 1 4 2.1.1 Stratified 4 2.1.2 Intermittent 5 2.1.3 Annular 5 2.1.4 Dispersed Bubble 5
2.2 Vertical Pipes: Fig. 2 5 2.2.1 Bubble Flow 5 2.2.2 Slug Flow 5 2.2.3 Chum Flow 6 2.2.4 Annular Flow 6
3 Flow-Pattern Detection 7 3.1 Visual Methods 7 3.2 Methods Based on Pressure Measurement 8 3.3 Methods Based on Photon Attenuation 11 3.4 Methods Based on Electrical Conductivity 12
4 Modeling Flow-Pattern Transitions: So me General Ideas 14 5 Horizontal and Slightly Inclined Pipes: Steady Motion without Mass
Transfer between Phases 16 5.1 Equilibrium Stratified Flow 16 5.2 Transition from Stratified Flow 19 5.3 Transition between Intermittent and Annular 22 5.4 Transition between Stratified-Smooth and Stratified-Wavy
Patterns 23 5.5 Transition between Intermittent and Dispersed Bubble
Patterns 25 5.6 The Flow Pattern Map: Summary 26
5.6.1 Comparison with Data 26
6 Effect of Flow Transients in Horizontal Pipes 29 6.1 Analysis 30 6.2 An Example: Liquid Feed Transients 33 6.3 An Example: Fast Gas Transients 34
7 Effects of Boiling and Condensation in Horizontal Pipes 37 7. 1 Analysis 37 7.2 Transition Criteria 41
v
vi Contents
8 Vertical Pipes: Steady Motion without Mass Transfer-Upflow and Downflow 46 8.1 Concurrent Upflow 47
8.1.1 Bubble-to-Slug Transition 47 8.1.2 Slug-to-Churn Transition 53 8.1.3 Transition from Annular Flow 57 8.1.4 Discussion 59
8.2 Concurrent Downflow 61 8.2.1 Transition from Annular Flow 61 8.2.2 Slug-to-Dispersed Bubble Transition 64
9 Effect of Pipe Inclination 65 9.1 Concurrent Upward Flow in an Inclined Tube 66
9.1.1 Bubble-to-Slug Transition and Minimum Inclination Angle for Bubbly Flow 67
9.1.2 Transition from Annular Flow 70 9.1.3 Slug-to-Churn Transition 70 9.1.4 Intermediate Angles of Inclination 70
9.2 Concurrent Downward Flow in an Inclined Tube 71 9.2.1 Stratified Smooth-to-Stratified Wavy Transition 73 9.2.2 Stratified-to-Annular Transition 73
10 Transition Mechanisms in Tubes: An Overview 76 11 Vertical Rod Bundles 77
11 . 1 Bubble Rise Velocities 78 11.2 Bubble-to-Slug Transition 82 11.3 Slug-to-Churn Transition 84 11.4 Churn-to-Annular Transition 84
Nomenclature 87 References 88
Chapter 2 A Critical Review of the Flooding literature S. George Bankoff and Sang Chun Lee 95
1 Introduction 95 1.1 Description of Vertical Countercurrent Annular Flow 96 1.2 Characteristics of the Flooding Phenomenon 97 1.3 Associated Phenomena 99 1.4 Classification of Previous Flooding Studies 102
2 Fundamentals of Countercurrent Flow 102 2.1 Pressure Drop 103
2.1.1 Adiabatic Flow 103 2.1.2 Condensing Flow 106
2.2 Mean Film Thickness 107 2.2.1 Falling Film without Gas Flow 107 2.2.2 Liquid Film with Countercurrent Gas Flow 109
2.3 Interfacial Shear Stress 110 2.3.1 Adiabatic Flow 111 2.3.2 Condensing Flow 114
3 Classification of Flooding Models 115
Contents vii
4 Brief Review of Analytical Models 116 4. 1 Stability Theory of a Traveling Wave 116
4.1 .1 Potential Flow Model 116 4. 1 .2 Viscous Flow Model 126 4.1.3 Finite-Amplitude Wave Model 127
4.2 Envelope Theories 129 4.2.1 Separate Cylinders Model 129 4.2.2 Orift-Flux Model 130 4.2.3 Separated-Flow Models 130
4.3 Static Equilibrium Theories 133 4.3.1 Stationary Wave Model 133 4.3.2 Hanging Film Model 134 4.3.3 Roll Wave Model 135
4.4 Theory of Slug Formation 136 4.4.1 Kordyban and Ranov Model 136 4.4.2 Wallis and Oobson Model 138 4.4.3 Taitel and Oukler Model 139 4.4.4 Gardner Model 140 4.4.5 Mishima and Ishii Model 141
5 Experimental Investigations 142 5.1 Experimental System 142 5.2 Empirical Correlations 143
6 Comparisons and Discussion 150 6.1 Flooding without Phase Change 150 6.2 Flooding with Phase Change 161
7 Further Aspects of Vertical Countercurrent Flooding 168 7. 1 Tube-End Conditions 168 7.2 Tube Length 169 7.3 Tube Diameter 169 7.4 Liquid Droplet Entrainment 170
8 Summary and Conclusions 171 Nomenclature 172 References 175
Chapter 3 A Comprehensive Examination of Heat Transfer Correlations Suitable for Reactor Safety Analysis D. C. Groeneveld and C. W. Snoek 181
1 Introduction 181 2 Single-Phase Heat Transfer 184
2.1 lntroduction 184 2.2 Subcooled Water Heat Transfer 184 2.3 Superheated Steam Heat Transfer 184 2.4 Bundle Geometry 186 2.5 Entrance and Spacer Effects 186
3 Nucleate Boiling and Convective Evaporation 188 3.1 Introduction 188
viii Contents
3.2 Prediction Methods 189 3.2.1 Nucleate Boiling Only 189 3.2.2 Saturated Boiling: Nucleate Boiling and Forced Convective
Evaporation 189
3.3 Conc!usions and Final Remarks 194 4 Criticai Heat Flux 195
4.1 Introduction 195 4.2 Correlations 195 4.3 Alternative Prediction Methods 202
4.3.1 Analytical Methods 202 4.3.2 Table Look-Up Technique 203 4.3.3 Graphical Techniques 210
4.4 Parametrie Trends 210 4.4.1 General 210 4.4.2 Cross-Section Geometry 214 4.4.3 Effect of Rod-Spacing Devices 215 4.4.4 Effect of Heat Flux Distribution 216 4.4.5 Transient Effects 217 4.4.6 Other Effects 217
4.5 Final Remarks 218 5 Transition Boiling 218
5.1 Introduction 218 5.2 Data Trends 219 5.3 Correlations 219 5.4 Prediction of the Critical Heat Flux Temperature 225 5.5 Discussion 226 5.6 Final Remarks 226
6 Minimum Film Boiling 227 6.1 Introduction 227 6.2 Minimum Film Boiling Types 227 6.3 Prediction Methods 233 6.4 Correlation Assessments 234
6.4. 1 Data Trends 234 6.4.2 Comparison with Data 235 6.4.3 Discussion 236
6.5 Final Remarks 237 7 Film Boiling 238
7.1 Introduction 238 7.2 Prediction Methods 238
7.2.1 Post-Dryout Models 238 7.2.2 Post-Dryout Correlations 239
7.3 Comparison with Experimental Data 250 7.3.1 Available Data 250 7.3.2 Comparison with Tube Data 250 7.3.3 Comparison with Rod Bundle Data 253 7.3.4 Miscel!aneous 255
7.4 Final Remarks 255 8 Summary of Conc!usions and Final Remarks 256 Acknowledgments 257
Nomenc!ature References
257 260
Contents
Chapter 4 Reboilers P. B. Whalley and G. F. Hewitt
1 Introduction 275 2 Types of Reboilers 275
2.1 Internal Reboiler 275 2.2 Kettle Reboiler 277 2.3 Vertical Thermosyphon Reboiler 278 2.4 Horizontal Thermosyphon Reboiler 281 2.5 Selection of Type 283
3 Detailed Experimental Studies 285 3.1 Kettle Reboilers 285 3.2 Vertical Thermosyphon Reboilers 292
4 Problems in Design 295 4.1 Kettle and Internal Reboilers 296 4.2 Vertical Thermosyphon Reboilers 296 4.3 Horizontal Thermosyphon Reboilers 296
5 A Design Strategy 297 5.1 Simulation Calculation 297 5.2 Design Calculation 297
6 Two-Phase Pressure Drop 298
275
6.1 Components of Two-Phase Pressure Drop 298 6.2 Two-Phase Frictional Pressure Drop in Tubes 299 6.3 Void Fraction in Tubes 300 6.4 Two-Phase Frictional Pressure Drop in Cross Flow 301 6.5 Void Fraction in Cross Flow 302 6.6 Use of the Homogeneous Model of Two-Phase Flow 303
7 Boiling Heat Transfer Coefficients 305 7.1 Boiling Inside Tubes 305 7.2 Boiling in Cross Flow 310
8 Critical Heat Flux 312 8.1 Critical Heat Flux Inside Tubes 312 8.2 Critical Heat Flux in Cross Flow 315
9 instability 318 1 0 Conclusions Nomenclature References
322 323
327
Chapter 5 Flow of Gas-Solid Mixtures through Stand pipes and Valves L. S. Leung and P. J. Jones 333
1 Introduction 333
ix
x Contents
2 Flow Regimes 337 2.1 Fluidized and Nonfluidized Regimes 337 2.2 Kojabashian's Classification 341
2.2.1 Fluidized Flow 341 2.2.2 Nonfluidized Flow 343 2.2.3 Summary of Kojabashian's Classification 343
2.3 Classification of leung and Jones in Fluidized Flow 343 2.4 Summary of the Classification of Flow Regimes 346
3 Demarcation between Flow Regimes 347
4
5
3.1 Demarcation between Fluidized and Nonfluidized Flow 347 3.2 Demarcation within the Fluidized Mode: Type I
and Type 11 350 3.3 Demarcation within the Nonfluidized Mode: TRANPACFLO and
PACFLO 355 Equations Describing Each Flow Regime 4.1 Equations for PACFLO 355 4.2 Equations for TRANPACFLO 357 4.3 Equations for Type I Fluidized Flow 4.4 Equations for Type 11 Fluidized Flow Coexistence of Flow Modes 359 5.1 Introduction 359
355
357 358
5.2 Coexistence of Flow Regimes at Constant Superficial Fluid Velocity 359 5.2.1 General Classification 359 5.2.2 Type I Lean-Phase Fluidized Flow Coexistence with
PACFLO/TRANPACFLO 360 5.2.3 Type I Fluidized Flow (Lean-Phasel Coexistence with Type 11 Fluidized
Flow (Dense-Phase) 362 5.2.4 Type I Dense-Phase Fluidized Flow Coexistence with
PACFLOITRANPACFLO 365
5.3 Coexistence of Flow Modes with Variation in the Superficial Velocity 366 5.3.1 General Classification 366 5.3.2 Coexistence of Flow Modes Caused by Gas Compression 366 5.3.3 Coexistence of Flow Modes Caused by Introduction of Aeration
Gas 368
6 Effects of Gas Compression and Aeration 372 6.1 Gas Compression 372 6.2 Aeration 374
6.2.1 Aeration Required for Counteracting Gas Compression 374 6.2.2 Aeration in Excess of that Required for Counteracting Gas
Compression 375
7 Flow of Gas-Solid Mixtures through an Orifice or a Valve 377 7. 1 Introduction 377 7.2 Flow of a Fluidized Mixture through an Orifice 378
7.2.1 Solids 378 7.2.2 Gas 381
Conients
7.3 Nonfluidized Flow through an Orifice 382 7.3.1 Nonfluidized Flow through an Orifice with No Fluid Drag
Effects 384 7.3.2 Nonfluidized Flow through an Orifice with Fluid Drag Effects 386
7.4 Flow through Land J Valves 387 7.5 Summary of Gas-Solid Flow through Valves 390
8 Stability of Standpipe Flow 391 8.1 Introduction 391 8.2 Stability of Uniform Suspension Flow 392 8.3 Flooding Instability 393 8.4 Stability fram Continuity (Kinematic) Wave Direction
Consideration 394 8.5 Ledinegg Supply-Demand Analysis of Flow Stability 8.6 Multiple Steady-State and Bifurcation-Type Instability
396 400
8.7 Oscillatory Steady State 400 9 Analyses of Industrial Standpipe Systems 401
9.1 Introduction 401 9.2 System with Fixed P" P3 , and z 402
9.2.1 One Fluidized Flow Mode Throughout 402 9.2.2 One Nonfluidized Mode Throughout 404 9.2.3 Multiple Steady States and Hysteresis 405 9.2.4 Coexistence of Two Flow Modes 406
9.3 System with Fixed Pl1 P3 , and Ws 407 9.3.1 Coexistence of Lean-Phase and Dense-Phase Fluidized Flow 9.3.2 Coexistence of Lean-Phase Fluidized Flow with TRANPACFLO 9.3.3 Summary of the Case Study for the Fig. 3 System 411
9.4 Stand pipe in Multiple Fluidized Beds 411 9.5 System with Fixed P, and z and with P3 Dependent
on Ws 415 9.6 Concluding Remarks 416
Nomenclature 417 References 419
Chapter 6 Core-Annular Flow of Oi! and Water through a Pipeline R. V. A. Gliemans and G. Goms 427
1 Introduction 427 2 Core Flow Characteristics and Literature Review 430
408 410
2.1 Criteria for the Existence of Stable Core-Ännular Flow 431 2.1.1 Practical Observations 431 2.1.2 Hydrodynamic Stability 431 2.1.3 Velocity Range for Stable Core Flow 432
2.2 Existing Theoretical Models and Correlation Methods 434 2.2.1 Hold-up 434 2.2.2 Pressure Loss for Stable Cora Flow 436
xi
xii Contents
2.3 Pressure Loss during Restart of Co re Flow from a Stratified Layer 443 2.3.1 Introduction 443 2.3.2 Completely Stratified Flow 443 2.3.3 Partially Stratified Flow 444 2.3.4 Comparison with Experimental Data 446
3 A New Theoretical Model: The Lubricating-Film Model 447 3.1 Model Description 448 3.2 Qualitative Predictions 450
3.2.1 Sensitivity Study 450 3.2.2 Conclusions 454
4 Experiments in 2- and 8-in Pipes 458 5 Comparison between the Theoretical Model and Experiments 459 6 Conclusions 467 Nomenclature 469 References 471 Appendix 1 Basic Equations of the Lubricating-Film Model 472
A 1.1 Derivation of Basic Equations 472 A 1.2 Solution Procedure 474
Index 477
Preface
This is the second volume of Multiphase Science and TechnoJogy, a new international series of books intended to provide authoritative overviews of important areas in multiphase systems. The alm is to have systematic and tutorial presentations of the state of knowledge in various areas. The objective of the chapters is to allow the nonspecialist reader to gain an up-to-date idea of the present state of development in a given subject. The response to Volume 1 of the se ries has been very positive, and we believe that the present volume will be equally weil received.
Volume 1 was concerned entirely with gas-liquid systems, and the first four chapters of the present volume also relate to such systems. However, the intention of the se ries is to cover a wide range of multiphase systems, and we are, therefore, pleased to include in the present volume chapters that refer to liquidliquid and gas-solid multiphase flows, respectively.
The first chapter in the present volume is by Professor A. E. Dukler of the University of Houston, Texas, and Professor Y. Taitel of Tel-Aviv University, Israel. This chapter summarizes work carried out in collaboration with these two universities over the past few years on the subject of flow pattern modeling in gasliquid flows. This work has given a new impetus to the interpretation of flow patterns, and the chapter brings together, in a complete coverage of the subject, all the various modeling schemes developed by the authors. Some previously unpublished information (e.g., on the effect of phase change on flow pattern) is included also.
An important phenomenon governing flow configuration in two-phase flows is that of "flooding" or "countercurrent flow limitation" (CCFL). A wide variety of experimental data, analytical interpretations, and empirical correlations exist in the literature, and an overall critical review of this information is given in Chapter 2, by Professor S. G. Bankoff and Dr. S. C. Lee of Northwestern University, llIinois. This chapter aims to classify the information in this difficult area and should provide a useful reference for the many people interested in this subject.
Chapter 3, by Dr. D. C. Groeneveld and Dr. C. W. Snoek of the Chalk River Laboratory of Atomic Energy of Canada, Ltd , presents a very detailed examination of the heat transfer correlations used in reactor safety analysis. Since the prediction of fuel temperature response following a postulated accident is the central objective of reactor safety analysis, the heat transfer correlations used in the prediction codes are obviously of key importance. Drs. Groeneveld and Lee have examined the wide range of alternative correlations available and make recommendations for prediction covering a wide range of regimes, in the particular context of nuclear safety prediction codes.
The final chapter on gas-liquid systems is Chapter 4 by Dr. P. B. Whalley of the University of Oxford, England, and Dr. G. F. Hewitt (one of the editors) from the Harweil Laboratory, England, and covers the subject of reboilers as used in
xiii
xiv Preface
the chemical processing industry. The inclusion of a chapter of this type, referring to equipment behavior and design, is in line with the editors' policy of covering the whole range from fundamental theory to application. Reboilers are of considerable importance in providing a reflux vapor stream in distillation processes and take a number of different forms. Alternative reboiler configurations are described, their operating problems discussed and, information on design approaches presented.
The fifth chapter is the first one in the series to be concerned with gas-solid flows and is written by Professors L. S. Leung and B. J. Jones of the University of Queensland, Australia. This chapter is concerned with gas-solid mixture flow in equipment, specifically in standpipes and valves.
Chapter 6 is by Dr. R. V. A. Oliemans of the Shell Petroleum Company, Amsterdam, Holland, and Professor G. Ooms of Delft University, Holland. It concerns the problems of simultaneous flow in a pipeline and of oi! and water in the core-annular regime. For highly viscous oils, the pressure gradient along the channel may be reduced by introducing water that flows at the surface of the tube and facilitates the passage of the oil. The chapter also describes experimental and analytical work on this topic, which is of increasing importance in the context of oil recovery.
The editors would like to thank the authors for their contributions, wh ich should combine to make this volume a useful contribution to the literature on multiphase systems. We are indebted to the many reviewers; their comments were taken into account by the authors in preparing the final vers ions of the text.
The Editors
Contents of Volume 1
Preface
Chapter 1 Spray Cooling of Hot Surfaces L. Bolle and J. C. Moureau
1 Introduction 2 Main Characteristics of a Liquid Spray 3 Hydrodynamic Behavior of Droplets Impinging on a Hot Plate 4 Heat Transfer during the Impact of a Drop 5 Heat Transfer between a Hot Plate and a Spray: Theoretical Model
and Experiments 6 Conclusions Nomenclature References
Chapter 2 The Spherical Droplet in Gaseous Carrier Streams: Review and Synthesis George Gyarmathy
1 Introduction 2 Statement of Problem, Dimensional Analysis 3 Transfer of Heat, Mass, and Momentum to a Sphere 4 Equilibrium and Stability of Droplets 5 Growth and Vaporization 6 Application 7 Critical Discussion and Conclusions Nomenclature References Appendix 1 Summary of Some Elementary Relationships
and of Representative Materials Data Appendix 2 Appendix 3 Appendix 4 Appendix 5
Balance Equations for the Two-Phase Fluid Sampie Free Molecular Transfer Processes in Mixture Carriers The Analysis of Droplet Surface Temperature Biographic Notes Concerning the Non-dimensional Named Groups Proposed
Chapter 3 Boiling in Multicomponent Fluids
1 Introduction 2 Phase Equilibrium 3 Onset of Boiling 4 Bubble Growth Dynamics 5 Nucleate Boiling Heat Transfer 6 Critical Heat Flux
R. A. W. Shock
xv
xvi
7 Film Boiling 8 Flow Boiling and Evaporation Conclusions Nomenclature References Appendix
Contents
Chapter 4 Contact Angles
1 Introduction
Jacques Chappuis
2 Liquid Surfaces 3 Solid Surfaces 4 Adsorption on Solid Surfaces 5 Contact Angles on Smooth and Homogeneous Solid Surfaces 6 Hysteresis of Contact Angles on Real Solid Surfaces 7 The Wetting Tensiometer: Analysis of a Method ,of Measuring
Contact Angles 8 Interpretation of Contact Angle Values 9 Nonequilibrium Contact Angles Nomenclature References
Subject Index
