FUNDAMENTALS OF MULTIPHASE FLOW by Christopher Earls Brennen © Cambridge University Press 2005 Preface Nomenclature CHAPTER 1. Introduction Scope Multiphase Flow Models Multiphase Flow Notation Size Distributions Equations of Motion Averaging Conservation of Mass Number Continuity Equation Fick's Law Equations of Motion Disperse Phase Momentum Equation On Disperse Phase Interaction Equations for Conservation of Energy Heat Transfer between Separated Phases Interaction with turbulence Particle and Turbulence Effect on Turbulence Stability On the equations of motion Comments Averaging Averaging Contributions to the Mean Motion Averaging in Pipe Flows Modeling with the Combined Phase Equations Mass, Force and Energy Interaction Terms CHAPTER 2. Single particle motion Introduction Sphere Flow - High Reynolds Number Sphere Flow - Low Reynolds Number Molecular Effects Unsteady Particle Motions Effect of Concentration on Added Mass Unsteady Potential Flow Unsteady Stokes Flow Particle Equation of Motion Magnitude of Relative Motion Effect of Concentration on Particle Motion Effect of Concentration on Particle Drag CHAPTER 3. Bubble or droplet translation Introduction Dimensional Analysis of Deformation due to Translation Bubble Shapes and Terminal Velocities Marangoni Effects Bjerknes Forces Growing Bubbles CHAPTER 4. Bubble growth and collapse Introduction Rayleigh-Plesset Equation Bubble Contents In the Absence of Thermal Effects Stability of Vapor/Gas Bubbles Thermal Effects on Growth Thermally Controlled Growth Cavitation and Boiling Bubble Growth by Mass Diffusion Bubble Natural Frequencies Nonlinear Effects Rectified Mass Diffusion CHAPTER 5. Cavitation Introduction Cavitation Inception Cavitation Bubble Collapse Shape during Bubble Collapse Cavitation Damage Cavitating Bubble Shapes Cavitation Noise Cavitation Luminescence Cavitation Chemistry Vapor Explosions Bubble Dynamics Videos Cavitating Flows Introduction Traveling Bubble Cavitation Bubble Flow Interactions Experimental Observations Large Scale Cavitation Structures Vortex Cavitation Cloud Cavitation Attached or Sheet Cavitation Cavitating Foils Cavity Closure Cavitating Flow Videos Free Streamline Flows Introduction Cavity Closure Models Cavity Detachment Models Wall Effects and Choked Flows Steady Planar Flows Some Nonlinear Results Linearized Methods Flat Plate Hydrofoil Cavitating Cascades Three Dimensional Flows Numerical Methods Unsteady Flows CHAPTER 6. Boiling and Condensation Introduction Pool Boiling on Horizontal Surface Nucleate Boiling on Horizontal Surface Film Boiling on Horizontal Surface Leidenfrost Effect Boiling on Vertical Surface Film Boiling on Vertical Surface Condensation Film Condensation CHAPTER 7. Flow patterns Multiphase Flow Patterns Examples of Flow Regime Maps Slurry Flow Regimes Vertical Pipe Flow Flow Pattern Classifications Disperse Phase Separation and Dispersion Example: Horizontal Pipe Flow Particle Size and Particle Fission Examples of Flow-determined Bubble Size Bubbly or Mist Flow Limits Other Bubbly Flow Limits Other Particle Size Effects Stability of Disperse Mixtures Inhomogeneity Instability of Vertical Flows Kelvin-Helmholtz Instability Stratified Flow Instability Annular Flow Instability Two-Component Flow Videos Three-Component Flow Videos CHAPTER 8. Energy conversion Introduction Disperse Horizontal Flow Friction Homogeneous Flow Friction Heterogeneous Flow Friction Vertical Flow Friction Two Component Separated Flow Friction Friction with Phase Change Multiphase Flow in Pumps CHAPTER 9. Homogeneous Flows Introduction Sonic Speed Sonic Speed at Higher Frequencies Sonic Speed with Phase Change Barotropic Relations Nozzle Flows Vapor/Liquid Nozzle Flow Condensation Shocks CHAPTER 10. Flows with bubble dynamics Introduction Basic Equations Acoustics of Bubbly Mixtures Comparison with Experiments Normal Shock Waves in Bubbly Flows Shock Waves Structure Oblique Shock Waves Spherical Bubble Cloud Modes Spherical Bubble Cloud Response CHAPTER 11.Flows with gas dynamics Introduction Equations for a Dusty Gas Homogeneous Flow with Gas Dynamics Velocity and Temperature Relaxation Normal Shock Wave Acoustic Damping Linear Stability of Laminar Flow Flow over a Wavy Wall Small Slip Perturbation CHAPTER 12.Sprays Introduction Ocean Spray Spray Formation by Bubbling Spray Formation by Wind Shear Spray Formation by Initially Laminar Jets Spray Formation by Turbulent Jets Single Droplet Mechanics Single Droplet Combustion Spray Combustion CHAPTER 13.Granular flows Introduction Particle Interaction Models Computer Simulations Wave Propagation Effects of Vibration Soil Liquefaction Flow Regimes Flow Regime Rheologies Flow Regime Boundaries Slow Granular Flow Mohr-Coulomb Models Hopper Flows Rapid Granular Flow Chute Flow Heat Transfer Examples of Rapid Flow Equations Boundary Conditions Rapid Flow Simulations Effect of Interstitial Fluid Particle Collisions Classes of Interstitial Fluid Effects Shear Flow Simulation Videos Chute Flow Simulation Videos Mixture Flow Simulation Videos Force Chain Videos Wave Propagation Videos Vibration Effects Videos Booming Dunes Videos CHAPTER 14.Drift flux models Introduction Drift Flux Method Vertical Pipe Flow Fluidized Bed Pool Boiling Crisis Corrections for Pipe Flows CHAPTER 15.System instablities Introduction System Structure Quasistatic Stability Turbomachine Surge Ledinegg Instability Geyser Instability Concentration Waves Dynamic Instabilities Cavitation Surge in Pumps Chugging and Condensation Oscillations Unsteady Internal Flow Methods Transfer Functions Uniform Homogeneous Flow Non-Cavitating Pumps Cavitating Inducers Bubbly Flow Model for Cavitating Inducers Cavitating Turbine Cavitating Propeller CHAPTER 16.Kinematic waves Introduction Kinematic Wave Analysis Kinematic Wave Speed at Flooding Kinematic Waves in Steady Flows Kinematic Shock Waves Kinematic Shock Stability Compressibility and Phase Change Effects Batch Sedimentation Dynamics of Cavitating Pumps Two-dimensional Shocks References N Last updated 4/9/04. Christopher E. Brennen