Multiphase Flows with Droplets and Particles

Cover
Half Title
Title
Copyright
Contents
Nomenclature
Foreword
About the Authors
Acknowledgments
Chapter 1 Introduction
1.1 Industrial Applications
1.1.1 Spray Drying
1.1.2 Materials Transport Systems
1.1.2.1 Pneumatic Transport
1.1.3 Slurry Transport
1.1.4 Manufacturing and Material Processing
1.1.4.1 Spray Forming
1.1.4.2 Plasma Spray Coating
1.1.4.3 Abrasive Water-Jet Cutting
1.1.4.4 Synthesis of Nanophase Materials
1.2 Energy Conversion and Propulsion
1.2.1 Pulverized-Coal-Fired Furnaces
1.2.2 Fluidized Beds
1.2.3 Solid Propellant Rockets
1.3 Environmental Applications
1.3.1 Pollution Control
1.3.1.1 Cyclone Separators
1.3.1.2 Electrostatic Precipitators
1.3.1.3 Scrubbers
1.3.2 Fire Suppression and Control
1.4 Bio-Medical Applications
1.4.1 Dry Powder Inhalers
1.4.2 Airway Deposition
1.5 Summary and Objectives of This Book
References
Chapter 2 Properties of Dispersed Phase Flows
2.1 The Continuum Hypothesis
2.2 Density and Volume Fraction of Dispersed Flows
2.3 Inter-Particle Distance—Dilute and Dense Flows
2.4 Response Times, the Stokes Number, Collisions
2.4.1 The Stokes Number
2.4.2 Dilute Flows and Dense Flows
2.5 Thermodynamic and Transport Properties
2.6 Phase Interactions—Coupling
2.6.1 Mass Coupling
2.6.2 Momentum Coupling
2.6.3 Energy Coupling
Summary
Note
References
Problems
Chapter 3 Distributions and Statistics of Particles and Droplets
3.1 The “Size” of Particles
3.1.1 Fractal Dimension
3.2 Discrete Size Distributions
3.2.1 Frequency Distribution
3.2.2 Cumulative Distribution
3.3 Continuous Size Distributions
3.4 Statistical Parameters
3.4.1 Mode, Mean, and Median
3.4.2 Variance and Standard Deviation
3.5 Analytical Size Distributions
3.5.1 Log-Normal Distribution
3.5.2 Upper-Limit Log-Normal Distribution
3.5.3 Square-Root Normal Distribution
3.5.4 Rosin-Rammler Distribution
3.5.5 Nukiyama-Tanasawa Distribution
3.5.6 Log-Hyperbolic Distribution
Summary
References
Problems
Chapter 4 Forces on Single Particles and Drops
4.1 Steady Drag on Spherical Particles and Drops
4.1.1 Drag at Very Small Reynolds Numbers—Creeping or Stokes Flow
4.1.2 Steady Drag on Spherical at Finite Reynolds Numbers
4.1.2.1 The Flow Field Around the Solid Sphere
4.1.2.2 Steady Drag on Solid Spheres
4.1.2.3 Steady Drag on Liquid Spheres
4.1.2.4 The Drag Factor, f
4.1.3 Steady Drag with Velocity Slip at the Interface
4.2 Compressibility and Rarefaction Effects
4.2.1 The Cunningham Correction Factor
4.2.2 Effects of the Mach Number
4.3 Non-Spherical Particles
4.3.1 Particles of Regular Shapes
4.3.2 Particles with Irregular Shapes
4.3.3 The Stokes or Hydrodynamic Diameter
4.4 Effects of Flow Turbulence
4.5 Blowing Effects
4.6 Transverse (Lift) Forces Due to Particle Rotation and Flow Shear
4.6.1 The Magnus Force
4.6.2 The Saffman Force
4.7 Effects of Solid Boundaries
4.7.1 Effect of Enclosures
4.7.2 Effect of Solid Boundaries
4.8 Electrical Forces
4.8.1 The Zeta Potential
4.8.2 Electrophoresis
4.9 Body Forces
4.9.1 Terminal Velocity
4.9.2 Centrifuging
4.10 Brownian Movement
4.10.1 Brownian Diffusion
4.10.2 Thermophoresis
4.11 Transient Drag-Added Mass and History (Basset) Force
4.11.1 Creeping (Stokes) Flow (Rer << 1)
4.11.2 Flow at Finite Reynolds Numbers
4.12 Summary
References
Problems
Chapter 5 Particle-Fluid Interactions
5.1 Fundamental Multiphase Flow Equations
5.1.1 Mass Conservation Equation
5.1.2 Linear Momentum Equation for the i-th Phase
5.1.3 Angular Momentum Equation
5.1.4 Energy Equation
5.1.5 The Entropy Inequality
5.1.6 Generalized Form of the Fundamental Equations
5.2 Applications in Evaporation and Combustion—Mass Coupling
5.2.1 Evaporation or Condensation
5.2.2 The D-Square Law
5.2.3 Mass Transfer from Slurry Droplets
5.2.4 Combustion
5.3 Linear Momentum Interactions
5.3.1 Momentum Interactions with Groups of Particles
5.4 Angular Momentum Interactions
5.4.1 Transient Rotation
5.5 Energy Interactions—Heat Transfer
5.5.1 Heat-Mass Transfer Similarity
5.5.2 Steady Heat Transfer from Spheres
5.5.2.1 Solid Spheres
5.5.2.2 Viscous Spheres
5.5.2.3 Mixed Convection
5.5.2.4 Velocity Slip and Temperature Difference (Temperature Slip)
5.5.2.5 Blowing Effects
5.5.2.6 Effects of Rotation
5.5.2.7 Effects of Flow Turbulence
5.5.3 Radiation
5.5.4 Dielectric Heating
5.5.5 Transient Heat Transfer
5.5.6 Energy Interactions with Groups of Particles
5.6 Turbulence Modulation by Particles
5.6.1 Experimental Studies
5.6.2 Turbulence Modulation Models
References
Problems
Chapter 6 Particle-Particle Interactions
6.1 Binary Hard-Sphere Particle Collisions
6.1.1 Binary Collision Detection
6.1.2 Impact Efficiency
6.1.3 Particle Velocity Change
6.1.4 Physical Effects of Inter-Particle Collisions
6.2 Soft-Sphere Particle Collision/Contact
6.2.1 Elastic Deformation
6.2.2 Dissipation in the Normal Direction
6.2.3 Rotation
6.2.4 Adhesion
6.2.5 Dissipation in the Tangential Direction
6.2.6 Particle Coordinate Reference Frame
6.2.7 Integration of the Equations of Motion
6.3 Agglomeration and Flocculation Modelling
6.3.1 Characteristics of Agglomerates
6.3.2 Models of the Agglomeration Process
References
Chapter 7 Particle-Wall Interactions
7.1 Momentum and Energy Exchanges
7.2 Wall Roughness Effects and Irregular Bouncing
7.2.1 Modelling Approaches for Irregular Bouncing
7.2.2 Wall Roughness Normal PDF Model
7.3 Particle Deposition and Wall Adhesion
7.4 Wall Erosion by Particle Impact
7.4.1 The Finnie Model
7.4.2 The Neilson and Gilchrist Model
7.4.3 The Chen Model
7.4.4 The Zhang Model
7.4.5 The Oka et al. Model
References
Chapter 8 Numerical Methods and Modelling Approaches
8.1 Summary of Numerical Methods for Single-Phase Flows
8.2 Hierarchy of Numerical Methods for Multiphase Flows
8.3 Particle-Scale Simulation Methods
8.3.1 Summary Resolved Rigid Particles
8.3.2 Lattice-Boltzmann Method
8.3.2.1 Treatment of Solid-Fluid Boundaries
8.3.2.2 Description of the Particle Motion
8.3.2.3 Moving Solid-Fluid Boundaries
8.3.2.4 Solid Boundaries in Close Contact
8.3.2.5 Examples of LBM Applications
8.3.3 Immersed Boundary Methods
8.3.3.1 Fundamentals of the Immersed Boundary Methods
8.3.3.2 Applications of the Immersed Boundary Methods
8.4 Point-Particle DNS
8.4.1 Examples of Point-Particle DNS
8.5 Point-Particle LES
8.5.1 Examples of a Point-Particle LES
8.6 Euler/Euler or Multi-Fluid Approach
8.6.1 Volume Averaging Over an Indicator Function
8.6.2 Averaging Over an Ensemble of Particles
8.6.3 Probability Density Function
8.6.4 The Boltzmann Equation
8.6.5 The Eulerian-Eulerian Governing Equations
8.6.6 Mixture Models
8.7 Hybrid Euler-Lagrange Approaches
8.7.1 RANS Continuous-Phase Equations
8.7.2 Particle Tracking Concepts
8.7.3 Generation of Fluid Turbulent Velocities
8.7.4 Point-Mass Coupling Approaches
8.7.5 Mesh Size Requirements in Two-Way Coupled Euler-Lagrange Simulations
8.7.6 Example Euler-Lagrange Simulations: Pneumatic Conveying
8.8 Applications of Numerical Methods to Fluidized Bed Reactors
8.8.1 Eulerian-Eulerian Prediction of Fluidized Beds
Frictional Stress
Solving the Eulerian-Eulerian Equations
Boundary Conditions
Initial Conditions
Example Simulations
Results: Slugging Fluidized Beds
Results: Bubbling Fluidized Beds
Results: Bubble Injection
8.8.2 Eulerian-Lagrangian Predictions for Fluidized Beds
CFD-DEM Model
8.8.3 Example of Simulations
References
Chapter 9 Experimental Methods
9.1 Light Scattering Fundamentals
9.2 Sampling and Offline Methods
9.2.1 Imaging Methods, Microscopy
9.2.2 Sieving Analysis
9.2.3 Sedimentation Methods
9.2.4 Cascade Impactor
9.2.5 Electric Sensing Zone Method (Coulter principle)
9.2.6 Laser-Diffraction Method
9.3 Online Integral Methods
9.3.1 Light Attenuation
9.3.2 Cross-Correlation Method
9.4 Local Measurement Techniques
9.4.1 Isokinetic Sampling
9.4.2 Optical Fiber Probes
9.4.3 Light Scattering Instruments
9.4.4 Laser-Doppler Anemometry
9.4.5 Phase-Doppler Anemometry
9.5 Imaging Techniques and PTV/PIV
9.6 Summary
Note
References
Problems
Chapter 10 Nanoparticles and Nanofluids
10.1 Characteristics of Nanoparticles and Nanofluids
10.2 Effective Transport Properties of Nanofluids
10.3 Effective Viscosity
10.3.1 Experimental Data and Correlations
10.3.2 Non-Newtonian Behavior
10.4 Effective Thermal Conductivity
10.4.1 Experimental Studies
10.4.2 Analytical Expressions
10.4.3 Mechanisms of Thermal Conductivity Enhancement
10.5 Forced Convection
10.6 Natural Convection
10.7 Boiling
10.7.1 Pool Boiling
10.7.2 Convective Boiling
10.7.3 Critical Heat Flux
10.8 Effective Diffusivity and Mass Transfer
10.8.1 Analytical Results
10.8.2 Experimental Methods and Results
10.9 Specific Heat Capacity
Summary
References
Index