CFD–DEM simulation of a pseudo-two-dimensional spouted bed comprising coarse particles

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CFD–DEM simulation of a pseudo-two-dimensional spouted bed comprising coarse particles B. Mahmoodi a , S.H. Hosseini b,∗ , G. Ahmadi c a b c

Ilam Gas Treating Company, Ilam, Iran Department of Chemical Engineering, Ilam University, Ilam 69315-516, Iran Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725, USA

a r t i c l e

i n f o

Article history: Received 7 November 2017 Received in revised form 14 December 2017 Accepted 26 December 2017 Available online xxx Keywords: CFD–DEM Pseudo-2D spouted bed Hydrodynamics Coarse particles

a b s t r a c t In the present study, computational fluid dynamics (CFD) and the discrete element method (DEM) are used in conjunction with the Eulerian–Lagrangian method to simulate a pseudo-two-dimensional spouted bed comprising coarse 6-mm particles. The open-source OpenFOAM code is used to solve the governing equations. The predicted vertical particle velocity along the bed axis, particle velocity profiles in the radial direction, power spectral density, time-averaged particle velocity vectors, bed pressure drop, and solid flow pattern are evaluated and compared with existing experimental data. Good agreement is found between the CFD–DEM results and the measured data. It is also shown that the present CFD–DEM model accurately predicts the particle flow pattern throughout the bed. It is found that the drag force, solid stresses, and gravity play important roles in the CFD–DEM simulation of a spouted bed comprising coarse particles. © 2018 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

Introduction The original spouted bed (SB) was developed as an alternative method to the fluidized bed for drying moist wheat particles (Gishler, 1983). Because of the vigorous particle circulation in SBs, the air much hotter than that in conventional wheat driers could be used without damaging the grains (Mathur & Gishler, 1955). The use of SBs is increasing because they provide good mixing and effective heat transfer. Some industrial applications of SBs are grain drying, spray drying, coating, heterogeneous catalysis, and gasification of biomass and coal (Al-Mayman & Al-Zahrani, 2003; Harvie, Langrish, & Fletcher, 2002; Ichikawa, Arimoto, & Fukumori, 2003; Kersten, Prins, van der Drift, & van Swaaij, 2003; Kmiec & Szafran, 2000; Luo, Aoki, Uemiya, & Kojima, 1998). Advances in measurement techniques have provided certain crucial information regarding the flow behavior and stability of SBs. In recent years, computational fluid dynamics (CFD) has also emerged as an effective numerical method for simulating gas–solid flows in SBs. Two important classes of models that are used to simulate multiphase flows are Eulerian–Eulerian and Eulerian–Lagrangian approaches. In the former so-called two-fluid

∗ Corresponding author. E-mail address: [email protected] (S.H. Hosseini).

models (TFM), the gas and the particulate phase are described as interpenetrating continua, whereas in the latter the fluid phase is simulated by the Eulerian technique and the solid phase by Lagrangian particle-trajectory analysis (known as the discrete element method (DEM)). The difference between these approaches lies in how the particulate phase is treated. The DEM approach is able to capture more accurately the physics of gas–solid processes. However, DEM simulations become computationally more expensive with more particles. In the present study, we used the CFD–DEM approach to capture more accurately the features of an SB. Among the different types of SB, the pseudo-two-dimensional SB (P2DSB) has been used to visualize the particulate flow pattern conveniently and to measure its hydrodynamic properties. However, most reported data in the literature are for beds with particles smaller than 2.5 mm. For instance, Liu, Li, Zhao, and Yao (2008) and Zhao, Li, Liu, Song, and Yao (2008) used particle image velocimetry (PIV) to measure the velocity distributions and flow patterns in a P2DSB of 2-mm particles, without and with draft plates, respectively. The experimental conditions of the SBs of Liu et al. (2008) and Zhao, Li, Liu, Song et al. (2008) were simulated to assess the accuracy of different CFD models (Hosseini, Ahmadi, Razavi, & Zhong, 2010; Hosseini, Fattahi, & Ahmadi, 2015; Moradi, Yeganeh, & Salimi, 2013; Wang et al., 2010; Zhao, Li, Liu, Yao, and Marshall, 2008).

https://doi.org/10.1016/j.partic.2017.12.014 1674-2001/© 2018 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

Please cite this article in press as: Mahmoodi, B., et al. CFD–DEM simulation of a pseudo-two-dimensional spouted bed comprising coarse particles. Particuology (2018), https://doi.org/10.1016/j.partic.2017.12.014

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Nomenclature CD C␮ C1 , C2 dp E Fc Fd Fp

Drag force coefficient A constant in Eq. (3) Model constants in Eq. (5) Particle diameter, m Young’s modulus Contact force, N Drag force, N Far-field pressure force, N

g H Hb Ip k KH e12 E mp n P r R Rep Sp t t T Ug g u vp Vp V

Acceleration due to gravity, m/s2 Bed height Still bed height Particle moment of inertia, kg m2 Turbulence kinetic energy, m2 /s2 Spring coefficient in normal direction, N/m Unit vector Young’s modulus, Pa Particle mass, kg Total number of particles located in a specific cell Pressure, Pa Position, m Particle radius, m Particle Reynolds number Gas–solid interaction force per unit volume, N/m3 Time step, s Time, s Torque on particle, N m Spouting velocity, m/s Fluid velocity in current cell, m/s Particle velocity, m/s Particle volume, m3 Volume of current cell, m3

→

Greek symbols ˛ Gas volume fraction ˇgp Interphase momentum transfer coefficient, kg/(m3 s)  Damping coefficient, kg/s ı Particle–particle and particle–wall penetration depth Restitution coefficient  ε Turbulence energy dissipation rate, m2 /s3  Gas dynamic viscosity, kg/(m s) s Static friction coefficient rolling Rolling friction coefficient t Turbulent gas viscosity, kg/(m s)  Poisson’s ratio Gas density, kg/m3 g p Particle density, kg/m3 Turbulent Prandtl number Particle angular velocity, s–1 ω Subscripts c Contact force d Drag force g Luid phase i Particle i Particle j j p Particle phase

Hosseini et al. (2010) used the TFM approach embedded in the MFIX CFD code and studied the hydrodynamics of the P2DSB of Liu

et al. (2008) for relatively fine particles. They showed that the CFD results are quite sensitive to the choices of particle–particle restitution coefficient, drag function, and frictional stresses. Recently, Hosseini et al. (2015) showed that the TFM simulation of the P2DSB of Liu et al. (2008) overestimates the solid velocity and fountain height. They also showed that two-dimensional (2D) simulation of a thin SB is inadequate for predicting three-dimensional (3D) experimental data because the front and back walls exert an important effect. Zhao, Li, Liu, Yao et al. (2008) performed a series of CFD–DEM simulations of a P2DSB comprising 2-mm glass beads. They reported the distribution of drag forces acting on the particles and the particle velocity profiles in the spout and annulus regions of the bed. Using the TFM approach, Wang et al. (2010) studied the hydrodynamics of the P2DSB with draft plates reported by Zhao, Li, Liu, Song et al. (2008). It was found that considering the frictionalkinetic closure of the solid phase in the CFD model greatly improved the flow behavior through the bed. In addition to obtaining experimental data, Zhao, Li, Liu, Song et al. (2008) simulated a P2DSB with draft plates by using the CFD–DEM approach for 2-mm particles (relatively fine particles). They studied the impact of entrainment height on the vertical velocity and circulation rate of the particles. Using the CFD–DEM approach, Swasdisevi et al. (2005) studied the mixing of binary particle mixtures in a P2DSB with draft plates. They considered the case in which the static bed height (BH) was considerably higher than the conical section height. The particle flow pattern in the conventional cylindrical spouted beds, in which the particles fill the conical and a large portion of cylindrical section of the bed, were studied by Ren, Zhong, Jin, Yuan, and Lu (2011), Du, Bao, Xu, and Wei (2006), and Hosseini, Ahmadi, and Olazar (2013). Those studies used relatively fine particles (dp < 2.5 mm) and found that the spout, annulus, and fountain shapes in such beds remain quite steady with time. In addition, the bed pressure drop remains fairly constant. However, Liu et al. (2008) and Zhao, Li, Liu, Yao et al. (2008) observed incoherent spouting experimentally in P2DSBs with relatively fine particles (dp < 2.5 mm). Using the TFM, Hosseini et al. (2010) predicted incoherent spouting in the P2DSB comprising 2-mm particles as studied earlier experimentally by Liu et al. (2008). Using CFD–DEM, Zhao, Li, Liu, Yao et al. (2008) also predicted incoherent spouting in a P2DSB with 2-mm particles. Using the TFM, Setarehshenas, Hosseini, Nasr Esfahany, and Ahmadi (2016, 2017) simulated fully 3D conical–cylindrical SBs comprising heavy zirconia particles having a density of 6000 kg/m3 ; they also observed unstable spouting in their simulations. San Jose, Olazar, Alvarez, Morales, and Bilbao (2005) argued that the geometrical features and operating conditions of an SB significantly affect the shapes of its spout, fountain, and core and peripheral zones. All the aforementioned simulations were performed for P2DSBs comprising relatively fine particles (dp < 2.5 mm). To the best of our knowledge, CFD simulations of P2DSBs comprising coarse particles are rather scarce. Coarse particles that can be used in SBs include beans, corn, pharmaceuticals, and polymer spheres in applications such as agriculture and medicine (Marreto, Freire, & Freitas, 2006; Neuwirth, Antonyuk, Heinrich, & Jacob, 2013; Ren et al., 2012; Vieira Neto, Duarte, Murata, & Barrozo, 2008; Yang, Luo, Fang, & Fan, 2013). In addition to SBs, the pneumatic conveying of absorber spheres in a high-temperature gas-cooled reactor involves coarse particles. Moreover, a draft tube feeder is used for the vertical pneumatic conveying of coarse particles (Tan, Williams, Jones, & Krull, 2008; Zhang et al., 2016), and coarse polymer particles are fluidized and dried by an air spout in rotor granulation (Neuwirth et al., 2013). In the present study, we use a CFD–DEM model to explore the hydrodynamics of a P2DSB. We use the Gidaspow drag model to compute the gas–solid momentum exchange coefficient. We pay

Please cite this article in press as: Mahmoodi, B., et al. CFD–DEM simulation of a pseudo-two-dimensional spouted bed comprising coarse particles. Particuology (2018), https://doi.org/10.1016/j.partic.2017.12.014

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particular attention to the particle velocities in the axial and radial directions and also to the particle flow pattern in the SB. We show that the CFD–DEM simulation results for a P2DSB with coarse 6mm particles agree well with available experimental data while incurring quite reasonable computational cost. Numerical procedure

In the CFD–DEM approach, the continuous gas phase is governed by the generalized Navier–Stokes equations, but the particulate phase is treated as a discrete phase with the motion of an individual particle being evaluated using Newton’s Second Law. To account for the effect of the particulate phase on the continuous phase, the volume fraction of the gas phase is evaluated in each computational cell. Accordingly, the mass and momentum equations for the gas phase are given as (1)

(2)

where g is the gas density, ˛g is the gas volume fraction (porosity), g is the gas dynamic viscosity, t is the turbulent (eddy) viscosity,  g is the gas velocity vector. In Eq. (2), p is the static pressure, and u S p is the source term for momentum, representing the gas–particle interaction force per unit volume. Also, we use the standard k–ε model to simulate the turbulent nature of the bed flow. The eddy viscosity is computed as 2

t = C␮ g k /ε,

(3)

where C␮ is a constant that we set to 0.09 in all simulations, and k and ε are the turbulence kinetic energy and turbulence energy dissipation rate, respectively, which are governed by the following transport equations:

∂   g ) = ∇ · [˛g ( + t )∇ k] (˛g g k) + ∇ · (˛g g ku k ∂t +˛g Gk − ˛g g k ,

∂   g ) = ∇ · [˛g ( + t )∇ ε] (˛g g ε) + ∇ · (˛g g εu ε ∂t

T

(6)

Ii

dt

dωpi dt

E E 4  1 2   3 E2 1 − v2 + E1 1 − v2 1 2

 = −2



r1 r2 , r1 + r2

(11)

m m

KH m 1+m2 ln ()



1

2

2

+ ln()2

(12)

,

where m1 and m2 are the masses of particles 1 and 2, respectively. Here,  is the damping coefficient and  is the restitution coefficient. In this study, we evaluate the friction force between the particles based on the Coulomb friction law: Ffr = (s + rolling )Fnormal ,

(13)

where s is the static friction coefficient, rolling denotes the rolling friction coefficient, and Fnormal is the magnitude of the normal force at the contact surface. The friction force is directed opposite to the relative tangential motion and may or may not inhibit the relative tangential motion depending on the magnitudes of the tangential momentum and forces. Finally, the drag force exerted on the particles by the fluid phase, Fd in Eq. (7), is calculated as (14)

where ˇgp is the interphase momentum exchange coefficient and is calculated by the Gidaspow correlation as (Gidaspow, 1994) ˛g g (1 − ˛g ) −2.65 3 ˛g , ˛g ≥ 0.8 CD 4 dpi 150(1 − ˛g )2 g 2 ˛g dpi

+

 g − vpi | 1.75g (1 − ˛g )|u

24 0.687 (1 + 0.15Repi ), CD = { 4 0.44, Repi =

 g − vpi |dpi ˛g g |u g

,

dpi Repi < 1000

,

, (15) , ˛g < 0.8

(16)

Repi ≥ 1000 (17)

where CD is the drag force coefficient, dpi is the diameter of particle i, and Repi is the particle Reynolds number.

The translation and rotation of particle i are governed by Newton’s Second Law and the balance of angular momentum: dvpi

KH =

(5)

Equations of particle motion

mi

(10)

where ı is the particle–particle and particle–wall penetration depth, e12 is the unit vector, and KH is the effective modulus that is computed from the respective Young’s moduli E1 and E2 of the two colliding particles and their Poisson’s ratios v1 and v2 :

ˇgp = {

where k = 1 and ␧ = 1.3 are the turbulent Prandtl numbers for k and ε, respectively. In Eq. (5), C1 = 1.44 and C2 = 1.92 are model constants, and Gk denotes the generation of turbulence kinetic energy by the mean velocity gradient and is given as  g + (∇ u g) ) : ∇u g. Gk = t (∇ u

F1,2 = (KH ı3/2 + ((v2 − v1 ) · e12 ))e12 ,

 g − vpi )Vpi /(1 − ˛g ), Fd,i = ˇgp (u (4)

ε +˛g (C1 Gk − C2 g ε), k

(9)

where Vpi is the particle volume. To model particle collisions, we use the soft-sphere contact model proposed by Cundall and Strack (1979). We use a nonlinear Hertzian-dashpot collision law (Hertz, 1881) in which the force of particle 1 on particle 2 is described as



∂  g ) + ∇ · (˛g g u gu  g ) = −˛g ∇ p + ∇ · [˛g (t + g ) (˛g g u ∂t g + ∇u  Tg )] + ˛g g g + Sp , (∇ u

→

where mi , vp , g , Ii , and ωi are the particle mass, particle translational velocity, acceleration due to gravity, particle rotational inertia, and particle angular velocity, respectively. Here, Ti denotes the total torque exerted on the particle by the contacting particles and the wall. In Eq. (7), Fp is the pressure-gradient force exerted on the particle and is given as Fp = Vpi ∇ p,

Equations governing gas phase

∂  g ) = 0, (˛g g ) + ∇ · (˛g g u ∂t

3

= mi g − Fp + Fd + Fc + Ffr ,

(7)

= Ti ,

(8)

Computational conditions In the present study, we use geometry identical to the experimental 2D bed operated by Zhang et al. (2017). The configuration is a P2DSB with a conical base made of Plexiglas, in which the initial bed height just covers the part of the bed corresponding to

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Table 2 Numerical parameters used in present study. Young’s modulus, E (Pa) Poisson’s ratio,  Restitution coefficient,  Friction coefficient, s Numerical schemes Spatial discretization Transient formulation Particle time step size (s) Fluid flow time step size (s) Number of simulated particles for H0 12.4 and 8 cm

50 × 109 0.23 0.66 0.3 PIMPLE (PISO + SIMPLE) QUICK Bounded second order implicit 1.0 × 10−7 5.0 × 10−6 2809, 1405

other important modeling parameters are listed in Table 2. All simulations are performed using the OpenFOAM code. Results and discussion

Fig. 1. (a) Main components of bed geometry and (b) computational grid.

Table 1 Geometrical components of two-dimensional conical spouted bed and fluid properties. Gas density, g (kg/m3 ) Gas viscosity, g (Pa s) Particle diameter, dp (mm) Particle density, p (kg/m3 ) Gas superficial velocity, Ug (m/s) Static bed depth, H0 (cm) Total solid mass (kg) Slot width, (mm) Column height, Hc (m) Column depth, Lz (mm) Column width, Lc (mm) Inclined angle,  (◦ )

1.205 18.1 × 10−6 6 2518 3.2, 3.72, 4.39 8, 12.4 4, 8 30 1.2 36 210 60

the inclined wall with heights of Hb = 8 cm and 12.4 cm. The main components of the bed geometry are shown in Fig. 1(a) and the corresponding dimensions are listed in Table 1. To establish a grid for DEM simulations, the mesh dimension should exceed the particle diameter (Esmaili & Mahinpey, 2011; Guo, Wu, & Thornton, 2013; Ren et al., 2011). We used a grid with 2964 hexahedral cells as shown in Fig. 1(b). Furthermore, because the particle diameter is 6 mm (similar to the experiments), the numbers of particles used in the current simulations are 1405 and 2809 for the two stagnant bed heights as listed in Table 2, which are identical to those in the experiment. Because we do not use too many particles, the computational cost for this study is quite modest. In the experiment, the inlet gas velocity and outlet pressure were known conditions that we use as the inlet boundary conditions for the computational model. As noted earlier, we use the standard k–ε turbulence model for the turbulent motion of the fluid phase, and we use the Hertzian-dashpot model to resolve particle–particle and particle–wall collisions. The values of the

We performed a series of simulations of a P2DSB with 6-mm particles under various operating conditions, and we present the results in this section. We characterize the flow stability by evaluating the pressure drop (i.e., the uniformity and amplitude of the fluctuations) and via visual observations, which are easy for slot rectangular beds (Gryczka et al., 2009; Pietsch et al., 2017; Salikov, Antonyuk et al., 2015; Salikov, Heinrich et al., 2015). Therefore, in this study we model the pressure drop, power spectral density (PSD), and particle distribution. For a gas speed of Ug = 4.39 m/s and an initial bed height of Hb = 12.4 cm, Fig. 2 shows the time evolution of the bed pressure drop, the pressure-drop PSD, and the solid concentration in the P2DSB. Fig. 2(a) shows the particle distribution in the 2D bed as measured experimentally and as predicted by the CFD–DEM simulation. As described by Liu et al. (2008), the spout has a dynamic ‘X’ shape marked with a neck. Over the cycle time T, the spout changes shape, and the strongest particle entrainment appears in the neck at the end of the spout. It is interesting to note that an explosion of particle clusters occurs in the neck region of the spout. Fig. 2(a) shows close agreement between the CFD–DEM simulation and the experimental findings. As shown in Fig. 2(a), the spout end is choked with particle clusters, thereby increasing the overall pressure drop. This is followed typically by an explosion of particle clusters in the neck with the air flow and a decrease in the bed pressure drop. As shown in Fig. 2(b), this trend is roughly periodic, which is quite similar to the experimental data. According to Fig. 2(b), the computed cycle period is T = 0.171 s, which is slightly shorter than the measured value of 0.204 s. Fig. 2(c) shows the PSD of the bed pressure drop. The dominant frequency is Fd = 6.22 Hz, which is consistent with the aforementioned cycle period of incoherent spouting, namely T = 1/Fd = 0.161 s. The measured dominant frequency of 4.8 Hz is lower than the DEM-predicted one. Note that for the sake of brevity we refer to Zhang et al. (2017) for the measured PSD of the bed pressure drop and also the bed pressure drop versus time. According to the simulation results of Liu et al. (2008) for finer particles (dp = 2 mm) at roughly the same static bed height, the dominant frequency decreases with increasing particle diameter; this trend was also reported by Zhang et al. (2017). The reason for this behavior is that changing the particle diameter changes the minimum spouting velocity, the gravitational force, and many other parameters related to the bed hydrodynamics, thereby affecting the bed pressure drop. In particular, the particle diameter affects the drag force and solid stresses appreciably (Hosseini et al., 2015; Wang et al., 2010). The drag force and solid stresses exert a marked influence on the dominant frequency of incoherent spouting for both coarse and fine particles. Pietsch et al. (2017) studied the hydrodynamics of a 3D prismatic spouted bed with two horizontal

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Fig. 2. Measured (Zhang et al., 2017) and DEM results for (a) particle flow pattern, (b) evolution of bed pressure drop with time, and (c) predicted pressure drop power spectral density at Ug = 4.39 m/s and Hb = 12.4 cm.

gas inlets experimentally and computationally using the CFD–DEM approach. They examined various drag functions and found that those of Koch and Hill (2001) and Beetstra, van der Hoef, and Kuipers (2007) gave accurate predictions of the bed expansion and spouting behavior in the bed. For Ug = 4.39 m/s and Hb = 12.4 cm, Fig. 3(a) shows the computed and measured particle flow patterns in the bed at different times. Incoherent spouting with dynamic change in the spout geometry is clearly seen in both the CFD–DEM simulations and the experimental results. As observed in the second and third images from the left-hand side, the particles move upward in the spout, collect additional particles from the annulus region, and form clusters that grow in size and become denser in the spout “neck.” For the CFD–DEM results (shown in the above row), particles are colored by their velocity magnitudes. It is seen that the location of maximum particle velocity changes along the spout region with time. Also, the spout shows a slight deviation from the bed axis at certain times. A close examination of Fig. 3(a) indicates that the bed surface is not flat but concave in both the experimental and numerical results. Fig. 3(a) shows good overall agreement between the numerical prediction and the experimental result for the particle flow pattern. For Ug = 4.39 m/s and Hb = 8 cm, Fig. 3(b) shows the CFD–DEM predictions against measured snapshots of the particle distribution

in the bed at different times. It is seen that the predicted and measured particle distributions in the bed are quite similar. The spout and fountain in this case are slightly more stable than those for Hb = 12.4 cm shown in Fig. 3(a). It is interesting to note that Hosseini et al. (2010) and Liu, Wen, Liu, Liu, and Shao (2015) used respectively the TFM and CFD–DEM to show that the inlet gas velocity and stagnant bed height affect the stability of the spout for P2DSBs comprising 2-mm particles. To provide a better understanding of the solid concentration distribution in the bed, a series of instantaneous solid-volumefraction contour plots is presented in Fig. 4 for Ug = 4.39 m/s and Hb = 12.4 cm. In these figures, the dilute bed regions are the spout and fountain, while the annulus is the densest zone. Similar trends were observed earlier for P2DSBs comprising fine particles (Zhao, Li, Liu, Song et al. (2008); Hosseini et al., 2010). It should be noted that the spout is more dilute compared with the fountain region of the bed. The processes leading to the formation of the spout, annulus, and fountain for the bed with coarse particles are clearly seen in Fig. 4; the “X” spout geometry is also clearly observed in this figure. Fig. 4 also shows that the annulus and spout shapes change gradually with time, while the fountain height remains roughly constant. As mentioned before, the random deviation of the spout from the bed axis is clearly seen in Fig. 4. Note that the unsteady spout behavior observed in Figs. 3 and 4 is consistent with the previous DEM

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Fig. 3. Computed and measured particle flow pattern in bed for Ug = 4.39 m/s with (a) Hb = 12.4 cm and (b) Hb = 8 cm.

simulations of Zhao, Li, Liu, Yao et al. (2008) for a P2DSB comprising 2-mm particles. For Ug = 4.39 m/s and Hb = 12.4 cm, Fig. 5 shows the CFD–DEM prediction for the mean-particle-velocity vector field in a plane across the bed against the time-averaged measured data. In addition, a sample instantaneous-particle-velocity vector field as predicted by CFD–DEM is shown in this figure for comparison. The experimental data and the CFD–DEM results clearly show that the particle velocities in the spout are approximately 10 times higher than those in the annulus. The particle-velocity magnitude is low in the annulus region whereas the solid concentration is high, as was shown in Figs. 3 and 4. The contact forces balance the particle weight in the annulus region, but in the spout region the particles move upward because of the strong gas drag force. Also, both the experimental and simulation results show the rain of particles to the periphery of the central axis in the fountain region. Two large vortices are seen in this figure for both the experimental and numerical results. The particle circulation patterns observed in the computational results are quite similar to those in the experiment. The instantaneous-particle-velocity vector shown in Fig. 5 is from a time after the explosion of particle clusters in the neck.

Quantitative comparisons of the time-averaged axial particle velocities along the bed axis and distributed in the radial direction are presented in this section. For Ug = 4.39 m/s and Hb = 12.4 cm, Fig. 6(a) shows the predicted time-averaged axial particle velocities along the bed axis against the experimental data. The CFD–DEM predicted reasonable results in the spout region but overestimated the particle velocities in the fountain region. This trend is consistent with the CFD–DEM results of Zhao, Li, Liu, Yao et al. (2008) for their P2DSB comprising 2-mm particles. In earlier studies of cylindrical–conical spouted beds (Ren et al., 2011; Du et al., 2006; Hosseini et al., 2013), the particles accelerated rapidly along the central line of the bed to their maximum velocity at certain heights near the orifice; afterward, the particles decelerated gradually and came to rest in the fountain zone. In contrast with those findings for cylindrical–conical spouted beds, Fig. 6(a) shows that the coarse particles accelerated rapidly near the inlet orifice, maintain a nearly constant velocity in the spout region, and then decelerated gradually in the fountain region. For superficial gas velocities of 4.39, 3.73, and 3.2 m/s and a static bed height of Hb = 8 cm, Fig. 6(b) shows the time-averaged axial particle velocities on the spout centerline as predicted by CFD–DEM against the experimental data. The sharp increase of par-

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Fig. 4. Instantaneous contour plots of solid volume fraction for Ug = 4.39 m/s and Hb = 12.4 cm.

Fig. 5. Computed instantaneous and mean particle–velocity vector field and measured particle–velocity vector for Ug = 4.39 m/s and Hb = 12.4 cm.

ticle velocity in the lower part of the spout (near the inlet zone up to 3 cm) is almost identical for the different superficial gas velocities for the same static bed height. The CFD–DEM predictions and the measured data deviate at higher heights, especially in the fountain region. It should be noted that with increasing superficial gas velocity, the particle velocity increases for heights above 3 cm. Fig. 6(b) shows that the CFD–DEM overestimated the experimental axial velocity data for a gas velocity of 3.2 m/s but underestimated it for higher gas velocities. The difference between the measured and CFD–DEM results increased with gas velocity, especially in the fountain region. We conjecture that these differences may be attributed to the turbulence model used in the simulation. Such differences between DEM results and experimental data were also observed by Zhao, Li, Liu, Yao et al. (2008) in their study of a P2DSB comprising finer particles. Overall, the CFD–DEM simulation with the k–ε turbulence model predicts the trend of axial particle velocity along the spout centerline reasonably well. Examination of the influence of different turbulence models on the simulation results is left for future work.

For Ug = 4.39 m/s and Hb = 12.4 cm, Fig. 7 shows the radial profiles of axial particle velocity across the bed at various still bed heights and bed heights. The maximum particle velocity was at the bed axis (center of the spout) and decreased to zero at the boundary between the spout and annulus zones. The particle velocity then became negative, indicating downward flow in the annulus region for all bed heights as shown in the CFD–DEM results and the measured data. Good agreement is found between the particle velocity profiles across the bed at different heights. Some researchers determined the spout diameter by tracing the particle velocities over the spout and annulus regions and identifying where they passed through zero (Hosseini et al., 2013). Using this method while increasing the bed height H from 3.85 to 9.35 cm, Fig. 7 shows that the spout radius increased from 2.1 to 2.75 cm experimentally and from 2.2 to 3.18 cm in the CFD–DEM results. The model overestimated the spout diameter especially at higher bed heights. For finer particles, Zhao, Li, Liu, Yao et al. (2008), Hosseini et al. (2013), and Liu et al. (2014) reported similar trends

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Fig. 8. Radial profiles of vertical particle velocity in the annulus at various bed heights for Ug = 4.39 m/s and Hb = 12.4 cm.

Fig. 6. Calculated and measured time-averaged axial particle velocities along bed axis for (a) Ug = 4.39 m/s, Hb = 12.4 cm and (b) Ug = 4.39, 3.73, 3.2 m/s, Hb = 8 cm.

in CFD–DEM and TFM predictions of the variation of spout diameter with bed height. Finally, the time-averaged axial particle velocities as predicted by CFD–DEM in the annulus region at different bed heights H are shown in Fig. 8. Near the spout region, the magnitude of the downward particle velocity increased rapidly to its maximum value and then decreased more slowly toward the inclined wall. It is also observed that the particle velocity near the wall was roughly the same for different bed heights. Therefore, the peak downward velocity occurred at a certain location between the spout region and the inclined wall. It is also observed that with increasing bed height, the location of peak downward velocity moved toward the wall and the peak amplitude increased slightly. The results for particle velocity in the annulus presented in Fig. 8 are quite similar to the results reported by Liu et al. (2008) and Zhao, Li, Liu, Yao et al. (2008). However, in their experiments, Zhang et al. (2017) found lower particle velocity near the inclined wall. Providing more

accurate values to model parameters such as the friction and restitution coefficients (i.e., by direct experimental measurement) could improve the model predictions. However, such fine-tuning of the model parameters is left for future work. Comparing the velocities predicted herein for coarse particles in the annulus region with those of Liu et al. (2008) and Zhao, Li, Liu, Yao et al., 2008 for spouted beds comprising finer particles shows that the present predictions are considerably higher. We conjecture that this is due to the higher force of gravity on the coarse particles in the annulus. Contour plots of the mean airflow velocity, interphase momentum exchange coefficient, and drag force for the coarse particles are shown in Fig. 9 for Ug = 4.39 m/s and Hb = 12.4 cm. As shown in Fig. 9(a), the gas flows much faster in the spout than it does in the other regions of the bed. In other words, most of the gas flows through the spout while a small amount flows through the annulus. The calculated results for the interphase momentum exchange coefficient are shown in Fig. 9(b). The highest value of ˇgp occurs in the annulus region where the particle concentration is highest. The calculated drag force is shown in Fig. 9(c). The maximum drag force appears in the spout region, which is consistent with the results of Zhao, Li, Liu, Yao et al., 2008. Conclusions In this study, the CFD–DEM was used to simulate a P2DSB comprising coarse 6-mm (Geldart D) particles. The simulation results were compared with experimental data published recently by

Fig. 7. Measured (right plot) and model predicted (left plot) radial profiles of vertical particle velocity in spout at various bed heights for Ug = 4.39 m/s and Hb = 12.4 cm.

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Fig. 9. Contour plots of (a) mean air velocity, (b) interphase momentum exchange coefficient, and (c) drag force for coarse particles at Ug = 4.39 m/s and Hb = 12.4 cm.

Zhang et al. (2017) for pressure drop, axial velocity profiles in the axial and radial directions, pressure-drop PSD, and particle flow pattern in the bed. It was found that the presented CFD–DEM model could accurately predict the particle motions in the bed. In particular, the incoherent spouting that was observed experimentally was properly predicted. In addition, the flow patterns of coarse particles presented herein were consistent with those of finer particles (smaller than 2.5 mm). It was also found that the differences between the results for coarse and finer particles were due to the drag and gravity forces and the solid stresses. It was concluded that the CFD–DEM could predicted the behavior of course particles in an SB with good accuracy and at reasonable computational cost. For future improvement of the CFD–DEM predictions in the fountain region, we suggest optimizing the drag function and exploring various turbulence models. In addition, implementing instantaneous turbulence fluctuation on DEM is left for future work. Finally, because the higher diameter of the particles under study requires coarser grids, we recommend using the mesh-free lattice Boltzmann method to simulate such flows of gas and coarse particles.

References Al-Mayman, S. I., & Al-Zahrani, S. M. (2003). Catalytic cracking of gas oils in electromagnetic fields: Reactor design and performance. Fuel Processing Technology, 80, 169–182. Beetstra, R., van der Hoef, M. A., & Kuipers, J. A. M. (2007). Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres. AIChE Journal, 53, 489–501. Cundall, P. A., & Strack, O. D. L. (1979). A discrete numerical model for granular assemblies. Geotechnique, 29, 47–65. Du, W., Bao, X. J., Xu, J., & Wei, W. S. (2006). Computational fluid dynamics (CFD) modeling of spouted bed: Assessment of drag coefficient correlations. Chemical Engineering Science, 61, 1401–1420. Esmaili, E., & Mahinpey, N. (2011). Adjustment of drag coefficient correlations in three dimensional CFD simulation of gas–solid bubbling fluidized bed. Advances in Engineering Software, 42, 375–386. Gidaspow, D. (1994). Multiphase flow and fluidization: Continuum and kinetic theory descriptions. New York: Academic Press. Gishler, P. E. (1983). The spouted bed technique–discovery and early studies at N. R. C. Canadian Journal of Chemical Engineering, 61, 267–268.

Gryczka, O., Heinrich, S., Deen, N. G., van Sint Annaland, M., Kuipers, J. A. M., Jacob, M., et al. (2009). Characterization and CFD-modeling of the hydrodynamics of a prismatic spouted bed apparatus. Chemical Engineering Science, 64, 3352–3375. Guo, Y., Wu, C. Y., & Thornton, C. (2013). Modeling gas–particle two-phase flows with complex and moving boundaries using DEM–CFD with an immersed boundary method. AIChE Journal, 59, 1075–1087. Harvie, D. J. E., Langrish, T. A. G., & Fletcher, D. F. (2002). A computational fluid dynamics study of a tall-form spray dryer. Food and Bioproducts Processing, 80, 163–175. Hertz, H. (1881). Über die Berührung fester elastischer Körper. Journal für die Reine und Angewandte Mathematik, 92, 156–171. Hosseini, S. H., Ahmadi, G., & Olazar, M. (2013). CFD simulation of cylindrical spouted beds by the kinetic theory of granular flow. Powder Technology, 246, 303–316. Hosseini, S. H., Ahmadi, G., Razavi, B. S., & Zhong, W. (2010). Computational fluid dynamic simulation of hydrodynamic behavior in a two-dimensional conical spouted bed. Energy & Fuels, 24, 6086–6098. Hosseini, S. H., Fattahi, M., & Ahmadi, G. (2015). Hydrodynamics studies of a pseudo 2D rectangular spouted bed by CFD. Powder Technology, 279, 301–309. Ichikawa, H., Arimoto, M., & Fukumori, Y. (2003). Design of microcapsules with hydrogel as a membrane component and their preparation by spouted bed. Powder Technology, 130, 189–192. Kersten, S. R. A., Prins, W., van der Drift, B., & van Swaaij, W. P. M. (2003). Principles of a novel multistage circulating fluidized bed reactor for biomass gasification. Chemical Engineering Science, 58, 725–731. Kmiec, A., & Szafran, R. G. (2000). Kinetics of drying of microspherical particles in a spouted bed dryer with a draft tube. Proceedings of the 12th International Drying Symposium (IDS2000). Koch, D. L., & Hill, R. J. (2001). Inertial effects in suspension and porous-media flows. Annual Review of Fluid Mechanics, 33, 619–647. Liu, G. Q., Li, S. Q., Zhao, X. L., & Yao, Q. (2008). Experimental studies of particle flow dynamics in a two-dimensional spouted bed. Chemical Engineering Science, 63, 1131–1141. Liu, M., Wen, Y., Liu, R., Liu, B., & Shao, Y. (2015). Investigation of fluidization behavior of high density particle in spouted bed using CFD–DEM coupling method. Powder Technology, 280, 72–82. Liu, X., Zhong, W., Shao, Y., Ren, B., & Jin, B. (2014). Evaluation on the effect of conical geometry on flow behaviours in spouted beds. Canadian Journal of Chemical Engineering, 92, 768–774. Luo, C., Aoki, K., Uemiya, S., & Kojima, T. (1998). Numerical modeling of a jetting fluidized bed gasifier and the comparison with the experimental data. Fuel Processing Technology, 55, 193–218. Marreto, R. N., Freire, J. T., & Freitas, L. A. P. (2006). Drying of pharmaceuticals: The applicability of spouted beds. Drying Technology, 24, 327–338. Mathur, K. B., & Gishler, P. E. (1955). A study of the applications of the spouted bed technique to wheat drying. Journal of Applied Chemistry, 5, 624–636. Moradi, S., Yeganeh, A., & Salimi, M. (2013). CFD-modeling of effects of draft tubes on operating condition in spouted beds. Applied Mathematical Modelling, 37, 1851–1859.

Please cite this article in press as: Mahmoodi, B., et al. CFD–DEM simulation of a pseudo-two-dimensional spouted bed comprising coarse particles. Particuology (2018), https://doi.org/10.1016/j.partic.2017.12.014

G Model PARTIC-1119; No. of Pages 10 10

ARTICLE IN PRESS B. Mahmoodi et al. / Particuology xxx (2018) xxx–xxx

Neuwirth, J., Antonyuk, S., Heinrich, S., & Jacob, M. (2013). CFD–DEM study and direct measurement of the granular flow in a rotor granulator. Chemical Engineering Science, 86, 151–163. Pietsch, S., Heinrich, S., Karpinski, K., Müller, M., Schönherr, M., & Jäger, F. K. (2017). CFD–DEM modeling of a three-dimensional prismatic spouted bed. Powder Technology, 316, 245–255. Ren, B., Zhong, W., Chen, Y., Chen, X., Jin, B., & Yuan, Z. (2012). CFD–DEM simulation of spouting of corn-shaped particles. Particuology, 10, 562–572. Ren, B., Zhong, W., Jin, B., Yuan, Z., & Lu, Y. (2011). Computational fluid dynamics (CFD)–discrete element method (DEM) simulation of gas–solid turbulent flow in a cylindrical spouted bed with a conical base. Energy & Fuels, 25, 4095–4105. Salikov, V., Antonyuk, S., Heinrich, S., Sutkar, V. S., Deen, N. G., & Kuipers, J. A. M. (2015). Characterization and CFD–DEM modelling of a prismatic spouted bed. Powder Technology, 270, 622–636. Salikov, V., Heinrich, S., Antonyuk, S., Sutkar, V. S., Deen, N. G., & Kuipers, J. A. M. (2015). Investigations on the spouting stability in a prismatic spouted bed and apparatus optimization. Advanced Powder Technology, 26, 718–733. San Jose, M. J., Olazar, M., Alvarez, S., Morales, A., & Bilbao, J. (2005). Spout and fountain geometry in conical spouted beds consisting of solids of varying density. Industrial & Engineering Chemistry Research, 44, 193–200. Setarehshenas, N., Hosseini, S. H., Nasr Esfahany, M., & Ahmadi, G. (2016). Impacts of solid-phase wall boundary condition on CFD simulation of conical spouted beds containing heavy zirconia particles. Journal of the Taiwan Institute of Chemical Engineers, 64, 146–156. Setarehshenas, N., Hosseini, S. H., Nasr Esfahany, M., & Ahmadi, G. (2017). Threedimensional CFD study of conical spouted beds containing heavy particles: Design parameters. Korean Journal of Chemical Engineering, 34, 1541–1553.

Swasdisevi, T., Tanthapanichakooni, W., Charinpanitkul, T., Kawaguchi, T., Tanaka, T., & Tsugi, Y. (2005). Prediction of gas–particle dynamics and heat transfer in a two-dimensional spouted bed. Advanced Powder Technology, 16, 275–293. Tan, S. M., Williams, K. C., Jones, M. G., & Krull, T. (2008). Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying. Particuology, 6, 307–315. Vieira Neto, J. L., Duarte, C. R., Murata, V. V., & Barrozo, M. A. S. (2008). Effect of a draft tube on the fluid dynamics of a spouted bed: Experimental and CFD studies. Drying Technology, 26, 299–307. Wang, S., Hao, Z., Sun, D., Liu, Y., Wei, L., & Wang, S. (2010). Hydrodynamic simulations of gas–solid spouted bed with a draft tube. Chemical Engineering Science, 65, 1322–1333. Yang, S., Luo, K., Fang, M., & Fan, J. (2013). Discrete element simulation of the hydrodynamics in a 3D spouted bed: Influence of tube configuration. Powder Technology, 243, 85–95. Zhang, H., Liu, M., Li, T., Huang, Z., Bo, H., & Dong, Y. (2016). Experimental study on plug formation characteristics of a novel draft tube type feeder for vertical pneumatic conveying of coarse particles. Powder Technology, 301, 730–736. Zhang, H., Liu, M., Li, T., Huang, Z., Sun, X., Bo, H., et al. (2017). Experimental investigation on gas-solid hydrodynamics of coarse particles in a two-dimensional spouted bed. Powder Technology, 307, 175–183. Zhao, X. L., Li, S. Q., Liu, G. Q., Song, Q., & Yao, Q. (2008). Flow patterns of solids in a two-dimensional spouted bed with draft plates: PIV measurement and DEM simulations. Powder Technology, 183, 79–87. Zhao, X. L., Li, S. Q., Liu, G. Q., Yao, Q., & Marshall, J. S. (2008). DEM simulation of the particle dynamics in two-dimensional spouted beds. Powder Technology, 184, 205–213.

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