Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study

PTEC-14552; No of Pages 14 Powder Technology xxx (2019) xxx

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Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study Xuejiao Liu a,b, Jieqing Gan c, Wenqi Zhong a,b,⁎, Aibing Yu b,c a b c

Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, PR China Center for Simulation and Modelling of Particulate Systems, Southeast University-Monash University Joint Research Institute, Suzhou, PR China ARC Research Hub for Computational Particle Technology, Department of Chemical Engineering, Monash University, Clayton, Vic 3800, Australia

a r t i c l e

i n f o

Article history: Received 31 May 2019 Received in revised form 22 July 2019 Accepted 27 July 2019 Available online xxxx Keywords: Gas-solid flow Cylindroid particle Spouted bed CFD-DEM

a b s t r a c t The Computational Fluid Dynamics-Discrete Element method (CFD-DEM) approach for cylindroid particles was developed to study the effects of particle shape on spouting behaviors in a flat-bottomed spouted bed. The gas motion was modelled with k-ε turbulent model, and the particles was represented with the realistic cylindroid shapes. The various particle contact scenarios and contact forces between cylinders, as well as the drag force model for non-spherical particles were comprehensively involved to describe the particle motions more accurately. With the aspect ratio of particle varying from L/d = 0.25 to 3.0, spouting behaviors including flow pattern, particle velocity, orientation and contact details were studied. Results found that cylindroid particles show the clear different orientations in the three regions of spouted bed. In spout, cylindroid particles tend to put their longer dimension parallel to the (vertical) flow direction, while in annulus the orientation tendency is contrary and particles tend to put their larger dimension perpendicular to their falling direction. The particle with L/d = 1.0 obtains the maximum projected area in spout and thus the largest drag force and the highest particle velocities. When L/d deviates from 1.0, with particle shape becoming flatter or longer, the particle projected area in spout accordingly decreases, resulting in the decreasing particle velocity and particle circulation rate. On the other hand, when aspect ratio deviates from 1.0, the obviously increasing particle contact number in annulus reflects their increasing interlocking effects and worse flowability. © 2019 Elsevier B.V. All rights reserved.

1. Introduction As the effective fluidization device used in a wide range of power-handling processes, e.g. drying, blending, coating, combustion, gasification, etc., spouted bed or spout-fluid bed has been proved of extraordinary advantages to treat the particles with the larger sizes and extremely non-spherical shapes by providing strong particle circulation, effective fluid-particle contact and high rates of mass and heat transfer [1–5]. One of the typical potential applications is to produce (e.g., dry, torrefy) [6,7] and use (e.g. combust, gasify or pyrolyze) [8,9] the biomass pellet fuel. This is one of the most important biomass utilization modes in nowadays benefiting from the regular geometries, standard sizes (mostly cylindrical solid particles) and especially the significant energy-densification of biomass pellets which provide the remarkable convenience in the storage, transportation of biomass and the automatic feeding for large-scale unit operations [10,11]. However, when it comes to such specific non-spherical particles like cylindroid biomass pellets, ⁎ Corresponding author at: Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, PR China. E-mail address: [email protected] (W. Zhong).

spouted bed technology is now still hindered by the severe lack of understanding on the complex hydrodynamic behaviors because of the special particle properties. Compared to spherical particles, the motion modality and coexistence forms of the non-spherical particles are more various with the extreme diversities in the geometrical contact scenario with their neighboring particles or walls, as well as the interactions with the surrounding fluid [12,13]. This leads to the more complicated spouting dynamics of non-spherical particles than that of spherical particles. For example, angular particles (e.g., elongated and flatted biomass particles, irregular solid waste particles or others) are likely to produce dilute packing fractions, or to interlock each other to form solid-like assemblies showing the stronger resistance to the shearing flows in reactors than smooth spheres, which will significantly affect their performances of spouting, heat transfer and reaction in the spouted beds [14]. On the other hand, the various orientations of non-spherical particles also remarkably increase the complexity of the gas-solid flow dynamics [15,16]. Up to now studies on the spouting of non-spherical particles in spouted beds is very limited, mostly focusing on the mesoscale and macroscale gas-solid flow and reaction characteristics including spouting patterns, pressure drops, minimum spouting velocity, mixing behaviors, reaction efficiency and product features and so on

https://doi.org/10.1016/j.powtec.2019.07.099 0032-5910/© 2019 Elsevier B.V. All rights reserved.

Please cite this article as: X. Liu, J. Gan, W. Zhong, et al., Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study, Powder Technol., https://doi.org/10.1016/j.powtec.2019.07.099

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[2–5,17,18]. The in-depth understanding in the micro scale is especially insufficient. Many fundamental issues, for example, how the particle shape and size affect the spouting behaviors, that are closely related to the design, operating and optimization of spouted bed reactors, still have no clear answers. Spouted bed is a cyclic gas-solid system, in which particles usually rapidly rise in the central spout under the carry of the spouting gas, and then rain back onto the annulus region between the spout and the column wall where they slowly travel downward and inward as loosely packed bed [1,3]. In such a unique system combining the dilute-phase gas-solid concurrence in the central spout and the densephase countercurrent in annulus region, the motion states of nonspherical particles and their interactions with fluids become significantly more complex and diverse. To obtain the thorough insight into the motion details and mechanisms of non-spherical particles is very crucial. With the rapid developments of computer technology, the discrete element method (DEM) coupling with Computational fluid dynamics (CFD) is being vigorously developed as a powerful tool to study the complex dynamics of gas-solid multiphase flows in such as pneumatic transmission and fluidization processes involving nonspherical particles, benefiting from its advantageous abilities to consider the shapes, properties and forces of individual particles and exhibit these in the macroscale dynamics. The important contributions of many researchers to CFD-DEM simulations of non-spherical particles have been fully reviewed by Lu et al. [12] and Zhong et al. [13] in the aspects of particle representations and contact detections, force calculations for particle-particle and particle-fluid, fluid-particle coupling schemes and important applications. Typically, Zhong et al. [19] and Oschmann et al. [20] simulated the fluidization of cylinders in fluidized beds and regarding the spouted beds, Ren et al. [3,21,22] have realized the CFD-DEM simulations on the spouting behaviors of the cornshaped particles, cylindroid particles and their mixtures with spherical bed materials. In these works, the non-spherical particles were constructed by the Multi-Sphere Method. This method can explicitly and flexibly construct particles with arbitrary shape, and converts the complicated contact detections and parameter calculations between the non-spherical particles into the simple problems between spheres, which remarkably increases the computational efficiency of nonspherical particle simulations, showing significant advantages to treat the large-scale industrial progresses involving the particles with large quantities or diverse shapes [12,13]. However, in the Multi-Sphere Method, the introduce of some artificial roughness when depicting the particle shapes and the simplification of contact scenario and force calculations between particles will inevitably affect the microscopic motions and coexisting forms of the non-spherical particles [19,22,23], and limit its applications in the fundamental studies dealing with the motion mechanisms of the non-spherical particles, especially when the particle orientations and particle contacts need to be fully consider to investigate the qualities of spouting process and the mass/heat transfer. On the other hand, Vollmari et al. [24] developed the coupled DEMCFD approach to study the dynamic behaviors of some non-spherical particles such as cylinders, cuboids in fluidized beds. In their studies, the fluid phase was usually assumed as the laminar flow and the complex shaped particles were modelled by the polyhedron method with the common plane algorithm being used as a basis to fast detect the contacts between non-spherical particles. Ma et al. [25,26] simulated the fluidizations of rod-like particles in a typical fluidized bed, as well as a fluidized bed of complex geometry using the CFD-DEM coupling approach, with the particles being described by the super-ellipsoid model. Mahajan et al. [27] numerically studied the fluidization behavior of spherocylindrical particles which were represented through analytical calculation, and proposed new voidage correction models for dense gas-solid flows with rod-like particles. In these works, the detailed contact scenarios of non-spherical particles have also usually not been fully taken into account. As in the DEM scheme, many detailed factors in particle properties such as the location of contact point, the

overlap geometry and volume (or area in 2D case) that are closely related to the particle shape, the motion states and the relative motion tendencies of the contacting particles, will influence the interactions of particles and then their motions, more accurate considerations on these factors worth further trying. In this study, the CFD-DEM simulations were developed to study the spouting behaviors of real cylindroid particles, which particles were chosen here due to their abundant applications in practice, as well as their typical non-spherical features with the comprehensive geometric elements such as curves, planes and curved surfaces and the achievable wide sphericity range. The cylindroid particles including rod-like particles and disc-like particles were accurately constructed by combining the two circular planes and one cylindrical curved surface, and the various different contact criteria including edge-edge, face-face, bandband, edge-face, edge-band, face-band and so on were comprehensively involved. With the more accurate and detailed particle shape representation and forces calculations, spouting features of cylindroid particles with varying shapes were studied and the gas and solid dynamic mechanisms, as well as the effects of particles shapes on the spouting behaviors would be figured out in particle scale. 2. Model descriptions 2.1. Turbulence motion of gas phase The k-ε model was adopted to simulate the turbulent gas flow in the non-spherical particulate systems, with the detailed continuity equation, momentum conservation equation and k-ε equations are as follows: 
 ∂
α f ρg þ ∇∙ α f ρg ug ¼ 0 ∂t

ð1Þ


 ∂
α f ρg ug þ ∇∙ α f ρg ug ug ¼ −∇p þ ∇∙ðα f τÞ þ α f ρg g−Sp ∂t

ð2Þ

with.  
−1 2 − ∇ug I ; τ ¼ ðμ þ μ t Þ ∇ug þ ∇ug 3

2

μ t ¼ Cμ ρg k =ε

where ρg is the gas density, kg/m3; ug is gas velocities, m/s; α is the volume fraction of gas; p is the gas pressure, Pa; τ is the gas viscous stress tensor, Pa; μ and μt are the gas kinetic viscosity and turbulent viscosity, respectively, Pa∙s; Cμ is the empirical coefficient and Cμ = 0.09 in the current simulations [28]; Sp is the volumetric fluid-particle interaction in a computational fluid cell volume ΔV and Sp=ð∑particles F pf;i Þ=ΔV , with the Fpf,i being the interaction forces between fluid and a particle. k and ε are the turbulent energy and turbulent dissipation rate, respectively, with their governing transport equations being:     
 ∂
μ ρg α f k þ ∇ α f ρg kug ¼ ∇ α f μ þ t ∇k þ α f Gk þ α f ρg εk þ Skd εk ∂t ð3Þ      
 ∂
μ ε
ρg α f ε þ ∇ α f ρg εug ¼ ∇ α f μ þ t ∇ε þ α f C1 Gk −C2 ρg ε þ Sεd εε k ∂t

ð4Þ here Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients with Gk ¼

μt ρg

( " 2  2 #  2 ) ∂u ∂v ∂u ∂v 2 þ þ þ ∂x ∂y ∂y ∂x

ð5Þ

εk = 1.0 and εε = 1.33 are the turbulent Prandtl constant [28], and Skd

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and Sεd give the influence of the particles to the gas motion, calculated by [28,29]:  2 Skd ¼ βu−vp  þ βðΔvΔv−ΔuΔvÞ Sεd ¼ C3

ð6Þ

εε k S k d

ð7Þ

where Δu and Δv are the instantaneous velocity pulsations of gas phase and solid phase, respectively. The first term on the right of Eq. (6) is the solid particle resistance production term, and the second is the redistribution term to describe the transformation relationship of kinetic energies between the solid particles and gas phase with the detailed calculation as follows:   τl τl βðΔvΔv−ΔuΔvÞ ¼ −2βk 1− τl þ τd τl þ τd τd ¼

ð8Þ

4dp ρp   3CD ρg ug −vp 

τl ¼ 0:35

ð9Þ

k ε

curved surface (cylinder band) and their intersecting lines being really described as shown in Fig. 1. The location of each particle in the space coordinate system is defined by the position of particle centroid, O′, and the particle shape is characterized by the length of the cylindrical surface, L, and the diameter of the circular plane, d. The particle orientation in the space is defined by the vector O'A, as seen in Fig. 1. Researchers have proposed several methods to detect the contacts between cylindroid particles [31–35]. Typically, Kodam et al. [33,34] and Guo et al. [35] comprehensively considered the various contact scenarios of the real-shaped cylinders and proposed the detailed detection criteria for each possible contact scenario as well as the corresponding determinations of the contact information such as the location of contact point, contact direction and the quantitative particle deformations. Mainly based on the works of Kodam et al. [33,34] and Guo et al. [35], this work further developed the more comprehensive contact scenarios for the real cylindroid particles with some special contact scenario for disc-like particles being supplemented as shown in Fig. 2. The detailed contact criteria and the corresponding determinations of contact parameters could be found in reference [33–35]. Here the maximum overlap of the particles is restricted to 1% of the particle diameter to avoid unrealistic behaviors [24,27].

ð10Þ

where τl and τd are the Lagrange time scale of gas phase and the solid particle response time, respectively. In these equations, the related empirical constants are set as: C1 = 0.09, C2 = 1.44, C3 = 1.92 [28,30].

(2) Motion equations and forces of cylindroid particles.

The two motion types of a particle, viz translation and rotation, can be governed by the Newton's second law of motion as below: mi

2.2. Particle phase (1) Representation and contact detection of cylindroid particles

The accurate representation of particle properties like shape, density distribution, etc. is fundamentally important to model the behaviors of non-spherical particles as in the DEM the particle contact forces, torques and thus the particle trajectories are obtained by minutely evaluating the detailed information of the individual particle-particle (wall) contact. In the current study, two kinds of typical cylindroid particles, namely the disc-like particles and rod-like particles, were respectively constructed by combining the two circular planes and one cylindrical curved surface, with the three main geometric factors, viz. the planes,

3

Ii

dvi ki ¼ mi g þ ∑ j¼1 F c;ij þ F pf;i dt

 dωi ki
¼ ∑ j¼1 Mt;ij þ Mr;ij þ Mn;ij dt

ð11Þ ð12Þ

where mi, Ii, vi and ωi are the mass, moment of inertia, translational velocity and angular velocity of the particle i, respectively. The forces acting on a particle considered in this study are the gravitational force mig, the contact force Fc,ij from its ki neighboring particles, and the particle-fluid interaction force Fpf,i which mainly consists of the drag force (Fd,i) and the pressure gradient force (F▽p,i) and is assumed to act at the center of mass of the particle [15,16]. The torques acting on the particle i mainly come from the contact interactions with the neighboring particles. Specifically, Mt,ij, is generated by the tangential force and causes particle i to rotate. Mr,ij is the rolling friction torque.

Fig. 1. Representation of the realistic cylindroid particles in DEM.

Please cite this article as: X. Liu, J. Gan, W. Zhong, et al., Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study, Powder Technol., https://doi.org/10.1016/j.powtec.2019.07.099

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Fig. 2. Contact scenario between cylindroid particles used in the current study [33–35].

The additional torque Mn,ij for non-spherical particles must also be involved when the normal contact force does not pass through the particle center. The effect of hydrodynamic torque is neglected here considering the low gas density and the approximately parallel flow

of fluid in spout, as well as the very short particle mean free path between collisions especially when particle volume fraction is large [15,27]. The detailed components of forces and torques acting on particle i are shown in Table 1.

Table 1 Forces and torques acting on cylindroid particle i [15,16]. Force and Torques

Equations

Contact force [22,33]

Fc,ij = Fcn,ij + Fct,ij Fcn,ij = (kn,ijδn,ij-γnvij·n)·n Fct,ij = −min [(kt,ijδt,ij-γtvij·t), μs|·Fcn,ij|]·t where k and γ are the spring coefficient and viscous damping coefficient for the contact model, respectively, and the subscripts of n or t indicate the variables are in the normal or tangential directions. They are assumed to be as constants during the collisions of particles. δij is the displacement of the two contacting particles and vij is the relative velocity; μs is the friction coefficient. Mt,ij = Rc,ijFct,ij Mn,ij = Rc,ijFcn,ij ^ nij Mr,ij = μr,ij·|Fcn,ij|ω

Torque by tangential force Torque by normal force, Rolling friction forque

^ nij ¼ ωnij =jωnij j ω Drag force between fluid and particle

Syamlal-O'Brien drag model [34]: 3 ρ f α f ð1−α f Þ Re j u−vp j C D ðu−vp Þ F d;i ¼ 4 vr v2r ∙dp ρ f α f ju−vp jdp Re ¼ μf  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi vr ¼ 0:5 A−0:06 Re þ ð0:06 ReÞ2 þ 0:12 Reð2B−AÞ þ A2

0:8α f 1:28 α f ≤0:85 A ¼ α f 4:14 , B ¼ α f N0:85 α f 2:65 CD calculated by Holzer-Sommerfeld correlation [35]: 0:2 1 8 1 16 1 3 1 qffiffiffiffiffiffi þ pffiffiffiffi þ pffiffiffiffiffiffiffiffi 3=4 þ 0:42100:4ð− logϕÞ CD ¼ Re ϕ Re ϕ ϕ⊥ Re ϕ ‖

Pressure gradient force

With Fd,i being the fluid-particle drag force acting on the particle, u and vp being the fluid velocity and the particle velocity in the current fluid cell, αf the volume fraction of fluid, ϕ‖ the lengthwise sphericity, and ϕ⊥is the crosswide sphericity. F▽p,i = ▽p·ΔV

Please cite this article as: X. Liu, J. Gan, W. Zhong, et al., Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study, Powder Technol., https://doi.org/10.1016/j.powtec.2019.07.099

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Fig. 3. flow sheet for the numerical procedure of the CFD-DEM simulations on non-spherical particles.

As during the calculating process, the moment of inertia of the nonspherical particles usually changes at each time step, the additional body-fixed coordinate system, of which the axes are chosen as the principle axes of inertia of particle, is introduced to conveniently describe the rotation of the non-spherical particle and determine its orientation. In the body-fixed frame, the rotation motion of non-spherical particles is described as [24]: I0i


 dWi þ Wi  I0i Wi ¼ Λi −1 Mi dt

equations of particle motion on GPU. Specifically, for gas phase, the finite volume method is implemented to solve the conservative and constitutive equations with the first-order upwind discretization being used to convert the partial differential equations to algebraic forms. The SIMPLE algorithm is adopted for the pressure-velocity coupling

ð13Þ

where, Wi is the angular velocity in the body-fixed frame, and Mi is external moment in the inertia frame. Ii is the inertia tensor along the principle axis and Λ−1 is the transformation matrix to convert a vector from i the inertia frame into the body-fixed frame and it is determined by the three Euler angles (φ, θ, ψ) of the particle [36,37]. At each time step, the inertia tensor Ii in the space-fixed coordinate system will be converted to Ii' in the body-fixed coordinate system by the transformation matrix Λ−1 and then the angular velocity Wi of particles in body-fixed frame i can be calculated by Eq. (13). As angular velocity is closely related to the changed of Euler angles, three new Euler angles can be calculated and then the spatial orientation of particles can be determined on the basis of the quaternion method [38]. More details about this approach can be found in references [13, 36]. 2.3. Solution techniques The flowchart of the CFD-DEM simulations on non-spherical particles in this study is shown in Fig. 3. The gas flow field is firstly obtained by CFD on CPU and particle trajectories are then obtained by solving the

Fig. 4. The sampling method to calculate the solid volume fraction in CFD-DEM scheme.

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X. Liu et al. / Powder Technology xxx (2019) xxx Table 3 The main physical and numerical parameters for simulations.

Fig. 5. Geometry of the pseudo 2D rectangular spouted bed and grid for gas phase.

and correction. The convergence criterion of 10−4 is set for each scaled residual component to check the relative error between successive iterations and evaluate whether the calculation is convergent. The time step of gas phase was set as 5 × 10−5 with that of the particle phase being 10−6 s. For the particle phase, the grid element method is used to coarsely detect the particle pairs that possibly contact. In this method, the space occupied by the particle system was divided into regular grids, and only those particles located in the same grid unit and adjacent units would be further handled with the fine contact detection. Their detailed position information of edges, planes and faces will be checked to determine which contact criterion (in Fig. 2) they match and then to determine the corresponding contact parameters. The gas phase and particle phase were two-way coupled by the Averaged volume method (AVM) [13]. In the AVM, the cell size of gas phase is usually larger than the size of particle. The information of particles is firstly mapped into the corresponding CFD cell according to their locations and then the contact forces of particles and the interaction force of particle-fluid could be calculated according to the particle information and fluid information within the current CFD grid. In a CFD grid cell, the gas-solid interaction force exerting on the fluid is equal to the sum of that acting on all particles within this grid cell. The volume fractions of gas and solid required to solve the conservation equations and calculate the gas-solid interaction forces were obtained with the sampling statistical method [27]. A certain number of sample points were evenly set within the bounding box of a particle as shown in Fig. 4 and each point would be checked to determine which CFD

Properties

Values

Section dimensions of spouted bed, A Bed height, Hb Grid size (Δx × Δy × Δz) Static bed height, H0 Gas density, ρg Gas viscosity, μg Inlet-based gas velocity, us Number of particle, N Possion's ratio: Particle-particle, σp Particle-wall, σw Friction coefficient: Particle-particle, μp Particle-wall, μw Rolling friction, μr Spring constant: Particle-particle, kp Particle-wall, kw Damping coefficient: Particle-particle, γp Particle-wall, γw

0.2 m × 0.024 m 1.0 m See Fig. 5 0.21 m 1.205 kg/m3 1.8 × 10−5 Pa/s 6.0 m/s 15,000–17,000 0.4 0.4 0.4 0.4 0.002dp 104 N/m 104 N/m 102 kg/s 102 kg/s

cell it lied in. For a particle, its volume within the current CFD cell could be got by calculating the ratio between the number of sample points lying in the current CFD cell and the total number set in the particle. Then for the current CFD cell, the solid volume fraction could be figured out as:

α s ¼ 1−α ¼

X ns Vp N particles s

ð14Þ

ΔV

where Ns and nc are the total number of sample points set in one particle and that lying in the current CFD, respectively, and Vp, ΔV are the particle volume and CFD cell volume. 3. Simulation conditions The Geometry of the pseudo 2D rectangular spouted bed and its grids for the gas phase are shown in Fig. 5. The periodic boundary conditions are used to eliminate the effects of walls at the front and rear directions [27]. The dimensional sizes of the spouted bed are 200 mm × 24 mm × 1000 mm. At the bottom of the bed there is a gas inlet with the dimensions of 20 mm × 24 mm. The finer grid size, namely 6.67 mm × 10 mm, is adopted in the middle zone of the bed for spout region where the gas is of relatively higher velocity and intensive turbulence, while in the other zone, the grid size is 10 mm × 10 mm.

Table 2 Properties of cylindroid particles used in the current study. Particles

ρp (kg/m3)

V (mm3)

L(mm)

d (mm)

L/d

Sphericity

1

1200

42.39

1.5

6.0

0.25

0.693

2

1200

42.39

2.38

4.76

0.5

0.825

3

1200

42.39

3.78

3.78

1.0

0.874

4

1200

42.39

4.95

3.30

1.5

0.859

5

1200

42.39

6.0

3.0

2.0

0.832

6

1200

42.39

6.96

2.78

2.5

0.804

7

1200

42.39

7.86

2.62

3.0

0.779

Please cite this article as: X. Liu, J. Gan, W. Zhong, et al., Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study, Powder Technol., https://doi.org/10.1016/j.powtec.2019.07.099

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Fig. 6. Comparisons between experimental results and CFD-DEM simulations in the fluidized bed with cylindroid particles [19]: (a) the structures and dimensional sizes of the fluidized bed and cylindroid particles; (b) Comparisons of the simulated flow behaviors with experiments with U = 1.5 m/s and U = 2.0 m/s.

Fig. 7. Macroscale flow patterns of cylindroid particles with varying aspect ratios (us = 6 m/s, H0 = 0.21 m, ρp = 1200 kg/m3, Vp = 42.39 mm3).

Fig. 8. Fountain height of cylindroid particles with varying aspect ratios (us = 6 m/s, H0 = 0.21 m, ρp = 1200 kg/m3, Vp = 42.39 mm3).

Fig. 9. Spout shapes of cylindroid particles with varying aspect ratios (us = 6 m/s, H0 = 0.21 m, ρp = 1200 kg/m3, Vp = 42.39 mm3).

Please cite this article as: X. Liu, J. Gan, W. Zhong, et al., Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study, Powder Technol., https://doi.org/10.1016/j.powtec.2019.07.099

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Fig. 10. The time-averaged radial particle velocity distributions of three typical particles (L/d = 0.25, 1.0 and 2.0) at the varying bed heights (us = 6 m/s, H0 = 0.21 m, ρp = 1200 kg/m3, Vp = 42.39 mm3).

Seven kinds of cylindroid particles with the same volume and density but different shapes are involved in the current study. Their aspect ratios (L/d) vary from 0.25 to 3.0, and the detailed properties are shown in Table 2. In each simulation case, the packed bed with the expected static bed height is firstly obtained with about 15,000–17,000 particles of random orientations successively generating at the certain height within the bed and freely falling down under gravity force. When the velocities of all particles packed in the bed approach to zero, the spouting gas with the specified velocity (us) is then injected into the bed from the gas inlet at the bed bottom and the stable external spouting will finally establish. After this, a real calculation time of about 10 s is continued to carry out to obtain the time-averaged information for fluid and particles. Table 3 lists the main physical and numerical parameters used in simulations. To study the detailed particle behaviors in the spouted bed, a series of evenly distributed sample points were respectively set at some heights of the bed such as h = 0.06, 0.12, 0.18, 0.24 m. At a certain moment the particle information (velocity, orientation, coordinate number, etc.) at a simple point is obtained by averaging the information of all particles that are within the neighborhood of this sample point at the current moment. The time-averaged particle information at sampling points in a period time of stable spouting (about 10 s)

are finally adopted to characterize the particle behaviors in the spouted bed. 4. Results and discussion 4.1. Model validation Fig. 6 showed the typical comparisons of the flow patterns and pressure drop of a fluidized bed with cylindroid particles between experimental results [19] and the simulations. The structures and dimensional sizes of the fluidized bed and cylindroid particles were illustrated in Fig. 6(a) with the particle density and static bed height respectively being 850 kg/m3 and 0.08 m. The linear spring-damper model was adopted to calculated the contact force between particles and the friction coefficient between particle and particle (wall), Poisson ratio, spring constant and damping coefficient were set as 0.4, 0.4, 104 N/m, 100 kg/s, respectively according to the sensitivity analysis. Fig. 6(b) showed the simulation results and experimental results with the fluidizing gas velocity being U = 1.5 m/s and U = 2.0 m/s. The satisfactory agreements indicated that the above CFD-DEM models and numerical solutions were able to successfully predict the fluidization

Fig. 11. The radial time-averaged velocity distributions of particles with the varying L/d at the same bed height (us = 6 m/s, H0 = 0.21 m, ρp = 1200 kg/m3, Vp = 42.39 mm3): (a) h = 0.06 m; (b) h = 0.18 m.

Please cite this article as: X. Liu, J. Gan, W. Zhong, et al., Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study, Powder Technol., https://doi.org/10.1016/j.powtec.2019.07.099

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Fig. 12. The radial time-averaged velocity distributions of particles with the varying L/d (us = 6 m/s, H0 = 0.21 m, ρp = 1200 kg/m3, Vp = 42.39 mm3).

behaviors, as well as the dynamics of gas and cylindroid particles in the dense gas-solid two-phase turbulent flows. 4.2. Macroscale flow patterns The different spouting patterns of seven kinds of particles with different shapes were shown in Fig. 7 with the static bed height H0 = 0.21 m and the inlet-based spouting gas velocity us = 6.0 m/s. All these seven kinds of particles were able to form typical external spouting with the distinct spout, fountain and annular region in the bed. When the particle aspect ratio L/d is around 1.0, such as L/d = 0.5–1.5, the spouting was relatively more stable with the central stream being vertical in spout and fountain. When L/d gradually deviates from 1.0, with the particle shape becoming flatter or longer, the stability of the spouting gradually deteriorated, and the upward flow in the center region of bed obviously twisted with the fountain continuously wagging. With the increasing deviation of L/d from 1.0, the non-spherical features of particles became more obvious, and their increasingly strong interactions, for example, collision, friction and interlocking would damage the fluidity of particle assemblies causing the increasing instability of spouting in the bed. On the other hand, the particles with L/d = 1.0 reached the highest fountain height; as the L/d of particles gradually deviated from 1.0, the fountain height in the bed also decreased, as shown in Fig. 8. The effect of the aspect ratio of the particles on the fountain height was very remarkable when the L/d was around 1.0, and when L/d N 2.0, it significantly weakened.

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Under the bed surface, particles with the aspect ratio of L/d = 1.0 performed the widest spout region, as well as the maximum jet width, as seen in Fig. 7 and Fig. 9. This larger jet width namely the wider spout meant more particles were moving upward in the rapid spout, and the bed had the higher solid circulation rate. When the particle became longer or flatter with the aspect ratio gradually deviating from 1.0, the width of the spout region thereupon decreased. Above the bed surface, the width of central stream in fountain showed the similar trend with that in spout as a whole. A difference was that when the aspect ratio of the particle was quite large, such as L/d = 3.0, the timeaveraged width of the central stream in the fountain would increase to a certain extent. This was because when the particle aspect ratio was large, the fountain became unstable and constantly swayed around, which resulted in the larger average-width over a period of time. In addition, when the particle aspect ratio was relatively larger, for example, L/d = 2.5 or 3.0, the spout width near the bottom of the bed showed a remarkable increase, because the stronger interactions between the elongated particles caused more particles entrain into the spout near the nozzle (namely gas inlet). In general, for the particle with the smaller aspect ratio, the boundaries of central stream in the bed were relatively smoother, and when the aspect ratio increased, the boundaries became more zigzag. For particles with L/d = 1.0, the highest fountain height and the widest spout width meant more particles in the spout and fountain region, resulting in an obviously lower bed surface in the annulus.

4.3. Particle velocity The time-averaged radial particle velocity distributions of three typical cylindroid particles with L/d = 0.25, 1.0 and 2.0 at the bed heights of h = 0.06, 0.12, 0.18 and 0.24 m were shown in Fig. 10 under the conditions of H0 = 0.21 m and us = 6 m/s. These three kinds of particles with different shapes showed the similar velocity distribution characteristics when spouted in the rectangular spouted bed. Specifically, under the bed surface, the particles in the spout moved upward with the relatively higher velocities, while that in the annulus moved downward with the lower velocities. As a whole, with the increasing bed height, both the particle velocities in the spout and annulus increased. Only an exception appeared in the velocity distributions of the particles with L/d = 1.0 at the heights of h = 0.18 m and h = 0.24 m. In this case the bed surface was under h = 0.18 m, particles at the heights of h = 0.18 m and h = 0.24 m already located in the fountain, and thus the particle velocities upward in the central stream started to decelerate, while that downward in the lateral region were increasing.

Fig. 13. The time-averaged radial orientation distributions of three kinds of cylindroid particles with varying shapes (us = 6 m/s, H0 = 0.21 m, ρp = 1200 kg/m3, Vp = 42.39 mm3).

Please cite this article as: X. Liu, J. Gan, W. Zhong, et al., Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study, Powder Technol., https://doi.org/10.1016/j.powtec.2019.07.099

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Fig. 14. The time-averaged radial CN distributions of three kinds of cylindroid particles with varying shapes (us = 6 m/s, H0 = 0.21 m, ρp = 1200 kg/m3, Vp = 42.39 mm3).

Although the velocity distributions of particles with varying shapes shared the similar trend, the values of their velocities performed remarkable differences. The specific velocity values of different particles at the same bed heights, for example, h = 0.06 m and h = 0.18 m, were shown in Fig. 11. For the disk-like particles (L/d ≤ 1.0), with the increasing L/d, their velocities in the spout and annulus obviously increased at both the bottom of the bed (h = 0.06 m) and the upper part of the bed (h = 0.18 m), and meanwhile the width of the spout widened, as shown in the left parts of Fig. 11 (a) and (b). That meant the particles with the flatter shape performed the smaller velocities and formed the narrower spout in the spouted bed. However, the rod-like particles (L/d ≥ 1.0) showed the opposite variation trends in particle velocities. With the increasing L/d, the particle velocities in the spout and annulus decreased and the spout in the bed became narrower, as seen in the right parts of Fig. 11 (a) and (b). That was, for rod-like particles, if the particle shape became thinner and longer, they would perform the smaller velocities and formed the narrower spout when spouting in the bed. Fig. 12 showed the time-averaged axial velocity distributions of the seven kinds of particles spouting in the bed. Along the central axis of the spouted bed, the seven kinds of particles showed the similar variation trend: the particle velocities firstly increased from zero to the peak values, and then gradually reduced to zero. For the disc-like particles, when L/d decreased with the particle shape becoming flatter, the particle velocity ascended slowly along the central axis of the bed and

the velocity peak decreased; for the rod-like particles, the similar trend occurred when the L/d increased with the particle shape being thinner and longer. When L/d = 1.0, the particle velocity showed the fastest raise and the highest peak along the central axis of the bed. In general, the spouting of the particle with L/d = 1.0 had the largest particle velocities in the spout and the annulus, the widest spout width, and thus the largest particle circulation rate. When the particle aspect ratio gradually deviated from 1.0 with the particle shape becoming flatter or longer and further deviating from the sphere, their velocities in the bed reduced and correspondingly the spout width also became narrower resulting in the decreasing particle circulation rate in the spouted bed. 4.4. Orientations of cylindroid particles in the spouted bed Different from the usual isotropic nature of spherical particles, nonspherical particles showed distinct orientations in the particulate systems, which not only determined the forces and motions of particles, but also significantly affected the mass and heat transfer between the particle and particle, or particle and fluid [15,16,39]. For the cylindroid particles such as the disc-like particles or rod-like particles, the effects of orientations were particularly pronounced. As the cylindroid particles were centrally symmetric, in this study the angle between the principal axis of a particle (namely O'A) and the vertical direction was defined as the direction angle of this particle, α.

Fig. 15. The time-averaged CN distributions of the particles with varying shapes in the spout region (us = 6 m/s, H0 = 0.21 m, ρp = 1200 kg/m3, Vp = 42.39 mm3): (a) disc-like particles; (b) rod-like particles (“Pct” in Y-axial represents “percentage”. This will be consistent across following figures).

Please cite this article as: X. Liu, J. Gan, W. Zhong, et al., Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study, Powder Technol., https://doi.org/10.1016/j.powtec.2019.07.099

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Fig. 16. The time-averaged CN distributions of the particles with varying shapes in the annulus region (us = 6 m/s, H0 = 0.21 m, ρp = 1200 kg/m3, Vp = 42.39 mm3): (a) disc-like particles; (b) rod-like particles.

Based on the above definition, the time-averaged radial particle angle distributions of three typical cylindroid particles with L/d = 0.25, 1.0 and 2.0 at the different bed heights (h = 0.06, 0.12, 0.18, 0.24 m) were shown in Fig. 13. Particles with different shapes demonstrated the completely different orientation distribution characteristics in the spouted bed. For the disc-like particle with L/d = 0.25, the particle angles varied significantly in the bottom and middle parts of the bed: in the spout the angles between the principal axes of the particles and the vertical direction were N70°, indicating the disc-like particles tend to “stand” on their bands in the spout as shown in Fig. 13 left, while in the lateral annulus, the particle angles were only about 30–40° and the particles preferred to “lay” on their planes in this region; however, the particles near the wall usually stood by their bands against the wall with the particle angles of 90°. Generally, the angle of disc-like particle showed the W– shaped radial distributions in the bottom and middle parts of the spouted bed as seen in Fig. 13 left. In the bottom region of bed, the particle orientation variation between the spout and annulus was more obvious. In the annulus, the particles slowly moved downward in the loose packing state. As their velocities gradually decreased from the bed surface to the bottom as seen in Fig. 10, the particles would contact more and more closely. In this process, the particles tend to adjust their orientations to lay with their longer dimensions as they were closely packing according to the stable principle of minimum gravitational potential. This led to the larger angles of disc-like particles in the bottom region of annulus, which was significantly different from that in spout region

where the particles were affected mainly by the vertical spouting gas. With the increasing bed height, this variation in radial direction gradually weakened mainly due to the looser contacts between particles in the upper region of annulus. At the space that above the bed surface, for example h = 0.24 m, the radial particle orientations became uniform and only slightly fluctuated in the range of 60–70°. For the rod-like particle, such as L/d = 2.0, their orientation distributions in the radial direction also showed the obvious variations: in the bottom and middle regions of the bed the particles tended to “stand upright” on their planes in the spout with the particle angle being quite small (about 40°), while in the annulus the particles preferred to “lay” on their bands with the particle angle being larger (60–70°); the angles of particles near the wall were also relatively smaller (about 55°). The angle of rod-like particle generally showed the M –shaped distributions in the radial direction in the bottom and middle regions of the spouted bed as shown in Fig. 13 right. Similar to that of disc-like particles, this angle variation of rod-like particles in the radial direction also weakened with the increase of bed height. In summary, the typical cylindroid particles had the distinct orientation variations in the spouted bed, especially in the bottom and middle regions of the bed. In the vertical upward stream of the spout, the particles tended to put their larger dimension parallel to the stream direction, while in the annulus where the particles were slowly falling, the particles tended to lay with their larger dimension especially in the bottom region. When L/d = 1.0, the particle angles were fairly evenly distributed in the bed as shown in Fig. 13 middle, and the averaged angle of the particles in the entire bed level only slightly fluctuated between 55° and 60°.

4.5. Coordination numbers (CN) of cylindroid particles in the spouted bed

Fig. 17. The time-averaged CN distributions of the particles with varying shapes in the fountain region (us = 6 m/s, H0 = 0.21 m, ρp = 1200 kg/m3, Vp = 42.39 mm3).

Coordination number (CN) of a given particle is defined as the total number of contacts between this particle and other objects such as particles, walls at a moment [15,40]. The larger CN usually indicates the more frequent contacts (or collisions) and the closer interactions between particles; this may result in more intensive mass and heat transfer between particles. For the systems in which conductivity between particles plays an important role, the CN is of the remarkable significance to analyze the thermal behaviors. CN depends on the definition of critical separation. When the distance of the boundaries of two particles is less than the defined critical separation, they are considered in contact. The critical separation should be zero in theory when the real contact occurs between particles. But in practical computation, it is often defined as a small value slightly larger than zero. This treatment does not affect the analysis as long as the

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definition is consistent. In this work, the critical separation is set to be 1%dv (equivalent volume diameter of particle) [15]. Fig. 14 showed the time-averaged radial CN distributions of the three typical cylindroid particles (L/d = 0.25, 1.0 and 2.0) at different bed heights (h = 0.06, 0.12, 0.18, 0.24 m) in the spouted bed. In the bed levels, these three kinds of particles presented the similar distribution with the lower CNs in the central spout region and the higher in the lateral annulus region. The particle contacts in the spout were obviously less than that in the lateral annulus. With the bed height increasing from 0.06 m to 0.12 or 0.18 m, the CNs both in the spout and annulus decreased, indicating that the particle contacts obviously reduced in the upper part of the bed level. In the fountain region outside the bed (such as h = 0.24 m), CN showed little difference in the radial direction, and the time-averaged CN was b1. This meant there was almost no contact between the particles in the fountain region. It could also be seen from Figs. 14 that for the particles with different shapes, their CN distributions under the same conditions showed significant differences in value. Figs. 15, 16 and 17 showed the detailed CN distributions of particles with different shapes in the spout, annulus and fountain regions, respectively. When the spouted bed was in the spouting state, in the spout region, the cylindroid particles with CN = 0, viz., that did not contact with other particles, usually accounted for the largest proportion; particles with the CN between 0–4 were in the majority and that with CN larger than 6 only accounted for the very small proportion (b5%). For different particles, as L/d deviated from 1.0, the CN curves would shift to the right gradually. The proportions of the particles with the smaller CN decreased and that with the larger CN increased, as shown in Fig. 15. This indicated that when particles tended to be flatter or to be longer and thinner, the contacts between particles would increase generally. Compared to the situations of packing, the probability distribution curves of CN in the spout region of spouting states showed the very different configurations with the main bodies of curves obviously shifting to the left and proportions of CN = 0 rapidly increasing. This revealed the remarkable less particle contacts in the spout region under the spouting states than that under the packing states. Differently, the probability distribution curves of CN in the annulus region presented the very similar configurations to that under the packing states, as shown in Fig. 16, but the positions of the former curves also shifted to the left obviously in the coordinate system. Under the spouting states, the proportions of particles with CN between 3~6 were highest in the annulus and that with CN exceeding 7 were very low, while under the packing states, it was the particles with CN between 5 and 9 that usually accounted for the highest proportions. The downward movements of particles reduced the contacts between them to some extent in the annulus. Additionally, for different particles, as L/d deviated from 1.0, their CN curves shifted to right with the proportions of particles with the large CN slightly increasing both in the spout and annulus region. This meant with the shapes of particles becoming flatter or longer, their contacts in the spouted would increase. In the fountain region, the majority of the particles (about 70%) were not in contact with any other particles (CN = 0). The proportion of particles with CN N 1 was quite small as shown in Fig. 17. This determined that the shapes of the particles had little effect on the CN distributions in the fountain region, and all of the particles showed the similar probability distribution curves of CN. 5. Conclusions The CFD-DEM models for the dense gas-solid flow systems of cylindroid particles were developed in the current study with the gas motion modelled with k-ε turbulent model, and the particles represented with realistic cylindroid shapes by the combined geometric element method. With comprehensively analyzing the various contact scenarios and improving the interactions models for the gas and the

real cylindroid particles, the CFD-DEM modelling on “turbulent gas flow + real cylindroid particles + spouting” were achieved in a CPU + GPU computing platform. The spouting features of cylindroid particles with aspect ratios varying from 0.25–3.0 were studied in a rectangular spouted bed and the gas and solid dynamic characteristics and mechanisms, as well as the effects of particles shapes on the spouting dynamics were figured out in particle scale. The main findings are as follows: (1) In the macro scale, cylindroid particles have the similar gas and solid flow patterns with that of spherical particles in the spouted bed and three distinct three regions, namely the spout, annulus and fountain regions can form when the stable external spouting is established. The particle shapes have the obvious effects on the spouting characteristics: the particles with a L/d~1 perform the highest fountain and largest spout radius and thus the largest particles circulation rate in the spouted bed; as the cylindroid particles become flatter or longer with their shapes increasingly deviating from the sphere, the stability of the fountain will decrease and its height reduces; at the same time, the spout width, as well as the particle circulation rate also decreases. (2) In the particle scale, the cylindroid particles have the obvious orientations in the spouted bed: in the spout region, particles with remarkable difference in length and diameter tend to put their larger dimension parallel to the (vertical) flow direction, and obtained the minimum projected areas in the flow direction and thus the minimum drag forces; while in the annulus region these particles tend to put their larger dimension perpendicular to their falling direction. When particles are flatter or longer, such difference in orientation will be more obvious, and this would be increasingly unfavorable for the particle circulation motions in the spouted bed. (3) In the spout and annulus region, the particle contacts obviously reduce with the increasing bed height. The particle contacts in annulus are more intensive than that in spout region, while in the fountain region there is almost no contacts occurs between the particles. When the particles increasingly deviate from the sphere, their contacts obviously increase and the interactions including collision, friction, inter-locking, etc., become stronger. This may lead to the more intensive mass and heat transfer, but as well as the worse flowability and thus the less stable macro spoutings in the bed. Nomenclature CD CN d Fc,ij Fcn,ij Fct,ij Fpf,i Fd,i Gk Hb H0 h hF Ii I’i g k

Drag coefficient, Coordination numbers, 1 Diameter of the circular plane for a cylinder, m Contact force between particle i and j, N Contact force in normal direction between particle i and j, N Contact force in tangential direction between particle i and j, N Interaction force between particle and fluid acting on particle i, N Drag force acting on particle i, N Generation of turbulence kinetic energy, m2/s2 Height of bed vessel, m Static bed height, m Bed Height, m Height of fountain, m Particle motion of inertia in space-fixed coordinate system, N·m Particle motion of inertia in body-fixed coordinate system, N·m Gravitational acceleration, m/s2 Turbulent energy, m2/s2

Please cite this article as: X. Liu, J. Gan, W. Zhong, et al., Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study, Powder Technol., https://doi.org/10.1016/j.powtec.2019.07.099

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kn kt kp kw L Mn Mr Mt m ns p t U u us Vp vp

Spring coefficient in normal direction, − Spring coefficient in tangential direction, − Spring coefficient between particle and particle,Spring coefficient between particle and wall,The length of cylinder particle, m Torque by normal force, N·m Torque by rolling friction force, N·m Torque by tangential force, N·m Mass, kg Number of sample points within the CFD cell for a particle, 1 Pressure, Pa Time, s Superficial gas velocity in fluidized bed, m/s Gas velocity, m/s Spouting velocity based on spouting inlet for spouted bed, m/s Volume of cylinder particle, m3 Particle velocity, m/s

Greek letters α particle orientation angle, ° Volume fraction of fluid, − αf αs Volume fraction of solid, − γp Particle-particle damping coefficient,γw Particle-wall damping coefficient between particle and wall,δn,ij Normal displacement of two contacting particles, m δt,ij Tangential displacement of two contacting particles, m ε Turbulent dissipation rate, m2/s3 μ Gas kinetic viscosity, Pa·s μt Gas turbulent viscosity, Pa·s μf Friction coefficient, − μr Rolling friction coefficient, − μp Particle-particle friction coefficient, − μw Particle-wall friction coefficient, − ρ Density, kg/m3 σp Possion's ratio of particle, − σw Wall Possion's ratio of wall, − τ gas viscous stress tensor, Pa τl Lagrangian time scale of the gas phase τd Response time scale of the particle phase φ Sphericity, − ω Angular velocity of the particle, rad/s

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Please cite this article as: X. Liu, J. Gan, W. Zhong, et al., Particle shape effects on dynamic behaviors in a spouted bed: CFD-DEM study, Powder Technol., https://doi.org/10.1016/j.powtec.2019.07.099