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Vol. 9, Issue 1; January - February 2024; 
ISSN: 2837-2964 
Impact Factor: 6.67 
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26 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

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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.  

 DOI: https://doi.org/10.5281/zenodo.10592547 

  

 

Abstract: 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.  

Keywords: Computational fluid dynamics, fluidized bed, residence time distribution (RTD), gas-solids mixing, 

turbulence. 

  

INTRODUCTION  

Fluidization is the process whereby dense particles change into a fluid-like state over suspension in fluid. 

Fluidization entails delivering a flow of gas through a bed of granular substance at an adequate velocity, with the 

granulated bed being liquefied (Gidaspow, 1994; Richardson et al., 2008). Fluidized beds are common equipment 

in the industry and are used for catalytic reactions, increasing of size, element covering methods, heating 

system/chilling, drying, and mixing (Kunii and Levenspiel, 1991). Gas-solid fluidized beds are advantageous in 

many processes involving heat and/or  

mass transfer between phases. They provide efficient mixing, which results in excellent gas-solid contact and 

relatively uniform temperature/concentration profiles within the bed (Cui and Grace, 2007; Gidaspow, 1994). 

Indeed, the need for cleaner and sustainable energy source has led to the development of biomass gasifiers which 

employ fluidized bed technology. It is a hopeful tactic that specifies quick biomass central heating, effective heat, 

mass transfer and uniform reaction temperature (Salaices et al., 2012). Understandably, the physics behind 

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 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 1; January - February 2024; 
ISSN: 2837-2964 
Impact Factor: 6.67 
1252 Columbia Rd NW, Washington DC, United States 
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fluidization indicates theimportance of variable quantity such as pressure changes, minimum fluidization velocity, 

solid volume fraction profile, and particle velocity profile (Benzarti et al., 2012; Taghipour et al., 2005). Usually, 

fluidized bed reactors are chaotic in nature (Li et al., 2009). This is indicated by a turbulent fluidized bed. In 

addition, a fluidized bed is an intermediate that takes place in a chemical reaction involving gas and solid. The 

fluidized bed is mainly selected for the mixture of solid catalyzed gas segment reactions because it can regulate 

the temperature of the reaction zone well, and the situations in fluidized bed reactors are approximately 

isothermal.     

Nowadays, Computational Fluid Dynamics (CFD) is a powerful device used for the complex phenomena amongst 

air and solid element segments in the fluidized bed. CFD can be used to solve Navier-Stokes equations and has 

become a helpful device for investigating and developing different flow systems. Computational properties have 

improved substantially with sharp declining expenses, allowing the acquisition of detailed computational 

information about reactions and flows at a fraction of the cost of the corresponding experiments (Dutta et al., 

2010). It is possible to define a computational domain in which the geometry of the fluidized bed reactor can be 

incorporated and CFD approach can be used to solve the governing NavierStokes equations, using appropriate 

initial and boundary conditions. The results obtained from the numerical model can then be compared to 

experimental data for a necessary validation. Since computational assets have expanded significantly at forcefully 

diminishing costs, specified computational data about the flow can, these days, be acquired even with cheap 

experiments (Xia and Sun, 2002). The transient CFD simulations are performed to suggest the usability of the 

multiphase approach for the prediction of the solid phase mixing and residence time distribution in the riser 

(Andreux et al., 2008). Transient solution is always necessary because of the unsteady state nature of the fluidized 

bed. CFD is useful in understanding the quantitative hydrodynamics of fluidization and is needed for the design 

and scale-up of efficient reactors in several processes industries.   

The systematic method used to estimate the performance of a supplier and inclusive mixing actions of a fluidized 

bed entails quantifying and examining the residence time distribution (RTD) of the solid segment (Pant et al., 

2014).  The gas mixing in circular fluidized bed risers is evaluated as an overall behavior. The total mixing conduct 

is considered by determining the set time delivery of a gas tracer inserted at the feed inlet. The knowledge of RTD 

function is very important for the optimization of the operating parameters and equipment configuration (Idakiev 

and Morl, 2013). The tracer is 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, the samples are collected at 

the exit at fixed time intervals until tracer concentration goes to zero at the outlet (Lopez-Isunza, 1975). Using 

CFD, the flow of inert tracer units is determined using species transport equation, where the diffusion coefficient 

of elements, that is, the necessary parameter indicating particle diffusion capacity is investigated (Hua et al., 

2014). Typically, a CFD study should be conducted on a pilot scale fluidized bed, and numerical methods are 

used as prototypes of the experimental arrangements and to confirm the experimental outcomes. The main goal 

of this effort is to use the CFD program available in ANSYS FLUENT application to simulate the hydrodynamic 

performance of a fluidized bed. A first approach of the full-fledged CFD model is important to prove the modeling 

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 Academic Journal of Science, Engineering and Technology 

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through the investigational results presented. Due to the availability of residence time data, the CFD model is first 

validated with the RTD information obtained experimentally. The present study is divided into two main: 

validation of the two- and three-dimensions simulation of gas-solid fluidized bed with the RTD data and a 

subsequent study to identify the flow patterns of fluid-solid flow in the turbulent fluidized bed reactor.  The 

numerically predicted RTD outcomes are associated through the experimental results of Lopez-Isunza (1975). 

The target is to make a meaningful comparison between the predictions of the RTD at three different airflow rates 

that give the normalized velocity(U0 /Umf 9.5;8.0 and 6.4) . Note that the minimum fluidization velocity is 0.634 

cm/s. 

COMPUTATIONAL FLUID DYNAMICS (CFD) MODEL    

Geometry and mesh  

For the CFD simulations, initial mesh needs to be created. This mesh creates a geometry in which the calculations 

occur and furthermore is divided into several volumes according to the finite-volume methodology. These 

calculations are governed by the so-called  

Reynold’s averaged Navier-Stokes (RANS) equations. Dimensions of the fluidized bed reactor (1.5 m height and 

a radius of 0.1 m) are simulated. The particle diameter used in the gas-solid fluidized bed is between 175 and 200 

µm and falls in the Geldart group B particles (Geldart, 1973). The geometry is made in both 2D and 3D. The 

mesh consists of 12357 elements in 2D and 35616 elements in 3D, respectively. The mesh of the fluidized bed is 

as shown in Figure 1 as 2D and 3D.  

As shown in Figure 1, the initial bed height is fixed at 0.5 m. The solid particles can be seen over the distributor 

plate. The gas inlet is at the bottom and the gas outlet is at the upper part. A tracer monitoring point is also at the 

top outlet. 

Gas-solid model  

  
        

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

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 Academic Journal of Science, Engineering and Technology 

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2 

3  

For solutions in finite volume, an arrangement of balance and 3D, respectively.  

Equations is numerically solved for fluid flow over a number of control volumes, that is, over the so-called mesh 

cells. These balanced equations, calculated via the RANS approach for the conservation of mass, momentum and 

energy were used for CFD simulations. These equations are already implemented in the CFD software ANSYS 

Fluent® version 16.2. The CFD replication of the bed hydrodynamics is founded on the perception of Eulerian-

Eulerian different phase flow prototypical incorporated in the kinetic theory of granular flow (KTGF) (Gidaspow 

et al., 2004; Tartan and Gidaspow, 2004). This engineering method invented since the theory for non-ideal dense 

gases was developed by Chapman and Cowling (1970) is used for nearby solid segment calculations. A brief 

explanation of the underlying theory related to KTGF is subsequently discussed.   

Conservations of mass  

The sum of volume fraction for gas and solid phases must be equal to unity: 

g s 1                                                           (1)   

Where a subscript g and s stand for gas and solid phases.   

The continuity equation for a gas phase and a solid phase are expressed as follows:  

( g  g .( g 

t                                        (2)  

 

( s s .( s sv) 0 

t 

Conservation of momentum   

The momentum equation for the gas (g) phase is given as follows: 

 

t   ( g gvg) .( g gvgvg) g p g g gg Kgs (v g vs) 

                                                                                       (3) 

Momentum equation for solid phase: 

 

t   ( s svs) .( s svsvs) s p ps s s sg Kgs (v g vs) 

                                                                                       (4)   

  
Gas phase shear stress tensor, g g g( vg vT

g )   (5)               

Solid phase shear stress tensor,  

 
s s s( vs vs

T ) s( s s) vs.                    (6)  

The solid phase stress tensor consists of a shear viscosity and a bulk viscosity; it arises from solid particle 

momentum exchange due to kinetics and collision. A frictional viscosity is considered for viscous-plastic 

) 0 g v  

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translation. It occurs when a solid phase reaches the maximum volume fraction. The sum of collisional, kinetic 

and frictional viscosities gives the solids shear viscosity  

( s s, col s, kin s, fr ).  

Solid collision viscosity (Syamlal et al., 1993):  

s, col s sdgp o,   ss(1 ess)( )1
s
/2                           (7)  

Solid kinetic viscosity (Syamlal et al., 1993):  

6(3 s sedp)   1 2 sgo, ss(1 ess)(3ess 1)   (8)  

s, kin  s  5     

ss  

Solid frictional viscosity (Schaeffer, 1987):  

ps 

s, fr sin                                                      (9)  

2 2D 

  

where φ is the angle of internal friction.     Solid bulk viscosity (Lun et al., 1984):  

  

4   1/2                              (10) s s sdpgo,   ss(1 ess)( )s 

 

 
3  

  

Solid pressure is implemented according to   

  

ps s s s 2 sgo,   ss(1 ess) s
2 s                         (11)  

Radial distribution function is implemented according to   

  

1 

go,   ss 1 (
s, max )

1/3 
s                                            (12)  

 
Where the restitution coefficient for particle-particle impacts, ss 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 polymer 

elements (in this study polymeric silica gel is used).   

Wen-Yu and Gidaspow drag models are used for the momentum conversation coefficient. The Gidaspow effort 

model equation is a mixture of Wen-Yu and Ergun equations.   

Drag function  

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 Academic Journal of Science, Engineering and Technology 

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3 

Kgs 4CD dp g g s2.65
g vg vs                                       (13) Drag function (Gidaspow model, 1994):  

  

Kgs 150CD sd   2.g (1 g) 1.75 dg 
p   

g   vg vs for  

 

g p 

g 0.8                                                                    (14)  

  

when g 0.8 , Gidaspow drag model becomes Wen-Yu model.    

                   

24   0.687 

CD  Re   1 (0.15 g Res)  

 
g s   

and    

d p 

Re s g vg vs .  

g 

  

The coarse temperature is calculated by changeable kinetic energy equivalence for the particles, following the 

Kinetic Theory of Granular Flow (KTGF) belief. To require co×llisional energy dissipation, s, outstanding to 

inelastic collisions of elements and the granular conductivity, Ks, the equation is given as:  

 
3 t s s s s : Vs Ks s   (15)  

 
2  

Vs2  is the granular temperature.   

A list of sub-models used for the CFD model and their values are shown in Table 1. To simulate these equations 

inside the fluidized bed, various boundary conditions are required. The simulations in this study are done using 

gas phase (air) with density of 1.225 kg/m3 and viscosity of 1.785×10-5 Pa s and solid phase with particle diameter 

between 175 and 200 µm, and density of 2400 kg/m3. For tracer gas (Helium), the density and viscosity are 0.165 

kg/m3 and 2.0×10-5 Pa s, respectively.  

Gas-solid mixing studies  

Gas-solid fluidization is divided into several regimes depending on gas speed. In this study, the gas rate used falls 

within the bubble fluidized bed regime, that is, the range of Reynold number (Re) between 0.2 and 1000. Air 

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bubbles increase in the fluidized bed; there is continuous transference of gas to the solid phase by diffusion and 

convection modes. The gas that enters the fluidized bed passes through the granular particles in the column. The 

bubble pushes through the bed of the solid particles and stops at the top. Accordingly, the bubble is like the cloud 

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

  

Descriptions   Sub-model   

Granular viscosity     

Granular bulk viscosity   

Frictional viscosity   

Lun et al. (2009)   

  

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 transferred by convection inside the bubble. In the cloud, the 

contact between solid and gas takes residence. This implies that air exists in the cloud, which flows back to the 

bubble again. Part of it might be exchanged with the solid phase by diffusion or adsorption with the solid that is 

exchanged with the emulsion phase. Convection and diffusion mechanisms of exchange occur simultaneously. 

The gas exchange among bubble and suspension phases has been described in terms of mass transfer coefficient 

by Kunii and Levenspiel (1991):  

1   dNA 

k CAb CAe                           (16)  

 

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intrfacial area dt 

  

where k is mass transfer coefficient (cm/s). Interchange  

rate is defined as,   

  

1   dNA 

k CAb CAe                                     (17) volume dt 

 
  

Where k is mass transfer coefficient (s-1).  

Kunii and Levenspiel (1991) expected two transference steps, namely the transfer among bubble void and cloud 

particles intersection area and that between the cloud particles intersection area and the emulsion phase. They 

also presumed that the mass transfer quantity of bubblecloud and cloud-emulsion is given as in terms of gas 

transfer quantity per unit volume of bubble void.  

umf D1/2 g1/4  

kbc 4.5 Db 5.85 Db 5/4  from bubble to cloud                  

 

 
                                                                                     (18) 

mf ub De 1 / 2 

kce 6.78 Db3  from cloud to emulsion      (19)               

 
 

They defined the overall gas transfer coefficient of the bubble phase and emulsion phase as follows:  

   

kbck ce 

kb                                                                  (20)           kbc kce 

  
From the thorough information regarding the method of fluid (gas) in the cloud, it can carefully be expected that 

the gas structure in the cloud is roughly uniform. Chiba and Kobayashi (1970) used the analysis of Murray for 

the flow pattern around the spherical bubble to obtain the following expressions for the interchange coefficient:  

6.78 D mf u b                                             (21) kb   3  

Db 

Equation 23 indicates that there is no effect of the diffusion coefficient of the transferring species, nor any direct 

effect of the fluid mechanical phenomen. However, in this study, Gidaspow and Wen-Yu gas-solid interchange 

coefficients are used to observe the conduct of the hydrodynamics in a fluidized bed. 

Species transport model  

                                                      

1 g Db  

  
Finally, Kobayashi et al. (1967) determined the rate of  



 

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Species transport equation is used for the residence time distribution (RTD) study. The conservation equation for 

the species predicts the residence mass portion of each species, Yi, through the solution of a convection and 

diffusion equation from ith species. The general conservation equation is given as follows: 

  

i . vYi Ji Ri Si                         (23)  

 
t 

where i is density of species i,  is velocity vector,   is diffusion change of species i, Ri is the net rate of creation 

of species by chemical reaction and Si is the rate of creation by accumulation from the dispersed phase. In this 

situation, chemical reaction is not considered; therefore Ri and Si are ignored and Equation 24 is reduced to:  

  

  

i . vYi Ji 0                             (24)  

 
t  

where the diffusion flux of the species for turbulent flow is calculated by Fick’s law and CFD uses the dilute 

estimate of Fick’s law for prototypical mass diffusion due to the concentration difference and temperature. The 

diffusion flux might be given as follows: 

 
Ji .Yi Di, m Sct

t Dti TT                      (25)  

 

 
i 

where Sct is the turbulent Schmidt number Sct   Dt 

 
while the temperature gradient is negligible and combines Equations 25 and 26 form given as:  

exchanges of species at the inlets involves both convection and diffusion elements and compounds. That means 

the convection constituent is made static by the quantified inlet species mass fraction, while the diffusion factor 

depends on the difference of the calculated species’ amount (which is not known priori). 

Turbulent modeling  

In various industrial processes related to fluidization, turbulence behavior is observed. k -ε model is the commonly 

used engineering turbulent classical for industrial applications; it is robust and reasonable accurate.  

In this study, a standard k- ε model is used to calculate the transportation equation for turbulent kinetic energy (k) 

and dissipation rate of the turbulent kinetic energy (ε).  The k-ε model is given as follows:   

  

 exchange by measuring the RTD in a fluidized bed. They     Di, m Sctt  .                 (26) 

concluded that the interchange parameter could be  i . vY i .Y i      expressed as: 

 t   

 

 
     

11  During the simulation, diffusion at the inlet is important  

kb .                                                                     (22)                                 because the pressure -based solver 

calculating the net  

 



 

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.( mkvm) .( t,   m k) Gk, m m                   (27)  

  

.( mkvm) .( t, m k) (c1 Gk, m c2 m )  (28)               

 
 k 

  

where  is turbulent (eddy) viscosity computed from k k2 – ε, ( t, m mC )   

 
  

where C =0.09, C 1=1.44, C 2=1.92, =1 and Gk, m is classical of turbulent kinetic energy due to velocity 

difference.  

Residence time distribution (RTD)   

Residence time distribution (RTD) study is significant to describe the mixing and flow rate patterns of the inner 

apparatus, and to determine whether the unit would be an ideal apparatus in the future, that is, tubular reactor or 

mixed flow reactor. Besides, RTD is used to prototype the reactor as a mixture of ideal reactors. Residence time 

distribution data values are used to investigate any nonidealities similar to directing, by transient and quick 

circuiting existing in the reactor (Levenspiel, 1999). It can also be used to measure up or to project a reactor once 

the kinetics is attained. To accomplish RTD replications, the transient examination of a tracer is measured with 

the same physical properties as that of incessant phase. The t xj xj xj  Sct    

                                                                                     (29)   

where t is a turbulent viscosity and is given k2 

as t mC , and Ytr is mass fraction of tracer  

species.  

Numerical procedure for hydrodynamics    

Mathematical method   

ANSYS Fluent answers the main integral equations for mass conservation, conservation of momentum, kinetic 

theory of granular flow and turbulent simultaneously. This technique is used for finite volume approach for flow 

arrangements. 

Pressure based problem solver method  

 

 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  

Di, m t ]                                 bed and YThe solid capacity fractions in the freeboard are 

initially  -velocity of the air phase in the fluidized bed.  

mYtr   m  vm Y tr  [ Ytr   

 

 

 

 



 

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Pressure-based calculation employs phase momentum equations, collective pressure, and calculations of phase 

volume fractions in a separate way. The phase uses an implicit technique for pressure connected equations 

(PCSIMPLE). An extension of the SIMPLE system is established for polyphase flows. This consists of modifying 

the pressure and velocity which are functional to improve the limitation of the volume continuously.  

Three or two dimensions discretization 

Finite volume system used to conduct complex geometries is functional. The differentiation of the convective rate 

is first order exposed. Under transient formulation, the restricted second order implicit is used; this preparation 

would offer well stability, for time discretization to continuously confirm the bound variables. The bounded 

second order implicit is a better option for the fluidized bed to obtain stability and accurate results. A first order 

implicit transient design by means of the phase-Couple SIMPLE method is used to calculate the equations for 

both 2-dimensional and 3-dimensional cases.  

Initial values and boundary values conditions   

The initial condition might not influence the stable state solutions that may be favorable for the fluidized bed  set 

to zero (assuming only gas). The Y-velocity of the gas phase in the fluidized bed is computed completely with a 

steady state volumetric fluxes balance in which the flow rate going to the fluidized bed segment is linked to the 

volume flow rate leaving the fluidized bed segment (consisting of both solids and gas phase):  

 vinuin vgug                                                              (30)  

  

vinu in 

ug                                                                     (31) vg 

  

The situations represent that the superficial velocity of the gas is a proportion of the bed volume to the feed inlet 

volume which is identical with the void fraction: 

u 

ug 
in                                                                         (32)  

 

g  

Boundary conditions: At the inlet of the fluidized bed, there is gas superficial velocity for primary phase, while 

the secondary phase is zero inlet velocity. At the outlet of the fluidized bed there is atmospheric pressure. No slip, 

wall boundary condition is applied to the gas phase, while the partial slip condition is applied to the solid phase. 

A specularity coefficient (ϕ = 0.001) for a partial slip model is used based on the suggestion of Shi et al. (2015).  

PROBLEM DESCRIPTION AND CFD METHOD  

Problem identifications  

Figure 1 is the conceptual representation of the fluidized bed that is modelled and simulated using software. This 

figure characterizes a cylindrical container, that is, the gas-solid fluidization bed with superficial air velocity inlet 

at the bottom of the column. The solid particles are patched with s =0.577 at the initial bed height (ho) =  

0.5 m. The fluidizing gas causes the gas-solids mixing. The gravitational effect on the particles bed is taken into 

account as the bed is vertical.  

Simulation procedure  

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 inside the reactor after the tracer is presented. This assumption is used in many literature 



 

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studies (Hua et al., 2014; Shilapuram et al., 2011). The RTD analysis such as mean residence time, change, and 

leaving age distribution can be done.   

The tracer gas injection method involves:  

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Firstly, run the steady statesimulations 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 continuity, momentum, k-turbulent kinetic, - 

dissipation rate kinetic energy reduce in reaching steady state conditions.  

After it is achieved, it converges for the steady state simulation; the mass fraction of the tracer is made to 1 and 

the other equations are disabled. The tracer carries the properties of Helium gas, as mentioned in the experimental 

setup (Lopez-Isunza, 1975).  

Now the unsteady state equation for the tracer (Equation 29) is used for one iteration to imitate the Pulse method 

after which the mass fraction of the tracer is changed to 0.   

The flow equations (conservation of mass, conservation of momentum, k-turbulent kinetic, - dissipation rate 

kinetic energy species transport and tracer gas) are solved.  

Then, the mass density of the tracer is time monitored when leaving the fluidized bed.  

RESULTS AND DISCUSSION   

CFD reproductions of the fluidized bed are obtained by RTD validation study done by comparing the results with 

the experimental study done by Lopez-Isunza (1975). 

Gas-solid hydrodynamics   

Hydrodynamic characterization of gas-solid fluidized bed simulated by CFD in 2D with the drag equations of 

Gidaspow and Wen-Yu is done. Figure 2 represents the time used for the solids velocity profile in the radial path 

at 0.3 m. The motoring height is chosen arbitrarily but care is taken to ensure that it is below the top elevation of 

the fluidized bed. This is done to ensure that the gassolids mixing behavior is certainly investigated. It can be seen 

that the simulation results using Gidaspow and Wen-Yu gas-solid drag models are slightly different from each 

other. The solids axial velocity fluctuations along the radial position are larger in Wen-Yu model than in 

Gidaspow model. Experimental studies (Li et al., 2009; Loha et al., 2012) indicate that the variation in solids 

-0.10 -0.05 0.00 0.05 0.10  0.0  

0.1  

0.2  

0.3  

0.4  

0.5 

0.6  

 Wen-Yu model  
 Gidaspow model  

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.    



 

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velocity is similar to that exhibited by Gidaspow drag model. This indicates that the Gidaspow model could be 

more accurate in predicting the gas-solid solid hydrodynamics in this study. Moreover, Gidaspow drag equation 

is a modified form of Wen-Yu (and Ergun) drag equations as explained earlier.   

Figure 3 illustrates the time-averaged solid capacity fraction variation along the center of the fluidized bed. It 

shows the extreme solids volume fraction model equation of Wen-Yu ( s = 0.63) compared to the model of  

Gidaspow ( s = 0.59).         

This specifies the Wen-Yu model equation promotes solids clustering as compared to the Gidaspow model. It is 

probably due to the huge gas velocity escaping along the walls thereby pushing the solid particle together and 

forming cluster. Figure 4 indicates the profile of timeaveraged solid volume fraction outlined in the radial position 

at height of 0.4 m by Gidaspow and Wen-Yu drag models. 

Fraction contour in the fluidized column.  

The solids volume fraction shows even distribution along the radial direction for both models, while Wen-Yu 

model indicates comparatively larger variation of solids volume fraction along the radial direction as compared 

to Gidaspow model. To conclude from the aforementioned three figures, Gidaspow model seems to be preferable 

to We-Yu model as it indicates less variation along the radial and axial direction in gas and solid velocity. Also, 

literature studies (Sahoo and Sahoo, 2015; Loha et al., 2012; Hooyar et al., 2012) appreciate Gidaspow model for 

evaluation with investigational data. It must also be noted that the Gidaspow model is a modification of Ergun 

and Wen-Yu models. 

Residence time distribution (RTD) validation  

The species transport model in ANSYS Fluent® used for  the simulation of set time delivered (RTD) is 

implemented for the fluidized bed in 2D and 3D, respectively. In the RTD study, helium gas is considered as 

tracer gas. The concentration of the gas is measured when it is leaving, and the residence time predictions are 

given as Mean time distribution:t citi t i                          (33)  

ci ti 

Exit time distribution: E t c t                      (34)  

 
ci ti 

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 ratio of  U0 /Umf which is 0.634 cm/s. In all the three cases 

(U0 /Umf 9.5;8.0 and 6.4) , both the 2D and   

 

 

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

conditions(U0 /Umf 9.5).   

  

0 20 40 60 80 100  0  

100  

200  

300 

400  

500  

Time (s) 

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

  
  



 

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Figure 6. Experimental and predicted RTD response of the fluidized bed under normalized velocity conditions 

(U0 /Umf 8.0). 3D simulation results are in line with the experimental data (Figures 5 to 7, respectively) 

especially at lower simulation times; while it seems to over-predict the experimental data as the simulation time 

proceeds in the end. This is probably because of the numerical discrepancies associated with the CFD model 

while obtaining the final tracer concentration at the outlet. However, the peaks from the experimental data fit well 

with the numerical model, although the peaks from the 2D simulations are slightly lower than the peaks from the 

3D simualtions. This is probably because in 3D, tracer has enough space to pass through the fluidized bed.   

The validation of residence time distribution studies seems to be in line with the experimental study of 

LopezIsunza (1975) for the three different velocity conditions investigated (Figures 5 to 7). The theoretical mean 

residence time of the air in column is predicated in Kunii  
g h g 

and Levenspiel (1991) as t  . The results are U0 

Summarized in Table 2 for an initial solids bed height of 0.5 m.  

For U0 /Umf 9.5, the average residence time is the  fastest (compared to U0 /Umf 6.4 which is the slowest), which 

means that the mass transfer between the bubbles and emulsions phase is comparatively faster. 

Conclusion 

The gas-solid hydrodynamics using computation fluid dynamics (CFD) is important to identify the rate behavior 

of the inner fluidized column. The CFD implemented in this simulation work is a Eulerian-Eulerian multiphase 

flow fixed with the kinetic theory of granular flow and standard turbulence model used for closure. The two drag 

models, necessary for gas-solid interchange coefficient, that is, the Gidaspow and Wen-Yu models, simulate the 

gas-solids mixing in the bed. Although there is not much difference between the performance of these two models, 

Gidaspow model is recommended as it is able to correctly capture the hydrodynamics inside the fluidized bed. 

The simulations results studied are timeaveraged distributions of gas and solids velocity along the axial and radial 

directions. The simulation results related to residence time distribution (RTD) for three different velocity rations 

(U0 /Umf 9.5;8.0 and 6.4) , that is, at different degrees of gas-solids mixing, are evaluated in both 2-D and 3-D. 

The results are similar with the investigational data of Lopez-Isunza (1975). However, further research is still 

needed to understand the mass transport among the bubble and emulsion phases and connect them to the gas-solid 

hydrodynamics. It is important to investigate the relation between the mass transport and the residence time 

distribution, to have a meaningful fluidized column reactor.  

CONFLICT OF INTERESTS 

The author has not declared any conflict of interests. 

0 20 40 60 80 100 120  0  

100  

200  

300  

400  

Time (s) 

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

  



 

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