CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 57, 2017 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Sauro Pierucci, Jiří Jaromír Klemeš, Laura Piazza, Serafim Bakalis 
Copyright © 2017, AIDIC Servizi S.r.l. 

ISBN 978-88-95608- 48-8; ISSN 2283-9216 

CFD-DEM and TFM Simulations of Spouted Bed 
Shahab Golshan, Behrad Esgandari, Reza Zarghami 
Process Design and Simulation Centre, School of Chemical Engineering, College of Engineering, University of Tehran, 
Tehran, Iran  
rzarghami@ut.ac.ir 

This research compared TFM and CFD-DEM models for simulation of a slot-rectangular spouted bed. Limits, 
drawbacks and benefits of the models were discussed and compared. Results of the two models were 
compared with available experimental data in literature. Axial distributions of the axial component of particle 
velocity and solids hold-up at the center of the spout, as well as the radial distributions of the axial component 
of particle velocity at four heights were found and compared with experimental data. Similar increasing-
constant-decreasing trends were observed for both axial velocity and hold-up distributions in CFD and CFD-
DEM simulations. Decreasing-constant trends were observed for radial distributions of particle velocity at all 
heights in CFD and CFD-DEM simulations. Simulation times were also compared at equal condition for the 
two models. It was found that for all the studied velocity and voidage distributions, CFD-DEM model shows 
better accuracies.  

1. Introduction 

Several researches have been conducted on the simulation of multiphase flow systems and various models 
have been proposed. Among all the proposed models, Eulerian two fluid model (TFM) and Eulerian-
Lagrangian computational fluid dynamics – discrete element method (CFD-DEM) have attracted attentions of 
majority of the researchers and have been used for simulation of different gas-solid contactors, especially 
fluidized beds and spouted beds. In this research, a slot-rectangular spouted bed was utilized as the case 
study to compare TFM and CFD-DEM models. Spouted beds are gas-solid contactors which are being used in 
various industries such as gasification, pyrolysis, drying and coating. Spouted beds have special advantages 
comparing to other types of gas-solid contactors, including the ability to work with large distribution of particle 
size.  
Several researchers have been conducted investigations on the simulation of multiphase flow systems using 
TFM. Du et al. (2006a) studied the effect of different drag coefficient correlations on the simulation of spouted 
beds. In a similar research effects of frictional stress, maximum packing limit and coefficient of restitution of 
particles have been studied using TFM simulations (Du et al., 2006b). It was found that frictional stress only 
influences the annulus region in the simulation of large particles. On the other hand, changing the maximum 
packing limit showed significant impact on the radial distribution of the solids hold-up. Lan et al. (2012) studied 
influence of solid-phase wall boundary condition on the simulation of a spouted bed. Other researchers used 
TFM for simulation of spouted beds with and without draft tubes (Azizi et al., 2010, Wang et al., 2006). 
CFD-DEM, as a novel model, has attracted attention of many researchers in the field of multiphase flow 
simulation. CFD-DEM was utilized to study the gas-solid hydrodynamics of rectangular spouted bed (Saidi et 
al., 2015). Yang et al. (2013) used CFD-DEM to study the effects of operating conditions, flow regime and 
presence of draft tube on the hydrodynamics of spouted beds. Salikov et al. (2015) studied hydrodynamics of 
a prismatic spouted bed with two gas inlets using CFD-DEM simulations. Rong and Zhan (2010) proposed an 
improved CFD-DEM model and validated the model by simulation of a spouted bed.  
Despite all the conducted researches on proposing improved models and studying the effects of different 
parameters by means of TFM and CFD-DEM simulations, little has been published on the comparison of the 
mentioned models. This work compared TFM and CFD-DEM in simulation of a slot-rectangular spouted bed. 
Simulation results were compared with experimental results to evaluate the accuracy of each model. Required 
simulation times for different condition were compared for different models and some recommendations were 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1757209

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Golshan S., Esgandari B., Zarghami R., 2017, Cfd-dem and tfm simulations of spouted bed, Chemical Engineering 
Transactions, 57, 1249-1254  DOI: 10.3303/CET1757209 

1249



provided to choose the best method for other simulations. Limitations, drawbacks and benefits of the models 
in the simulation were also discussed.  

2. Model  

2.1 CFD (TFM) 

Two fluid model (TFM) was used for simulation of the spouted bed. In this paper, this model is referred to as 
CFD. Governing equations of the TFM can be found in literature (Ueyama, 2012). For calculation of the gas-
solid drag coefficient, the model proposed by Gidaspow et al. (2003) was used which considers a combination 
of Ergun and Wen-Yu models:  

(1 )
gs Ergun gs Wen Y u

    


    (1) 

in which: 

2

2
150 1.75 0.8

pp g
p g

Ergun g

g p p

u

d d

  
 

 


 



    
(2) 

2.653
0.8

4

pp g p

W en Y u D g g

p

u

C
d

   

  

 







   (3) 

0.68724
[1 0.15( Re ) ], Re 1000

Re

0.44 Re 1000

g p P

g pD

p

C




 
   

  
   

 (4) 

tan[150 1.75(0.2 )]
0.5

p

gs

Arc 




 
   (5) 

OpenFOAM® software was used for the CFD simulation in this work.  

2.2 CFD-DEM 

CFD-DEM model initially solves the local-averaged Navier-Stokes equation in the gas phase. After reaching 
convergence, the calculated drag force is used in the DEM part. DEM part solves the equation of motion for all 
the particles in the system. After calculation of the new position of particles in the bed, the voidage distribution 
is found and used in the next CFD iteration. It should be mentioned that a soft-sphere model is used based on 
Hertzian contact model in this research. The governing equations of CFD-DEM are shown in Table 2. Detailed 
information about the governing equations can be found in literature (Golshan et al., 2017). An open-source 
CFD-DEM code (Goniva et al., 2012) was used for CFD-DEM simulation in this research. Parameters which 
were used for the CFD and CFD-DEM simulation are shown in Table 1. 

3. Result and discussion 

In this work, we compared the simulation results with available experimental data of Zhao et al. (2008a and 
2008b) to find and compare the accuracies of the models. Schematics and dimensions of the bed are 
illustrated in Figure 1 and other details can be found in literature (Zhao et al., 2008b). Particle used in the 
simulations were glass beads with diameter of 1 mm. Properties of particles and bed where chosen based on 
the values used by Zhao et al. (2008a and 2008b). Particles were initially inserted into the bed without any gas 
flow in both CFD and CFD-DEM simulations and after finishing the insertion step the gas flow was inserted 
into the bed. Sensitivity analysis were performed on the mesh size to find the suitable mesh size in both CFD 
and CFD-DEM simulations. Four mesh sizes (dm/dp = 2, 3, 4 and 5) were used to find the effect of mesh size 
on the simulation results. The largest mesh size with no significant effect of decreasing the size on the results 
(dm/dp = 3) was chosen for both CFD and CFD-DEM simulations. 
  

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Table 1:  CFD-DEM governing equations. 

CFD 
g g

( ) .( u) 0
t
 


 


 

g g g
( u) .( uu) .( )

s g
P F g

t
    




      


 

DEM 
gmFF

dt

dv
m

i

T

ij

j

N

ij
i

i
  )(  

T ri
i ij ij

j

d
I M M

dt


   

 3/ 2 1/ 4
4

   
3

N

Neff eff rNN N ij
E v nRF   

  
  
 
  

 

  

1/ 216
  
3

eff e i

T

Tff jN
G RF t   

Table 2:  CFD and CFD-DEM simulation parameters. 

 

 

 

Figure 1: Schematics and dimensions of the simulated spouted bed. 

parameter value 

particle-particle particle-wall 
e 0.9 0.92 
μ 0.3 0.4 
μr 0.03 0.032 

E (GPa) 200 200 
ν 0.3 0.34 

ΔtDEM (s) 0.000001 
ΔtCFD (s) 0.0001 

ρp (kg/m
3) 2380 

ρg (kg/m
3) 1.22 

T.I. 0.06 
μg (Pa.s) 1.7894×10

-5 
U (m/s) 1.58 

tf (s) 5 

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Both CFD and CFD-DEM simulations were performed on seven CPUs (3.30 GHz). Required simulation time 
for CFD and CFD-DEM simulations were approximately 92 and 31 h. Both CFD and CFD-DEM models 
demonstrate some benefits and limitations during simulation which are discussed here. Both models are 
dependent on the mesh size, consequently performing a sensitivity analysis on the effect of mesh size is 
inevitable. As mentioned earlier required simulation time for the CFD-DEM simulation was considerably 
(approximately one third) less than CFD for this case. The required simulation time increases exponentially 
with the number of particles in the bed (Norouzi et al., 2016). In cases with low number of particles (similar to 
the case study in this research) CFD-DEM simulations are more computationally efficient. As the number of 
particles increases, required simulation time for CFD simulations become less than CFD-DEM. Additionally, 
input parameters of CFD-DEM simulations are more than CFD, which means more accurate information about 
the particle and bed properties should be known for a CFD-DEM simulation. However the accuracy of CFD-
DEM simulation is significantly higher than CFD which will be discussed in details. Moreover, some post-
simulation analysis can be performed only in CFD-DEM simulations such as calculation of solids circulation 
time and rate using the method used by Golshan et al. (2016). 
 

  

Figure 2: Axial distributions of (a) the axial component of particle velocity and (b) solids hold-up at the center 

of the spout (r = 0) in CFD and CFD-DEM simulations.  

  

  

Figure 3: Radial distributions of particle velocity at (a) z = 3.04 cm, (b) z = 4.56 cm, (c) z = 6.08 cm and (d) z = 

9.12 cm in CFD and CFD-DEM simulations. 

At t = 0 s, gas was inserted to the bed and opened its way to the bed surface. By reaching to the bed surface 
the spout region was observable in the bed. Particles which were initially located on the gas way, were 

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entrained with the gas to the surface. The gas jet scattered the particles over the annulus and stable spouting 
began.  
Axial distributions of the axial component of the particle velocity and solids hold-up for CFD and CFD-DEM 
simulations are illustrated in Figure 2. It can be observed that the axial distribution of particles velocity consist 
of three distinct increasing-constant-decreasing parts. Particles accelerate at lower heights due to high gas 
velocity. As the height increases, particles reach the maximum velocity (constant part in Figure 2a) and 
decelerate afterwards. CFD-DEM simulation predicts the mentioned trend (experimental trend) with high 
accuracy, however CFD results underestimate experimental results. The solids hold-up distribution results are 
also compared for CFD and CFD-DEM simulations with experiments. A similar increasing-constant-decreasing 
trend is also observed for the hold-up distribution. It should be mentioned that CFD-DEM simulations have 
better prediction of experimental results comparing to CFD simulations. Figure 3 shows radial distribution of 
the axial component of particle velocity at four heights (z = 3.04, 4.56, 6.08 and 9.12 cm). A decreasing-
constant trend is observed for the radial distributions. As the height increases, the accuracy of simulation 
decreases. It also can be observed that CFD-DEM simulation illustrate better predictions of experimental 
results similarly.  

4. Conclusions 

CFD (two fluid model) and CFD-DEM simulations of a slot-rectangular spouted bed were performed and 
compared with available experimental results. Axial distributions of axial component of particle velocity and 
solids hold-up and radial distributions of particle velocity at four heights were found and compared with 
experimental data. It was reported that both CFD and CFD-DEM could successfully predict the increasing-
constant-decreasing trends of axial velocity and hold-up distributions as well as decreasing-constant trends of 
radial particle velocity at all four heights. Results also show that CFD-DEM provides more accurate results 
comparing with CFD simulation. Required simulation time for CFD and CFD-DEM simulations were 
approximately 92 and 31 h, respectively For cases with low numbers of particles (such as case study in this 
research) CFD-DEM requires less time comparing to CFD. However as the number of particles increases in a 
system, the required time for CFD-DEM simulation increases exponentially and CFD becomes the efficient 
model. Other limitations, benefits and drawbacks of each model are discussed in this research.  

Nomenclature 

CD = drag coefficient, dimensionless 
dp =  diameter of particles, mm 
E =  Young’s modulus, Pa 
e =  coefficient of restitution, dimensionless 
Fij

N
 =  normal force, N 

Fij
T =  tangential force, N 

G =  shear modulus, Pa 
g =  gravity acceleration, m/s2 
Hs = static bed height, mm 
I =  moment of inertia, kg.m2 
Mij

T =  tangential torque, N.m 
Mij

r =  rolling friction torque, N.m 
m =  mass of particle, kg 
nij =  normal vector, dimensionless 
P = pressure, Pa 
Reff = effective diameter, m 
Rep = particle Reynolds number, dimensionless  
T.I.= turbulent intensity, dimensionless 
tij =  tangential vector, dimensionless 
U= minimum spouting velocity, m/s 
u =  gas velocity, m/s 
vp =  velocity of particle, m/s 
z = height, cm 

 
Greek letters: 

αg = gas volume fraction, dimensionless  

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αp = particle volume fraction, dimensionless  
β = gas/solid momentum exchange coefficient, kg/m3s 
ΔtCFD = CFD time step, s 
ΔtDEM = DEM time step, s 
δ =  overlap of particles, m 
ε =  voidage, dimensionless 
η̃n =  damping coefficient, kg/s.m

0.25 
μ =  friction coefficient, dimensionless 
μg = gas viscosity, Pa.s 
μr =  rolling friction factor, dimensionless 
ν =  Poisson’s ratio, dimensionless 
νrN =  relative velocity of particle in normal direction, m/s 
ρp =  density of particles, kg/m

3 
ρg = density of gas, kg/m

3 
φgs = switch function in the Gidaspow model, dimensionless  
ω =  angular velocity of particle, rad/s 

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