Vol. 13(2), pp.

10-22, July-December, 2022

DOI: 10.5897/JCEMS2021.0364
Article Number: DCA2C3F70078
ISSN: 2141-6605
Copyright ©2022 Journal of Chemical Engineering and Materials
Author(s) retain the copyright of this article
http://www.academicjournals.org/JCEMS
Science

Full Length Research Paper

Computational fluid dynamics (CFD) simulation of a

gas-solid fluidized bed: Residence time validation study
Baru Debtera
Chemical Engineering Department, College of Biological and Chemical Engineering,
Addis Ababa Science and Technology University, P. O. Box NO16417, Addis Ababa, Ethiopia.
Received 19 August, 2021; Accepted 8 March, 2022

In this work, the business Computational Fluid Dynamics (CFD) is used for the numerical simulations of
an air-solid fluidized bed container in the solid phase involving a multi-fluid Eulerian multiphase model
and the Kinetic Theory of Granular Flow (KTGF). The height of the fluidized bed setup is 1.5 m while its
diameter is 0.2 m. With it, a series of experimentations were obtained using Helium tracer to determine
the Residence Time Distribution (RTD) at various normalized velocities, that is, mixing of air-solids at
different degrees. 2 and 3 dimensions of the fluidized bed container are simulated. The main purpose of
this study is to understand the hydrodynamic behavior of air-solid fluidized bed container through a
framework of Eulerian multiphase model and to analyze the hydrodynamic behavior of the air-solids
mixing. As a first approach, the CFD model is validated using the experimental results of the residence
time study. The numerical results of RTD corresponded well with the experimental findings. This shows
that the CFD modeling might be used to indicate the performance of a fluidized bed reactor.

Key words: Computational fluid dynamics, fluidized bed, residence time distribution (RTD), gas-solids mixing,
turbulence.

INTRODUCTION

Fluidization is the process whereby dense particles mass transfer between phases. They provide efficient
change into a fluid-like state over suspension in fluid. mixing, which results in excellent gas-solid contact and
Fluidization entails delivering a flow of gas through a bed relatively uniform temperature/concentration profiles
of granular substance at an adequate velocity, with the within the bed (Cui and Grace, 2007; Gidaspow, 1994).
granulated bed being liquefied (Gidaspow, 1994; Indeed, the need for cleaner and sustainable energy
Richardson et al., 2008). Fluidized beds are common source has led to the development of biomass gasifiers
equipment in the industry and are used for catalytic which employ fluidized bed technology. It is a hopeful
reactions, increasing of size, element covering methods, tactic that specifies quick biomass central heating,
heating system/chilling, drying, and mixing (Kunii and effective heat, mass transfer and uniform reaction
Levenspiel, 1991). Gas-solid fluidized beds are temperature (Salaices et al., 2012). Understandably, the
advantageous in many processes involving heat and/or physics behind fluidization indicates theimportance of

E-mail: baru.debtera@aastu.edu.et.

Author(s) agree that this article remain permanently open access under the terms of the Creative Commons Attribution
License 4.0 International License
 Debtera 11

variable quantity such as pressure changes, minimum outlet (Lopez-Isunza, 1975). Using CFD, the flow of inert
fluidization velocity, solid volume fraction profile, and tracer units is determined using species transport
particle velocity profile (Benzarti et al., 2012; Taghipour et equation, where the diffusion coefficient of elements, that
al., 2005). Usually, fluidized bed reactors are chaotic in is, the necessary parameter indicating particle diffusion
nature (Li et al., 2009). This is indicated by a turbulent capacity is investigated (Hua et al., 2014). Typically, a
fluidized bed. In addition, a fluidized bed is an CFD study should be conducted on a pilot scale fluidized
intermediate that takes place in a chemical reaction bed, and numerical methods are used as prototypes of
involving gas and solid. The fluidized bed is mainly the experimental arrangements and to confirm the
selected for the mixture of solid catalyzed gas segment experimental outcomes. The main goal of this effort is to
reactions because it can regulate the temperature of the use the CFD program available in ANSYS FLUENT
reaction zone well, and the situations in fluidized bed application to simulate the hydrodynamic performance of
reactors are approximately isothermal. a fluidized bed. A first approach of the full-fledged CFD
Nowadays, Computational Fluid Dynamics (CFD) is a model is important to prove the modeling through the
powerful device used for the complex phenomena investigational results presented. Due to the availability of
amongst air and solid element segments in the fluidized residence time data, the CFD model is first validated with
bed. CFD can be used to solve Navier-Stokes equations the RTD information obtained experimentally. The
and has become a helpful device for investigating and present study is divided into two main: validation of the
developing different flow systems. Computational two- and three-dimensions simulation of gas-solid
properties have improved substantially with sharp fluidized bed with the RTD data and a subsequent study
declining expenses, allowing the acquisition of detailed to identify the flow patterns of fluid-solid flow in the
computational information about reactions and flows at a turbulent fluidized bed reactor. The numerically predicted
fraction of the cost of the corresponding experiments RTD outcomes are associated through the experimental
(Dutta et al., 2010). It is possible to define a results of Lopez-Isunza (1975). The target is to make a
computational domain in which the geometry of the meaningful comparison between the predictions of the
fluidized bed reactor can be incorporated and CFD RTD at three different airflow rates that give the
approach can be used to solve the governing Navier- normalized velocity (U0 / U mf  9.5;8.0 and 6.4) . Note
Stokes equations, using appropriate initial and boundary
conditions. The results obtained from the numerical that the minimum fluidization velocity is 0.634 cm/s.
model can then be compared to experimental data for a
necessary validation. Since computational assets have
expanded significantly at forcefully diminishing costs, COMPUTATIONAL FLUID DYNAMICS (CFD) MODEL
specified computational data about the flow can, these
days, be acquired even with cheap experiments (Xia and Geometry and mesh
Sun, 2002). The transient CFD simulations are performed
to suggest the usability of the multiphase approach for For the CFD simulations, initial mesh needs to be
the prediction of the solid phase mixing and residence created. This mesh creates a geometry in which the
time distribution in the riser (Andreux et al., 2008). calculations occur and furthermore is divided into several
Transient solution is always necessary because of the volumes according to the finite-volume methodology.
unsteady state nature of the fluidized bed. CFD is useful These calculations are governed by the so-called
in understanding the quantitative hydrodynamics of Reynold’s averaged Navier-Stokes (RANS) equations.
fluidization and is needed for the design and scale-up of Dimensions of the fluidized bed reactor (1.5 m height and
efficient reactors in several processes industries. a radius of 0.1 m) are simulated. The particle diameter
The systematic method used to estimate the used in the gas-solid fluidized bed is between 175 and
performance of a supplier and inclusive mixing actions of 200 µm and falls in the Geldart group B particles
a fluidized bed entails quantifying and examining the (Geldart, 1973). The geometry is made in both 2D and
residence time distribution (RTD) of the solid segment 3D. The mesh consists of 12357 elements in 2D and
(Pant et al., 2014). The gas mixing in circular fluidized 35616 elements in 3D, respectively. The mesh of the
bed risers is evaluated as an overall behavior. The total fluidized bed is as shown in Figure 1 as 2D and 3D.
mixing conduct is considered by determining the set time As shown in Figure 1, the initial bed height is fixed at
delivery of a gas tracer inserted at the feed inlet. The 0.5 m. The solid particles can be seen over the distributor
knowledge of RTD function is very important for the plate. The gas inlet is at the bottom and the gas outlet is
optimization of the operating parameters and equipment at the upper part. A tracer monitoring point is also at the
configuration (Idakiev and Morl, 2013). The tracer is top outlet.
introduced at the inlet and monitored at the outlet of the
column. The concentration of tracer is introduced as a
pulse into a fluidized bed column at the feed inlet. Then, Gas-solid model
the samples are collected at the exit at fixed time
intervals until tracer concentration goes to zero at the For solutions in finite volume, an arrangement of balance
12 J. Chem. Eng. Mater. Sci.

Figure 1. Mesh of the geometry of the fluidized bed reactor, as 2D

and 3D, respectively.

equations is numerically solved for fluid flow over a 

number of control volumes, that is, over the so-called ( g  g  .( g  g v)  0
t (2)
mesh cells. These balanced equations, calculated via the 
RANS approach for the conservation of mass, ( s  s  .( s  s v)  0
t
momentum and energy were used for CFD simulations.
These equations are already implemented in the CFD
software ANSYS Fluent® version 16.2. The CFD
Conservation of momentum
replication of the bed hydrodynamics is founded on the
perception of Eulerian-Eulerian different phase flow
The momentum equation for the gas (g) phase is given
prototypical incorporated in the kinetic theory of granular
as follows:
flow (KTGF) (Gidaspow et al., 2004; Tartan and
Gidaspow, 2004). This engineering method invented

since the theory for non-ideal dense gases was ( g  g vg )  .( g  g vg vg )   gp   g   g  g g  K gs (vg  vs )
developed by Chapman and Cowling (1970) is used for t
nearby solid segment calculations. A brief explanation of (3)
the underlying theory related to KTGF is subsequently
Momentum equation for solid phase:
discussed.

( s  svs)  .( s  svsvs)   sp  ps   s   s  s g  K gs (vg  vs)
Conservations of mass t
(4)
The sum of volume fraction for gas and solid phases
must be equal to unity:
Gas phase shear stress tensor,  g   g  g (vg  vTg ) (5)
g s  1 (1)
Solid phase shear stress tensor,
where a subscript g and s stand for gas and solid phases.
The continuity equation for a gas phase and a solid 2
 s   s  s (vs  vsT )   s ( s   s )vs. (6)
phase are expressed as follows: 3
 Debtera 13

The solid phase stress tensor consists of a shear Drag function (Gidaspow model, 1994):
viscosity and a bulk viscosity; it arises from solid particle
momentum exchange due to kinetics and collision. A  s g  gg
frictional viscosity is considered for viscous-plastic Kgs  150CD (1   g )  1.75 vg  vs for
translation. It occurs when a solid phase reaches the  gdp 2.
dp
maximum volume fraction. The sum of collisional, kinetic  g  0.8 (14)
and frictional viscosities gives the solids shear viscosity
(  s   s , col   s , kin   s , fr ). when  g  0.8 , Gidaspow drag model becomes Wen-Yu
Solid collision viscosity (Syamlal et al., 1993): model.

4
 s , col   s  sdpgo, ss(1  ess)()1/2 (7) CD 
24
1  (0.15 g Re s )0.687 
 g Re s 
s
5
Solid kinetic viscosity (Syamlal et al., 1993): and

 s  sdp  2 
 s , kin  s 1   sgo, ss(1  ess)(3ess  1)  (8)
Re s   g
dp
vg  vs .
6(3  ess)  5 
g
Solid frictional viscosity (Schaeffer, 1987):
The coarse temperature is calculated by changeable
kinetic energy equivalence for the particles, following the
ps
 s, fr  sin  (9) Kinetic Theory of Granular Flow (KTGF) belief. To require
2 2D co×llisional energy dissipation, 𝛾s, outstanding to inelastic
collisions of elements and the granular conductivity, Ks,
where φ is the angle of internal friction. the equation is given as:
Solid bulk viscosity (Lun et al., 1984):
3
   s  s   s  s   : V s    Ks   s  (15)
4
 s   s  sdpgo, ss (1  ess )( )1/2 (10) 2  t 
3  s
1
Solid pressure is implemented according to   Vs 2 is the granular temperature.
3
ps   s  ss  2 sgo, ss(1  ess) s2 s (11) A list of sub-models used for the CFD model and their
values are shown in Table 1. To simulate these equations
Radial distribution function is implemented according to inside the fluidized bed, various boundary conditions are
required. The simulations in this study are done using
1 gas phase (air) with density of 1.225 kg/m3 and viscosity
  1/3 
go , ss  1  ( ) (12) of 1.785×10-5 Pa s and solid phase with particle diameter
  s , max  s between 175 and 200 µm, and density of 2400 kg/m3. For
tracer gas (Helium), the density and viscosity are 0.165
where the restitution coefficient for particle-particle kg/m3 and 2.0×10-5 Pa s, respectively.
impacts, 𝒆ss is static at 0.9 for all the simulations in the
present work. This value is taken from literature studies
(Balakin et al., 2012; Hu et al., 2010) on glass and Gas-solid mixing studies
polymer elements (in this study polymeric silica gel is
used). Gas-solid fluidization is divided into several regimes
Wen-Yu and Gidaspow drag models are used for the depending on gas speed. In this study, the gas rate used
momentum conversation coefficient. The Gidaspow effort falls within the bubble fluidized bed regime, that is, the
model equation is a mixture of Wen-Yu and Ergun range of Reynold number (Re) between 0.2 and 1000. Air
equations. bubbles increase in the fluidized bed; there is continuous
Drag function transference of gas to the solid phase by diffusion and
convection modes. The gas that enters the fluidized bed
3  g s  g passes through the granular particles in the column. The
Kgs  CD vg  vs (13) bubble pushes through the bed of the solid particles and
4 dp g 2.65 stops at the top. Accordingly, the bubble is like the cloud
14 J. Chem. Eng. Mater. Sci.

Table 1. Summary of the numerically simulation boundary conditions and model parameters.

Descriptions Sub-model
Granular viscosity
Granular bulk viscosity Lun et al. (2009)
Frictional viscosity
Granular temperature KTGF
Drag law Gidaspow (1994)
Inlet boundary condition Velocity inlet
Outlet boundary condition Pressure outlet
Wall boundary condition No slip for air

Parameter Values
Bed height 0.5 m
Volume fraction of solid phase 0.577
Operating pressure 101325 Pa
Gas inlet velocity (0.065, 0.051 and 0.041) m/s
Turbulent kinetic energy 0.30554 m2/s2
Turbulent dissipation rate 0.30553 m2/s3
Angle of internal friction 30°
Particle-particle restitution coefficient 0.9
Specularity coefficient for solid phase 0.001

of dense segment, in which the gas is continuously umf  D1/ 2 g 1/ 4 

transferred by convection inside the bubble. In the cloud, kbc  4.5  5.85  5/ 4  from bubble to cloud
the contact between solid and gas takes residence. This
Db  Db 
implies that air exists in the cloud, which flows back to the
bubble again. Part of it might be exchanged with the solid (18)
phase by diffusion or adsorption with the solid that is
exchanged with the emulsion phase. Convection and
  mf ub De 
1/2

diffusion mechanisms of exchange occur simultaneously. kce  6.78  3  from cloud to emulsion (19)
The gas exchange among bubble and suspension  Db 
phases has been described in terms of mass transfer
coefficient by Kunii and Levenspiel (1991): They defined the overall gas transfer coefficient of the
bubble phase and emulsion phase as follows:
1 dNA
 k  CAb  CAe  (16)
intrfacial area dt kbc kce
kb  (20)
where k is mass transfer coefficient (cm/s). Interchange kbc  kce
rate is defined as,
From the thorough information regarding the method of
1 dNA
 k  CAb  CAe  (17) fluid (gas) in the cloud, it can carefully be expected that
volume dt the gas structure in the cloud is roughly uniform. Chiba
and Kobayashi (1970) used the analysis of Murray for the
where k is mass transfer coefficient (s-1). flow pattern around the spherical bubble to obtain the
Kunii and Levenspiel (1991) expected two transference following expressions for the interchange coefficient:
steps, namely the transfer among bubble void and cloud
particles intersection area and that between the cloud 6.78  D mf ub 
particles intersection area and the emulsion phase. They kb    (21)
also presumed that the mass transfer quantity of bubble-
1   g  Db 3 
cloud and cloud-emulsion is given as in terms of gas
transfer quantity per unit volume of bubble void. Finally, Kobayashi et al. (1967) determined the rate of
 Debtera 15

 t
 
  i   .  vYi  .Yi   Di , m   .
exchange by measuring the RTD in a fluidized bed. They
concluded that the interchange parameter could be (26)
expressed as: t  Sct 
During the simulation, diffusion at the inlet is important
11
kb  . (22) because the pressure-based solver calculating the net
Db exchanges of species at the inlets involves both
convection and diffusion elements and compounds. That
Equation 23 indicates that there is no effect of the means the convection constituent is made static by the
diffusion coefficient of the transferring species, nor any quantified inlet species mass fraction, while the diffusion
direct effect of the fluid mechanical phenomen. However, factor depends on the difference of the calculated
in this study, Gidaspow and Wen-Yu gas-solid species’ amount (which is not known priori).
interchange coefficients are used to observe the conduct
of the hydrodynamics in a fluidized bed. Turbulent modeling

In various industrial processes related to fluidization,

Species transport model turbulence behavior is observed. k -ε model is the
commonly used engineering turbulent classical for
Species transport equation is used for the residence time industrial applications; it is robust and reasonable
distribution (RTD) study. The conservation equation for accurate.
the species predicts the residence mass portion of each In this study, a standard k- ε model is used to calculate
species, Yi, through the solution of a convection and the transportation equation for turbulent kinetic energy (k)
diffusion equation from ith species. The general and dissipation rate of the turbulent kinetic energy (ε).
conservation equation is given as follows: The k-ε model is given as follows:


t, m
t
 
  i   .  vYi   Ji  Ri  Si (23) .(  mkvm)  .(

k )  Gk , m   m (27)

t, m 
.(  mkvm)  .( k )  (c1 Gk , m  c 2 m ) (28)
where 𝜌i is density of species i, is velocity vector, is  k
diffusion change of species i, Ri is the net rate of creation
of species by chemical reaction and Si is the rate of where is turbulent (eddy) viscosity computed from k
creation by accumulation from the dispersed phase. In
k2
– ε, (  t , m   mC 
this situation, chemical reaction is not considered;
)
therefore Ri and Si are ignored and Equation 24 is 
reduced to:
where C =0.09, C𝒆1=1.44, C𝒆2=1.92,  =1 and Gk, m is

t
 
  i   .  vYi   Ji  0 (24)
classical of turbulent kinetic energy due to velocity
difference.

where the diffusion flux of the species for turbulent flow is Residence time distribution (RTD)
calculated by Fick’s law and CFD uses the dilute estimate
of Fick’s law for prototypical mass diffusion due to the Residence time distribution (RTD) study is significant to
concentration difference and temperature. The diffusion describe the mixing and flow rate patterns of the inner
flux might be given as follows: apparatus, and to determine whether the unit would be
an ideal apparatus in the future, that is, tubular reactor or
 t  T mixed flow reactor. Besides, RTD is used to prototype the
Ji  .Yi   Di , m    Dti (25) reactor as a mixture of ideal reactors. Residence time
 Sct  T
distribution data values are used to investigate any non-
idealities similar to directing, by transient and quick
i circuiting existing in the reactor (Levenspiel, 1999). It can
where Sct is the turbulent Schmidt number Sct  also be used to measure up or to project a reactor once
 Dt the kinetics is attained. To accomplish RTD replications,
while the temperature gradient is negligible and combines the transient examination of a tracer is measured with the
Equations 25 and 26 form given as: same physical properties as that of incessant phase. The
16 J. Chem. Eng. Mater. Sci.

transportation calculation for the mass flow rate of a modeling. Notwithstanding, tactically estimate of initial
turbulent flow can be written thus: conditions confirms the meeting of the solution. They are
two kinds of initial conditions: solids volume fraction in the
    t
 
  mYtr    mvmYtr  [ Ytr   Di, m  ]
bed and Y-velocity of the air phase in the fluidized bed.
t xj xj xj  Sct  The solid capacity fractions in the freeboard are initially
set to zero (assuming only gas). The Y-velocity of the gas
(29) phase in the fluidized bed is computed completely with a
steady state volumetric fluxes balance in which the flow
where  t is a turbulent viscosity and is given rate going to the fluidized bed segment is linked to the
k2 volume flow rate leaving the fluidized bed segment
as  t   mC  , and Ytr is mass fraction of tracer (consisting of both solids and gas phase):

species. vin uin  vg ug (30)

Numerical procedure for hydrodynamics vin uin

ug  (31)
Mathematical method vg
ANSYS Fluent answers the main integral equations for The situations represent that the superficial velocity of the
mass conservation, conservation of momentum, kinetic gas is a proportion of the bed volume to the feed inlet
theory of granular flow and turbulent simultaneously. This volume which is identical with the void fraction:
technique is used for finite volume approach for flow
arrangements. uin
ug  (32)
g
Pressure based problem solver method
Boundary conditions: At the inlet of the fluidized bed,
Pressure-based calculation employs phase momentum there is gas superficial velocity for primary phase, while
equations, collective pressure, and calculations of phase the secondary phase is zero inlet velocity. At the outlet of
volume fractions in a separate way. The phase uses an the fluidized bed there is atmospheric pressure. No slip,
implicit technique for pressure connected equations (PC- wall boundary condition is applied to the gas phase, while
SIMPLE). An extension of the SIMPLE system is the partial slip condition is applied to the solid phase. A
established for polyphase flows. This consists of specularity coefficient (ϕ = 0.001) for a partial slip model
modifying the pressure and velocity which are functional is used based on the suggestion of Shi et al. (2015).
to improve the limitation of the volume continuously.

PROBLEM DESCRIPTION AND CFD METHOD

Three or two dimensions discretization
Problem identifications
Finite volume system used to conduct complex
geometries is functional. The differentiation of the Figure 1 is the conceptual representation of the fluidized bed that is
modelled and simulated using software. This figure characterizes a
convective rate is first order exposed. Under transient cylindrical container, that is, the gas-solid fluidization bed with
formulation, the restricted second order implicit is used; superficial air velocity inlet at the bottom of the column. The solid
this preparation would offer well stability, for time particles are patched with  s =0.577 at the initial bed height (ho) =
discretization to continuously confirm the bound 0.5 m. The fluidizing gas causes the gas-solids mixing. The
variables. The bounded second order implicit is a better gravitational effect on the particles bed is taken into account as the
option for the fluidized bed to obtain stability and accurate bed is vertical.
results. A first order implicit transient design by means of
the phase-Couple SIMPLE method is used to calculate Simulation procedure
the equations for both 2-dimensional and 3-dimensional
cases. The assumption of the tracer does not involve any chemical
reaction with the reactants to produce any product. The
smallamount of tracer component has the same physical properties
with the working fluid. That means the flow rate is not troubled
Initial values and boundary values conditions
inside the reactor after the tracer is presented. This assumption is
used in many literature studies (Hua et al., 2014; Shilapuram et al.,
The initial condition might not influence the stable state 2011). The RTD analysis such as mean residence time, change,
solutions that may be favorable for the fluidized bed and leaving age distribution can be done.
 Debtera 17

0.6

Wen-Yu model
0.5
Gidaspow model

0.4
Particle velocity(m/s)
0.3

0.2

0.1

0.0
-0.10 -0.05 0.00 0.05 0.10
Radial position(m)

Figure 2. Time-averaged (10 s) simulation of solid particles (a) axial velocity along
the radial height of 0.3 m and (b) velocity contour.

The tracer gas injection method involves: (5) Then, the mass density of the tracer is time monitored when
leaving the fluidized bed.
(1) Firstly, run the steady state simulations for the flow rate and
turbulence as shown in Table 1, for physical properties and
boundary conditions. It may be noted that the residuals of the RESULTS AND DISCUSSION

continuity, momentum, k-turbulent kinetic, - dissipation rate kinetic
energy reduce in reaching steady state conditions. CFD reproductions of the fluidized bed are obtained by
(2) After it is achieved, it converges for the steady state simulation; RTD validation study done by comparing the results with
the mass fraction of the tracer is made to 1 and the other equations the experimental study done by Lopez-Isunza (1975).
are disabled. The tracer carries the properties of Helium gas, as
mentioned in the experimental setup (Lopez-Isunza, 1975).
(3) Now the unsteady state equation for the tracer (Equation 29) is
used for one iteration to imitate the Pulse method after which the Gas-solid hydrodynamics
mass fraction of the tracer is changed to 0.
(4) The flow equations (conservation of mass, conservation of Hydrodynamic characterization of gas-solid fluidized bed

momentum, k-turbulent kinetic, - dissipation rate kinetic energy simulated by CFD in 2D with the drag equations of
species transport and tracer gas) are solved. Gidaspow and Wen-Yu is done. Figure 2 represents the
18 J. Chem. Eng. Mater. Sci.

Figure 3. Time-averaged (10 s) simulation of solid particle volume fraction (a) that changed
lengthways to center alliance of the fluidized bed and (b) contour in the fluidized bed.

time used for the solids velocity profile in the radial path equation is a modified form of Wen-Yu (and Ergun) drag
at 0.3 m. The motoring height is chosen arbitrarily but equations as explained earlier.
care is taken to ensure that it is below the top elevation of Figure 3 illustrates the time-averaged solid capacity
the fluidized bed. This is done to ensure that the gas- fraction variation along the center of the fluidized bed. It
solids mixing behavior is certainly investigated. It can be shows the extreme solids volume fraction model equation
seen that the simulation results using Gidaspow and of Wen-Yu (  s = 0.63) compared to the model of
Wen-Yu gas-solid drag models are slightly different from Gidaspow (  s = 0.59).
each other. The solids axial velocity fluctuations along the This specifies the Wen-Yu model equation promotes
radial position are larger in Wen-Yu model than in solids clustering as compared to the Gidaspow model. It
Gidaspow model. Experimental studies (Li et al., 2009; is probably due to the huge gas velocity escaping along
Loha et al., 2012) indicate that the variation in solids the walls thereby pushing the solid particle together and
velocity is similar to that exhibited by Gidaspow drag forming cluster. Figure 4 indicates the profile of time-
model. This indicates that the Gidaspow model could be averaged solid volume fraction outlined in the radial
more accurate in predicting the gas-solid solid position at height of 0.4 m by Gidaspow and Wen-Yu
hydrodynamics in this study. Moreover, Gidaspow drag drag models.
 Debtera 19

Figure 4. Time-averaged (10 s) simulation of solid (a) volume fraction change

along the circular position at 0.4 m of column height and (b) particle volume
fraction contour in the fluidized column.

The solids volume fraction shows even distribution along the simulation of set time delivered (RTD) is implemented
the radial direction for both models, while Wen-Yu model for the fluidized bed in 2D and 3D, respectively. In the
indicates comparatively larger variation of solids volume RTD study, helium gas is considered as tracer gas. The
fraction along the radial direction as compared to concentration of the gas is measured when it is leaving,
Gidaspow model. To conclude from the aforementioned and the residence time predictions are given as
three figures, Gidaspow model seems to be preferable to
We-Yu model as it indicates less variation along the Mean time distribution: t   c t t
i i i
(33)
radial and axial direction in gas and solid velocity. Also,  c t i i

literature studies (Sahoo and Sahoo, 2015; Loha et al.,

2012; Hooyar et al., 2012) appreciate Gidaspow model Exit time distribution: E  t   c t  (34)
for evaluation with investigational data. It must also be  c t i i
noted that the Gidaspow model is a modification of Ergun
and Wen-Yu models. Three cases with air velocities ranging from 6.4 to 9.5
times the minimum fluidization velocity are simulated in
this presented work. That means they are indicated as
Residence time distribution (RTD) validation ratio of U 0 / U mf which is 0.634 cm/s. In all the three

The species transport model in ANSYS Fluent® used for cases (U0 / U mf  9.5;8.0 and 6.4) , both the 2D and
20 J. Chem. Eng. Mater. Sci.

500

Normalized Concentration E(t).

400

3D CFD Result
2D CFD Result
300 Experimental data
Predicted by Prof.Felipe

200

100

0
0 20 40 60 80 100
Time (s)

Figure 5. Experimental and predicted RTD response of the fluidized bed

under normalized velocity conditions (U 0 / U mf  9.5) .

400
Normalized Concentration E(t)

300
3D CFD result
2D CFD result
Pred. by prof. Felipe
Experimental data
200

100

0
0 20 40 60 80 100 120
Time (s)

Figure 6. Experimental and predicted RTD response of the fluidized bed

under normalized velocity conditions (U 0 / U mf  8.0) .

3D simulation results are in line with the experimental The validation of residence time distribution studies
data (Figures 5 to 7, respectively) especially at lower seems to be in line with the experimental study of Lopez-
simulation times; while it seems to over-predict the Isunza (1975) for the three different velocity conditions
experimental data as the simulation time proceeds in the investigated (Figures 5 to 7). The theoretical mean
end. This is probably because of the numerical residence time of the air in column is predicated in Kunii
discrepancies associated with the CFD model while  g hg
obtaining the final tracer concentration at the outlet. and Levenspiel (1991) as t  . The results are
However, the peaks from the experimental data fit well U0
with the numerical model, although the peaks from the summarized in Table 2 for an initial solids bed height of
2D simulations are slightly lower than the peaks from the 0.5 m.
3D simualtions. This is probably because in 3D, tracer
For U 0 / U mf  9.5 , the average residence time is the
has enough space to pass through the fluidized bed.
 Debtera 21

400

350

Normalized Concentration E(t). 300

250 3D CFD result

2D CFD result
Pred.by prof.Felipe
200 Experimental data

150

100

50

0
0 20 40 60 80 100 120
Time (s)

Figure 7. Experimental and predicted RTD response of the fluidized bed under normalized
velocity conditions (U / U  6.4) .
0 mf

Table 2. Summary of the numerical outcomes of the mean residence time, compared with results from Lopez-Isunza (1975) and
Levenspiel (1999).

Mean residence time (s)

Fluidized bed (Lopez-Isunza, 1975) Theoretical mean CFD mean residence
Normalized residence time (s) time (s)
column height,
velocity
H (m) Experiment Predicted (Levenspiel, 1999)
2D 3D
1.5 9.5 19 14.05 20 22 24.13
1.5 8.0 23.297 18.796 25.490 25.3 28.8
1.5 6.4 25.402 22.320 31.707 29.5 33

fastest (compared to U 0 / U mf  6.4 which is the slowest), two models, Gidaspow model is recommended as it is
able to correctly capture the hydrodynamics inside the
which means that the mass transfer between the bubbles fluidized bed. The simulations results studied are time-
and emulsions phase is comparatively faster. averaged distributions of gas and solids velocity along
the axial and radial directions. The simulation results
related to residence time distribution (RTD) for three
Conclusion
different velocity rations (U0 / U mf  9.5;8.0 and 6.4) ,
The gas-solid hydrodynamics using computation fluid that is, at different degrees of gas-solids mixing, are
dynamics (CFD) is important to identify the rate behavior evaluated in both 2-D and 3-D. The results are similar
of the inner fluidized column. The CFD implemented in with the investigational data of Lopez-Isunza (1975).
this simulation work is a Eulerian-Eulerian multiphase However, further research is still needed to understand
flow fixed with the kinetic theory of granular flow and the mass transport among the bubble and emulsion
standard turbulence model used for closure. The two phases and connect them to the gas-solid
drag models, necessary for gas-solid interchange hydrodynamics. It is important to investigate the relation
coefficient, that is, the Gidaspow and Wen-Yu models, between the mass transport and the residence time
simulate the gas-solids mixing in the bed. Although there distribution, to have a meaningful fluidized column
is not much difference between the performance of these reactor.
22 J. Chem. Eng. Mater. Sci.

CONFLICT OF INTERESTS Lopez-Isunza F (1975). Determination of interchange parameter in

fluidized beds using pulse testing techniques. M.Eng Thesis,
McMaster University, Canada.
The author has not declared any conflict of interests. Pant HJ, Sharma VK, Goswami S, Samantray JS, Mohan IN, Naidu T
(2014). RTD in a pilot-scale gas–solid fluidized bed reactor using
radiotracer technique. Journal of Radioanalytical and Nuclear
REFERENCES Chemistry 302(3):1283-1288.
Richardson JF, Harker JH, Coulson JM, Richardson JF (2008). Particle
Andreux R, Petit G, Hemati M, Simonin O (2008). Hydrodynamic and technology and separation processes (5. ed.). Oxford: Butterworth
solid residence time distribution in a circulating fluidized bed: Heinemann.
Experimental and 3D computational study. Chemical Engineering and Sahoo P, Sahoo A (2015). A Comparative Study on Effect of Different
Processing: Process Intensification 47(3):463-473. Parameters of CFD Modeling for Gas–Solid Fluidized Bed.
Balakin B, Hoffmann AC, Kosinski P (2012). The collision efficiency in a Particulate Science and Technology 33(3):273-289.
shear flow. Chemical Engineering Science 68(1):305-312. Salaices E, de Lasa H, Serrano B (2012). Steam gasification of a
Benzarti S, Mhiri H, Bournot H (2012). Drag models for simulation gas- cellulose surrogate over a fluidizable Ni/α-alumina catalyst: A kinetic
solid flow in the bubbling fluidized bed of FCC particles. World model. AIChE Journal 58(5):1588-1599.
Academy of Science, Engineering and Technology 61:1138-1143. Schaeffer DG (1987). Instability in the evolution equations describing
Chapman S, Cowling TG (1970). The mathematical theory of non- incompressible granular flow. Journal of Differential Equations
uniform gases: an account of the kinetic theory of viscosity, thermal 66(1):19-50.
conduction and diffusion in gases. Cambridge University Press. Shi X, Sun R, LAN X, Liu F, Zhang Y, GAO J (2015). CPFD simulation
Chiba T, Kobayashi H (1970). Gas exchange between the bubble and of solids residence time and back mixing in CFB risers. Powder
emulsion phases in gas-solid fluidized beds. Chemical Engineering Technology 271:16-25.
science 25(9):1375-1385. Syamlal M, Rogers W, O'Brien TJ (1993). MFIX documentation.
Cui H, Grace JR (2007). Fluidization of biomass particles: A review of National Energy Technology Laboratory, Department of Energy,
experimental multiphase flow aspects. Chemical Engineering Science Technical Note No. DOE/MC31346-5824.
62(1-2):45-55. Taghipour F, Ellis N, Wong C (2005). Experimental and computational
Dutta A, Ekatpure RP, Heynderickx GJ, de Broqueville A, Marin GB study of gas–solid fluidized bed hydrodynamics. Chemical
(2010). Rotating fluidized bed with a static geometry: Guidelines for Engineering Science 60(24):6857-6867.
design and operating conditions. Chemical Engineering Science Tartan M, Gidaspow D (2004). Measurement of granular temperature
65(5):1678-1693. and stresses in risers. AIChE Journal 50(8):1760-1775.
Geldart D (1973). Types of gas fluidization. Powder Technology Wen CY, Yu YH (1966). Mechanics of Fluidization. Chemical
7(5):285-292. engineering progress symposium series 62:100-111.
Gidaspow D (1994). Multiphase flow and fluidization: continuum and Xia B. Sun DW (2002). Applications of computational fluid dynamics
kinetic theory descriptions. Boston: Academic Press. (CFD) in the food industry: a review. Computers and Electronics in
Gidaspow D, Jung J, Singh RK (2004). Hydrodynamics of fluidization Agriculture 34(1):5-24.
using kinetic theory: an emerging paradigm. Powder Technology
148(2-3):123-141.
Hu X, Zhang J, Dong C, Yang Y (2010). Simulation of Dense Gas-Solid
Fluidized Bed Based on Two-Fluid Model. In 2010 Asia-Pacific Power
and Energy Engineering Conference (pp. 1-4). IEEE.
Hua L, Wang J, Li J (2014). CFD simulation of solids residence time
distribution in a CFB riser. Chemical Engineering Science 117:264-
282.
Idakiev V, Morl L (2013). Study of Residence Time of Disperse
Materials in Continuously Operating Fluidized Bed Apparatus.
Journal of Chemical Technology and Metallurgy 48(5):451-456.
Kobayashi H, Arai F, Sunagawa T (1967). Kagaku Kogaku (Chemical
Engineering, Japan) 29:858.
Kunii D, Octave L (1991). Fluidization Engineering. 2. ed. Butterworth-
Heinemann Series in Chemical Engineering. Boston: Butterworth-
Heinemann.
Levenspiel O (1999). Chemical reaction engineering (3rd ed). New
York: Wiley.
Li P, Lan X, Xu C, Wang G, Lu C, Gao J (2009). Drag models for
simulating gas–solid flow in the turbulent fluidization of FCC particles.
Particuology 7(4):269-277.
Loha C, Chattopadhyay H, Chatterjee PK (2012). Assessment of drag
models in simulating bubbling fluidized bed hydrodynamics. Chemical
Engineering Science 75:400-407.