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<p>Cavitation and Bubble Dynamics</p> <p> CAVITATION AND </p> <p>BUBBLE DYNAMICS </p> <p>by Christopher Earls Brennen</p> <p>OPEN</p> <p> Oxford University Press 1995 Also available as a bound book </p> <p>ISBN 0-19-509409-3 </p> <p> 3:53:57 AM</p> <p>Contents - Cavitation and Bubble Dynamics</p> <p>CAVITATION AND BUBBLE DYNAMICS</p> <p>by Christopher Earls Brennen Oxford University Press 1995 </p> <p>Preface </p> <p>Nomenclature </p> <p>CHAPTER 1. </p> <p>PHASE CHANGE, NUCLEATION, AND CAVITATION </p> <p>1.1 Introduction </p> <p>1.2 The Liquid State </p> <p>1.3 Fluidity and Elasticity </p> <p>1.4 Illustration of Tensile Strength </p> <p>1.5 Cavitation and Boiling </p> <p>1.6 Types of Nucleation </p> <p>1.7 Homogeneous Nucleation Theory </p> <p>1.8 Comparison with Experiments </p> <p>1.9 Experiments on Tensile Strength </p> <p>1.10 Heterogeneous Nucleation </p> <p>1.11 Nucleation Site Populations </p> <p>1.12 Effect of Contaminant Gas </p> <p>1.13 Nucleation in Flowing Liquids </p> <p>1.14 Viscous Effects in Cavitation Inception </p> <p>1.15 Cavitation Inception Measurements </p> <p>1.16 Cavitation Inception Data </p> <p>1.17 Scaling of Cavitation Inception </p> <p>References </p> <p>CHAPTER 2. SPHERICAL BUBBLE DYNAMICS </p> <p>2.1 Introduction </p> <p>2.2 Rayleigh-Plesset Equation </p> <p> (1 of 5)7/8/2003 3:53:59 AM</p> <p>Contents - Cavitation and Bubble Dynamics</p> <p>2.3 Bubble Contents </p> <p>2.4 In the Absence of Thermal Effects </p> <p>2.5 Stability of Vapor/Gas Bubbles </p> <p>2.6 Growth by Mass Diffusion </p> <p>2.7 Thermal Effects on Growth </p> <p>2.8 Thermally Controlled Growth </p> <p>2.9 Nonequilibrium Effects </p> <p>2.10 Convective Effects </p> <p>2.11 Surface Roughening Effects </p> <p>2.12 Nonspherical Perturbations </p> <p>References </p> <p>CHAPTER 3. CAVITATION BUBBLE COLLAPSE </p> <p>3.1 Introduction </p> <p>3.2 Bubble Collapse </p> <p>3.3 Thermally Controlled Collapse </p> <p>3.4 Thermal Effects in Bubble Collapse </p> <p>3.5 Nonspherical Shape during Collapse </p> <p>3.6 Cavitation Damage </p> <p>3.7 Damage due to Cloud Collapse </p> <p>3.8 Cavitation Noise </p> <p>3.9 Cavitation Luminescence </p> <p>References </p> <p>CHAPTER 4. DYNAMICS OF OSCILLATING BUBBLES </p> <p>4.1 Introduction </p> <p>4.2 Bubble Natural Frequencies </p> <p>4.3 Effective Polytropic Constant </p> <p>4.4 Additional Damping Terms </p> <p>4.5 Nonlinear Effects </p> <p>4.6 Weakly Nonlinear Analysis </p> <p>4.7 Chaotic Oscillations </p> <p> (2 of 5)7/8/2003 3:53:59 AM</p> <p>Contents - Cavitation and Bubble Dynamics</p> <p>4.8 Threshold for Transient Cavitation </p> <p>4.9 Rectified Mass Diffusion </p> <p>4.10 Bjerknes Forces </p> <p>References </p> <p>CHAPTER 5. TRANSLATION OF BUBBLES </p> <p>5.1 Introduction </p> <p>5.2 High Re Flows around a Sphere </p> <p>5.3 Low Re Flows around a Sphere </p> <p>5.4 Marangoni Effects </p> <p>5.5 Molecular Effects </p> <p>5.6 Unsteady Particle Motions </p> <p>5.7 Unsteady Potential Flow </p> <p>5.8 Unsteady Stokes Flow </p> <p>5.9 Growing or Collapsing Bubbles </p> <p>5.10 Equation of Motion </p> <p>5.11 Magnitude of Relative Motion </p> <p>5.12 Deformation due to Translation </p> <p>References </p> <p>CHAPTER 6. HOMOGENEOUS BUBBLY FLOWS </p> <p>6.1 Introduction </p> <p>6.2 Sonic Speed </p> <p>6.3 Sonic Speed with Change of Phase </p> <p>6.4 Barotropic Relations </p> <p>6.5 Nozzle Flows </p> <p>6.6 Vapor/Liquid Nozzle Flow </p> <p>6.7 Flows with Bubble Dynamics </p> <p>6.8 Acoustics of Bubbly Mixtures </p> <p>6.9 Shock Waves in Bubbly Flows </p> <p>6.10 Spherical Bubble Cloud </p> <p>References </p> <p> (3 of 5)7/8/2003 3:53:59 AM</p> <p>Contents - Cavitation and Bubble Dynamics</p> <p>CHAPTER 7. CAVITATING FLOWS </p> <p>7.1 Introduction </p> <p>7.2 Traveling Bubble Cavitation </p> <p>7.3 Bubble/Flow Interactions </p> <p>7.4 Experimental Observations </p> <p>7.5 Large-Scale Cavitation Structures </p> <p>7.6 Vortex Cavitation </p> <p>7.7 Cloud Cavitation </p> <p>7.8 Attached or Sheet Cavitation </p> <p>7.9 Cavitating Foils </p> <p>7.10 Cavity Closure </p> <p>References </p> <p>CHAPTER 8. FREE STREAMLINE FLOWS </p> <p>8.1 Introduction </p> <p>8.2 Cavity Closure Models </p> <p>8.3 Cavity Detachment Models </p> <p>8.4 Wall Effects and Choked Flows </p> <p>8.5 Steady Planar Flows </p> <p>8.6 Some Nonlinear Results </p> <p>8.7 Linearized Methods </p> <p>8.8 Flat Plate Hydrofoil </p> <p>8.9 Cavitating Cascades </p> <p>8.10 Three-Dimensional Flows </p> <p>8.11 Numerical Methods </p> <p>8.12 Unsteady Flows </p> <p>References </p> <p>Back to front page </p> <p>Last updated 1/1/00. </p> <p> (4 of 5)7/8/2003 3:53:59 AM</p> <p>Contents - Cavitation and Bubble Dynamics</p> <p>Christopher E. Brennen</p> <p> (5 of 5)7/8/2003 3:53:59 AM</p> <p>Preface - Cavitation and Bubble Dynamics - Christopher E. Brennen</p> <p>CAVITATION AND BUBBLE DYNAMICS</p> <p>by Christopher Earls Brennen Oxford University Press 1995 </p> <p>Preface to the original OUP hardback edition</p> <p>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. </p> <p>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. </p> <p>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. </p> <p>Christopher Earls Brennen, Pasadena, Calif.June 1994 </p> <p>Preface to the Internet edition</p> <p> (1 of 2)7/8/2003 3:53:59 AM</p> <p>Preface - Cavitation and Bubble Dynamics - Christopher E. Brennen</p> <p>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. </p> <p>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. </p> <p>Christopher Earls Brennen, Pasadena, Calif.July 2002 </p> <p>Back to table of contents </p> <p> (2 of 2)7/8/2003 3:53:59 AM</p> <p>Nomenclature - Cavitation and Bubble Dynamics - Christopher E. Brennen</p> <p>CAVITATION AND BUBBLE DYNAMICS</p> <p>by Christopher Earls Brennen Oxford University Press 1995 </p> <p>Nomenclature</p> <p>ROMAN LETTERS </p> <p>a Amplitude of wave-like disturbance </p> <p>A Cross-sectional area or cloud radius </p> <p>b Body half-width </p> <p>B Tunnel half-width </p> <p>c Concentration of dissolved gas in liquid, speed of sound, chord</p> <p>ck Phase velocity for wavenumber k </p> <p>cP Specific heat at constant pressure</p> <p>CD Drag coefficient</p> <p>CL Lift coefficient</p> <p>, Unsteady lift coefficients</p> <p>CM Moment coefficient</p> <p>, Unsteady moment coefficients</p> <p>Cij Lift/drag coefficient matrix</p> <p>Cp Coefficient of pressure</p> <p>Cpmin Minimum coefficient of pressure</p> <p>d Cavity half-width, blade thickness to spacing ratio </p> <p>D Mass diffusivity </p> <p>f Frequency in Hz. </p> <p>f Complex velocity potential, +ifN A thermodynamic property of the phase or component, N </p> <p>Fr Froude number </p> <p>g Acceleration due to gravity </p> <p>gx Component of the gravitational acceleration in direction, x</p> <p> (1 of 6)7/8/2003 3:54:00 AM</p> <p>Nomenclature - Cavitation and Bubble Dynamics - Christopher E. Brennen</p> <p>gN A thermodynamic property of the phase or component, N </p> <p>(f) Spectral density function of sound </p> <p>h Specific enthalpy, wetted surface elevation, blade tip spacing</p> <p>H Henry's law constant </p> <p>Hm Haberman-Morton number, normally g4/S3 i,j,k Indices </p> <p>i Square root of -1 in free streamline analysis</p> <p>I Acoustic impulse</p> <p>I* Dimensionless acoustic impulse, 4I {\cal R} / L U RH2</p> <p>IKi Kelvin impulse vector </p> <p>j Square root of -1 </p> <p>k Boltzmann's constant, polytropic constant or wavenumber</p> <p>kN Thermal conductivity or thermodynamic property of N</p> <p>KG Gas constant </p> <p>Kij Added mass coefficient matrix, 3Mij/4R3 </p> <p>Kc Keulegan-Carpenter number</p> <p>Kn Knudsen number, /2R Typical dimension in the flow, cavity half-length</p> <p>L Latent heat of vaporization</p> <p>m Mass </p> <p>mG Mass of gas in bubble </p> <p>mp Mass of particle </p> <p>Mij Added mass matrix </p> <p>n Index used for harmonics or number of sites per unit area </p> <p>N(R) Number density distribution function of R</p> <p>Cavitation event rate </p> <p>Nu Nusselt number </p> <p>p Pressure </p> <p>pa Radiated acoustic pressure</p> <p>ps Root mean square sound pressure</p> <p>pS A sound pressure level </p> <p>pG Partial pressure of gas</p> <p> (2 of 6)7/8/2003 3:54:00 AM</p> <p>Nomenclature - Cavitation and Bubble Dynamics - Christopher E. Brennen</p> <p>P Pseudo-pressure </p> <p>Pe Peclet number, usually WR/L </p> <p>q Magnitude of velocity vector </p> <p>qc Free surface velocity </p> <p>Q Source strength </p> <p>r Radial coordinate</p> <p>R Bubble radius</p> <p>RB Equivalent volumetric radius, [3/4]1/3 RH Headform radius </p> <p>RM Maximum bubble radius</p> <p>RN Cavitation nucleus radius</p> <p>RP Nucleation site radius</p> <p>Distance to measurement point </p> <p>Re Reynolds number, usually 2WR/L </p> <p>s Coordinate measured along a streamline or surface </p> <p>s Specific entropy</p> <p>S Surface tension </p> <p>St Strouhal number, 2fR/W </p> <p>t Time </p> <p>tR Relaxation time for relative motion</p> <p>t* Dimensionless time, t/tR </p> <p>T Temperature </p> <p>u,v,w Velocity components in cartesian coordinates </p> <p>ui Velocity vector </p> <p>ur,u Velocity components in polar coordinates </p> <p>u Perturbation velocity in x direction, u-U U, Ui Fluid velocity and velocity vector in absence of particle </p> <p>V, Vi Absolute velocity and velocity vector of particle </p> <p>U Velocity of upstream uniform flow </p> <p>w Complex conjugate velocity, u-iv </p> <p>w Dimensionless relative velocity, W/WW Relative velocity of particle </p> <p> (3 of 6)7/8/2003 3:54:00 AM</p> <p>Nomenclature - Cavitation and Bubble Dynamics - Christopher E. Brennen</p> <p>W Terminal velocity of particle </p> <p>We Weber number, 2W2R/S z Complex position vector, x+iy </p> <p>GREEK LETTERS </p> <p> Thermal diffusivity, volume fraction, angle of incidence Cascade stagger angle, other local variables Ratio of specific heats of gas Circulation, other local parameters Boundary layer thickness or increment of frequency D Dissipation coefficient </p> <p>T Thermal boundary layer thickness </p> <p> Fractional volume Complex variable, +i Bubble population per unit liquid volume Coordinate in -plane Angular coordinate or direction of velocity vector Bulk modulus of compressibility Mean free path of molecules or particles Accommodation coefficient Dynamic viscosity </p> <p> Kinematic viscosity Coordinate in -plane </p> <p> Logarithmic hodograph variable, +i Density Cavitation number c Choked cavitation number </p> <p>ij Stress tensor </p> <p> Thermal parameter in bubble growth Volume of particle or bubble Velocity potential </p> <p> Acceleration potential </p> <p> (4 of 6)7/8/2003 3:54:00 AM</p> <p>Nomenclature - Cavitation and Bubble Dynamics - Christopher E. Brennen</p> <p> Fractional perturbation in bubble radius Potential energy </p> <p> log(qc/|w|) </p> <p> Stream function Radian frequency </p> <p>* Reduced frequency, c/U </p> <p>SUBSCRIPTS </p> <p>On any variable, Q: </p> <p>Qo Initial value, upstream value or reservoir value</p> <p>Q1,Q2,Q3 Components of Q in three Cartesian directions</p> <p>Q1,Q2 Values upstream and downstream of a shock </p> <p>Q Value far from the bubble or in the upstream flow</p> <p>QB Value in the bubble </p> <p>QC Critical values and values at the critical point </p> <p>QE Equilibrium value or value on the saturated liquid/vapor line</p> <p>QG Value for the gas</p> <p>Qi Components of vector Q </p> <p>Qij Components of tensor Q </p> <p>QL Saturated liquid value</p> <p>Qn Harmonic of order n </p> <p>QP Peak value </p> <p>QS Value on the interface or at constant entropy</p> <p>QV Saturated vapor value</p> <p>Q* Value at the throat </p> <p>SUPERSCRIPTS AND OTHER QUALIFIERS </p> <p>On any variable, Q: </p> <p>Mean value of Q or complex conjugate of Q </p> <p> (5 of 6)7/8/2003 3:54:00 AM</p> <p>Nomenclature - Cavitation and Bubble Dynamics - Christopher E. Brennen</p> <p>Complex amplitude of oscillating Q </p> <p>Laplace transform of Q(t) </p> <p>Coordinate with origin at image point</p> <p>Rate of change of Q with time</p> <p>Second derivative of Q with time</p> <p>Q+,Q- Values of Q on either side of a cut in a complex plane</p> <p>Q Small change in Q Re{Q} </p> <p>Real part of Q </p> <p>Im{Q} </p> <p>Imaginary part of Q </p> <p>UNITS </p> <p>In most of this book, the emphas...</p>


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