Transport Phenomena in Multiphase Systems (Mechanical Engineering Series)

Preface
Contents
Chapter 1: Introduction to Multiphase Flow Basic Equations
	1.1 Introduction
	1.2 Multiphase Conservations Laws
		1.2.1 Mass Balances
		1.2.2 Momentum Balances
			1.2.2.1 Incompressible Viscous Flow
			1.2.2.2 Incompressible Navier-Stokes Equation
			1.2.2.3 Compressible Viscous Flow
		1.2.3 Energy Balances
			1.2.3.1 Enthalpy Representation
			1.2.3.2 Entropy Representation
		1.2.4 Conservation of Species
	1.3 Exercises
		1.3.1 Ex. 1: Balances of Mass and Species in Multicomponent Systems
		1.3.2 Ex. 2: Momentum Balances for a Multicomponent System
		1.3.3 Ex. 3: Mixture Momentum Balance
		1.3.4 Ex. 4: Balance of Energy for a Multicomponent System
	References
Chapter 2: Multiphase Flow Kinetic Theory, Constitutive Equations, and Experimental Validation
	2.1 Introduction
	2.2 Elementary Multiphase Kinetic Theory
		2.2.1 Frequency Distributions
		2.2.2 Peculiar Velocity and Transport
		2.2.3 Granular Temperature and the Equation of State
		2.2.4 FCC Equation of State
		2.2.5 Particle and Molecular Velocities
		2.2.6 Maxwellian Distribution
		2.2.7 Restitution Coefficients
		2.2.8 Frequency of Binary Collisions
		2.2.9 Mean Free Path
		2.2.10 Elementary Treatment of Transport Coefficients
			2.2.10.1 Diffusion Coefficients
			2.2.10.2 Viscosity
			2.2.10.3 Thermal Conductivity
		2.2.11 Boundary Conditions
	2.3 Drag Expressions
	2.4 Multiphase Flow Experimental Verification
		2.4.1 Experimental
		2.4.2 Kinetic Theory-Based PIV
		2.4.3 Core-Annular Flow Regime Explanation
		2.4.4 Turbulent Granular Temperature
	2.5 Flow Regime Computation
	2.6 Wave Propagation
		2.6.1 Compression Wave Theory
		2.6.2 Experimental Equipment
		2.6.3 Pressure Wave Theory
		2.6.4 Pressure Wave Experimental Results
	2.7 Frictional Behavior of Granular Matters
	2.8 Drag Force for Homogeneous and Non-homogeneous Flow of the Particle Phase
		2.8.1 Filtered or Subgrid Model
		2.8.2 Energy Minimization Multi-scale (EMMS) Approach
	2.9 Modeling of Multi-type Particle Flow Using the Kinetic Theory Approach
		2.9.1 Multi-type Particle Flow Equations
			2.9.1.1 Continuity Equation
			2.9.1.2 Momentum Equation
			2.9.1.3 Fluctuating Energy Equation
			2.9.1.4 Kinetic Equation
	2.10 Heat Transfer
		2.10.1 Fluid/Particles Heat Transfer in Fluid/Particles Flow Systems
		2.10.2 Wall Heat Transfer in Fluid/Particles Flow Systems
	2.11 Mass Transfer
		2.11.1 Mass Transfer Coefficients
		2.11.2 Low Sherwood Number But Good Mass Transfer in Fluidized Beds
	2.12 Exercises
		2.12.1 Ex. 1: Alternate Definition of Granular Temperature
		2.12.2 Ex. 2: Diffusion Coefficients and Viscosities
		2.12.3 Ex. 3: Collision Theory for Reactions and Burning Rate
		2.12.4 Ex. 4: Apollo 13 Oxygen Tank Explosion
		2.12.5 Ex. 5: One-Dimensional Gas/Solid Flow
		2.12.6 Ex. 6: Three-Dimensional Gas/Solid Flow
		2.12.7 Ex. 7: Two-Dimensional Gas/Solid Flow
		2.12.8 Ex. 8: Two-Dimensional Transient Gas/Solid Flow
	References
Chapter 3: Multiphase Flow Phenomena (Gas/Solid and Gas/Liquid Systems)
	3.1 Introduction
	3.2 Gas/Solid Flows
		3.2.1 Introduction to Gas/Solid Flows
		3.2.2 Fluidization Concepts and Flow Regimes
		3.2.3 Geldart Particle Classification
		3.2.4 Standpipes, Non-mechanical Valves, and Cyclones
	3.3 Gas/Liquid Flows
		3.3.1 Overview and Fundamental Relations of Gas/Liquid Two-Phase Flows
		3.3.2 Some Differences Between Gas/Liquid Flows and Single-Phase Fluid Flows
		3.3.3 Modeling Gas/Liquid Flow in Pipes
		3.3.4 Flow Regimes and Flow Maps of Two-Phase Flows
			3.3.4.1 Overview of Various Flow Maps
			3.3.4.2 Classical Flow Maps of Two-Phase Regimes: A Summary of Applications and Limitations
			3.3.4.3 Industrial Application of Flow Maps
	3.4 Exercises
		3.4.1 Ex. 1: Minimum Fluidization Condition
		3.4.2 Ex. 2: Particle Terminal Velocity
		3.4.3 Ex. 3: Gas/Liquid Flow and Flow Regimes
	References
Chapter 4: Polymerization Process Intensification Using Circulating Fluidized Bed and Rotating Fluidized Bed Systems
	4.1 Introduction
	4.2 Circulating Fluidized Bed (CFB) Reactor for Polymerization
		4.2.1 Introduction
		4.2.2 Description of the Process
		4.2.3 Steady State Energy Balance for a Fluidized Bed Riser
		4.2.4 High Production Rate
		4.2.5 CFD Design of a Large Ethylene Reactor
			4.2.5.1 High Velocity
			4.2.5.2 Low Velocity
		4.2.6 CFD Design of Smaller Reactors
		4.2.7 Conclusion
	4.3 Rotating Fluidized Bed (RFB) Reactor for Polymerization
		4.3.1 Introduction
		4.3.2 Mathematical Modeling of a Rotating Fluidized Bed (RFB)
		4.3.3 Results and Discussion
		4.3.4 Conclusion
	4.4 Exercise
		4.4.1 Ex. 1: Polymerization Reactor with Downer
	References
Chapter 5: Circulating Fluidized Beds for Catalytic Reactors
	5.1 Introduction
	5.2 Catalytic Rates of Reactions
	5.3 Shrinking Core Model and Rates in Conservation of Species
	5.4 Denn Shrinking Core Model
	5.5 Combustion Reaction
	5.6 Gasification Reactions
	5.7 Circulating Fluidized Bed (CFD) Simulations for Synthesis Gas
	5.8 CFB Simulations for Sulfur Dioxide Capture
	5.9 Exercises
		5.9.1 Ex. 1: Catalytic Conversion of Methane to Synthesis Gas by Partial Oxidation
		5.9.2 Ex. 2: Catalytic Conversion of Methane to Synthesis Gas in a Riser No Bubbles
		5.9.3 Ex. 3: Catalytic Conversion of Methane to Synthesis Gas in a Circulating Fluidized Bed
		5.9.4 Ex. 4: Parabolic Rusting Law
		5.9.5 Ex. 5: CFD Scale-Up of a Fluidized Bed Coal Gasification Process, IGT U-GAS Process
	References
Chapter 6: Synthetic Gas Conversion to Liquid Fuel Using Slurry Bubble Column Reactors
	6.1 Introduction
	6.2 Diesel Fuel Reactor
	6.3 Reactor Model for Fischer-Tropsch Kinetics
	6.4 Potential High Production Reactor Simulation
	6.5 New Reactor Features
	6.6 Exercises
		6.6.1 Ex. 1: Computed Bubble Coalescence Explanation and Flow Regimes
		6.6.2 Ex. 2: Computation of Gas, Liquid, and Solid Volume Fractions
		6.6.3 Ex. 3: Computation of Gas Hold-Up (Effect of Pressure)
		6.6.4 Ex. 4: Elimination of Bubbles
	References
Chapter 7: Application of Multiphase Transport to CO2 Capture
	7.1 Introduction
	7.2 CO2 Capture Using Sodium or Potassium Carbonate Solid Sorbents
		7.2.1 Conceptual Design of Fluidized Bed Systems Based on the CFD Approach
			7.2.1.1 Bubbling Beds and Plug Flow Approximation
			7.2.1.2 CO2 Capture with Reduced Pressure in a Downer of a CFB
			7.2.1.3 CO2 Capture in a Multistage Sorber with Thermal Regeneration
		7.2.2 CFD Simulation of CO2 Capture Using Potassium Carbonate Sorbent
			7.2.2.1 Introduction
			7.2.2.2 Numerical Analysis
			7.2.2.3 Reaction Kinetic Model
			7.2.2.4 Simulation Results and Comparison with Experimental Data
	7.3 CO2 Capture by MgO-Based Sorbents Using a Circulating Fluidized Bed (CFB)
		7.3.1 Introduction
		7.3.2 Numerical Analysis and Simulation of Entire CFB Loop
		7.3.3 Numerical Simulation of Full CFB Loop for CO2 Capture and Sorbent Regeneration
	7.4 Use of Carbon Dioxide
	7.5 Exercises
		7.5.1 Ex. 1: Order of Magnitude Design of CO2 Capture Riser/Loop
		7.5.2 Ex. 2: CFD Design of CO2 Capture Loop
		7.5.3 Ex. 3: CFD Design of an Amine Sorber
	References
Chapter 8: Fluidized Bed Reactors for Solar-Grade Silicon and Silane Production
	8.1 Introduction
	8.2 Innovative Technology Description
	8.3 Exercises
		8.3.1 Ex. 1: Hydrochlorination of SiCl4
		8.3.2 Ex. 2: Design of Deposition Reactors for Silicon Production
	References
Chapter 9: Multiphase Hemodynamics Modeling (Blood Flow)
	9.1 Introduction
	9.2 Origins in Non-Newtonian Coal/Water Slurry Modeling
	9.3 Simulation of Concentrated Suspension Flows in Straight Pipe Geometries
		9.3.1 Analysis of Lovelace Medical Foundation Experiments
		9.3.2 Sinton and Chow Experiments Analysis
	9.4 Simulation of a Right Coronary Artery Using Basic Two-Phase Non-Newtonian and Kinetic Theory Models
		9.4.1 Idealized Model of a Right Coronary Artery
		9.4.2 Realistic Model of a Right Coronary Artery
		9.4.3 Realistic Model of a Right Coronary Artery Using Multiphase Kinetic Theory
	9.5 Multiphase CFD Analysis of Flow Through a Sudden-Expansion Flow Chamber
	9.6 Solutions to Two Important Phenomena
		9.6.1 Modeling of the Fahraeus-Lindqvist Effect
		9.6.2 Application to Platelet and RBC Transport
	9.7 Analysis of LDL and HDL Transport
	9.8 Application to Analysis of Monocyte Adhesion Data for Atherosclerosis
	9.9 Analysis of an Actual Right Carotid Artery
	9.10 Conclusion
	9.11 Exercises
		9.11.1 Ex. 1: Model the Altobelli and Sinton and Chow Experiments
		9.11.2 Ex. 2: Model the Realistic RCA Using the Carraeu-Yasuda Model
		9.11.3 Ex. 3: Model the Realistic RCA with Bifurcating Arteries
		9.11.4 Ex. 4: Extend the Fahraeus-Lidqvist Model
		9.11.5 Ex. 5: Extend the LDL and HDL Model
		9.11.6 Ex. 6: Model the Pritchard Experiment
	References
Chapter 10: Multiphase Flow Modeling of Explosive Volcanic Eruptions
	10.1 Introduction
	10.2 Scaling Properties and Regimes of Volcanic Gas/Particle Flows
		10.2.1 Scaling Properties
		10.2.2 Regimes in Multiphase Flows
		10.2.3 Grain-Size Distribution
	10.3 Eulerian-Eulerian Multiphase Flow Modeling
		10.3.1 Compressible Multiphase Flow Regime: Volcanic Jets and Blasts
			10.3.1.1 Volcanic Jets
			10.3.1.2 Volcanic Blasts
		10.3.2 Stratified Flow Regime: Pyroclastic Density Currents
	10.4 The Method of Moments
	10.5 The Equilibrium-Eulerian Multiphase Flow Model
		10.5.1 The Eulerian-Eulerian Model in Mixture Formulation
		10.5.2 The Equilibrium-Eulerian Model
		10.5.3 Application of the Equilibrium-Eulerian Model to Volcanic Plumes
	10.6 The Lagrangian Particle Approach
	10.7 Conclusion
	10.8 Exercises
		10.8.1 Ex. 1: Independent Eruption Source Parameters of Volcanic Plumes
		10.8.2 Ex. 2: Calculation of Stokes Time
		10.8.3 Ex. 3: Sauter Diameter of a Grain-Size Distribution
		10.8.4 Ex. 4: Numerical Simulation of Phreatic Explosions
	References
Chapter 11: Multiphase Flow Modeling of Wind Turbine Performance Under Rainy Conditions
	11.1 Introduction
	11.2 Numerical Modeling
	11.3 Numerical Simulation
	11.4 Results and Discussion
		11.4.1 S809 Airfoil
		11.4.2 NREL Phase VI Horizontal-Axis Wind Turbine
			11.4.2.1 Single-Phase (Air) Flow Simulation
			11.4.2.2 Two-Phase (Air and Rain) Flow Simulation
	11.5 Conclusion
	11.6 Exercises
		11.6.1 Ex. 1: Polar Curve
		11.6.2 Ex. 2: Calculation of Power Generation
		11.6.3 Ex. 3: Two-Dimensional Gas/Particle Flow
	References
Chapter 12: Application of Multiphase Flow Simulation in Pharmaceutical Processes
	12.1 Introduction
	12.2 Model Development for Pharmaceutical Bubbling Fluidized Bed Dryer
		12.2.1 Gas/Solid Flow Model
		12.2.2 Heat and Mass Transfer Model
		12.2.3 Drying Rate Model
	12.3 Numerical Simulation
		12.3.1 Three Different Scales of Drying Fluidized Beds
		12.3.2 Numerical Analysis
	12.4 Simulation Results and Discussion
		12.4.1 Gas/Solid Flow Patterns
		12.4.2 Heat and Mass Transfer During the Drying Process
	12.5 Comparison Between Simulation Results and Experimental Data
	12.6 Conclusion
	12.7 Exercises
		12.7.1 Ex. 1: Pneumatic Conveying Pharmaceutical Drying Process Modeling
		12.7.2 Ex. 2: Fluidized Bed Pharmaceutical Granulation Process
		12.7.3 Ex. 3: Pharmaceutical Drying Using Moving Packed-Bed Process
	References
Chapter 13: Hydrodynamics of Fluidization with Surface Charge
	13.1 Introduction
	13.2 Fluidized Bed to Determine Charge-to-Mass Ratio
	13.3 Experimental Bubbles and Bed Expansion
	13.4 Hydrodynamic Model with Surface Charge
	13.5 Surface Charge from Current Measurement
	13.6 Experiment and Simulation with Applied Electric Field
	13.7 Steady-State Conduction Model
	13.8 Simulation of Commercial Bed (Sheeting Behavior in Commercial Polymerization Reactor)
	13.9 Conclusion
	13.10 Exercise
		13.10.1 Ex. 1: Comparison Between Two Electrostatic Charging Models
	References
Appendix: A Generalization of Onsager´s Multicomponent Diffusion Equations
	A.1 Introduction
	A.2 Onsager´s Dissipation Function
	A.3 Entropy with Kinetic Energy of Diffusion
	A.4 Conservation of Species
	A.5 Mixture Energy Balance
	A.6 Entropy Production
	A.7 Isothermal Equations of Motion
	A.8 Fick´s Law: Zero Acceleration
	A.9 Perfect Gas Mixture
	A.10 Binary Diffusion with Inertia
	A.11 Inertial Correction of Fick´s Law
	References
Index