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Fundamentals of multiphase flow.pdf

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    Fundamentals of Multiphase Flows Christopher E. Brennen California Institute of Technology Pasadena, California Cambridge University Press 2005 ISBN 0521 848040 1
    Preface The subject of multiphase flows encompasses a vast field, a host of different technological contexts, a wide spectrum of different scales, a broad range of engineering disciplines and a multitude of different analytical approaches. Not surprisingly, the number of books dealing with the subject is volumi- nous. For the student or researcher in the field of multiphase flow this broad spectrum presents a problem for the experimental or analytical methodolo- gies that might be appropriate for his/her interests can be widely scattered and difficult to find. The aim of the present text is to try to bring much of this fundamental understanding together into one book and to present a unifying approach to the fundamental ideas of multiphase flows. Conse- quently the book summarizes those fundamental concepts with relevance to a broad spectrum of multiphase flows. It does not pretend to present a com- prehensive review of the details of any one multiphase flow or technological context though reference to books providing such reviews is included where appropriate. This book is targeted at graduate students and researchers at the cutting edge of investigations into the fundamental nature of multiphase flows; it is intended as a reference book for the basic methods used in the treatment of multiphase flows. I am deeply grateful to all my many friends and fellow researchers in the field of multiphase flows whose ideas fill these pages. I am particularly in- debted to my close colleagues, Allan Acosta, Ted Wu, Rolf Sabersky, Melany Hunt, 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 teaching and research at the California Institute of Technology. It was my privilege to have 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, Harri Kytomaa, Zhenhuan Liu, Beth McKenney, Sheung-Lip Ng, Tanh Nguyen, Kiam Oey, James Pearce, Garrett Reisman, Y.-C. Wang, Carl Wassgren, Roberto Zenit Camacho and Steve Hostler. To them I owe a special debt. Also, to Cecilia Lin who devoted many selfless hours to the preparation of the illustrations. A substantial fraction of the introductory material in this book is taken from my earlier book entitled “Cavitation and Bubble Dynamics” by Christopher Earls Brennen, c1995 by Oxford University Press, Inc. It is reproduced here by permission of Oxford University Press, Inc. The original hardback edition of this book was dedicated to my mother, Muriel M. Brennen, whose love and encouragement inspired me throughout my life. The paperback edition is dedicated to another very special woman, my wife Barbara, who gave me new life and love beyond measure. Christopher Earls Brennen California Institute of Technology December 2008. 3
    Contents 4 page 2 10 11 19 19 19 20 22 25 27 27 28 30 31 31 35 36 37 41 42 42 46 47 47 48 50 50 51 Preface Contents Nomenclature 1 INTRODUCTION TO MULTIPHASE FLOW 1.1 Scope 1.2 1.3 1.4 Fick’s law Equation of motion INTRODUCTION 1.1.1 1.1.2 Multiphase flow models 1.1.3 Multiphase flow notation 1.1.4 Size distribution functions EQUATIONS OF MOTION 1.2.1 Averaging 1.2.2 Conservation of mass 1.2.3 Number continuity equation 1.2.4 1.2.5 1.2.6 Disperse phase momentum equation 1.2.7 Comments on disperse phase interaction 1.2.8 1.2.9 Heat transfer between separated phases INTERACTION WITH TURBULENCE 1.3.1 1.3.2 COMMENTS ON THE EQUATIONS OF MOTION 1.4.1 Averaging 1.4.2 Averaging contributions to the mean motion 1.4.3 Averaging in pipe flows 1.4.4 Modeling with the combined phase equations 1.4.5 Mass, force and energy interaction terms Particles and turbulence Effect on turbulence stability Equations for conservation of energy
    2 SINGLE PARTICLE MOTION 2.1 2.2 3 BUBBLE OR DROPLET TRANSLATION 3.3 MARANGONI EFFECTS 3.4 3.5 BJERKNES FORCES GROWING BUBBLES 4 BUBBLE GROWTH AND COLLAPSE Equations of motion Effect of concentration on added mass INTRODUCTION DEFORMATION DUE TO TRANSLATION 3.2.1 Dimensional analysis 3.2.2 Bubble shapes and terminal velocities INTRODUCTION FLOWS AROUND A SPHERE 2.2.1 At high Reynolds number 2.2.2 At low Reynolds number 2.2.3 Molecular effects UNSTEADY EFFECTS 2.3.1 Unsteady particle motions 2.3.2 2.3.3 Unsteady potential flow 2.3.4 Unsteady Stokes flow PARTICLE EQUATION OF MOTION 2.4.1 2.4.2 Magnitude of relative motion 2.4.3 2.4.4 52 52 53 53 56 61 62 62 65 65 69 73 73 78 Effect of concentration on particle equation of motion 80 81 Effect of concentration on particle drag 86 86 86 86 88 91 95 97 100 100 100 100 103 106 109 110 113 113 115 118 118 120 120 INTRODUCTION BUBBLE GROWTH AND COLLAPSE 4.2.1 Rayleigh-Plesset equation 4.2.2 4.2.3 4.2.4 4.2.5 THERMAL EFFECTS 4.3.1 Thermal effects on growth 4.3.2 Thermally controlled growth 4.3.3 Cavitation and boiling 4.3.4 OSCILLATING BUBBLES 4.4.1 Bubble contents In the absence of thermal effects; bubble growth In the absence of thermal effects; bubble collapse Stability of vapor/gas bubbles Bubble growth by mass diffusion Bubble natural frequencies 5 2.3 2.4 3.1 3.2 4.1 4.2 4.3 4.4
    4.4.2 Nonlinear effects 4.4.3 Rectified mass diffusion 5 CAVITATION 5.1 5.2 5.3 Shape distortion during bubble collapse INTRODUCTION KEY FEATURES OF BUBBLE CAVITATION 5.2.1 Cavitation inception 5.2.2 Cavitation bubble collapse 5.2.3 5.2.4 Cavitation damage CAVITATION BUBBLES 5.3.1 Observations of cavitating bubbles 5.3.2 Cavitation noise 5.3.3 Cavitation luminescence 6 BOILING AND CONDENSATION 6.1 6.2 6.3 6.4 Pool boiling INTRODUCTION HORIZONTAL SURFACES 6.2.1 6.2.2 Nucleate boiling Film boiling 6.2.3 6.2.4 Leidenfrost effect VERTICAL SURFACES 6.3.1 Film boiling CONDENSATION 6.4.1 Film condensation 7 FLOW PATTERNS 7.1 7.2 7.3 Flow pattern classifications Examples of flow regime maps Slurry flow regimes INTRODUCTION TOPOLOGIES OF MULTIPHASE FLOW 7.2.1 Multiphase flow patterns 7.2.2 7.2.3 7.2.4 Vertical pipe flow 7.2.5 LIMITS OF DISPERSE FLOW REGIMES 7.3.1 Disperse phase separation and dispersion 7.3.2 7.3.3 7.3.4 7.3.5 Bubbly or mist flow limits 7.3.6 Other bubbly flow limits Example: horizontal pipe flow Particle size and particle fission Examples of flow-determined bubble size 6 124 126 128 128 128 128 131 133 136 139 139 142 149 150 150 151 151 153 154 155 157 158 160 160 163 163 163 163 165 168 169 173 174 174 176 178 179 181 182
    7.4 7.5 7.3.7 Other particle size effects INHOMOGENEITY INSTABILITY Stability of disperse mixtures 7.4.1 7.4.2 Inhomogeneity instability in vertical flows LIMITS ON SEPARATED FLOW 7.5.1 Kelvin-Helmoltz instability Stratified flow instability 7.5.2 7.5.3 Annular flow instability 8 INTERNAL FLOW ENERGY CONVERSION 8.1 8.2 INTRODUCTION FRICTIONAL LOSS IN DISPERSE FLOW 8.2.1 Horizontal Flow 8.2.2 Homogeneous flow friction 8.2.3 Heterogeneous flow friction 8.2.4 Vertical flow FRICTIONAL LOSS IN SEPARATED FLOW 8.3.1 Two component flow 8.3.2 ENERGY CONVERSION IN PUMPS AND TURBINES 8.4.1 Multiphase flows in pumps Flow with phase change 8.3 8.4 9 HOMOGENEOUS FLOWS 9.1 9.2 9.3 9.4 9.5 Basic analysis Sonic speeds at higher frequencies Sonic speed with change of phase INTRODUCTION EQUATIONS OF HOMOGENEOUS FLOW SONIC SPEED 9.3.1 9.3.2 9.3.3 BAROTROPIC RELATIONS NOZZLE FLOWS 9.5.1 One dimensional analysis 9.5.2 Vapor/liquid nozzle flow 9.5.3 Condensation shocks 10 FLOWS WITH BUBBLE DYNAMICS INTRODUCTION 10.1 10.2 BASIC EQUATIONS 10.3 ACOUSTICS OF BUBBLY MIXTURES 10.3.1 Analysis 10.3.2 Comparison with experiments SHOCK WAVES IN BUBBLY FLOWS 10.4 7 183 184 184 187 191 192 194 194 196 196 196 196 199 201 203 205 205 211 215 215 220 220 220 221 221 225 227 231 233 233 238 242 246 246 247 248 248 250 253
    10.4.1 Normal shock wave analysis 10.4.2 Shock wave structure 10.4.3 Oblique shock waves 10.5 FINITE BUBBLE CLOUDS 10.5.1 Natural modes of a spherical cloud of bubbles 10.5.2 Response of a spherical bubble cloud 11 FLOWS WITH GAS DYNAMICS INTRODUCTION 11.1 11.2 EQUATIONS FOR A DUSTY GAS 11.2.1 Basic equations 11.2.2 Homogeneous flow with gas dynamics 11.2.3 Velocity and temperature relaxation 11.3 NORMAL SHOCK WAVE 11.4 ACOUSTIC DAMPING 11.5 LINEAR PERTURBATION ANALYSES 11.5.1 Stability of laminar flow 11.5.2 Flow over a wavy wall SMALL SLIP PERTURBATION 11.6 12 SPRAYS INTRODUCTION 12.1 12.2 TYPES OF SPRAY FORMATION 12.3 OCEAN SPRAY 12.4 SPRAY FORMATION 12.4.1 Spray formation by bubbling 12.4.2 Spray formation by wind shear 12.4.3 Spray formation by initially laminar jets 12.4.4 Spray formation by turbulent jets SINGLE DROPLET MECHANICS 12.5.1 Single droplet evaporation 12.5.2 Single droplet combustion SPRAY COMBUSTION 12.5 12.6 13 GRANULAR FLOWS INTRODUCTION 13.1 13.2 PARTICLE INTERACTION MODELS 13.2.1 Computer simulations 13.3 FLOW REGIMES 13.3.1 Dimensional Analysis 13.3.2 Flow regime rheologies 13.3.3 Flow regime boundaries 8 253 256 259 259 259 264 267 267 268 268 269 271 272 275 279 279 280 282 285 285 285 286 288 288 289 292 293 299 299 301 305 308 308 309 311 312 312 313 316
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