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Cover
Title Page
About the Authors
Preface
1 Introduction
1. 1.1 Multiphase Coupling
2. 1.2 Modeling Approaches
3. 1.3 Modeling with DEM
4. 1.4 CFD-DEM Modeling
5. 1.5 Applications
6. 1.6 Scope and Overall Plan
7. 1.7 Online Content
8. References
Part I: DEM
1. 2 DEM Formulation
  1. 2.1 Hard-Sphere
  2. 2.2 Soft-Sphere
  3. 2.3 Force-Displacement Laws
  4. 2.4 Torque Expressions
  5. 2.5 Boundary and Initial Conditions
  6. Nomenclature
  7. References
2. 3 DEM Implementation
  1. 3.1 Computational View
  2. 3.2 Program Structure
  3. 3.3 Contact Search Algorithms
  4. 3.4 Integration Methods
  5. 3.5 Spring Stiffness
  6. 3.6 Wall Implementation
  7. 3.7 Parallelization
  8. Nomenclature
  9. References
3. 4 Non-Spherical Particles
  1. 4.1 Shape Representation
  2. 4.2 Kinematics and Dynamics of a Rigid Body
  3. 4.3 Superellipsoids
  4. 4.4 Multi-Sphere Method
  5. Nomenclature
  6. References
4. 5 DEM Applications to Granular Flows
  1. 5.1 Packing of Particles
  2. 5.2 Flow in Hoppers
  3. 5.3 Solid Mixing
  4. 5.4 Screw Conveying
  5. 5.5 Film Coating
  6. Nomenclature
  7. References
Part II: CFD-DEM
1. 6 CFD-DEM Formulation and Coupling
  1. 6.1 Multiphase Coupling
  2. 6.2 Momentum Coupling
  3. 6.3 Energy Coupling
  4. 6.4 Mass Coupling
  5. Nomenclature
  6. References
2. 7 CFD-DEM Applications to Multiphase Flow
  1. 7.1 Fluidization
  2. 7.2 Spouting
  3. 7.3 Pneumatic Conveying
  4. 7.4 Non-Isothermal Flows
  5. 7.5 Reactive Flows
  6. 7.6 Miscellaneous
  7. Nomenclature
  8. References
3. 8 Interparticle Forces and External Fields
  1. 8.1 Governing Equations
  2. 8.2 Interparticle Forces
  3. 8.3 External Fields
  4. 8.4 Applications
  5. Nomenclature
  6. References
Index
End User License Agreement

List of Tables

Chapter 01
1. Table 1.1 Open source and commercial software packages available for CFD-DEM simulation (accessed on November 2015)
Chapter 02
1. Table 2.1 Physical properties of the sphere used in normal and oblique collisions with wall
2. Table 2.2 Properties of sphere and wall used in elastic oblique tests
Chapter 03
1. Table 3.1 Various explicit numerical integration methods used in discrete element simulations
2. Table 3.2 Adams–Bashforth integration coefficients for various accuracy orders
3. Table 3.3 Adams–Moulton coefficients for various accuracy orders of integration
4. Table 3.4 Coefficients of the Gear’s method for various order of integration
5. Table 3.5 Relationships for evaluating collision time, maximum normal overlap, and maximum normal force in an elastic contact between two spherical particles for linear and non-linear contact models
6. Table 3.6 Variation of contact time, maximum overlap, and maximum contact force as a function of material stiffness and impact velocity in elastic collisions of two spherical particles with density of 2500 kg/m³ and diameter of 2 mm
Chapter 05
1. Table 5.1 Physical properties and operating conditions of simulations
2. Table 5.2 Properties of the particle and the walls used in simulation of the Nauta mixer
3. Table 5.3 Parameters of the dispersion model and other variables extracted from DEM simulations
4. Table 5.4 Experimental and theoretical studies on the screw conveyors
5. Table 5.5 Physical properties of particles and walls used in the screw conveyor simulation
Chapter 06
1. Table 6.1 Governing equations of three types of CFD-DEM models
Chapter 08
1. Table 8.1 Permittivity ϵ, refractive index n, and main absorption frequency ν_e in UV for various solids, liquids, and polymers at 20 °C [18]
2. Table 8.2 Simulation and operating condition of the tribocharger
3. Table 8.3 Magnetic susceptibility of various materials [48]

List of Illustrations

Chapter 01
1. Figure 1.1 Momentum, energy, and mass transport between solid and fluid phases
2. Figure 1.2 Modeling scales in fluid–particulate systems
3. Figure 1.3 Different modeling approaches for fluid–solid systems
4. Figure 1.4 Different scales in a fluid–solid system
5. Figure 1.5 A typical bubbling gas–solid fluidized bed. Averaged fluid fields (pressure, velocity, porosity, etc.) are calculated in a fluid cell at the meso-scale. The cells are small enough to capture all properties of the flow (e.g., bubbles) and large enough to contain a number of particles to ensures proper averaging. Vectors show the fluid velocity interpolated on the center of fluid cells
Chapter 02
1. Figure 2.1 Successive steps in an instantaneous collision between two spherical particles in the hard-sphere formulation. and are translational velocities, and are rotational velocities, and are normal and tangential impulse forces. Superscripts 0 and 1 refer to pre- and post-collision velocities, respectively
2. Figure 2.2 Square-well potential used for simulating instantaneous and cohesive forces between particles. When the separation distance is longer than d₀, no cohesive interaction exists between particles. Once the separation distance is d₀, a cohesive collision occurs and thereafter particles undergo an elastic collision
3. Figure 2.3 Schematic illustration of colliding particles i and j and forces acting on particles as a result of collision
4. Figure 2.4 Schematic of a viscoelastic collision model in normal direction. The elastic force is repulsive and conserves the kinetic energy of collision while the viscous force resists the motion and dissipates kinetic energy of the collision
5. Figure 2.5 Dimensionless normal force versus dimensionless normal overlap in the linear spring-dashpot model for various normal coefficients of restitutions. is the ratio of normal collision force to maximum elastic normal force and is the ratio of normal overlap to maximum normal overlap of an elastic collision
6. Figure 2.6 Different elastic oblique collision regimes in the LSD model. The collision angle is (a) 5° (first regime), (b) 25° (second regime), and (c) 65° (third regime)
7. Figure 2.7 The normal pressure distribution in the contact area of an elastic sphere as a function of contact radius
8. Figure 2.8 Dimensionless normal force-displacement curves for (a) KKn model and (b) TTIn model. is the ratio of normal collision force to maximum elastic normal force (Hertz’s theory) and is the ratio of normal overlap to maximum normal overlap of an elastic collision
9. Figure 2.9 Predictions of different nonlinear viscoelastic models (a) collision duration and (b) normal coefficient of restitution, versus normal impact velocity. The FEM data are collected from [65]
10. Figure 2.10 The procedure for calculating tangential forces based on LTH and ZZYt models
11. Figure 2.11 Schematic of an oblique impact of a sphere with a flat wall. The rotation speed is zero before the collision. The impact angle may range from 0 to 90° and different collision regimes may occur. At low impact angles (near normal) sticking regime occurs and at high impact angles (near horizontal) sliding regime occurs
12. Figure 2.12 Tangential coefficient of restitution as a function of impact angle for elastic particle–wall collisions. The dashed curve shows (Equation 2.88) corresponding to the sliding regime. Experimental data are collected from Kharaz et al. [40]
13. Figure 2.13 (a) Dimensionless contact parameter as a function of dimensionless rebound parameter at contact point and (b) rebound angle as a function of impact angle. Experimental data are collected from Kharaz et al. [40]
14. Figure 2.14 Typical force-displacement curves for normal elastic perfectly plastic collisions at different maximum normal force. Results are based on finite-element analysis. As the normal applied force becomes larger, more energy is dissipated in the plastic deformation of sphere
15. Figure 2.15 Schematic of a force-displacement law with different spring stiffnesses in loading and unloading phases corresponding to the model proposed by Walton and Braun [74]
16. Figure 2.16 The normal pressure distribution in the contact area of an elastic perfectly plastic sphere based on the model of Thornton [73]
17. Figure 2.17 Representation of real and granular walls in the discrete-element methods
Chapter 03
1. Figure 3.1 Algorithm of the DEM program for the flow of non-cohesive spherical particles without heat or mass transfer and fluid inertial effects
2. Figure 3.2 Different steps in a contact detection algorithm for finding contacts between a target particle (cross-hatched body) and other particles in the system. Left-hand section shows all particles with bounding spheres. Middle section shows the process of broad search that identifies all particles near the target particle. Right-hand section shows the fine search phase. First, the particles whose bonding spheres touch each other are determined. Then, geometric resolution is performed to find the exact contact point
3. Figure 3.3 Bounding spheres in 3D Cartesian coordinates enclosed by simulation domain
4. Figure 3.4 Discretized simulation domain and bounding sphere in 2D space
5. Figure 3.5 The linked list constructed based on the NBS method for the particulate system shown in Figure 3.4
6. Figure 3.6 The NBS masks in 2D space (a) and 3D space (b)
7. Figure 3.7 Constructed Y-lists of the particulate system of Figure 3.4
8. Figure 3.8 X-lists of the second row of the particulate system of Figure 3.4
9. Figure 3.9 A hierarchical contact search with variation of sphere size. Three levels with different cell sizes are considered and spheres are assigned to each level based on their size
10. Figure 3.10 Method of performing cross-search between a target sphere of target level (smaller grid) and spheres of cross level (larger grid). The target sphere is mapped onto the cross-level grid and target cell in the cross level is determined. All larger spheres in this cell and its surrounding cells (nine shaded cells in total) are checked for possible contacts
11. Figure 3.11 Variation of (a) computation time of contact search stage and (b) total RAM requirement for simulation versus number of particles for two different cell-based algorithms. Total number of iterations was 30,000
12. Figure 3.12 Variation of (a) computation time of contact search and (b) average potential contacts for 30,000 iterations of simulations containing 5000 particles versus the size ratio. Numbers in the parentheses show the number of grid levels used in each simulation
13. Figure 3.13 Schematics of the DESS algorithm in 2D space
14. Figure 3.14 Partitioning of the simulation domain and positioning of particles into a binary tree
15. Figure 3.15 Binary tree and static linked list of the particulate system shown in Figure 3.14
16. Figure 3.16 Quadtree of the particulate system shown in Figure 3.14
17. Figure 3.17 The average relative deviation of normal coefficient of restitution for oblique impact between exact solution and results of various numerical integrators (a) single-step, (b) multi-step, and (c) predictor-corrector methods. Integration was started at the incipient of collision.
18. Figure 3.18 Effect of using a fixed time step in DEM simulations on detection of correct moments of collision and rebound
19. Figure 3.19 Execution time of integration step for various methods in a DEM simulation with 8000 spherical particles and 30,000 iterations
20. Figure 3.20 Comparison of memory requirement, computation time of integration step, and required time step resolution for different integration methods. All parameters are normalized with respect to the corresponding maximum value
21. Figure 3.21 Various wall geometries that can be created directly in the program (a,b) or can be imported from external files with STL format (c,d)
22. Figure 3.22 The initial hexahedron around the wall element and the enlarged hexahedron for finding the particle list of the wall element
23. Figure 3.23 The parametric representation of a triangle with barycentric coordinates that divides the plane into seven regions
24. Figure 3.24 The process of contact detection between a spherical particle and triangular and quadrilateral wall elements
25. Figure 3.25 Testing a sphere against one edge of the wall element
26. Figure 3.26 Message passing parallelization of a typical DEM code based on the space decomposition approach with overlapping regions. Each processor has its own set of particles and simulation domain. Each processor performs typical steps of a serial code independently to find the trajectory and velocities of its dedicated particles. Dashed lines show the points that processors exchange data of particles in the overlapping region. The output module is not shown here. Writing to the file is logically serial and data from all processors are sent to a target processor and then the target processor writes data into a file
27. Figure 3.27 Typical orthogonal recursive bisection domain decomposition for six processors (left). The computational load of processors is diverse that leads to idle time of some processors. The boundaries are shifted to redistribute particles among processors (right). The computational load of processors is balanced now.
28. Figure 3.28 The execution paths of serial and parallel regions of the code. Execution proceeds with thread 0 in serial region. Once this thread reaches the parallel region, it creates a team of N_t threads that are executed concurrently and thread 0 becomes the master thread in this team. At the end of parallel region, all private variables are deleted and all threads except the master thread are destroyed. Thread 0 continues the execution of the next serial region. At the end of the parallel region, master thread waits for other threads to finish their execution (implicit synchronization)
Chapter 04
1. Figure 4.1 Rolling of a spherical and a non-spherical particle over a slope. Both particles are initially at rest and they are allowed to roll down the surface due to gravity
2. Figure 4.2 Three different methods to representing the shape of a bi-convex tablet (a) intersecting surfaces: the surface of tablet is formed by intersecting surfaces of three spheres, (b) multi-sphere: the surface of tablet is approximated by gluing small spheres, and (c) polyhedral: the surface of tablet is covered by triangles
3. Figure 4.3 Three subsequent rotations (zxz convention) based on Euler angles. (a) rotation by φ around the z-axis, (b) rotation by θ around the x′-axis, and (c) rotation by ψ around teh z″-axis
4. Figure 4.4 Steps to integrate/solve equations of motion of a non-spherical rigid particle in 3D space. This flow chart corresponds to steps 5–7 in Figure 3.1
5. Figure 4.5 A superellipse can change gradually from a star-shape to a circle and to a square in the limit by changing the value of m from near zero to infinity in Equation 4.30 with
6. Figure 4.6 Some shapes that can be generated by superellipsoid equation by changing values of size parameters a, b, c, and exponents ε₁ and ε₂
7. Figure 4.7 Schematic illustration of colliding superellipsoid i, j, and the forces acting on them in the space-fixed frame
8. Figure 4.8 The procedure of calculating the curvatures of two ellipsoidal particles and the inclined angle at their contact point
9. Figure 4.9 Contact detection of superellipsoids according to the geometrical potential concept
10. Figure 4.10 Contact detection of superellipsoids according to the common normal concept
11. Figure 4.11 Schematic of dilated surface algorithm to find the possible contact point between two ellipsoidal particles
12. Figure 4.12 Some regular and irregular shapes that can be generated by assembling spheres. (a) Ellipsoidal particles with 5 and 11 spheres (b) cylindrical particle (c) angular particle with 121 sphere, (d) equant particle with 150 spheres, and (e) elongated particles with 247 spheres
13. Figure 4.13 Two non-spherical particles i and j are in contact via their constituent spheres ik and jl
14. Figure 4.14 The evolution of height of particle in free fall tests with single-sphere and multi-sphere particles. Spheres in the multi-sphere particle are identical to sphere used in the single-sphere free fall
15. Figure 4.15 The schematic of possible contact conditions between a multi-sphere particle and a flat wall. With more contact points between particle and wall, the equivalent spring would be stiffer
Chapter 05
1. Figure 5.1 Formation of packed bed under gravity. Particles are inserted into the simulation through the insertion plane (rectangle with light shading at top) at a specified rate
2. Figure 5.2 Packing of (a) monodispersed spherical particles with the size of 7 mm, (b) binary mixture of spherical particles with the diameters of 7 mm (dark gray) and 3.5 mm (light gray), and (c) cylindrical particles with the aspect ratio of 5. The average porosity in (a) is 0.41, in (b) is 0.38, and in (c) is 0.45
3. Figure 5.3 Pile formation of (a) 9 mm spherical particles, (b) biconvex particles, and (c) 9 mm spherical particles without rolling friction
4. Figure 5.4 Packing of 1200 flexible fibers which comprise of five sphero-cylinders. The length to diameter ratio is 30. Bending that from the joint points between segments and it was shown that the flexible fiber model has better capabilities to predict dynamics and packing condition of long rods.
5. Figure 5.5 Discharge flow patterns of particles in various hoppers. (a) Discharge of spherical particles in a cylindrical hopper, (b) spherical particle in a conical hopper with , (c) spherical particle in a conical hopper with , (d) spherical particles in a conical hopper with obstacle, and (e) biconvex particles in conical hopper with . All snapshots are clipped in the middle to make the inside of the bed visible
6. Figure 5.6 Snapshots of discharge of a binary mixture from a cylindrical hopper. Small particles (4.5 mm) are light gray and large particles (9 mm) are black. (a) shows 18% mass out (b) shows 50% mass out, and (c) 85% mass out
7. Figure 5.7 Segregation profile during the discharge of two binary mixtures of particles with 11 and 50 wt% of small particle in a cylindrical hopper. Diameters of small and large particles are 4.5 and 9 mm, respectively
8. Figure 5.8 Effect of aspect ratio of particles and orifice diameter on the normalized discharge rate (normalized with discharge rate of spherical particle) of 9 mm particles in a cylindrical hopper. Data were created using Equations 5.4, 5.6a, and 5.6b
9. Figure 5.9 Different types of mixtures
10. Figure 5.10 Upper and lower limits for expected variance of a sample as a function of number samples
11. Figure 5.11 Various flow regimes in a rotating drum with inner diameter of 0.45 m, filled with 9 mm spherical particles, (a) rolling regime with and , (b) cascading regime with and , (c) cataracting regime with and , and (d) centrifuging regime with and . Particles are colored based on their velocity magnitude (the graduated shaded bar shows the velocity magnitude) and small pictures show the instantaneous velocity vectors. Vectors are not scaled and all have the same length
12. Figure 5.12 Rotating drum at and different Froude numbers, (a) , (b) , and (c)
13. Figure 5.13 Time averaged velocity profile of particles at the surface of the active layer in a drum with inner diameter of 45 cm and fill level of 0.15. () Spherical, () oval, () biconvex, and (×) oblong particles.
14. Figure 5.14 Mixing mechanism of 3-mm monodispersed spherical particles in a rotating drum with the diameter of 0.2 m and the rotation speed of 10 rpm (rolling regime), (a) instantaneous non-scaled velocity vectors of particles and (b) the schematic of motion streamlines in active and passive layers. Particles are shown by gray dots in these snapshots and tracers by darker shaded spheres. Snapshots show the position of tracers at the reference time of (c) 0 s, (d) 0.2 s, (e) 0.8 s, (f) 1.6 s, (g) 3.2 s, and (h) 9 s
15. Figure 5.15 Radial segregation process for a 1:1 binary mixture of small (3 mm, light gray) and large (4.5 mm, black) particles in a rotating drum (10 rpm and 0.2 m diameter). Small particles accumulate in the middle of the drum while larger particles accumulate in the periphery of the bed
16. Figure 5.16 Inverted size segregation after five revolutions in the cataracting regime ( ) in a drum with the diameter of 0.2 m. Particles are of the same density with diameters 3 mm (gray) and 4.5 mm (black)
17. Figure 5.17 Variation of steady state mixing index in a 0.07 m diameter rotating drum filled with small (1 mm) and large (1.5 mm) particles with the volume ratio of 1:1 as a function of Froude number for various fill ratios.
18. Figure 5.18 Progress of diffusive and convective dominant mixing of identical particles in a V-blender
19. Figure 5.19 Instantaneous velocity vector of particles during one revolution of the V-blender. Vectors are scaled and shaded based on their velocity magnitude
20. Figure 5.20 Snapshots of mixing evolution in the Nauta mixer
21. Figure 5.21 Granular temperature distribution on a vertical plane crossing the screw axis in the Nauta mixer. The shaded bar shows the granular temperature in m²/s²
22. Figure 5.22 Position of marked groups during the operation of the Nauta mixer
23. Figure 5.23 Evolutions of Lacey mixing index during the operation of the Nauta mixer at (a) various primary rotation speeds and (b) various sweeping rotation speeds. Symbols are obtained from DEM simulations and lines are the fitted exponential decay model (Equation 5.28)
24. Figure 5.24 DEM simulation of a continuous mixer. Two separate streams of small (3 mm) and large (5 mm) particles are fed into the mixer ( ). Particles are shaded based on their velocity magnitudes in (a) and (b) and particles are shaded based on their sizes in (c): light gray for small particles and black for large particles
25. Figure 5.25 The residence time distribution of large and small particles in a continuous mixer. Markers show the pulse injection obtained from post processing DEM results and curves show the fitted dispersion model on the simulation results
26. Figure 5.26 Schematic of (a) a horizontal screw conveyor and (b) a screw feeder with its wedge hopper
27. Figure 5.27 Snapshots of the solids flow in a screw conveyor at various rotational speed with constant solid flow rate (0.7 kg/s). Left-hand images (a–c) show the cross-sectional views and the right-hand side shows the side views of the conveyor
28. Figure 5.28 A typical pan coater with spray zone
29. Figure 5.29 Distribution of various parameters in a pan coater with a 0.45 m drum at 9 rpm rotation speed (a) circulation time, (b) spray zone time, (c) cascading velocity, and (d) axial velocity
30. Figure 5.30 The flowchart of the Monte-Carlo method for calculating inter-particle variability [170]
Chapter 06
1. Figure 6.1 Exchange of momentum, energy, and mass between phases
2. Figure 6.2 Various coupling strategies
3. Figure 6.3 Various flow conditions based on the particle–particle interaction
4. Figure 6.4 Velocity fluctuations and different resolved turbulence scales in a steady turbulent flow. While RANS resolves integral scales, LES resolves only the largest scales, and DNS resolves all scales
5. Figure 6.5 An overview of the different turbulent models.
6. Figure 6.6 Different representations of the particle treatment: (a) unresolved surface method ( ) and (b) resolved surface method ( ). Arrows show the local fluid velocity vectors
7. Figure 6.7 Estimation of fluid volume fraction by (a) exact method, (b) PCM, and (c) PCM with the offset method.
8. Figure 6.8 The sub-element method for calculating the fluid volume fraction
9. Figure 6.9 Framework of explicit coupling in the CFD-DEM model
10. Figure 6.10 Drag coefficient for an incompressible flow over a smooth sphere as a function of Reynolds number obtained from experimental data [83], Stokes’ theory [23], Cheng’s correlation [84], Di Felice’s correlation [85], and Schiller–Naumann’s correlation [86]
11. Figure 6.11 Comparison of normalized drag force calculated from LB simulations and correlations versus particle diameter for bidispersed system at and (a) , (b) , (c) , and (d) . The size ratio of the smallest to largest particle was varied between 1 : 5 and 1 : 10. Symbols represent the results of LB simulations [8], dashed lines represent the ad hoc procedure, and solid lines represent the correlation of Beetstra et al. [93, 95].
12. Figure 6.12 Drag coefficient of particles with different shapes as a function of Reynolds number of particle. (----) Stokes; (–) sphere; (◊) disk and plate; (×) isometric bodies; (|) minerals; and (o) spheroids and streamline bodies.
13. Figure 6.13 Saffman lift force on a particle in a non-uniform flow field
14. Figure 6.14 Magnus lift force on a particle rotating in a uniform flow field
15. Figure 6.15 Various mechanisms of heat exchange between/in phases
16. Figure 6.16 The fluid computational cell and corresponding particles for calculating the fluid–particle convective heat transfer
17. Figure 6.17 Different heat exchange mechanisms between particles and surrounding objects
18. Figure 6.18 Relative position of two spherical particles: (a) non-colliding and (b) colliding with overlap.
19. Figure 6.19 Comparison between various correlations for convective heat transfer coefficient. Pr = 0.7, ε_f = 0.7 obtained from correlations of Ranz and Marshall [128], Li and Mason [129], Gunn [130], Sun et al. [131], and Tavassoli et al. [132]
20. Figure 6.20 Heat exchange/generation mechanisms for the fluid phase
21. Figure 6.21 Coupling procedure for the thermal CFD-DEM model
22. Figure 6.22 Mass exchange mechanisms and reaction in fluid phase. Possible mass transfer between fluid and wall is not considered here
23. Figure 6.23 Comparison between various correlations for mass transfer coefficient. Sc = 0.7, ε_f = 0.7 obtained from correlations of Froessling [134], Kunii and Levenspiel [135], Gunn [130], and La Nauze et al. [136]
24. Figure 6.24 Coupling procedure for the CFD-DEM model combined by heat and mass transfer and reactions
Chapter 07
1. Figure 7.1 Local bed gas volume fraction distribution at different operating pressures.
2. Figure 7.2 Typical trajectory of a particle in physical experiments obtained by radioactive particle tracking technique and that obtained from the CFD-DEM simulation.
3. Figure 7.3 A typical conical spouted bed
4. Figure 7.4 Gas streamlines in conical spouted bed
5. Figure 7.5 Representation of corn-shaped particles with (a) four spheres and (b) seven spheres.
6. Figure 7.6 Percentage of time averaged forces acting on particles in the spouted bed (H/D = 1.6, d_p = 2–3 mm, ).
7. Figure 7.7 Time-smoothed streamlines of particles and mixing mechanism in different regions of a spouted bed.
8. Figure 7.8 Solid flow patterns in a spouted bed at various spouting gas velocities: (a) , (b) , (c) , (d) , (e) , and (f) .
9. Figure 7.9 Time-smoothed vector field of particle velocity of a fully developed spout ( at t = 3 seconds).
10. Figure 7.10 Flow pattern in double slot, rectangular spouted bed with a vertical partition plate at a superficial gas velocity 1 m/s, (a) t = 0.1 s; (b) t = 0.2 s; (c) t = 0.3 s; (d) t = 0.4 s; (e) t = 0.5 s; and (f) t = 0.6 s.
11. Figure 7.11 Flow patterns in a pseudo-2D spouted bed at the superficial gas velocity of 1.58 m/s (minimum spouting velocity is 0.91 m/s), (a) t = 2.0 s; (b) t = 2.05 s; (c) t = 2.1 s; and (d) t = 2.15 s. Top row shows the gas velocity magnitude contour and particles and bottom row shows the local-averaged velocity vector of particles
12. Figure 7.12 Comparison between experimental particle velocity along the bed vertical axis [49] and the simulation performed by the code accompanying this book. The superficial velocity is 1.58 m/s and the minimum spouting velocity is 0.91 m/s
13. Figure 7.13 Phase diagram for horizontal conveying at constant solids feed rate
14. Figure 7.14 The horizontal slug flow patterns predicted by CFD-DEM at simulation times of (a) 14.236 s, (b) 14.498 s, and (c) 14.760 s.
15. Figure 7.15 Predicted particle flow patterns at different gas velocities (a) 10 m/s, (b) 13 m/s, (c) 18.5 m/s, (d) 30.5 m/s, and (e) 30.5 m/s.
Chapter 08
1. Figure 8.1 Physical and non-physical contacts between two particles. A physical contact happens when the surfaces of two particles touch each other. It is used to calculate collisional interactions between particles. A non-physical contact happens when long-range interactions between particles exist. R_LR is the maximum distance at which the interparticle force is still significant
2. Figure 8.2 The Verlet list of the target particle i. This list includes all particles around the target particle whose center to center distance (or surface to surface distance, depending on the type of interparticle force) is less than R_cut-off
3. Figure 8.3 Calculation sequence of the main steps of a DEM code including interparticle forces. Note that the calculation sequence for solving fluid phase equations and interphase coupling remain intact, hence not shown here
4. Figure 8.4 Relative distance between two particles’ surfaces and particle’s surface and wall for calculating van der Waals force
5. Figure 8.5 Dimensionless van der Waals force against the distance between two 60 µm particles in air and water
6. Figure 8.6 Schematic of a liquid bridge between two particles
7. Figure 8.7 Dimensionless liquid bridge force against the distance between two 1 mm glass beads for various liquids: water (ρ_f = 1000 kg/m³, μ_f = 0.001 Pa · s, σ = 0.073 N/m), glycerin (ρ_f = 1260 kg/m³, μ_f = 0.95 Pa · s, σ = 64 N/m), and n-hexane (ρ_f = 655 kg/m³, μ_f = 0.000297 Pa · s, σ = 18 N/m)
8. Figure 8.8 Two charged particles that exert electric force on each other. Geometric parameters required for calculation of electric force are shown in this figure
9. Figure 8.9 Dimensionless electrostatic force against the distance between two 1 mm particles at various particle charges
10. Figure 8.10 (a) Snapshot of the tribocharger. Particles are shaded based on their surface charge and their sizes are doubled in the figure for visibility, (b) distribution of particle charge in the exit, and (c) distribution of number of particle–wall contacts
11. Figure 8.11 A particle placed in an electric field. Geometric parameters required for calculation of electric field induced interparticle force are shown in this figure
12. Figure 8.12 Dimensionless electrostatic force exerted on a 1 mm glass bead placed in an electric field. Horizontal axis shows the distance of particle from a dielectric wall
13. Figure 8.13 Dimensionless repulsive and attractive magnetic forces as a function of the distance between two 1 mm ferromagnetic particles in the presence of 0.01 T uniform magnetic field
14. Figure 8.14 Repulsive and attractive magnetic force between two ideal dipoles under the influence of a uniform external magnetic field

COUPLED CFD-DEM MODELING

FORMULATION, IMPLEMENTATION AND APPLICATION TO MULTIPHASE FLOWS

About the Authors

Preface