Cavitation and Bubble Dynamics CAVITATION AND BUBBLE DYNAMICS by Christopher Earls Brennen OPEN © Oxford University Press 1995 Also available as a bound book ISBN 0-19-509409-3 http://caltechbook.library.caltech.edu/archive/00000001/00/bubble.htm7/8/2003 3:53:57 AM Contents - Cavitation and Bubble Dynamics CAVITATION AND BUBBLE DYNAMICS by Christopher Earls Brennen © Oxford University Press 1995 Preface Nomenclature CHAPTER 1. PHASE CHANGE, NUCLEATION, AND CAVITATION 1.1 Introduction 1.2 The Liquid State 1.3 Fluidity and Elasticity 1.4 Illustration of Tensile Strength 1.5 Cavitation and Boiling 1.6 Types of Nucleation 1.7 Homogeneous Nucleation Theory 1.8 Comparison with Experiments 1.9 Experiments on Tensile Strength 1.10 Heterogeneous Nucleation 1.11 Nucleation Site Populations 1.12 Effect of Contaminant Gas 1.13 Nucleation in Flowing Liquids 1.14 Viscous Effects in Cavitation Inception 1.15 Cavitation Inception Measurements 1.16 Cavitation Inception Data 1.17 Scaling of Cavitation Inception References CHAPTER 2. SPHERICAL BUBBLE DYNAMICS 2.1 Introduction 2.2 Rayleigh-Plesset Equation http://caltechbook.library.caltech.edu/archive/00000001/00/content.htm (1 of 5)7/8/2003 3:53:59 AM Contents - Cavitation and Bubble Dynamics 2.3 Bubble Contents 2.4 In the Absence of Thermal Effects 2.5 Stability of Vapor/Gas Bubbles 2.6 Growth by Mass Diffusion 2.7 Thermal Effects on Growth 2.8 Thermally Controlled Growth 2.9 Nonequilibrium Effects 2.10 Convective Effects 2.11 Surface Roughening Effects 2.12 Nonspherical Perturbations References CHAPTER 3. CAVITATION BUBBLE COLLAPSE 3.1 Introduction 3.2 Bubble Collapse 3.3 Thermally Controlled Collapse 3.4 Thermal Effects in Bubble Collapse 3.5 Nonspherical Shape during Collapse 3.6 Cavitation Damage 3.7 Damage due to Cloud Collapse 3.8 Cavitation Noise 3.9 Cavitation Luminescence References CHAPTER 4. DYNAMICS OF OSCILLATING BUBBLES 4.1 Introduction 4.2 Bubble Natural Frequencies 4.3 Effective Polytropic Constant 4.4 Additional Damping Terms 4.5 Nonlinear Effects 4.6 Weakly Nonlinear Analysis 4.7 Chaotic Oscillations http://caltechbook.library.caltech.edu/archive/00000001/00/content.htm (2 of 5)7/8/2003 3:53:59 AM Contents - Cavitation and Bubble Dynamics 4.8 Threshold for Transient Cavitation 4.9 Rectified Mass Diffusion 4.10 Bjerknes Forces References CHAPTER 5. TRANSLATION OF BUBBLES 5.1 Introduction 5.2 High Re Flows around a Sphere 5.3 Low Re Flows around a Sphere 5.4 Marangoni Effects 5.5 Molecular Effects 5.6 Unsteady Particle Motions 5.7 Unsteady Potential Flow 5.8 Unsteady Stokes Flow 5.9 Growing or Collapsing Bubbles 5.10 Equation of Motion 5.11 Magnitude of Relative Motion 5.12 Deformation due to Translation References CHAPTER 6. HOMOGENEOUS BUBBLY FLOWS 6.1 Introduction 6.2 Sonic Speed 6.3 Sonic Speed with Change of Phase 6.4 Barotropic Relations 6.5 Nozzle Flows 6.6 Vapor/Liquid Nozzle Flow 6.7 Flows with Bubble Dynamics 6.8 Acoustics of Bubbly Mixtures 6.9 Shock Waves in Bubbly Flows 6.10 Spherical Bubble Cloud References http://caltechbook.library.caltech.edu/archive/00000001/00/content.htm (3 of 5)7/8/2003 3:53:59 AM Contents - Cavitation and Bubble Dynamics CHAPTER 7. CAVITATING FLOWS 7.1 Introduction 7.2 Traveling Bubble Cavitation 7.3 Bubble/Flow Interactions 7.4 Experimental Observations 7.5 Large-Scale Cavitation Structures 7.6 Vortex Cavitation 7.7 Cloud Cavitation 7.8 Attached or Sheet Cavitation 7.9 Cavitating Foils 7.10 Cavity Closure References CHAPTER 8. FREE STREAMLINE FLOWS 8.1 Introduction 8.2 Cavity Closure Models 8.3 Cavity Detachment Models 8.4 Wall Effects and Choked Flows 8.5 Steady Planar Flows 8.6 Some Nonlinear Results 8.7 Linearized Methods 8.8 Flat Plate Hydrofoil 8.9 Cavitating Cascades 8.10 Three-Dimensional Flows 8.11 Numerical Methods 8.12 Unsteady Flows References Back to front page Last updated 1/1/00. http://caltechbook.library.caltech.edu/archive/00000001/00/content.htm (4 of 5)7/8/2003 3:53:59 AM Contents - Cavitation and Bubble Dynamics Christopher E. Brennen http://caltechbook.library.caltech.edu/archive/00000001/00/content.htm (5 of 5)7/8/2003 3:53:59 AM Preface - Cavitation and Bubble Dynamics - Christopher E. Brennen CAVITATION AND BUBBLE DYNAMICS by Christopher Earls Brennen © Oxford University Press 1995 Preface to the original OUP hardback edition 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 multiphase 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 seminar 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 immensely from their scholarship and their friendship. I also owe much to my many colleagues in the American Society of Mechanical Engineers whose insights 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. Christopher Earls Brennen, Pasadena, Calif. June 1994 Preface to the Internet edition http://caltechbook.library.caltech.edu/archive/00000001/00/preface.htm (1 of 2)7/8/2003 3:53:59 AM Preface - Cavitation and Bubble Dynamics - Christopher E. Brennen Though my conversion of "Cavitation and Bubble Dynamics" from the hardback book to HTML is rough in places, I am so convinced of the promise of the web that I am pleased to offer this edition freely to those who wish to use it. This new medium clearly involves some advantages and some disadvantages. The opportunity to incorporate as many color photographs as I wish (and perhaps even some movies) is a great advantage and one that I intend to use in future modifications. Another advantage is the ability to continually correct the manuscript though I will not undertake the daunting task of trying to keep it up to date. A disadvantage is the severe limitation in HTML on the use of mathematical symbols. I have only solved this problem rather crudely and apologize for this roughness in the manuscript. In addition to those whom I thanked earlier, I would like to express my thanks to my academic home, the California Institute of Technology, for help in providing the facilities used to effect this conversion, and to the Sherman-Fairchild Library at Caltech whose staff provided much valuable assistance. I am also most grateful to Oxford University Press for their permission to place this edition on the internet. Christopher Earls Brennen, Pasadena, Calif. July 2002 Back to table of contents http://caltechbook.library.caltech.edu/archive/00000001/00/preface.htm (2 of 2)7/8/2003 3:53:59 AM Nomenclature - Cavitation and Bubble Dynamics - Christopher E. Brennen CAVITATION AND BUBBLE DYNAMICS by Christopher Earls Brennen © Oxford University Press 1995 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 c k Phase velocity for wavenumber k c P Specific heat at constant pressure C D Drag coefficient C L Lift coefficient , Unsteady lift coefficients C M Moment coefficient , Unsteady moment coefficients C ij Lift/drag coefficient matrix C p Coefficient of pressure C pmin 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 f N A thermodynamic property of the phase or component, N Fr Froude number g Acceleration due to gravity g x Component of the gravitational acceleration in direction, x http://caltechbook.library.caltech.edu/archive/00000001/00/nomen.htm (1 of 6)7/8/2003 3:54:00 AM Nomenclature - Cavitation and Bubble Dynamics - Christopher E. Brennen g N A thermodynamic property of the phase or component, N (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 g• 4 /ρS 3 i,j,k Indices i Square root of -1 in free streamline analysis I Acoustic impulse I * Dimensionless acoustic impulse, 4πI {\cal R} / ρ L U ∞ R H 2 I Ki Kelvin impulse vector j Square root of -1 k Boltzmann's constant, polytropic constant or wavenumber k N Thermal conductivity or thermodynamic property of N K G Gas constant K ij Added mass coefficient matrix, 3M ij /4ρπR 3 Kc Keulegan-Carpenter number Kn Knudsen number, λ/2R • Typical dimension in the flow, cavity half-length L Latent heat of vaporization m Mass m G Mass of gas in bubble m p Mass of particle M ij Added mass matrix n Index used for harmonics or number of sites per unit area N(R) Number density distribution function of R Cavitation event rate Nu Nusselt number p Pressure p a Radiated acoustic pressure p s Root mean square sound pressure p S A sound pressure level p G Partial pressure of gas http://caltechbook.library.caltech.edu/archive/00000001/00/nomen.htm (2 of 6)7/8/2003 3:54:00 AM [...]... 1 - Cavitation and Bubble Dynamics - Christopher E Brennen CAVITATION AND BUBBLE DYNAMICS by Christopher Earls Brennen © Oxford University Press 1995 CHAPTER 1 PHASE CHANGE, NUCLEATION, AND CAVITATION 1.1 INTRODUCTION This first chapter will focus on the mechanisms of formation of two-phase mixtures of vapor and liquid Particular attention will be given to the process of the creation of vapor bubbles... Weber (1926), Farkas (1927), Becker and Doring (1935), Zeldovich (1943), and others For reviews of the subject, the reader is referred to the books of Frenkel (1955) and Skripov (1974), to the recent text by Carey (1992) and to the reviews by Blake (1949), Bernath (1952), Cole (1970), Blander and Katz (1975), and Lienhard and Karimi (1981) We present here a brief and simplified version of homogeneous...Nomenclature - Cavitation and Bubble Dynamics - Christopher E Brennen P Pseudo-pressure Pe Peclet number, usually WR/αL q qc Magnitude of velocity vector Q r R RB Source strength Radial coordinate Bubble radius RH Headform radius RM Maximum bubble radius RN Cavitation nucleus radius RP Nucleation site radius Free surface velocity Equivalent... magnitude of the latent heat of vaporization and the critical temperature, it fails dismally to predict the tensile strength that a liquid can withstand One must conclude that unlike the http://caltechbook.library.caltech.edu/archive/00000001/00/chap1.htm (6 of 33)7/8/2003 3:54:07 AM Chapter 1 - Cavitation and Bubble Dynamics - Christopher E Brennen latent heat and critical temperature, the tensile strength... cavitation number σij Stress tensor Σ Thermal parameter in bubble growth τ ø Volume of particle or bubble Velocity potential ø′ Acceleration potential http://caltechbook.library.caltech.edu/archive/00000001/00/nomen.htm (4 of 6)7/8/2003 3:54:00 AM Nomenclature - Cavitation and Bubble Dynamics - Christopher E Brennen φ Fractional perturbation in bubble radius Φ Potential energy χ log(qc/|w|) ψ Stream function... three different water tunnels (Peterson et al 1975, Gates and Bacon 1978, Katz 1978) at the cavitation numbers, σ, as shown) and in the ocean off Los Angeles, Calif (O'Hern et al 1985, 1988) http://caltechbook.library.caltech.edu/archive/00000001/00/chap1.htm (18 of 33)7/8/2003 3:54:07 AM Chapter 1 - Cavitation and Bubble Dynamics - Christopher E Brennen It is much more difficult to identify the character... incipient cavitation number and denoted by σi For the moment we shall ignore the practical difficulties involved in observing cavitation inception Further reduction in σ below σi causes an increase in the number and extent of vapor bubbles Figure 1.9 Schematic of pressure distribution on a streamline In the hypothetical flow of a liquid that cannot withstand any tension and in which vapor bubbles appear... http://caltechbook.library.caltech.edu/archive/00000001/00/chap1.htm (5 of 33)7/8/2003 3:54:07 AM Chapter 1 - Cavitation and Bubble Dynamics - Christopher E Brennen completely rupture the liquid or solid since for x>x1 the attractive force is insufficient to counteract that tensile force In fact, liquids and solids have compressibility moduli, κ, which are usually in the range of 1010 to 1011 kg/m s2 and since the pressure, p=-κ(∆V/Vo), it follows that the... during http://caltechbook.library.caltech.edu/archive/00000001/00/chap1.htm (9 of 33)7/8/2003 3:54:07 AM Chapter 1 - Cavitation and Bubble Dynamics - Christopher E Brennen the available time It is of interest to substitute a typical surface tension, S=0.05 kg/s2, and a critical vacancy or bubble size, RC, comparable with the intermolecular distance of 10-10 m Then the calculated tensile strength, ∆pC,... superheat at atmospheric pressure is about 300°C and the maximum that has been attained experimentally is 280°C The reasons for this http://caltechbook.library.caltech.edu/archive/00000001/00/chap1.htm (13 of 33)7/8/2003 3:54:07 AM Chapter 1 - Cavitation and Bubble Dynamics - Christopher E Brennen discrepancy do not seem to be well understood (Eberhart and Schnyders 1973) The above remarks addressed . coefficient , Unsteady lift coefficients C M Moment coefficient , Unsteady moment coefficients C ij Lift/drag coefficient matrix C p Coefficient of pressure C pmin Minimum coefficient. AM Chapter 1 - Cavitation and Bubble Dynamics - Christopher E. Brennen CAVITATION AND BUBBLE DYNAMICS by Christopher Earls Brennen © Oxford University Press 1995 CHAPTER 1. PHASE CHANGE, NUCLEATION,. by increasing the temperature. Then an equivalent description of the state at D is to call it superheated and to refer to the difference between the temperatures at D and D′ as the superheat.