Fundamentals of Multiphase Flows - …

1 Fundamentals ofMultiphase FlowsChristopher E. BrennenCalifornia Institute of TechnologyPasadena, CaliforniaCambridge University Press 2005 ISBN 0521 8480401 PrefaceThe subject of Multiphase Flows encompasses a vast field, a host of differenttechnological contexts, a wide spectrum of different scales, a broad range ofengineering disciplines and a multitude of different analytical surprisingly, the number of books dealing with the subject is volumi-nous. For the student or researcher in the field of Multiphase flow this broadspectrum presents a problem for the experimental or analytical methodolo-gies that might be appropriate for his/her interests can be widely scatteredand difficult to find.

2 The aim of the present text is to try to bring muchof this fundamental understanding together into one book and to presenta unifying approach to the fundamental ideas of Multiphase Flows . Conse-quently the book summarizes those fundamental concepts with relevance toa broad spectrum of Multiphase Flows . It does not pretend to present a com-prehensive review of the details of any one Multiphase flow or technologicalcontext though reference to books providing such reviews is included whereappropriate. This book is targeted at graduate students and researchers atthe cutting edge of investigations into the fundamental nature of multiphaseflows; it is intended as a reference book for the basic methods used in thetreatment of Multiphase am deeply grateful to all my many friends and fellow researchers in thefield of Multiphase Flows whose ideas fill these pages.

3 I am particularly in-debted to my close colleagues, Allan Acosta, Ted Wu, Rolf Sabersky, MelanyHunt, Tim Colonius and the late Milton Plesset, all of whom made my pro-fessional life a real pleasure. This book grew out of many years of teachingand research at the California Institute of Technology. It was my privilege tohave worked on Multiphase flow problems with a group of marvelously tal-ented students including Hojin Ahn, Robert Bernier, Abhijit Bhattacharyya,David Braisted, Charles Campbell, Steven Ceccio, Luca d Agostino, Fab-rizio d Auria, Mark Duttweiler, Ronald Franz, Douglas Hart, Steve Hostler,2 Gustavo Joseph, Joseph Katz, Yan Kuhn de Chizelle, Sanjay Kumar, HarriKytomaa, Zhenhuan Liu, Beth McKenney, Sheung-Lip Ng, Tanh Nguyen,Kiam Oey, James Pearce, Garrett Reisman, Wang, Carl Wassgren.

4 Roberto Zenit Camacho and Steve Hostler. To them I owe a special , to Cecilia Lin who devoted many selfless hours to the preparation ofthe substantial fraction of the introductory material in this book is takenfrom my earlier book entitled Cavitation and Bubble Dynamics byChristopher Earls Brennen,c 1995 by Oxford University Press, Inc. It isreproduced here by permission of Oxford University Press, original hardback edition of this book was dedicated to my mother,Muriel M. Brennen, whose love and encouragement inspired me throughoutmy life.

5 The paperback edition is dedicated to another very special woman,my wife Barbara, who gave me new life and love beyond Earls BrennenCalifornia Institute of flow flow distribution OF of continuity s of phase momentum on disperse phase for conservation of transfer between separated WITH and on turbulence ON THE EQUATIONS OF contributions to the mean in pipe with the combined phase , force and energy interaction terms5142 SINGLE PARTICLE AROUND A high Reynolds low Reynolds particle of concentration on added potential Stokes EQUATION OF of of relative of concentration on particle equation of motion of concentration on particle drag813 BUBBLE OR DROPLET DUE TO shapes and terminal BUBBLES974 BUBBLE GROWTH AND GROWTH AND the absence of thermal effects; bubble the absence of thermal effects.

6 Bubble of effects on controlled and growth by mass natural mass diffusion1265 FEATURES OF BUBBLE bubble distortion during bubble of cavitating luminescence1496 BOILING AND condensation1607 FLOW OF Multiphase flow of flow regime flow pipe pattern OF DISPERSE FLOW phase separation and : horizontal pipe size and particle of flow-determined bubble or mist flow bubbly flow particle size of disperse instability in vertical ON SEPARATED flow flow instability1948 INTERNAL FLOW ENERGY LOSS IN DISPERSE flow flow LOSS IN SEPARATED component with phase CONVERSION IN PUMPS AND TURBINES Flows in pumps2159 HOMOGENEOUS OF HOMOGENEOUS speeds at higher speed with change of dimensional nozzle shocks24210 Flows WITH BUBBLE BASIC ACOUSTICS OF

7 BUBBLY Comparison with SHOCK WAVES IN BUBBLY Normal shock wave Shock wave Oblique shock FINITE BUBBLE Natural modes of a spherical cloud of Response of a spherical bubble cloud26411 Flows WITH GAS EQUATIONS FOR A DUSTY Basic Homogeneous flow with gas Velocity and temperature NORMAL SHOCK ACOUSTIC LINEAR PERTURBATION Stability of laminar Flow over a wavy SMALL SLIP PERTURBATION28212 TYPES OF SPRAY OCEAN SPRAY Spray formation by Spray formation by wind Spray formation by initially laminar Spray formation by turbulent SINGLE DROPLET Single droplet Single droplet SPRAY COMBUSTION30513 GRANULAR PARTICLE INTERACTION Computer FLOW Dimensional Flow regime Flow regime SLOW GRANULAR Equations of Mohr-Coulomb Hopper RAPID GRANULAR Example of rapid flow Boundary Computer EFFECT OF INTERSTITIAL Particle Classes of interstitial fluid

8 Effects32914 DRIFT FLUX DRIFT FLUX EXAMPLES OF DRIFT FLUX Vertical pipe Fluidized Pool boiling CORRECTIONS FOR PIPE FLOWS34315 SYSTEM SYSTEM QUASISTATIC QUASISTATIC INSTABILITY Turbomachine Ledinegg Geyser CONCENTRATION DYNAMIC Multiphase FLOW Dynamic Cavitation surge in cavitating Chugging and condensation TRANSFER Unsteady internal flow Transfer Uniform homogeneous flow36216 KINEMATIC TWO-COMPONENT KINEMATIC Basic Kinematic wave speed at Kinematic waves in steady TWO-COMPONENT KINEMATIC Kinematic shock Kinematic shock Compressibility and phase change EXAMPLES OF KINEMATIC WAVE Batch Dynamics of cavitating TWO-DIMENSIONAL SHOCKS383 Bibliography385 Index40710 NomenclatureRoman lettersaAmplitude of wave-like disturbanceACross-sectional area or cloud radiusAAttenuationbPower law indexBaBagnold number.

9 SD2 / LcConcentrationcSpeed of soundc Phase velocity for wavenumber cpSpecific heat at constant pressurecsSpecific heat of solid or liquidcvSpecific heat at constant volumeCComplianceCDamping coefficientCDDrag coefficientCijDrag and lift coefficient matrixCLLift coefficientCpCoefficient of pressureCpminMinimum coefficient of pressuredDiameterdjJet diameterdoHopper opening diameterDParticle, droplet or bubble diameterDMass diffusivityDmVolume (or mass) mean diameterDsSauter mean diameter11D(T)Determinant of the transfer matrix [T]

10 DThermal diffusivityeSpecific internal energyERate of exchange of energy per unit volumefFrequency inHzfFriction factorfL,fVLiquid and vapor thermodynamic quantitiesFiForce vectorFrFroude numberFInteractive force per unit volumegAcceleration due to gravitygL,gVLiquid and vapor thermodynamic quantitiesGNiMass flux of componentNin directioniGNMass flux of componentNhSpecific enthalpyhHeightHHeightHTotal head,pT/ gHeHenry s law constantHmHaberman-Morton number, normallyg 4/ S3i, j, k, m, nIndicesiSquare root of 1 IAcoustic impulseIRate of transfer of mass per unit volumejiTotal volumetric flux in directionijNiVolumetric flux of componentNin directionijNVolumetric flux of componentNkPolytropic constantkThermal conductivitykBoltzmann s constantkL,kVLiquid