Cavitation and Bubble Dynamics Christopher E. Brennen California Institute of Technology Pasadena, California New York Oxford Oxford University Press 1995 Oxford University Press Oxford New York Athens Auckland Bangkok Bombay Calcutta Cape Town Dar-es-Salaam Delhi Florence Hong Kong Istanbul Karachi Kuala Lumpur Madras Madrid Melbourne Mexico City Nairobi Paris Singapore Taipei Tokyo Toronto and associated companies in Berlin Ibadan Copyright c 1995 by Oxford University Press, Inc. Published by Oxford University Press, Inc., 200 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Brennen, Christopher Earls, 1941- Cavitation and bubble dynamics / Christopher Earls Brennen. p.cm.—(Oxford engineering science series; 44) Includes bibliographical references and index. Cavitation and bubble dynamics / Christopher Earls Brennen. 1. Multiphase flow. 2. Cavitation 3. Bubbles I. Title II. Series TA357.5.M84B74 1995 620.1’064–dc20 94-18365 ISBN 0-19-509409-3 (alk. paper) Printing(lastdigit):987654321 Printed in the United States of America on acid-free paper Preface This book is intended as a combination of a reference book for those who work with cavitation or bubble dynamics and as a monograph for advanced students interested in some of the basic problems associated with this category of multi- phase flows. A book like this has many roots. It began many years ago when, as a young postdoctoral fellow at the California Institute of Technology, I was asked to prepare a series of lectures on cavitation for a graduate course cum sem- inar series. It was truly a baptism by fire, for the audience included three of the great names in cavitation research, Milton Plesset, Allan Acosta, and Theodore Wu, none of whom readily accepted superficial explanations. For that, I am immensely grateful. The course and I survived, and it evolved into one part of a graduate program in multiphase flows. There are many people to whom I owe a debt of gratitude for the roles they played in making this book possible. It was my great good fortune to have known and studied with six outstanding scholars, Les Woods, George Gadd, Milton Plesset, Allan Acosta, Ted Wu, and Rolf Sabersky. I benefited im- mensely from their scholarship and their friendship. I also owe much to my many colleagues in the American Society of Mechanical Engineers whose in- sights fill many of the pages of this monograph. The support of my research program by the Office of Naval Research is also greatly appreciated. And, of course, I feel honored to have worked with an outstanding group of graduate students at Caltech, including Sheung-Lip Ng, Kiam Oey, David Braisted, Luca d’Agostino, Steven Ceccio, Sanjay Kumar, Douglas Hart, Yan Kuhn de Chizelle, Beth McKenney, Zhenhuan Liu, Yi-Chun Wang, and Garrett Reisman, all of whom studied aspects of cavitating flows. The book is dedicated to Doreen, my companion and friend of over thirty years, who tolerated the obsession and the late nights that seemed necessary to bring it to completion. To her I owe more than I can tell. Pasadena, Calif. C.E.B. June 1994 3 Contents Nomenclature 9 1 PHASE CHANGE, NUCLEATION, AND CAVITATION 15 1.1INTRODUCTION.......................... 15 1.2THELIQUIDSTATE........................ 16 1.3FLUIDITYANDELASTICITY.................. 17 1.4 ILLUSTRATION OF TENSILESTRENGTH....................... 19 1.5CAVITATIONANDBOILING................... 21 1.6TYPESOFNUCLEATION..................... 22 1.7 HOMOGENEOUS NUCLEATION THEORY............................... 23 1.8COMPARISONWITHEXPERIMENTS............. 25 1.9 EXPERIMENTS ON TENSILE STRENGTH............................. 28 1.10HETEROGENEOUSNUCLEATION............... 28 1.11NUCLEATIONSITEPOPULATIONS............... 30 1.12 EFFECT OF CONTAMINANT GAS . ........... 33 1.13NUCLEATIONINFLOWINGLIQUIDS............. 34 1.14 VISCOUS EFFECTS IN CAVITATIONINCEPTION..................... 36 1.15 CAVITATION INCEPTION MEASUREMENTS......................... 37 1.16CAVITATIONINCEPTIONDATA................ 40 1.17SCALINGOFCAVITATIONINCEPTION............ 43 REFERENCES............................ 43 2 SPHERICAL BUBBLE DYNAMICS 47 2.1INTRODUCTION.......................... 47 2.2RAYLEIGH-PLESSETEQUATION................ 47 2.3BUBBLECONTENTS........................ 50 2.4 IN THE ABSENCE OF THERMAL EFFECTS............................... 53 2.5STABILITYOFVAPOR/GASBUBBLES............ 57 5 2.6GROWTHBYMASSDIFFUSION................. 61 2.7THERMALEFFECTSONGROWTH............... 63 2.8THERMALLYCONTROLLEDGROWTH............ 65 2.9NONEQUILIBRIUMEFFECTS.................. 67 2.10CONVECTIVEEFFECTS..................... 68 2.11SURFACEROUGHENINGEFFECTS............... 70 2.12NONSPHERICALPERTURBATIONS.............. 71 REFERENCES............................ 75 3 CAVITATION BUBBLE COLLAPSE 79 3.1INTRODUCTION.......................... 79 3.2BUBBLECOLLAPSE........................ 79 3.3THERMALLYCONTROLLEDCOLLAPSE........... 83 3.4 THERMAL EFFECTS IN BUBBLECOLLAPSE........................ 84 3.5 NONSPHERICAL SHAPE DURING COLLAPSE.............................. 84 3.6CAVITATIONDAMAGE...................... 91 3.7DAMAGEDUETOCLOUDCOLLAPSE............. 94 3.8CAVITATIONNOISE........................ 96 3.9CAVITATIONLUMINESCENCE.................104 REFERENCES............................107 4 DYNAMICS OF OSCILLATING BUBBLES 113 4.1INTRODUCTION..........................113 4.2BUBBLENATURALFREQUENCIES...............114 4.3EFFECTIVEPOLYTROPICCONSTANT............118 4.4ADDITIONALDAMPINGTERMS................120 4.5NONLINEAREFFECTS......................122 4.6 WEAKLY NONLINEAR ANALYSIS . ...............123 4.7CHAOTICOSCILLATIONS....................126 4.8 THRESHOLD FOR TRANSIENT CAVITATION............................127 4.9RECTIFIEDMASSDIFFUSION..................128 4.10BJERKNESFORCES........................131 REFERENCES............................133 5 TRANSLATION OF BUBBLES 137 5.1INTRODUCTION..........................137 5.2HIGHReFLOWSAROUNDASPHERE.............138 5.3LOWReFLOWSAROUNDASPHERE.............140 5.4MARANGONIEFFECTS......................145 5.5MOLECULAREFFECTS......................147 5.6UNSTEADYPARTICLEMOTIONS................148 5.7UNSTEADYPOTENTIALFLOW.................151 5.8UNSTEADYSTOKESFLOW...................154 5.9GROWINGORCOLLAPSINGBUBBLES............158 5.10EQUATIONOFMOTION.....................160 5.11MAGNITUDEOFRELATIVEMOTION.............164 5.12 DEFORMATION DUE TO TRANSLATION...........................166 REFERENCES............................171 6 HOMOGENEOUS BUBBLY FLOWS 175 6.1INTRODUCTION..........................175 6.2 SONIC SPEED . .........................176 6.3 SONIC SPEED WITH CHANGE OFPHASE..............................179 6.4BAROTROPICRELATIONS....................183 6.5NOZZLEFLOWS..........................185 6.6VAPOR/LIQUIDNOZZLEFLOW.................190 6.7 FLOWS WITH BUBBLE DYNAMICS . ...........194 6.8ACOUSTICSOFBUBBLYMIXTURES..............196 6.9SHOCKWAVESINBUBBLYFLOWS..............199 6.10SPHERICALBUBBLECLOUD..................205 REFERENCES............................212 7 CAVITATING FLOWS 217 7.1INTRODUCTION..........................217 7.2TRAVELINGBUBBLECAVITATION..............218 7.3BUBBLE/FLOWINTERACTIONS................219 7.4EXPERIMENTALOBSERVATIONS................220 7.5 LARGE-SCALE CAVITATION STRUCTURES............................227 7.6VORTEXCAVITATION......................227 7.7CLOUDCAVITATION.......................232 7.8ATTACHEDORSHEETCAVITATION..............233 7.9CAVITATINGFOILS........................237 7.10CAVITYCLOSURE.........................238 REFERENCES............................240 8 FREE STREAMLINE FLOWS 245 8.1INTRODUCTION..........................245 8.2CAVITYCLOSUREMODELS...................248 8.3CAVITYDETACHMENTMODELS................251 8.4 WALL EFFECTS AND CHOKEDFLOWS..........................256 8.5 STEADY PLANAR FLOWS . ..................259 8.6SOMENONLINEARRESULTS..................262 8.7LINEARIZEDMETHODS.....................267 8.8FLATPLATEHYDROFOIL....................270 8.9CAVITATINGCASCADES.....................272 8.10THREE-DIMENSIONALFLOWS.................278 8.11NUMERICALMETHODS.....................278 8.12UNSTEADYFLOWS........................280 REFERENCES............................284 INDEX 291 Nomenclature ROMAN LETTERS a Amplitude of wave-like disturbance A Cross-sectional area or cloud radius b Body half-width B Tunnel half-width c Concentration of dissolved gas in liquid, speed of sound, chord ck Phase velocity for wavenumber k cP Specific heat at constant pressure CD Drag coefficient CL Lift coefficient C˜Lh, C˜Lp Unsteady lift coefficients CM Moment coefficient C˜Mh, C˜Mp Unsteady moment coefficients Cij Lift/drag coefficient matrix Cp Coefficient of pressure Cpmin Minimum coefficient of pressure d Cavity half-width, blade thickness to spacing ratio D Mass diffusivity f Frequency in Hz. f Complex velocity potential, φ + iψ fN A thermodynamic property of the phase or component, N Fr Froude number g Acceleration due to gravity gx Component of the gravitational acceleration in direction, x gN A thermodynamic property of the phase or component, N G(f) Spectral density function of sound h Specific enthalpy, wetted surface elevation, blade tip spacing H Henry’s law constant Hm Haberman-Morton number, normally gµ4/ρS3 i,