boiling heat transfer and two-phase flow, second edition

Series in Chemical and Mechanical Engineering G F Hewitt and C L Tien, Editors Carey, Liquid-Vapor Phase-Change Phenomena: An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment Diwekar, Batch Distillation: Simulation, Optimal Design and Control FORTHCOMING TITLES Tong and Tang, Boiling Heat Transfer and Two-Phase Flow, Second Edition BOILING HEAT TRANSFER AND TWO-PHASE FLOW Second Edition L S Tong, Ph.D Y S Tang, Ph.D Publishing Office USA Taylor & Francis 1101 Vermont Avenue, N.W, Suite 200 Washington, D.C 20005-3521 Tel: (202) 289-2174 Fax: (202) 289-3665 Distribution Center: Taylor & Francis 1900 Frost Road, Suite 101 Bristol, PA 9007-1598 Tel: (215) 785-5800 Fax: (215) 785-5515 Taylor & Francis Ltd UK Gunpowder Square London EC4A 3DE Tel: 171 583 0490 Fax: 71 583 0581 BOILING HEAT TRANSFER AND TWO-PHASE FLOW, Second Edition Copyright © 1997 Taylor & Francis All rights reserved Printed in the United States of America Except as permitted under the United States Copyright Act of 976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher 1234567890 BR BR 987 The editors were Lynne Lackenbach and Holly Seltzer Cover design by Michelle Fleitz Prepress supervisor was Miriam Gonzalez A CIP catalog record for this book is available from the British Library @> The paper in this publication meets the requirements of the ANSI Standard Z39.48-1984 (Permanence of Paper) Library of Congress Cataloging-in-Publication Data Boiling heat transfer and two-phase flow/L S Tong and Y S Tang p cm Includes bibliographical references Tong, L S (Long-sun) Heat-Transmission Ebullition I Tang, Y S (Yu S.) II Title QC320.T65 1997 536' 2-dc20 ISBN 1-56032-485-6 (case) Two-phase flow 96-34009 CIP In Memory of Our Parents CONTENTS xv Preface Preface to the First Edition Symbols xix xxix Unit Conversions xvii INTRODUCTION 1.1 Regimes of boiling 1.2 Two-Phase Flow 3 Flow Boiling Crisis 4 Flow Instability POOL BOILING 2.1 Introduction 2.2 Nucleation and Dynamics of Single Bubbles 2.2.1 Nucleation 2.2.1 Nucleation i n a Pure Liquid 2.2.1 Nucleation at Surfaces 8 10 2.2.2 Waiting Period 2.2.3 Isothermal Bubble Dynamics 23 2.2.4 Isobaric Bubble Dynamics 26 2.2.5 Bubble Departure from a Heated Surface 37 19 vii viii CONTENTS 37 2.2.5.1 Departure Frequency 40 2.2.5.3 Boiling Sound 44 2.2.5.4 Latent Heat Transport and Microconvection by Departing Bubbles 45 2.2.5.5 2.3 Bubble Size at Departure 2.2.5.2 Evaporation-of-Microlayer Theory 45 Hydrodynamics of Pool Boiling Process 50 2.3.1 50 2.3.2 2.4 The Helmholtz Instability The Taylor Instability 52 Pool Boiling Heat Transfer 2.4.1 Dimensional Analysis 54 55 2.4.1.1 55 2.4.1.2 2.4.2 Commonly Used Nondimensional Groups Boiling Models 58 Correlation of Nucleate Boiling Data 60 2.4.2.1 Nucleate Pool Boiling of Ordinary Liquids 60 2.4.2.2 Nucleate Pool Boiling with Liquid Metals 71 Pool Boiling Crisis 80 2.4.3.1 Pool Boiling Crisis in Ordinary Liquids 81 2.4.3.2 2.4.3 Boiling Crisis with Liquid Metals 97 Film Boiling in a Pool 102 2.4.4.1 Film Boiling in Ordinary Liquids 103 2.4.4.2 2.4.4 Film Boiling in Liquid Metals 109 Additional References for Further Study 116 HYDRODYNAMICS OF T WO-PHASE FLOW 119 3.1 Introduction 119 3.2 Flow Patterns in Adiabatic and Diabatic Flows 120 2.5 3.2.1 Flow Patterns in Adiabatic Flow 120 3.2.2 Flow Pattern Transitions in Adiabatic Flow 128 3.2.2.1 Pattern Transition in Horizontal Adiabatic Flow 130 3.2.2.2 Pattern Transition in Vertical Adiabatic Flow 133 3.2.2.3 Adiabatic Flow in Rod Bundles 136 3.2.2.4 Liquid Metal-Gas Two-Phase Systems 140 3.2.3 3.3 Flow Patterns in Diabatic Flow Void Fraction and Slip Ratio in Diabatic Flow 140 147 3.3.1 Void Fraction in Subcooled Boiling Flow 152 3.3.2 Void Fraction in Saturated Boiling Flow 155 3.3.3 Diabatic Liquid Metal-Gas Two-Phase Flow 159 3.3.4 Instrumentation 161 3.3.4.1 Void Distribution Measurement 161 3.3.4.2 Interfacial Area Measurement 163 3.3.4.3 Measurement of the Velocity of a Large Particle 164 3.3.4.4 Measurement of Liquid Film T hickness 166 CONTENTS ix 3.4 Modeling of Two-Phase Flow 68 3.4.1 Homogeneous Model/Drift Flux Model 68 3.4.2 Separate-Phase Model (Two-Fluid Model) 70 3.4.3 Models for Flow Pattern Transition 72 3.4.4 Models for Bubbly Flow 73 3.4.5 Models for Slug Flow (Taitel and Barnea, 990) 74 3.4.6 Models for Annular Flow 77 3.4.6.1 Falling Film Flow 77 3.4.6.2 Countercurrent Two-Phase Annular Flow 80 3.4.6.3 Inverted Annular and Dispersed Flow 80 3.4.7 Models for Stratified Flow (Horizontal Pipes) 82 3.4.8 Models for Transient Two-Phase Flow 83 3.4.8.1 85 3.4.8.2 Transient Slug Flow 86 3.4.8.3 3.5 Transient Two-Phase Flow in Horizontal Pipes Transient Two-Phase Flow in Rod Bundles 86 Pressure Drop in Two-Phase Flow 87 3.5.1 Local Pressure Drop 87 3.5.2 Analytical Models for Pressure Drop Prediction 88 3.5.2.1 Bubbly Flow 88 3.5.2.2 Slug Flow 90 3.5.2.3 Annular Flow 91 3.5.2.4 Stratified Flow 91 3.5.3 Empirical Correlations 94 96 3.5.3.1 Bubbly Flow in Horizontal Pipes 3.5 3.2 Slug Flow 200 3.5.3.3 Annular Flow 201 3.5.3.4 Correlations for Liquid Metal and Other Fluid Systems 3.5.4 Pressure Drop in Rod Bundles 202 207 3.5.4.1 207 3.5.4.2 3.5.5 Steady Two-Phase Flow Pressure Drop in Transient Flow 209 Pressure Drop in Flow Restriction 21 3.5.5.1 21 3.5.5.2 3.6 Steady-State, Two-Phase-Flow Pressure Drop Transient Two-Phase-Flow Pressure Drop 21 Critical Flow and Unsteady Flow 21 3.6.1 Critical Flow in Long Pipes 220 3.6.2 Critical Flow in Short Pipes, Nozzles, and Orifices 225 3.6.3 Blowdown Experiments 228 3.6.3.1 Experiments with Tubes 228 3.6.3.2 Vessel Blowdown 230 Propagation of Pressure Pulses and Waves 231 3.6.4.1 Pressure Pulse Propagation 231 3.6.4.2 Sonic Wave Propagation 236 3.6.4.3 3.6.4 Relationship Among Critical Discharge Rate, Pressure Propagation Rate, and Sonic Velocity 3.7 Additional References for Further Study 239 242 x CONTENTS FLOW BOILING 245 4.1 Introducton 245 4.2 Nucleate Boiling in Flow 248 248 Partial Nucleate Flow Boiling 248 4.2.1.2 4.2.2 Subcooled Nucleate Flow Boiling 4.2.1.1 4.2.1 Fully Developed Nucleate Flow Boiling 257 Saturated Nucleate Flow Boiling 258 4.2.2.1 Liquids 259 4.2.2.2 4.3 Saturated Nucleate Flow Boiling of Ordinary Saturated Nucleate Flow Boiling of Liquid Metals 265 Forced-Convection Vaporization 265 4.3.1 266 4.3.2 Effect of Fouling Boiling Surface 268 4.3.3 4.4 Correlations for Forced-Convection Vaporization Correlations for Liquid Metals 268 Film Boiling and Heat Transfer in Liquid-Deficient Regions 274 4.4.1 Partial Film Boiling (Transition Boiling) 275 4.4.2 Stable Film Boiling 276 4.4.2.1 Film Boiling in Rod Bundles 277 4.4.3 Mist Heat Transfer in Dispersed Flow 277 4.4.3.1 Dispersed Flow Model 279 4.4.3.2 Dryout Droplet Diameter Calculation 281 283 Blowdown Heat Transfer 283 4.4.4.2 Heat Transfer in Emergency Core Cooling Systems 287 4.4.4.3 4.4.5 Transient Cooling 4.4.4.1 4.4.4 Loss-of-Coolant Accident (LOCA) Analysis 288 Liquid-Metal Channel Voiding and Expulsion Models 297 Additional References for Further Study 299 FLOW BOILING CRISIS 303 5.1 Introduction 303 5.2 Physical Mechanisms of Flow Boiling Crisis in Visual Observations 304 4.5 5.2.1 304 5.2.2 Evidence of Surface Dryout in Annular Flow 309 5.2.3 5.3 Photographs of Flow Boiling Crisis Summary of Observed Results 309 Microscopic Analysis of CHF Mechanisms 5.3.1 Liquid Core Convection and Boundary-Layer Effects 317 318 5.3.1 Liquid Core Temperature and Velocity Distribution Analysis 319 5.3.1.2 Boundary-Layer Separation and Reynolds Flux 320 5.3.1.3 Subcooled Core Liquid Exchange and Interface Condensation 5.3.2 Bubble-Layer Thermal Shielding Analysis 5.3.2.1 323 328 Critical Enthalpy in the Bubble Layer (Tong et aI., 1996a) 329 530 REFERENCES Weisman, J , 985, Theoretically Based Predictions of Critical Heat Flux in Rod Bundles, Third Int Conf on Reactor Thermal Hydraulics, Newport, RI (5) Weisman, J , 992, The Current Status of Theoretically Based Approaches to the Prediction of the Critical Heat Flux in Flow Boiling, Nuclear T echnol 99: 1-2 ( ) Weisman, J , A Husain, and B Harshe, 978, Two-Phase Pressure Drop Across Abrupt Changes and Restriction, in Two-Phase Transport and Reactor Saf ety, T N Vezetroglu and S Kakac, Eds., Taylor & Francis, Inc., Washington, DC (3) Weisman, J., and B S Pei, 983, Prediction of CHF in Flow Boiling at Low Qualities, Int J Heat Mass Trans er 26: 463 (5) f Weisman, J , A H Wenzel, L S Tong, D Fitzsimmons, W Thorne, and J Batch, 968, Experimental Determination of the Departure from Nucleate Boiling in Large Rod Bundles at High Pressures, AIChE Chern Eng Prog Symp Ser 64(82): 14- 25 (5) Weisman, J., J Y Yang, and S Usman, 994, A Phenomenological Model for Boiling Heat Transfer and the CHF in Tubes Containing Twisted Tapes, Int J Heat Mass Trans er 37( ):69-80 (4) f Weisman, 1., and S H Ying, 983, Theoretically Based CHF Prediction at Low Qualities and Interme­ diate Flows, Trans Am Nuclear Soc 45:832 (5) Weisman, J., and S H Ying, 985, A Theoretically Based Critical Heat Flux Prediction for Rod Bun­ dles at PWR Conditions, Nuclear Eng Design 85:239-250 (5) Westendorf, W H., and W F Brown, 966, Stability of Intermixing of High-Velocity Vapor with Its Subcooled Liquid in Cocurrent Streams, NASA TN D-3553, Lewis Res Ctr., Cleveland, OH (6) Westinghouse Electric Corp., 969, Thermal Conductivity of Crud, Rep WAPD-TM-9 8, Pittsburgh, PA ( 14) Westwater, W, 956, Boiling of Liquids, Adv Chem Eng 1:2-76 (2) Westwater, W, and D B Kirby, 963, Bubble and Vapor Behavior on a Heated Horizontal Plate during Pool Boiling near Burnout, AIChE Preprint 4, 6th Natl Heat Transfer Conf., Boston, MA (5) Westwater, J W, A J Lowery, and F S Pramuk, 955, Sound of Boiling, Science 122:332-333 (2) Westwater, J W, and J G Santangelo, 955, Photographic Study of Boiling, Ind Eng Chem 47: 605 (2) Westwater, J W, J C Zinn, and K Brobeck, 989, Correlation of Pool Boiling Curves for the Nomo­ logous Group-Freons, Trans A SME, J Heat Trans er 1 : 204-207 (2) f Whalley, P B., 976, The Calculation of Dryout in a Rod Bundle, Rep UK AERE-R-83 9, UK AERE, Harwell, England (5) Whalley, P B., P Hutchinson, and G F Hewitt, 973, The Calculation of Critical Heat Flux in Forced Convective Boiling, Rep AERE-R-7520, European Two Phase Flow Group Meeting, Brussels (5) Whalley, P B., P Hutchinson, and G F Hewitt, 974, The Calculation of Critical Heat Flux in Forced Convection Boiling, Heat Transf 1974, vol IV, pp 290-294, Int Heat Transfer Conf., Tokyo (5) er Wichner, R P , and H W Hoffman, 965, Pressure Drop with Forced Convection Boiling of Po­ tassium, Proc Con! on Applications of Heat Transf Instrumentation to Liquid Metals Experi­ er ments, ANL-7 00, p 535, Argonne National Lab., Argonne, IL (3) Williams, C L., and A C Peterson, Jr., 978, Two Phase Flow Patterns with High Pressure Water in a Heated Four-Rod Bundle, Nuclear Sci Eng 68: 55 (3) Wilson, R H., L J Stanek, J S Gellerstedt, and R A Lee, 969, Critical Heat Flux in a Nonuniformly Heated Rod Bundle, in Two Phase Flow and Heat Trans er in Rod Bundles, pp 56-62, ASME, f New York (5) Witte, L c., J W Stevens, and P J Hemingson, 969, The Effect of Subcooling on the Onset of Transi­ tion Boiling, Am Nuclear Soc Trans 12(2) 806 (4) Wong, Y L., D C Groeneveld, and S C Cheng, 990, Semi-analytical CHF Predictions for Horizontal Tubes, Int J Multiphase Flow 16: 23-1 38 (5) Wright, R M., 96 , Downflow Forced Convection Boiling of Water in Uniformly Heated Tubes, USAEC Rep UCRL-9744, Los Angeles, CA (4) REFERENCES 531 Wulff, W, 978, Lump-Parameter Modeling of One-Dimensional Two-Phase Flow, in Transient Two­ Phase Flow, Proc 2nd Specialists Meeting, vol , pp -2 9, OECD Committee on Safety of Nuclear Installations, Paris (3) Wurtz, 1., 978, An Experimental and Theoretical Investigation of Annular Steam-Water Flow in Tubes and Annular Channels, Riso Natl Lab , Oslo, Norway (5) Wyllie, G , 965, Evaporation and Surface Structure of Liquid, Proc Roy Soc A 19 7: 383 (2) Yadigaroglu, G., 993, Instabilities in Two-Phase Flow, in Workshop on Multiphase Flow and Heat Trans er: Bases, Modeling and Applications, chapter 2, University of California, Santa Barbara, f CA (4) Yadigaroglu, G., and M Andreani, 989, Two Fluid Modeling of Thermal-Hydraulic Phenomena for Best Estimate LWR Safety Analysis, Proc 4th Int Topical Meeting on Nuclear Reactors Thermal­ Hydraulics, Karlsruhe, U Mueller, K Rehnee, and K Rust, Eds., Rep NURETH-4, pp 980996 (3) Yadigaroglu, G., and A E Bergles, 969, An Experimental and Theoretical Study of Density-Wave Oscillation in Two-Phase Flow, M I.T Rep DSR 74629-3 (HTL 74629-67), Massachusetts Insti­ tute of Technology, Cambridge, MA (6) Yadigaroglu, G , and A E Bergles, 972, Fundamental and Higher-Mode Density-Wave Oscillation in Two-Phase Flow: The Importance of Single Phase Region, Trans A SME, J Heat Transf er 94: 89-1 95 (6) Yang, , L C Chow, and M R Pais, 993, Nucleate Boiling Heat Transfer in Spray Cooling, ASME Paper 93-HT-29, Natl Heat Transfer Conf , Atlanta, GA, ASME, New York (4) Ying, S H , and Weisman, 986, Prediction of the CHF in Flow Boiling at Intermediate Qualities, Int J Mass Transf 29( 1 ) : 639- 648 (5) er Yoder, G L., Jr., and W M Rohsenow, 980, Dispersed Flow Film Boiling, MIT Heat Transfer Lab Rep 85694- 03, Massachusetts Institute of Technology, Cambridge, MA (4) Zaker, T A., and A H Wiedermann, 966, Water Depressurization Studies, I1TRI-578-P, pp 1-26, lIT Res Inst , Chicago, Illinois (3) Zaloudek, F R., 963, The Critical Flow of Hot Water through Short Tubes, USAEC Rep HW-77594, Hanford, WA (3) Zeigarnick, Y A., and V D Litvinov, 980, Heat Transfer and Pressure Drop in Sodium Boiling in Tubes, Nuclear Sci Eng 73: 9-28 (4) Zeng, L Z., and F Kausner, 993, Nucleation Site Density in Forced Convection Boiling, Trans A SME, J Heat Transf 15: 5-22 (4) er Zenkevich, B A., and V I Subbotin, 959, Critical Heat Fluxes in Subcooled Water Forced Circula­ tion, J Nuclear Energy, Part B, Reactor T echnol 1: 34-140 (5) Zenkevich, B A., et aI., 969, An Analysis and Correlation of the Experimental Data on Burnout in the Case of Forced Boiling Water in Pipes, Physico Energy Institute, Afomizdat, Moscow, HTFS Transl 2022 (5) Zernick, W, H B Curren, E Elyash, and G Prevette, 962, THINe, A Thermal Hydraulic Interaction Code for Semi-open or Closed Channel Cores, Rep WCAP-3704 Westinghouse Electric Corp., Pittsburgh, PA (App.) Zetzmann, K., 98 , Flow Pattern of Two Phase Flow inside Cooled Tubes, in Two-Phase Flow and Heat Trans er in the Power and Processing Industries, Hemisphere, Washington, DC (3) f Zivi, S M , and A B Jones, 966, An Analysis of EBWR Instability by FABLE Program, Trans Am Nuclear Soc , ANS 966 Annual Meeting, American Nuclear Society, LaGrange Park, IL (6) Zuber, N , 958, On Stability of Boiling Heat Transfer, Trans A SME, J Heat Trans er 80:7 1-720 (2) f Zuber, N., 959, Hydrodynamic Aspects of Boiling Heat Transfer, USAEC Rep AECU-4439, Ph.D thesis, University of California, Los Angeles, CA (2) Zuber, N., 96 , The Dynamics of Vapor Bubbles in Non-uniform Temperature Fields, Int J Heat Mass Transf 2:83-98 (2) er Zuber, N., and A Findlay, 965, Average Volumetric Concentration in Two-Phase Flow System, Trans ASME, J Heat Transf 7:453 (3) er 532 REFERENCES Zuber, N., M Tribus, and W Westwater, 96 , The Hydrodynamics Crisis in Pool Boiling of Satu­ rated and Subcooled Liquids, in International Develvpments in Heat Trans er Part II, pp 230-236, f ASME, New York (2) Zun, I., 985, The Transverse Migration of Bubbles Influenced by Walls in Vertical Two-Phase Bubbly Flow, 2nd Int Conf on Multiphase Flow, London, pp 27-1 39, BHRA, The Fluid Engineering Center, Cranfield, England (3) Zun, I., 988, Transition from Wall Void Peaking to Core Void Peaking in Turbulent Bubbly Flow, in Transient Phenomena in Multiphase Flow, ICHMT Int Seminar, N H Afgan, Ed., pp 225-245, Hemisphere, Washington, DC (3) Zun, I., 990, The Mechanism of Bubble Non-homogenous Distribution in 2-Phase Shear Flow, Nu­ clear Eng Design 118: 55-1 62 (3) INDEX Accommodation coefficient, , 34 Alkali metals, 7, 39, 1-73, 79, 1 , 1 0-1 2, 40, 252, 266, 272, 364, 462 Analysis, one dimensional, 29 Anemometer, hot wire, Anemometry: Doppler, 64 optical, 64 thermal, 64 Apex angle, 3, Area: of influence, 60, 62 local preferable, 37 Attenuation coefficient, 63 Bernoulli effect, 146 Blowdown, 225, 227-228, 230, 283, 286-288 experiments, 9-220, 222 heat transfer, 283 Boiling, flow, 4, 7, 44, 80, 86, 1 7, 245, 249, 25 burnout, (5ee flow boiling crisis) crisis, 4, 303-3 0, 1-322, 328, 33 , 333-334, 338, 342-343, 346-348, 352, 353, 357, 361-363, 366-367, 370, 378-380, 382384, 388, 392, 399-40 , 404-406, 428, 433, 440, 454, 458 460, 466, 469, 473, 479 critical heat flux (CHF), 258, 272-274, 283, 286, 303-305, 309, 4, 7, 322-329, 332-334, 336, 338, 342, 344, 348-35 , 357-363, 366-37 , 373-399, 40 406, 4 7, 420-433, 436, 438, 44 443, 452-455, 460, 46 , 467 film, 274, 277, 279, 283, 306, 307, 1 , 3, 459, 478, 479 departure from, (DFB), 258, 287 dispersed flow, 82, 277 inverted annular, 301 partial, 245, 248, 283, 286, 289 stable, 245, 27 , 274, 276, 283, 306, 307 with liquid metals, 252, 258, 265, 268, 27 , 274 (See also Liquid metals) local, 2, 43, 144, 52, 246, 249, 258, 259, 30 , 1 , 331 nucleate, 202, 245, 248, 25 , 252, , 266, 283, 303, 306, 307, 3 departure from, (DNB), 258, 287, 288, 303307, 0-3 2, 4, 5, 8, 365, 40 , 402, 408 41 partial, 245, 248, 249, 250, 252 subcooled, 143, 248, 249, 257, 258, 305, 338, 34 , 454 (See also local flow boiling) saturated, 143, 144, 55, 258, 266, 30 , 304, 305, 2, 326 transition, (see partial film boiling) Boiling, pool, 4, 7, 5, 44, 46, 50, 54-55, 65, , 72, 78, 80-8 , 83, 86, 99 burnout, 44, 80, 87-88, 93, 97, 1 7, 259 crisis, 5, 50, 56, 80-8 , 99, 1 (See also burnout) 533 534 INDEX Boiling, pool (continued) critical heat flux, 3-4, 54, , 83-86, 88, 90, , 95, 97, 99-1 02, 1 6-I l 7, 393 hydrodynamic prediction of, 88 film, 44, 50, 52, 57, 87-88, 02, 04, 08-1 09, I l 2, 1 5, 277 partial, 2-3, 44, 50, 52, 57, , 84-88, 021 04, 06, I l 2, 1 6- I l stable, 2-3, , 86-87, 22 incipient, 14, 6-19, 79, 80, 59-1 , 248, 255, 298 liquid metals, with, 6- 7, 20, 43, 48, 72, 74, 75, 78, 00-1 02, I lO-1 2, 1 4-I l (See also Liquid metals) nucleate, 1-3, 7, 22, 39, 44-46, 50, 55, 60, 62, 65-67, 69-74, 79, 80, 84, 86-88, 95, 97, 1 , 02, 1 6, 26 , 299 departure from, (DNB), 3, 80 with liquid metals, 14, 39, 44, 48-49, , 7780, 02, 248 saturated, , 39, , 82, 98, 287 stable, 7, 72, 74 subcooled, 25, 44, 83-84, 93, 97, 98 unstable, 72-74, 02 Boiling regimes, 1-3 Boiling sound, 37, 44, 45 Boiling superheat, 7, 79, 80, 252-254, 256 incipient, 59-1 , 252, 254-257, 300 Boiling surface, fouling, 268 thermal conductivity of, 269 Boiling suppression, 8, 9, 260, 266 Boltzmann constant, 8, 38 Boltzmann distribution, Boundary layer, 262, 27 , separation, 320, 32 technique, 73 Bubble: activation, agglomeration, 26 agitation, 58, 59, 248 blanket, 326, 328 (See also vapor blanket) boundary layer, 43, 54, 73, 257, 27 counts, departure, , 2, 7, 6, 9, 37, 38, 40, , 50, 58, 60, 62, 67, 54, 32 , 340, diameter, 299, 340 deposition theory, 74 detached, 143, 53, 54, 33 , 343 diameter, 38, , 43, 56, 60, 62, 03, 22, 300, 369 dispersed, 24, 35, 75 dynamics, 23-25 elongated, 75, 300 embryo, I I , equilibrium equation, 7, 74 frequencies, 24, 25, 40, 67, generation, I , 7, , , 47, 245, 326 growth, , 4, 7, 0, 2, 4, 5, 7, 20, 22-28, 30-34, 37-39, 49, 62, 68, , , 88, 42, 246, 250, 263, 264, 300 interface, 8, 23, 25-27, 29 isolated, 22 layer, 143, 45, 48, 304, 307, 320, 326, 328334, 336, 337, 340, 342, 343, 367, 405, 455 life, 26, 300 nucleation, I , 6, 7, 5, 9, 20, 23, I l 6, 250 population, 9, 40, 50, 67, 245, 246 radius, 25, 35, , 237, 238, 300 release, 03 Reynolds number, 57, 89, 209 (See also boiling Reynolds number) rise velocity, 40, 43, 57, 89 segregation, 43 shape, 19, 22, 300 slip velocity, 57 site, 8, 14, size, , , 24-26, 29, 34, 36, 37, 40, , 50, 54, , 237, 300, 323, , 352, 357, 369, 392 equilibrium, 0, Taylor, 37, 90, unstable, 22 Bubbly flow (,