Cover
Multiphysics Modelling
of Fluid-Particulate
Systems
Copyright
Contributors
Introduction
Part I: Computational Fluid Dynamics: Discrete Element Modeling of Fluidized Beds
1 - Introduction: discrete element modeling-computational fluid dynamics of fluidized beds
1.1 - Fluidization and fluidized beds
1.2 - Application of the fluidized beds
1.3 - Geldart grouping
1.4 - Minimum fluidization velocity
1.5 - Brief overview of research efforts in the area of fluidization
1.6 - Numerical modeling of the fluidized beds
1.7 - Contact modeling of solid spherical particles
1.8 - Computation of voidage in computational fluid dynamics-discrete element modeling simulation
1.9 - The phenomenon of bubbling in fluidized beds
1.10 - Speed of sound in the fluidized medium
References
2 - Methodology: computational fluid dynamics-discrete element modeling of fluidized beds
2.1 - Introduction to computational fluid dynamics-discrete element modeling
2.2 - Computational fluid dynamics
2.2.1 - Volume-averaged fluid equations
2.2.2 - Discretization of fluid equations
2.2.3 - Numerical methods
2.2.3.1 - Pressure-driven method: semi-implicit pressure linked equation
2.2.3.2 - Density-driven method
2.2.4 - Discrete element modeling
2.3 - Particle-particle interactions
2.3.1 - Discrete element modeling simulation of time step size
2.3.2 - Modeling of fluid-particle interactions
2.4 - Computational algorithms and flow charts
2.5 - Parallelization/optimization
References
3 - Validation case study: bubbling in the fluidized bed
3.1 - Introduction
3.2 - Computational fluid dynamics-discrete element modeling numerical simulation setup
3.3 - Computational fluid dynamics-discrete element modeling numerical simulation results
3.4 - Experimental setup
3.5 - Experimental results
3.6 - Comparison of CFD-DEM numerical simulation and experimental results
3.7 - Conclusion
References
4 - Validation case study: sound waves in a fluidized medium
4.1 - Introduction
4.2 - Experimental verification of speed of sound in a fluidized medium
4.3 - Computational fluid dynamics-discrete element method numerical simulation setup
4.4 - Computational fluid dynamics-discrete element numerical simulation results
4.5 - Analytical study of standing waves in a fluidized medium
4.6 - Linearization of two-phase equations
4.6.1 - Scaling analysis of linearized two-phase equations
4.6.2 - Substitution of the computational fluid dynamics-discrete element method solution into linearized two-phase equations
4.7 - Conclusion
References
Part II: Large (non-)spherical particle modelling in the context of fluid filtration applications (resolved eulerian-lagrangian)
5 - Introduction: Large, (non-)spherical particle modeling in the context of fluid filtration applications
References
6 - Methodology: large (non)spherical particle modeling in the context of fluid filtration applications
6.1 - Fundamentals and modeling task
6.1.1 - Prevailing physical conditions in fluid filtration
6.1.2 - Fiber reconstruction and fluid structure interaction
6.1.3 - Why nonspherical particle modeling?
6.1.3.1 - Drag forces and particle relaxation times
6.1.3.2 - The nonspherical particle slip effect
6.1.3.3 - The nonspherical particle bulk effect
6.2 - Basic concepts of the large Lagrangian dirt particle and deposition model
6.2.1 - Lagrangian particle modeling approach
6.2.2 - The force to motion concept
6.2.3 - The large-particle model
6.3 - The (non)spherical dirt particle deposition solvers
6.3.1 - A spherical particle solver
6.3.1.1 - Particle momentum equation behind the spherical solver
6.3.1.2 - Particle-fluid interaction: drag forces on small particles
6.3.1.3 - Spherical particle event forces: particle-wall interaction
6.3.1.4 - Spherical particle event forces: particle-fiber interaction
6.3.1.5 - Impact forces: particle-particle interaction
6.3.1.6 - Spherical large-particle effects: drag force via pressure gradient
6.3.1.7 - Spherical large-particle effects: plugging effect
6.3.1.8 - Combined spherical filtration solver
6.3.2 - Advanced nonspherical particle solver
6.3.2.1 - Going from spherical to nonspherical particles
6.3.2.2 - Crucial concepts and implementation schemes
6.3.2.2.1 - Particle geometry: ellipsoid shape
6.3.2.2.2 - Euler and Lagrange coordinate systems
6.3.2.2.3 - Six degrees of freedom solver
6.3.2.2.3.1 - Lagrangian equations of motion for ellipsoids
6.3.2.2.3.2 - Moment of inertia tensor
6.3.2.2.4 - Nonspherical particle shape concepts
6.3.2.2.4.1 - Nonspherical surface and pressure-velocity help points
6.3.2.2.4.2 - Panel method
6.3.2.3 - The particle momentum equation behind the nonspherical solver
6.3.2.4 - Nonspherical particle-fluid interaction
6.3.2.5 - Free flow particle-fluid interaction module
6.3.2.5.1 - Free flow module force calculation
6.3.2.5.2 - Weighing method and torque effect calculation
6.3.2.6 - The fiber vicinity particle-fluid interaction module
6.3.2.6.1 - Fiber vicinity module implementation
6.3.2.6.2 - Results and verification
6.3.2.6.2.1 - Drag on coarse particles and smooth surface correction
6.3.2.6.2.2 - Nonspherical drag and lift characteristics in the fiber vicinity module
6.3.2.6.2.2.1 - Proposal for descriptive formulation of drag and lift force characteristics
6.3.2.6.2.3 - Validation of the (non)spherical fiber vicinity drag model: terminal settling velocity
6.3.2.6.2.3.1 - Spherical settling
6.3.2.6.2.3.2 - Nonspherical settling
6.3.2.7 - Nonspherical particle interaction effects: event forces
6.3.2.7.1 - Nonspherical event forces: particle-wall interaction
6.3.2.7.2 - Particle-fiber interaction and particle deposition model
6.3.2.7.2.1 - Impact phase
6.3.2.7.2.2 - Gliding phase
6.3.2.7.2.3 - Full stop deposition phase
6.3.2.7.3 - Particle-particle interaction
6.3.2.8 - Qualitative examples of nonspherical dirt particle standard filtration solver application
6.4 - Adaptive time-stepping for explicit Euler temporal discretization of spherical and nonspherical particle speed-up
6.4.1 - Introduction
6.4.2 - Explicit Euler temporal discretization of drag force effect on (non)spherical particles
6.4.2.1 - Particle-fluid interaction: drag forces
6.4.2.2 - Particle speed-up
6.4.2.2.1 - Speed-up of spherical particles
6.4.2.2.2 - Speed-up of nonspherical particles
6.4.2.3 - Numeric instability of explicit Euler drag force effect implementation
6.4.3 - Particle relaxation time and study of nonspherical speed-up behavior
6.4.3.1 - Spherical particle relaxation time
6.4.3.2 - Nonspherical particle relaxation time and speed-up behavior
6.4.3.3 - Generalized particle relaxation time
6.4.4 - Adaptive time-stepping
6.4.4.1 - One parameter to define numeric stability
6.4.4.2 - Describing the instabilities
6.4.4.3 - Quantification of numeric error
6.4.4.3.1 - Quantification of spherical numeric error
6.4.4.3.2 - Quantification of nonspherical numeric error
6.4.4.3.3 - Evaluation of a quantified numeric error
6.4.4.4 - Simple linear correlation for deviation
6.4.4.4.1 - Slope dependence on reference value, โtp,0/ฯp
6.4.4.4.2 - Slope dependence on M = tend/ฯp
6.4.4.4.3 - Slope dependence on โtend/ฯp
6.4.4.5 - Adaptive time-stepping of user-defined accuracy
6.4.5 - Adaptive time-stepping and event forces
6.4.5.1 - The particle event force relaxation time
6.4.5.1.1 - The spatially bounded, event forceโadapted, time-stepping scheme
6.4.5.1.2 - The temporally bounded, event forceโadapted, time-stepping scheme
6.4.5.1.3 - Event forceโadapted, time-stepping scheme versus static time-stepping
6.4.6 - Adaptive time-stepping: conclusion
6.5 - Extension modules: electrostatic module and bacteria module
6.5.1 - The bacteria module
6.5.2 - The E-static module
6.6 - Workflow, C++ program structure, and how to use the solver
6.6.1 - Overall workflow
6.6.2 - Workflow for the dirt particle and deposition solvers
6.6.3 - Workflow for particle movement calculation
6.6.4 - Inheritance structure and basic functionality of solver-relevant C++ classes
6.6.5 - User options and dictionary
6.6.6 - The graphic user interface
References
7 - Validation: experimental and semianalytical
7.1 - Semianalytical validation scheme for simplified geometries
7.1.1 - Simplified geometry
7.1.2 - Semianalytical approach
7.1.2.1 - Inertial impact effects
7.1.2.2 - Particle fiber adhesion and blow-off due to particle momentum or interactions
7.1.2.3 - Sieving due to pore sizes
7.1.2.4 - Comparing computational fluid dynamics and analytical results
7.2 - Validation by comparison to data from literature
7.3 - Experimental filter fiber analysis and validation
7.3.1 - The oil fiber test facility
7.3.2 - Particle distribution detection facility
7.3.2.1 - Measurement principle
7.3.2.2 - Experimental procedure
7.3.3 - The optical evaluation algorithm
7.3.4 - Qualitative verification of the three-dimensionless reconstruction method
7.3.5 - Two modes of measurement
7.3.5.1 - Particle distribution detection mode
7.3.5.2 - Filter fiber efficiency mode
7.3.6 - Experimental verification of simulation results
7.3.6.1 - Pressure drop
7.3.6.2 - Filter fiber efficiency curve
References
8 - Application and results: filter fiber engineering
8.1 Comparison of material with and without adhesional effects
8.2 Comparison of (non)spherical particle filter fiber efficiency
8.3 Comparison of (non)spherical particle penetration depth
8.4 Comparison of fiber materials: Ahlstrom A55 and Fulda A43
8.5 Effect of dirt predeposition
Reference
9 - Conclusion and vision
Reference
Part III: Modeling Shocks through Multiphase Media with Smoothed Particle Hydrodynamics
10 - Introduction: smoothed particle hydrodynamics modeling of shocks
10.1 - Overview of smoothed particle hydrodynamics
10.1.1 - Convergence, consistency, and stability
10.1.2 - Boundary conditions
10.1.3 - Adaptivity
10.1.4 - Coupling to other models
10.1.5 - Applicability to industry
10.2โMultiphase compressible smoothed particle hydrodynamics
References
11 - Methodology: smoothed particle hydrodynamics modeling of shocks
11.1 - Weakly compressible smoothed particle hydrodynamics from Newtonian mechanics
11.1.1 - Particle approximation
11.1.2 - Convergence and renormalization techniques
11.1.3 - Weakly compressible smoothed particle hydrodynamics approximation of Euler equations
11.1.4 - Monaghan artificial viscosity
11.1.5 - Variable smoothing length
11.1.6 - Neighbors search algorithms
11.1.7 - Ghost particles for boundary conditions
11.2 - Fully compressible smoothed particle hydrodynamics from Lagrangian mechanics
11.2.1 - Density estimates
11.2.2 - Variationally consistent smoothed particle hydrodynamics schemes
11.2.3 - Artificial dissipation
11.3 - Time integration, algorithm details, and code implementation
11.3.1 - Leapfrog time integration
11.3.2 - Neighbors search algorithm: KD-Tree2
11.3.3 - Structure of the serial code
References
12 - Validation: smoothed particle hydrodynamics modeling of shocks
12.1 - Multimaterial arbitrary Lagrangian-Eulerian method formulation
12.1.1 - Equations of state
12.2 - One-dimensional test cases
12.2.1 - Multiphase shock tubes
12.2.2 - One-dimensional underwater explosive shock testing
12.2.3 - Isothermal impact into inhomogeneous structure
12.2.4 - Isentropic impact into an inhomogeneous structure
12.2.5 - Conclusions
12.3 - Two-dimensional test cases
12.3.1 - Air-air shock chambers
12.3.2 - Two-dimensional underwater explosive shock testing near planar wall
12.3.3 - Two-dimensional hypervelocity impacts
References
13 - Conclusion: smoothed particle hydrodynamics modeling of shocks
Index
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