Gas-Particle and Granular Flow Systems: Coupled Numerical Methods and Applications

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Gas-Particle and
Granular Flow Systems:

Coupled Numerical Methods
and Applications
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Contents
Part 1: Theories & models
1 Introduction to two-phase flow
	1.1 Flow classifications
		1.1.1 Single-phase flow
		1.1.2 Gas-particle flow
		1.1.3 Granular flow
		1.1.4 Pebble flow
	1.2 Flow regimes
		1.2.1 Dilute and dense flows
		1.2.2 Inertial and elastic flows
	1.3 Numerical methods
		1.3.1 Methods for single-phase flow
		1.3.2 Methods for two-phase flow
	1.4 Summary
2 Discrete particle model
	2.1 Spherical particle model
	2.2 Generalized hard particle model (GHPM)
		2.2.1 Governing equations
		2.2.2 Consistency with the hard sphere model
		2.2.3 Numerical procedures for implementation
		2.2.4 GHPM model validation
			Theoretical validation
			Experimental validation
		2.2.5 Application in a lifting hopper
		2.2.6 Application for the particle-wall collision
		2.2.7 Numerical procedure for multiple contacts
		2.2.8 Simulation test and experimental validation
		2.2.9 Application in the particle-wall collision
			Case 1: Multiple particle-wall collisions
			Case 2: With wall roughness
	2.3 SIPHPM model
		2.3.1 Description of the model basis
		2.3.2 Governing equation
		2.3.3 Equation of motion
		2.3.4 Numerical procedures and techniques
			Collision detection
			Three-dimensional extension
		2.3.5 SIPHPM model validation
			2.3.5.1 Case 1: Pair collision
			2.3.5.2 Cases 2-4: Jamming of cubes in silo discharge
			2.3.5.3 Case 5: Free discharge of cubes in silos
	2.4 EHPM-DEM model
		2.4.1 Extended general hard particle model (EHPM)
		2.4.2 Extended discrete element method
		2.4.3 EHPM-DEM coupling strategy
		2.4.4 Collision detection strategy
		2.4.5 Governing equations of motion
		2.4.6 Demonstration and validation of EHPM-DEM
			Case 1: Pair collision
			Case 2: Hopper discharge
		2.4.7 Simulation efficiency
			2.4.7.1 Case 1: Hopper discharge
			2.4.7.2 Case 2: Particle deposition
	2.5 Heat transfer extensions
		2.5.1 Particle-particle conduction
	2.6 Summary
3 Coupled methods
	3.1 LES-DEM coupled methods
		3.1.1 Governing equations
		3.1.2 Discrete element method (DEM)
		3.1.3 Approach A: conventional method
		3.1.4 Approach B: smoothed void fraction method
			3.1.4.1 Virtual void fraction model
			3.1.4.2 Drag force computation
			3.1.4.3 Feedback force and the subparticle scale four-way coupling
	3.2 DNS-DEM coupled methods
		3.2.1 Immersed boundary method
		3.2.2 Point-force method
			3.2.2.1 Governing equations of fluids
			3.2.2.2 Motion equations of particles
			3.2.2.3 Particle-particle collision model
			3.2.2.4 Particle-particle collision detection
	3.3 LBM-DEM coupled methods
		3.3.1 Recovery of governing equation
			3.3.1.1 Chapman-Enskog analysis
			3.3.1.2 Inperfect equilibrium distribution function
			3.3.1.3 Considering the interphase force
		3.3.2 Coupled with heat transfer
		3.3.3 Multiple schemes LBM-IBM-DEM
	3.4 Summary
Part 2: Applications
4 Application in gas-particle flows
	4.1 Homogeneous turbulence
		4.1.1 Governing equations
		4.1.2 Collision rates and statistics
			4.1.2.1 Particle-particle collision rate Rc
			4.1.2.2 Mean free path
			4.1.2.3 Flatness factor F
			4.1.2.4 Comparison with the no-collision case
	4.2 Planar jets
		4.2.1 2D case with the heat transfer
			4.2.1.1 Vortex structure and temperature fields
			4.2.1.2 Fractal characteristics of the heat transfer interface
			4.2.1.3 Effect of the inflow momentum thickness θ
		4.2.2 3D case with the two-way coupling
			4.2.2.1 3D fluid vortex structure
			4.2.2.2 Fluid velocity profiles
	4.3 Swirling jets
		4.3.1 Vortex breakdown
		4.3.2 Coherent oscillation
			4.3.2.1 Auto-correlation
			4.3.2.2 Cross-correlation
		4.3.3 Particle-vortex interaction
			4.3.3.1 Instantaneous characteristics
			4.3.3.2 Fλ2(k,t)  in the spectrum space
			4.3.3.3 Fλ2,(k,t)  for case 1
			4.3.3.4 Fλ2,(k,t)  for case 2
			4.3.3.5 Fλ2(k,t)  for case 1
			4.3.3.6 Fλ2(k,t)  for case 2
			4.3.3.7 The energy spectrum
		4.3.4 Four-way coupling
			4.3.4.1 Dependency on TKE and TDR
			4.3.4.2 Dependency on the Reynolds stress tensor
	4.4 Bubbling fluidized bed
		4.4.1 3D bubbling fluidized testing bed
			4.4.1.1 Computation of ε3D and configuration
			4.4.1.2 Force behavior analysis
		4.4.2 Pulsed fluidization
			4.4.2.1 Pressure drop
			4.4.2.2 Force behavior analysis
			4.4.2.3 Collision on immersed tubes
			4.4.2.4 Particle phase fluctuation
	4.5 Spouted bed
		4.5.1 CFD-DEM vs. SVFM-based fine LES-DEM
			4.5.1.1 Comparison with experimental results
		4.5.2 Particle phase behavior
			4.5.2.1 Mean velocity field comparison: 2D, 3D vs. Exp
			4.5.2.2 Longitudinal profile comparison: fine scale δ1 vs. coarse scale δ2, and LES vs. no LES
			4.5.2.3 Lateral profile of the particle mean velocity
		4.5.3 Gas phase behavior
			4.5.3.1 Pressure drop: 2D, 3D vs. Exp
			4.5.3.2 Velocity of gas phase: 2D
			4.5.3.3 Void fraction of the gas phase: 2D
			4.5.3.4 The effect of the parameter τ: 3D
		4.5.4 Additional remark
	4.6 Summary
5 Application in granular flows
	5.1 Some functions
		5.1.1 Evaluation functions of mixing degree
			5.1.1.1 Dimensionless concentration difference
			5.1.1.2 Radial distribution function (RDF)
			5.1.1.3 Mixing information entropy via RDF
			5.1.1.4 Mixing information entropy via local concentration
			5.1.1.5 Improved information entropy via coordination number fraction (CnIE)
			5.1.1.6 General mixing information entropy for Na : N b <>1 : 1 and multiple particle system (GMIE)
			5.1.1.7 Lacey mixing index (LMI)
			5.1.1.8 Improved mixing index for multiple particle systems (MPMI)
		5.1.2 Evaluation functions of heat transfer degree
			5.1.2.1 Weighted temperature (WT) and temperature discrepancy function (TDF)
			5.1.2.2 Dimensionless temperature probability density function (TPDF)
			5.1.2.3 Mean temperature discrepancy (MTD)
			5.1.2.4 Thermal radial distribution function (TRDF) and thermal information entropy (TIE) ST
	5.2 Circular drum mixers
		5.2.1 Flow pattern and mixing evolution
		5.2.2 Dimension analysis
		5.2.3 Information entropy analysis
			5.2.3.1 Radial distribution function
		5.2.4 Heat conduction features
			5.2.4.1 Motion of gyration
			5.2.4.2 After the same evolution time
			5.2.4.3 After the same revolution
			5.2.4.4 Probability density function of temperature discrepancy functions (TDF)
			5.2.4.5 Thermal radial distribution function
			5.2.4.6 Entropy analysis
			5.2.4.7 Mean temperature differences and increasing rates
	5.3 Wavy drum mixers
		5.3.1 Wavy wall configuration
		5.3.2 Analysis and prediction
		5.3.3 Effects of phase velocity, wave number and amplitude
			5.3.3.1 Case 1: Effect of phase velocity
			5.3.3.2 Case 2: Effect of the wave numbers kλ ( ωa=Const.)
			5.3.3.3 Case 3: Effect of boundary amplitudes A
		5.3.4 Driven force analysis
			5.3.4.1 Effective driven force (EDF)
		5.3.5 Heat conduction features
			5.3.5.1 With different wave numbers
			5.3.5.2 With different rotating speeds
			5.3.5.3 Probability density function of temperature (T-PDF)
			5.3.5.4 Mean temperature discrepancy (MTD)
	5.4 Mixing of nonspherical particles
		5.4.1 Polygonal particle mixing in 2D drum
			5.4.1.1 Simulation configurations
			5.4.1.2 Mixing processes
			5.4.1.3 Mixing index
			5.4.1.4 Mixing entropy analysis
			5.4.1.5 Velocity fields
			5.4.1.6 Kinetic energies
		5.4.2 Cubic particle mixing in one layer
			5.4.2.1 Numerical setup
			5.4.2.2 Motion process and flow pattern comparisons
			5.4.2.3 Effect of cubic shape on velocity distribution
			5.4.2.4 Effect of friction from front and rear walls
			5.4.2.5 Effect of filling levels and driving modes
		5.4.3 Tetrahedral particle mixing in one layer tumbler
			5.4.3.1 The observation of mixing of tetrahedrons
			5.4.3.2 Mixing index and entropy analyses
			5.4.3.3 Probability density function of velocity
			5.4.3.4 Mean and variance of velocity
		5.4.4 Cubic particle mixing in 3D cylinder
			5.4.4.1 Three kinds of mixing patterns
			5.4.4.2 Mixing indices
			5.4.4.3 Mixing information entropies
			5.4.4.4 Normalized values of entropy
			5.4.4.5 Particle trajectories analysis
	5.5 Hopper discharge
		5.5.1 Geometric features on quasi-static discharge
			5.5.1.1 Particle trajectories
			5.5.1.2 Probability density function
			5.5.1.3 Comparison with experiments
			5.5.1.4 Geometrical models for explanation
			5.5.1.5 The ideal dispersion process based on the model
		5.5.2 Shaken discharge
			5.5.2.1 Model validation and simulation conditions
			5.5.2.2 Discharge process under rocking and flow pattern
			5.5.2.3 Effect of rocking amplitude
			5.5.2.4 Effect of rocking frequency
			5.5.2.5 Kinetic energy of the resident particles
			5.5.2.6 Trajectory of the discharged particles
		5.5.3 Discharge of 2D polygonal particles
			5.5.3.1 Discharge process
			5.5.3.2 Discharge fraction
			5.5.3.3 Discharge number flow rate
			5.5.3.4 Mean voidages in discharge
			5.5.3.5 Effect of initial packing condition
	5.6 Summary
Bibliography
Index
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