Dynamics of Multiphase Flows

Cover
Half-title page
Series page
Title page
Copyright page
Dedication
Contents
Preface
Part I Principles
1 Introduction to Multiphase Flows
1.1 Multiphase Flow Phenomena
1.1.1 Sedimentation in a Particulate Flow
1.1.2 Dispersion by Sprays or Multiphase Jets
1.1.3 Mixing and Material Processing
1.1.4 Pipeline Transport
1.1.5 Flows with Charged Particles
1.1.6 Flows with Chemical Reactions
1.2 Definition of Multiphase Flow
1.2.1 Multiphase Flows versus Multicomponent Flows
1.2.2 Dilute Phase versus Dense Phase
1.3 Modeling Approaches
1.3.1 Eulerian–Lagrangian Modeling
1.3.2 Eulerian–Eulerian Modeling
1.4 Case Studies: Peculiarities of Multiphase Flows
1.4.1 Bubble Acceleration
1.4.2 Pressure Drop Reduction in Pneumatic Transport
1.4.3 Acceleration of Solids in a Dense Gas–Solid Riser
1.4.4 Cluster Formation and Instability
1.4.5 Wake-Induced Phenomena
1.4.6 Particle Trajectories in a Cyclone Separator
1.5 Summary
Nomenclature
Problems
References
2 Continuum Modeling of Single-Phase Flows
2.1 Introduction
2.2 Flow of a Viscous Fluid
2.2.1 Constitutive Relation of a Viscous Fluid
2.2.2 General Transport Theorem
2.2.3 Governing Equations of Viscous Flows
2.2.4 Interfacial Phenomena and Boundary Conditions
2.2.5 Theory Simplifications and Limitations
2.3 Turbulence
2.3.1 Turbulent Flows
2.3.2 Length Scales in Turbulence
2.3.3 Reynolds-Averaged Navier–Stokes Equations
2.3.4 Turbulence Modeling
2.3.5 Large Eddy Simulation
2.4 Flows in Porous Media
2.4.1 Darcy's Law
2.4.2 Ergun's Equation
2.4.3 Brinkman Equation
2.5 Kinetic Theory of Collision-Dominated Granular Flows
2.5.1 Regimes of Granular Flows
2.5.2 Transport Theorem of Collision-Dominated Granular Particles
2.5.3 Governing Equations
2.5.4 Constitutive Relations
2.5.5 Advancement in Kinetic Theory for Granular Flow
2.6 Case Studies
2.6.1 Model Closure of a Multicomponent Single-Phase Reacting Flow
2.6.2 Smallest Characteristic Length of a Continuum-Based CFD
2.6.3 Flow into a Spherical Cavity in an Infinite Porous Medium
2.6.4 Electroosmotic Flow
2.7 Summary
Nomenclature
Problems
References
3 Transport of Isolated Objects: Solid Particles, Droplets, and Bubbles
3.1 Introduction
3.2 Momentum Transfer
3.2.1 Drag Force
3.2.2 Basset Force and Carried Mass
3.2.3 Saffman Force and Other Gradient-Related Forces
3.2.4 Magnus Force
3.2.5 Field Forces
3.2.6 Coriolis Force
3.3 Heat Transfer
3.3.1 Heat Conduction of a Sphere in Quiescent Fluid
3.3.2 Convective and Radiant Heat Transfer of a Sphere
3.4 Mass Transfer
3.4.1 Mass Fluxes in a Multicomponent Fluid
3.4.2 Stefan Flux
3.4.3 Evaporation of a Droplet
3.5 Equation of Motion
3.5.1 Basset–Boussinesq–Oseen Equation
3.5.2 General Equation of Motion
3.6 Advanced Topics
3.6.1 Characteristics and Shape Regime of Fluid Particles
3.6.2 Orientation and Path Instability of Nonspherical Particles
3.7 Case Studies
3.7.1 Particle Trajectory in a Rotating Fluid
3.7.2 Motion of a Charged Particle between Parallel Electric Plates
3.7.3 Motion of a Parachuted Object from an Airplane
3.7.4 Motion of an Evaporating Droplet
3.8 Summary
Nomenclature
Problems
References
4 Interactions of Particles, Droplets, and Bubbles
4.1 Introduction
4.2 Transport Properties of a Cloud of Particles
4.2.1 Hydrodynamic Forces of a Pair of Spheres
4.2.2 Hydrodynamic Forces on a Sphere in a Swamp of Spheres
4.2.3 Heat Transfer of Suspended Particles
4.2.4 Mass Transfer of a Cluster
4.2.5 Charge Effect due to Interparticle and Particle–Wall Interactions
4.3 Collision of a Pair of Solid Spheres
4.3.1 Hertzian Contact of Frictionless Spheres
4.3.2 Frictional Contact of Spheres
4.3.3 Normal Collision of Elastic Spheres
4.3.4 Oblique and Rotational Collisions
4.3.5 Collision of Inelastic Spheres
4.3.6 Heat Transfer by Collision of Solids
4.3.7 Charge Transfer by Collision of Solids
4.4 Other Interaction Forces between Solid Particles
4.4.1 Van der Waals Force
4.4.2 Liquid–Bridge Force
4.5 Interactions between Fluid Particles
4.5.1 Droplet Impact on a Flat Solid Surface
4.5.2 Binary Droplet Collision
4.5.3 Breakup of Fluid Particles
4.5.4 Coalescence of Fluid Particles
4.6 Case Studies
4.6.1 Settling of Suspended Particles in Column
4.6.2 Wake-Induced Motion of a Pair of Spheres
4.6.3 Collision of Elastic Spheres in Fluid
4.6.4 Leidenfrost Collision of a Drop with a Flat Surface
4.7 Summary
Nomenclature
Problems
References
5 Continuum-Discrete Tracking Modeling of Multiphase Flows
5.1 Introduction
5.2 Lagrangian Trajectory Modeling
5.2.1 Deterministic Trajectory Models
5.2.2 Stochastic Trajectory Models
5.2.3 Particle Cloud Tracking Models
5.3 Discrete Element Method
5.3.1 Hard-Sphere Model
5.3.2 Soft-Sphere Model
5.4 Coupling in Eulerian–Lagrangian Model
5.4.1 Mass Coupling
5.4.2 Momentum Coupling
5.4.3 Energy Coupling
5.4.4 Coupling due to Charge-Induced Electric Field
5.5 Case Studies
5.5.1 Flow over Airfoil in Rain
5.5.2 Inhalation of Ultrafine Particulates
5.5.3 Solar-Absorbing Particulate-Laden Flow
5.5.4 Transport of Charged Particles in Chamber
5.6 Summary
Nomenclature
Problems
References
6 Continuum Modeling of Multiphase Flows
6.1 Introduction
6.2 Averages and Averaging Theorems
6.2.1 Phase and Intrinsic Averaging
6.2.2 Volume-Averaging Theorems
6.3 Volume-Averaged Equations
6.3.1 General Volume-Averaged Equations
6.3.2 Volume-Averaged Continuity Equation
6.3.3 Volume-Averaged Momentum Equation
6.3.4 Volume-Averaged Energy Equation
6.4 Volume–Time-Averaged Equations
6.4.1 Volume–Time Averages and Covariance
6.4.2 Volume-Time-Averaged Continuity Equation
6.4.3 Volume-Time-Averaged Momentum Equation
6.4.4 Volume–Time-Averaged Energy Equation
6.4.5 Closure of Volume–Time-Averaged Equations
6.5 Constitutive Relations in Multifluid Model
6.5.1 Pressure
6.5.2 Molecular Fluxes
6.5.3 Eddy Diffusivities
6.5.4 Interfacial Transport
6.5.5 Turbulence Modeling
6.6 Constitutive Relations for Fluid–Solid Flows
6.6.1 Stresses of Solid Particles
6.6.2 Turbulent Diffusion of Particulates
6.7 Advanced Topics
6.7.1 Effect of Mesoscale Structures on Phase Interaction
6.7.2 Particle Size Distribution and Interfacial Area Concentration
6.7.3 Turbulence Modulation
6.8 Case Studies
6.8.1 Particle Suspension in a Stirred Tank
6.8.2 Bubble Plume Flow in Bubble Column
6.8.3 Heat Transfer of Immersed Tubes in Dense Gas–Solid Fluidized Bed
6.8.4 Evaporating Spray in Gas–Solid Suspension Flow
6.9 Summary
Nomenclature
Problems
References
7 Numerical Modeling and Simulation
7.1 Introduction
7.2 General Procedure of Numerical Modeling and Simulation
7.3 Numerical Solutions of Partial Differential Equations
7.3.1 Numerical Solution of General Transport Equation
7.3.2 Numerical Methods for Single-Phase Flow
7.3.3 Boundary Conditions
7.4 Resolved Interface Approach for Dispersed Phase Objects
7.4.1 Conformal Mesh Methods
7.4.2 Nonconformal Mesh Methods
7.5 Eulerian–Lagrangian Algorithms for Multiphase Flows
7.5.1 Governing Equations
7.5.2 Continuous-Discrete Phase Coupling
7.5.3 Particle–Particle Interactions
7.6 Eulerian–Eulerian Algorithms for Multiphase Flows
7.6.1 Calculation of Velocity and Pressure Field
7.6.2 Volume Fraction
7.6.3 Pressure and Volume Fraction for Dense Solid Phase
7.7 Lattice Boltzmann Method
7.7.1 LBM for Single-Phase Flows
7.7.2 LBM for Particle Suspensions
7.7.3 LBM with Two Fluid Phases
7.8 Case Studies
7.8.1 Particle–Fluid Force in LBM
7.8.2 Modeling of Aerosol Delivery by a Powder Inhaler
7.8.3 Air Entrainment in a Hydraulic Jump
7.8.4 Evaluation of Sparger in Bubble Column
7.9 Summary
Nomenclature
Problems
References
8 Measurement Techniques
8.1 Introduction
8.2 Particle Size and Morphology Measurement
8.2.1 Optical Visualization Methods
8.2.2 Microscopy Methods
8.2.3 Sieving Analysis
8.2.4 Sedimentation Methods
8.2.5 Cascade Impaction
8.2.6 Phase Doppler Method
8.2.7 Particle Size Distribution and Averaged Size
8.3 Volume Fraction Measurement
8.3.1 Beam Attenuation Method
8.3.2 Permittivity Measurement Method
8.3.3 Transmission Tomography
8.3.4 Electrical Impedance Tomography
8.4 Mass Flow Measurement
8.4.1 Overall Mass Flow Measurement
8.4.2 Isokinetic Sampling Method
8.4.3 Ball Probe Method
8.5 Velocity Measurement
8.5.1 Cross-correlation Method
8.5.2 Venturimeter
8.5.3 Laser Doppler Velocimetry
8.5.4 Corona Discharge Method
8.5.5 Particle Image Velocimetry
8.6 Charge Measurement
8.6.1 Sampling with Faraday Cup
8.6.2 Induction Probe
8.7 Case Studies
8.7.1 Particle Size Distribution by Deconvolution Method
8.7.2 Optical Measurement of Microbubbles and Droplets
8.7.3 Volume Fraction in a Pressurized Slurry-Bubble Column
8.8 Summary
Nomenclature
Problems
References
Part II Application-Based Analysis of Multiphase Flows
9 Separation of Multiphase Flows
9.1 Introduction
9.2 Separation by Phase Inertia
9.2.1 Phase-Inertia Separation Methods
9.2.2 Modeling Approaches
9.3 Filtration
9.3.1 Collection Efficiency of a Single Fiber or Granular Particle
9.3.2 Collection Efficiency of a Filter
9.3.3 Pressure Drop through a Filter
9.4 Separation by External Electric Field
9.4.1 Electrostatic Precipitation
9.4.2 Separation by Polarization of Dielectric Particles
9.5 Case Studies
9.5.1 Cyclone Collection Efficiency for a Polydispersed Particulate Flow
9.5.2 Inertial Impaction-Dominated Fibrous Filtration of Fine Particles
9.5.3 Numerical Modeling of Gas–Solid Flow in a Cyclone Separator
9.5.4 Numerical Modeling of Particulate Removal by Electrostatic Precipitator
9.6 Summary
Nomenclature
Problems
References
10 Fluidization
10.1 Introduction
10.2 Dense Phase Gas–Solid Fluidized Beds
10.2.1 Classifications of Particles for Fluidization
10.2.2 Dense Phase Fluidization
10.2.3 External Field Modulated Fluidization
10.2.4 Fluidization of Nanoparticles
10.3 Circulating Fluidized Beds
10.3.1 Components of a Circulating Fluidized Bed
10.3.2 Fast Fluidization Regime
10.3.3 Fast Fluidization Structure and Transition to Choking
10.3.4 Modeling of Flow in Fast Fluidization
10.4 Gas–Liquid Bubbling Flows
10.4.1 Bubble Formation and Shape Regime
10.4.2 Bubble Wake Dynamics and Interaction
10.4.3 Bubble Columns
10.5 Gas–Liquid–Solid Fluidization
10.5.1 Pressure Drop and Phase Holdup
10.5.2 Incipient Fluidization and Flow Regimes
10.5.3 Bed Contraction and Moving Packed Bed
10.6 Case Studies
10.6.1 Pressure Balance in CFB
10.6.2 Energy Partitions in Riser Transport
10.6.3 Kinetic Theory Model for Bubbling Fluidization
10.7 Summary
Nomenclature
Problems
References
11 Pipe Flow
11.1 Introduction
11.2 Multiphase Flow Patterns in Pipeline Transport
11.2.1 Flow Regimes in Horizontal Pneumatic Conveying
11.2.2 Flow Regimes in Horizontal Slurry Pipe Flows
11.2.3 Gas–Liquid Flow Regimes in Pipes
11.3 Saltation and Pickup Velocities
11.3.1 Critical Transport Velocity
11.3.2 Pickup Velocity
11.4 Pressure Drop
11.4.1 Pressure Drop of a Fully Developed Suspension Flow
11.4.2 Pressure Drop in Dilute Gas–Solid Flows
11.4.3 Pressure Drop in Slurry Flows
11.4.4 Pressure Drop in Gas–Liquid Flows
11.4.5 Drag Reduction
11.5 Phase Distributions of Suspended Pipe Flows
11.5.1 Fully Developed Dilute Pipe Flows
11.5.2 Effect of Electrostatic Charge on Phase Transport
11.5.3 Dilute Transport in a Vertical Pipe
11.6 Stratified Flows in Pipes and Ducts
11.6.1 Regional-Averaged Theories of Stratified Flows
11.6.2 Stratified Gas–Liquid Flows
11.6.3 Stratified Gas–Solids Flow
11.7 Flows in Bends
11.7.1 Single-Phase Flow in a Pipe Bend
11.7.2 Particulate Flow in a Pipe Bend
11.7.3 Bend Erosion by Particle Collision
11.8 Case Studies
11.8.1 Particle–Laden Gas Flow and Erosion in a Bend
11.8.2 Modeling of Slurry Flow over a Bend
11.8.3 Modeling of Transition of Stratified to Nonstratified Flow
11.8.4 Modeling of Fully Suspended Slurry Pipe Flow
11.9 Summary
Nomenclature
Problems
References
12 Flows with Phase Changes and/or Reactions
12.1 Introduction
12.2 Boiling in Vapor–Liquid Flows
12.2.1 Boiling in Stagnant Liquid
12.2.2 Boiling in Liquid Pipe Flow
12.3 Liquid Spray Dispersion and Evaporation
12.3.1 Spray Atomization
12.3.2 Evaporating Spray Jets
12.3.3 Spray Drying
12.3.4 Spray on a Heated Surface
12.3.5 Evaporating Spray in Gas–Solid Flows
12.3.6 Modeling of Spray Transport and Phase Interactions
12.4 Bubbling Reactors in Liquid and Liquid–Solid Media
12.4.1 Mass Transfer in Gas–Liquid Media
12.4.2 Sparged Stirred Tank
12.4.3 Fischer–Tropsch Synthesis in Slurry Bubble Column
12.5 Reactive Flows in Gas–Solid Fluidized Beds
12.5.1 Fluid Catalytic Cracking
12.5.2 Vaporization and Reaction in a Riser
12.5.3 Gas Phase Polymerization
12.6 Dispersed Fuel Combustion
12.6.1 Combustion of a Fuel Droplet
12.6.2 Combustion of a Solid Fuel Particle
12.7 Case Studies
12.7.1 Motion of a Condensing Bubble in a Solution
12.7.2 Modeling of FCC Reacting Flow
12.7.3 Modeling of Fisher–Tropsch Slurry Bubble Reactor
12.7.4 Modeling of Reacting Flow in Coal Gasifier
12.8 Summary
Nomenclature
Problems
References
Index