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Chemical Engineering Journal 171 (2011) 301–313

Contents lists available at ScienceDirect

Chemical Engineering Journal

journa l homepage: www.e lsev ier .com/ locate /ce j

wo- and three-dimensional CFD modeling of Geldart A particles in a thinubbling fluidized bed: Comparison of turbulence and dispersion coefficients

enjapon Chalermsinsuwana,b,∗, Dimitri Gidaspowc, Pornpote Piumsomboona,b

Fuels Research Center, Department of Chemical Technology, Faculty of Science, Chulalongkorn University, 254 Phayathai Road, Patumwan, Bangkok 10330, ThailandCenter for Petroleum, Petrochemicals, and Advanced Materials, Chulalongkorn University, 254 Phayathai Road, Patumwan, Bangkok 10330, ThailandDepartment of Chemical and Biological Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, IL 60616, USA

r t i c l e i n f o

rticle history:eceived 15 October 2010eceived in revised form 30 March 2011ccepted 3 April 2011

eywords:ubbling fluidized bedomputational fluid dynamics (CFD)ispersion coefficientydrodynamicsultiphase flow

urbulence

a b s t r a c t

A comprehensive understanding of turbulence and dispersion is essential for the efficient design of aconventional fluidized bed reactor. However, the available information is restricted to that in a two-dimensional (2-D) plane, because of the experimental and simulation limitations. It is, therefore, ofimportance to evaluate the remaining third dimension of the system and compare these results withthe corresponding data obtained from the 2-D analysis for validation. In this study, computational fluiddynamics (CFD) based upon the kinetic theory of granular flow with a modified interphase exchangecoefficient was successfully used to compute the system hydrodynamics of fluid catalytic cracking (FCC)particles in a thin bubbling fluidized bed with 2-D and three-dimensional (3-D) computational domains.In addition, the shortcoming of the current CFD model was evaluated. With respect to the bed height, thebed expansion ratio and solid volume fraction revealed similar results from both 2-D and 3-D computa-tional domains. The turbulent granular temperature was higher than that of the laminar ones in the lowersection of the bed while the laminar granular temperature dominates the system in the upper section.

However, the granular temperatures obtained from the 3-D computational domain were slightly lowerthan that from the 2-D computational domain. The computation also showed that the dispersion coeffi-cients are in good agreement with the literature measurements and so the 2-D computational domain canbe used to simulate the bubbling fluidized bed system. Finally, all the evaluated system hydrodynamicvalues in the thin radial system direction were lower in the 3-D computational domain than in the thickradial system direction.

. Introduction

Fluidized beds are types of reactor that can be used to per-orm a variety of gas–solid multiphase reacting flows, such asuid catalytic cracking (FCC) and coal combustion units [1,2]. Inhese types of reactor, a gas is passed through solid particles atigh enough velocities to suspend the solids and cause them toehave as a fluid. As the gas velocity passing through the solid

articles increases, a series of changes in the motion of the solids

s formulated as flow regimes. These regimes, arranged in order ofncreasing velocities are; bubbling, turbulent, fast fluidization andneumatic transport [3].

∗ Corresponding author at: Department of Chemical Technology, Faculty of Sci-nce, Chulalongkorn University, 254 Phayathai Road, Patumwan, Bangkok 10330,hailand. Tel.: +66 2218 7682; fax: +66 2255 5831.

E-mail address: benjapon.c@chula.ac.th (B. Chalermsinsuwan).

385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.cej.2011.04.007

© 2011 Elsevier B.V. All rights reserved.

At present, the bubbling regime has received more attentionthan the other three regimes because of its unique characteristics.The occurrence of bubbles is the major characteristic of thisregime which then exerts an influence on the gas–solid mixingand reaction conversion. For Geldart B and D particles, the gasvelocity, when in excess of the required velocity to maintain thedense phase of the minimum fluidization condition, flows throughthe solids in the form of a bubble [4]. For Geldart A particles,the solid does not start bubbling as the gas velocity reaches theminimum fluidization condition, but the bed starts expanding [5]due to the role of the interparticle forces. The solid starts to bubblewhen the gas velocity exceeds the minimum bubbling condition.For Geldart C particles, the solids are very fine and very difficultto fluidize and so there is no bubbling regime [6]. Although therehave been a number of published studies on the bubbling regime,most of them have been focused on the macroscopic viewpoint,

such as the alteration of the flow pattern with operating conditions[7–9]. Studies from a microscopic viewpoint are still lacking inthe literature, despite the fact that this will allow a better under-standing of the fundamental parameters describing the system

302 B. Chalermsinsuwan et al. / Chemical Engin

Nomenclature

C Scale factor (–)CD0 Drag coefficient (–)dp Particle diameter (m)D Dispersion coefficient (m2/s)e Restitution coefficient between solids or particles

(–)eW Restitution coefficient between particle and wall (–)g Gravity force (m/s2)g0 Radial distribution function (–)h Height of system outlet (m)H Height of system (m)Hi Height of quasi-steady state solid bed (m)H0 Height of initial solid bed (m)I Unit tensor (–)I2D Second invariant of the deviator of the rate of strain

tensor (Pa)l Thickness of system (m)n Unit vector (–)P Pressure (kPa)Re Reynolds number (–)t Time (s)TL Lagrangian integral time scale (s)u Superficial velocity (m/s)v Velocity (m/s)vs,slip Slip velocity of solid phase at the wall (m/s)vs,W Velocity of solid phase at the wall (m/s)vt,W Tangential velocity of solid phase at the wall (m/s)v′

Velocity fluctuation (m/s)W Width of system (m)x Radial x-direction (–)y Axial y-direction (–)z Radial z-direction (–)

Greek lettersˇgs Interphase exchange coefficient (kg/m3 s)ˇgs,new Modified interphase exchange coefficient (kg/m3 s)ε Volume fraction (–)εs,max Volume fraction of solid phase at maximum packing

(–)� Specularity coefficient (–)ϕ Angle of internal friction (◦)�s Collisional dissipation of solid fluctuating energy

(kg/m s3)�W Collisional dissipation of solid phase fluctuating

energy at the wall (kg/m s3)�s Conductivity of solid fluctuating energy (kg/m s)� Viscosity (kg/m s)� Granular temperature (m2/s2)�t Turbulent granular temperature (m2/s2)�W Granular temperature at the wall (m2/s2) Density (kg/m3) Stress tensor (Pa)ω Correction factor correlation (–)� Bulk viscosity (kg/m s)

Subscriptsg Gas phases Solid phasex Radial x-directiony Axial y-directionz Radial z-direction

eering Journal 171 (2011) 301–313

hydrodynamics, and so enable scientists and engineers to designbetter and more efficient reactors [10].

The hydrodynamics of bubbling fluidized bed reactors dealswith the dynamic phenomena of the gas–solid suspension insidethe reactor. The parameters describing these hydrodynamicsinclude the turbulence and dispersion coefficients. Tartan andGidaspow [11] stated that using a kinetic theory based particleimage velocimetry apparatus, there are two kinds of turbulencein the fluidization, as measured by granular temperature. A “lam-inar” granular temperature, which represents random oscillationsof individual solids and measures the solid’s fluctuating kineticenergy, and a “turbulent” granular temperature, which representsthe motion of the bubble or cluster of solids and measures thenormal Reynolds stress. These terminologies are named after themethod to compute the oscillations or movements. The laminaroscillation is obtained by computing the instantaneous velocitywhile the turbulent oscillation is obtained by the hydrodynam-ics or averaged instantaneous velocity, which is typically used asthe turbulent velocity in turbulence theory. This methodology hasthen been applied to characterize the information in many flu-idization systems in both experimental and simulation conditions[12–16]. Dispersion coefficients are a parameter for measuring thequality of mixing and their definition is based on the kinetic the-ory of granular flow [17]. As such it is a measure of the spread ofsolids with reference to the spatial location. Similar to turbulence,there are two kinds of mixing; a “laminar” type due to individualparticle oscillations and a “turbulent” type due to bubble or clus-ter of solid oscillations [15,18]. In addition, many researchers havetried to compute these parameters using other methodologies, suchas tracer injection [19–22] and thermal inspection [23]. However,these methodologies were mainly restricted to considering the dis-persion coefficient only in the axial direction, ignoring all otherdirections. Recently, Breault [24] summarized that the reporteddispersion coefficients (from the available literature) can vary upto five orders of magnitude. Given that our current understand-ing of both turbulence and dispersion coefficients is somewhatrestricted to a two-dimensional (2-D) plane, albeit due to the exper-imental and simulation limitations, the values in the other systemdimensions are interesting to discover and compare with the dataobtained from 2-D studies.

Computational fluid dynamics (CFD) is a branch of fluid mechan-ics that uses numerical methods and algorithms to solve problemsand analyze phenomena that involve fluid and chemically reactingflows [25]. For gas–solid systems, two different approaches mightbe used for the calculation, namely the Lagrangian and the Eule-rian approaches. The Lagrangian approach should be used whenthe solids in the system occupy a low volume fraction while theEulerian approach should be used when the solid volume frac-tion in the system is high. For the bubbling fluidized bed, theEulerian approach is thus more suitable for the calculation. Thisapproach separately solves the conservation equations for eachphase. Among the various attempts to close the gas–solids flow,the kinetic theory of granular flow is the most widely applied the-ory as a constitutive equation [26–30]. This theory is basically anextension of the classical kinetic theory of gases with the addition ofthe solid fluctuating kinetic energy and the solids collision descrip-tions. Although CFD is anticipated to make valuable contributionsin predicting the performance of a bubbling fluidized bed, there arecurrently no universal CFD models that can be applied to all systems[31–34], as will be discussed in the following sections. Therefore,more attention should be focused in this area.

This study aims to determine the turbulence or granular tem-

perature and the axial and radial dispersion coefficients for gas andsolids in a thin bubbling fluidized bed using CFD simulation with 2-D and three-dimensional (3-D) computational domains. As statedabove, it was the first literature that studies and compares these

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B. Chalermsinsuwan et al. / Chemica

alues. In addition, the other hydrodynamic information on the bedxpansion was validated with our experimental data so as to eval-ate the current CFD model and the solid volume fraction patternas discussed based on the new computational domain.

. Experimental setup

Experiments were conducted in a thin Plexiglas bubbling flu-dized bed of 1.28 m height (H), 0.30 m width (W) and 0.05 mhickness (l), as shown schematically in Fig. 1(a). At the base ofhe system, there was a fine stainless steel wire support grid thatas used to support the solids and a gas distributor was locatedirectly below this. Compressed gas was conditioned prior to enter-

ng the system. First, the gas was blown through a silica bed toemove water vapor from the stream. Next, the gas pressure wasdjusted to the desired value by a pressure regulator. Finally, the gasow rate to the system was regulated by directing the gas streamhrough a rotameter with a manual valve. Gas from the systemas discharged to the atmosphere through a 0.15 m diameter (h)

xhaust.The gas fed to the system was air at ambient conditions with

density of 1.20 kg/m3 and a viscosity of 2.00 × 10−5 kg/m s. Theolid bed was the FCC catalyst with a mean particle diameter of5 �m and a density of 1654 kg/m3, classified as commonly usedeldart A particles. Initially, the solid bed height was at 0.24 m (H0).o validate the CFD simulation results, the experimental analysesere performed to identify the quasi-steady state bed height (Hi)

nd the expansion ratio at different superficial gas velocities (ug),anging from 0.08 to 0.35 m/s. The quasi-steady state bed heightas measured by observing the solid bed expansion and was used

o calculate the expansion ratio by dividing it with initial solid bedeight (Hi/H0).

. Computational fluid dynamics simulation setup

Advances in computational methodology have provided theasis for further insight into the dynamics of multiphase flows. Forbubbling fluidized bed, as in this study, the Eulerian model in

he commercial CFD program FLUENT 6.2.16 was used for mod-ling the system. The main governing equations, the so calledonservation equations, are then closed by providing constitutivequations based on the kinetic theory of granular flow, as reviewedy Gidaspow [17] and Gidaspow and Jiradilok [35]. The conser-ation and constitutive equations for each phase are summarizedelow.

.1. Conservation equations

The mass and momentum conservations for the gas and solidhases as well as for the solid fluctuating kinetic energy conserva-ion were considered based upon the assumption that the systemas isothermal. Under this assumption, the energy conservation

an be ignored.

.1.1. Mass conservation equationsThe accumulation of mass in each phase is balanced by the con-

ective mass fluxes.The mass conservation equation for the gas phase, g, is:

∂

∂t

(εgg

)+ ∇ ·

(εggvg

)= 0 (1)

The mass conservation equation for the solid phase, s, is:

∂

∂t(εss) + ∇ · (εssvs) = 0 (2)

eering Journal 171 (2011) 301–313 303

where εg and εs are the volume fraction of the gas and solidphases, respectively, g and s are the density of the gas and solidphases, respectively, vg and vs are the velocity of the gas and solidphases, respectively, and t is the time.

Each computational cell is shared by the inter-penetratingphases, so that the summation of all volume fractions is unity.

εg + εs = 1 (3)

3.1.2. Momentum conservation equationsThe accumulation of momentum in each phase is balanced by

the convective momentum fluxes and the related forces inside thesystem, which are the forces due to pressure, stress tensor, gravityand momentum interphase exchange coefficient.

The momentum conservation equation for the gas phase is:

∂

∂t

(εggvg

)+ ∇ ·

(εggvgvg

)= −εg∇P + ∇ · g + εggg

− ˇgs

(vg − vs

)(4)

The momentum conservation equation for the solid phase is:

∂

∂t(εssvs) + ∇ · (εssvsvs) = −εs∇P + ∇ · s − ∇Ps + εssg

+ ˇgs

(vg − vs

)(5)

where P is the pressure of the gas phase, g and s are the stresstensor of the gas and solid phase, respectively, Ps is the pressure ofsolid phase, g is the gravity forces and ˇgs is the interphase exchangecoefficient.

3.1.3. Solid fluctuating kinetic energy conservation equationThe fluctuating kinetic energy conservation equation for the

solids, as derived from the kinetic theory of granular flow [17], canbe expressed as:

32

[∂

∂t

(εss�

)+ ∇ ·

(εss�

)vs

]=(−∇PsI + s

): ∇vs + ∇·

(�s∇�

)− �s (6)

where � is the solid fluctuating kinetic energy or granular tem-perature, �s is the conductivity of solid fluctuating kinetic energyand �s is the collisional dissipation of solid fluctuating kineticenergy.

3.2. Constitutive equations

Constitutive equations, based on the kinetic theory of granu-lar flow, are needed to close conservation equations. The behaviorof the solid phase is described by taking into account the energyassociated with solid particles that arises out of collisions and fluc-tuating motions of the solids. The following are the constitutiverelations were used in this study.

The stress tensor can be expressed as the sum of deviatoric andspherical stresses which tend to change the volume of the stressedbody.

The stress tensor for the gas phase is described as:

g = εg�g

[∇vg +

(∇vg

)T]

− 23

εg�g

(∇ · vg

)I (7)

while the stress tensor for the solid phase is:

s = εs�s

[∇vs + (∇vs)T]

− εs

(�s − 2

3�s

)∇ · vsI (8)

304 B. Chalermsinsuwan et al. / Chemical Engineering Journal 171 (2011) 301–313

dimen

wau

nc

P

wp

sdire

�

wat

t

�

ip

g

Fig. 1. (a) Schematic, (b) two-dimensional computational domain and (c) three-

here �g is the viscosity of the gas phase, �s and �s are the shearnd bulk viscosities, respectively, of the solid phase and I is thenit tensor.

The solid pressure is composed of a kinetic term that domi-ates in the dilute regions and a second term due to solid particleollisions that is significant in the dense regions:

s = εss� [1 + 2g0εs(1 + e)] (9)

here g0 is the radial distribution function and e is thearticle–particle restitution coefficient.

The solid shear viscosity is also composed of kinetic and colli-ional terms arising from the solid particle momentum exchangeue to translation and collision. A frictional component of viscosity

s included to account for the transition that occurs when solidseach the maximum solid volume fraction, as suggested by Khoet al. [36] for Geldart A particles:

s = 45

εssdpg0(1 + e)

√�

�+ 10sdp

√��

96(1 + e)g0εs

[1 + 4

5g0εs(1 + e)

]2

+ Ps sin ϕ

2√

I2D

(10)

here dp is the particle diameter, ϕ is the angle of internal frictionnd I2D is the second invariant of the deviator of the rate of strainensor [37].

The solid bulk viscosity accounts for the resistance of the solidso compression and expansion:

s = 43

εssdpg0(1 + e)

√�

�(11)

The radial distribution function is a correction factor that mod-fies the probability of collisions between solids when the solid

hase becomes dense:

0 =[

1 −(

εs

εs,max

)1/3]−1

(12)

sional computational domain of a thin Plexiglas bubbling fluidized bed system.

where εs,max is the volume fraction of the solid phase at maximumpacking.

The conductivity of the solid fluctuating kinetic energy describesthe diffusion of granular energy as:

�s = 150sdp

√��

384 (1 + e) g0

[1 + 6

5εsg0 (1 + e)

]2+ 2sε

2s dp (1 + e) g0

√�

�(13)

The collisional dissipation of the solid fluctuating kinetic energyrepresents the rate of energy dissipation within the solid phase dueto collisions between solid particles:

�s = 3(

1 − e2)

ε2s sg0�

(4dp

√�

�

)(14)

Many researchers have successfully performed the bubbling flu-idized bed simulations of coarse Geldart B and D particles [38–40].However, only a few successful simulations on the bubbling flu-idized bed of fine Geldart A particles have been reported [41,42],and they all reported a severe over-estimation of the bed expansion.van Wachem et al. [43] reported a high sensitivity to the interphaseexchange coefficient model when compared with the other param-eters. McKeen and Pugsley [32] and Taghipour et al. [44] reportedthat the generally poor simulation results for Geldart A particlescan be attributed to the existence of significant interparticle forcesthat are neglected in most CFD simulations. The existence of cohe-sive interparticle forces would lead to grouping of solids or particleclusters, resulting in an effectively larger particle diameter and alower interphase exchange coefficient, which would in turn resultin a reduced bed expansion. The non-modified interphase exchangecoefficient could not capture the observed realistic phenomenon.

In this study, the Energy Minimization Multi-Scale (EMMS) inter-phase exchange coefficient model, pioneered by Yang et al. [45,46],was selected. The EMMS interphase exchange coefficient modelwas developed below using the concept of particle clusters.

B. Chalermsinsuwan et al. / Chemical Engineering Journal 171 (2011) 301–313 305

Table 1Summary of grid resolutions.

No. (–) Computational domaindimensions (–)

Grid number (–)

x-direction y-direction z-direction

1 2 22 50 –2 2 33 75 –

a

ˇ

ˇ

w

a

R

R

eetHhpu[nUa

3

sttcfltvsatwDFtoig

Table 2Summary of system descriptions and variables.

Symbol Description Value

g Gas density 1.20 kg/m3

�g Gas viscosity 2.00 × 10−5 kg/m ss Particle density 1654 kg/m3

dp Diameter of particle 75 �mvg Gas inlet velocity 0.25, 0.28, 0.35 m/sH0 Initial bed height 0.24 mεs Initial solid volume fraction 0.50εs,max Solid inlet volume fraction at maximum

packing limit0.64

e Restitution coefficient between particles 0.70eW Restitution coefficient between particle and

wall0.70

� Specularity coefficient 0.0001

3 2 (Base case) 44 100 –4 3 44 100 10

The EMMS interphase exchange coefficient model is expresseds follows:

For εg ≤ 0.74,

gs = 150

(1 − εg

)2�g

εgd2p

+ 1.75

(1 − εg

)g

∣∣vg − vs

∣∣dp

(15)

For εg > 0.74,

gs = 34

(1 − εg

)εg

dpg

∣∣vg − vs

∣∣CD0ω(ε) (16)

ith

when 0.74 ≤ εg ≤ 0.82, ω(εg ) = −0.5760 + 0.0214

4(εg − 0.7463)2 + 0.0044

when 0.82 ≤ εg ≤ 0.97, ω(εg ) = −0.0101 + 0.0038

4(εg − 0.7789)2 + 0.0040

when εg > 0.97, ω(εg ) = −31.8295 + 32.8295εg

nd Re < 1000, CD0 = 24/Re(1 + 0.15Re0.687);

e = gεg

∣∣vg − vs

∣∣dp/�g;

e ≥ 1000, CD0 = 0.44.

There is a simplification in the development stage of themployed EMMS interphase exchange coefficient model. Zhangt al. [47] and Nikolopoulos et al. [48] suggested that the sys-em heterogeneity depended on the void fraction and slip velocity.owever, this model neglects the effect of slip velocity on theeterogeneity structure [45,46]. The void fraction is the onlyarameter in the correction factor correlation (ω). The large val-es of the slip velocity render cluster structures relatively unstable48]. Since the EMMS interphase exchange coefficient model isot available in the FLUENT 6.2.16 program, the new additionalDF (user-defined function) code in C programming language wasdded.

.3. Computational domain conditions

The simulations were carried out for the bubbling fluidized bedystem shown in Fig. 1(a). Xie et al. [49] studied the effect of compu-ational domains on bubbling fluidized bed simulations and foundhat the 2-D computational domain with Cartesian coordinatesould be successfully used to simulate the results of the bubblinguidized bed from a macroscopic viewpoint. Since a 3-D computa-ional domain requires a much longer computation time, the modelalidation section used a 2-D computational domain with Carte-ian coordinates for the simulation. The obtained results were thenpplied to a 3-D computational domain with Cartesian coordinateso compute the microscopic viewpoint. The results were comparedith those obtained from the 2-D computational domain. Both 2-and 3-D computational domains are displayed schematically in

ig. 1(b) and (c), respectively. The gas phase was fed at the bot-

om and exited through the non-symmetric side outlet at the topf the system. Throughout the simulation, the solid phase remainednside the system and uniform grids were used. A summary of therid resolution used is given in Table 1. The effect of grid number

ϕ Angle of internal friction 30◦

or grid independence study is described in the model validationsection.

According to the previous literature [32,43], the alteration ofthe CFD tuning variables, which are the particle–particle restitu-tion, particle–wall restitution and specularity coefficients will notprovide a better prediction of the FCC particles in a bubbling flu-idized bed system. The restitution coefficients express the amountof the energy dissipation by collisions, where a zero and unit valuesimply very high and low dissipation levels, respectively. McKeenand Pugsley [32] and Almuttahar and Taghipour [50] observedthat changing the restitution coefficients from 0.5 to 0.99 did notsignificantly affect the model predictions. The specularity coeffi-cient measures the fraction of collisions which transfer momentumto wall. As the specularity coefficient approaches zero or one, asmall or large amount, respectively, of momentum is transferred.Although there is not much difference in the model predictions,Almuttahar and Taghipour [50] and Benyahia et al. [51] reportedthat a higher solid concentration near the wall is obtained witha smaller specularity coefficient (varying from 0 to 1). Therefore,those values found to be reasonable in the existing literature [32,50]were selected for use in this study, and the system descriptions andvariables used are defined in Table 2. The used time step shouldbe limited by a Courant number in order to ensure the numericalaccuracy, convergence and stability [52]. This number is a func-tion of the smallest cell dimension and the largest instantaneousvelocity. Therefore, a time step of 1.00 × 10−3 s with 100 itera-tions per time step was used in the simulation. The models weresolved by using a computer with Pentium 1.80 GHz CPU 2 GB RAM,which, for a typical 2-D computational domain with Cartesian coor-dinates, took around 5 days of computer time for 20 s of simulationtime.

3.4. Initial and boundary conditions

The definition of appropriate initial and boundary conditionsis crucial for carrying out a realistic simulation. Initially, thesolid was filled inside the system with an initial 0.24 m (exper-imentally determined) bed height. At the inlet, the velocity andvolume fraction in each phase were specified. In this study, a non-uniform parabola inlet velocity profile was applied. The averageinlet velocities were determined from the experimental values.On the other hand, at the outlet, the outflow boundary conditionwas selected. This boundary condition is obeyed in fully devel-oped flows where the diffusion fluxes for all flow variables in

the exit direction are zero. At the wall, a no-slip condition wasapplied for all velocities, except for the tangential velocity (vt,W)of the solid phase and the granular temperature (�W). Here, the

306 B. Chalermsinsuwan et al. / Chemical Engin

F

bf

v

�

wvwt

4

eesfievaarsrbftw

4

t

TTv

ig. 2. Experimental bed expansion ratio with different superficial gas velocities.

oundary conditions of Johnson and Jackson [53] were used asollows:

t,W = − 6�sεs,max

��sεsg0√

3�

∂vs,W

∂n(17)

W = −�s�

�W

∂�W

∂n+

√3��sεsv2

s,slipg0�32

6εs,max�W(18)

ith �W =√

3�(

1 − e2W

)εssg0�3/2/4εs,max where vs,W is the

elocity of solid phase at the wall, vs,slip is the slip velocity at theall, � is the specularity coefficient, eW is the particle–wall resti-

ution coefficient and n is the unit vector.

. Results and discussion

As already discussed in Section 3.2 above, the values for the bedxpansion for Geldart A particles tend to be over-estimated. Thus,xperimental analyses were performed to identify the quasi-steadytate bed height and the bed expansion ratio at six different super-cial gas velocities ranging from 0.08 to 0.35 m/s. The obtainedxperimental bed expansion ratio with different superficial gaselocities is displayed in Fig. 2, while the values of bed heightnd bed expansion ratio with different superficial gas velocitiesre compared in Table 3. The results reveal a similar trend to thateported in the previous literature [32,43], in that the bed expan-ion ratio increases with superficial gas velocity due to the higherepulsive forces acting on the solid particles. Then, these results cane used to compare with those predicted by CFD simulation. In theollowing section, the CFD simulations were only performed withhree highest superficial gas velocities, at 0.25, 0.28 and 0.35 m/s,hich are the high bed expansion ratio conditions.

.1. Model validation

In the preliminary study, we performed a numerical simula-ion with the stated EMMS interphase exchange coefficient model.

able 3he values of the bed height and bed expansion ratio with different superficial gaselocities.

No. (–) Superficial gasvelocity (m/s)

Bed height (m) Bed expansionratio (–)

Minimum Maximum Average

1 0.08 0.27 0.28 0.27 1.132 0.15 0.27 0.30 0.29 1.183 0.18 0.28 0.32 0.30 1.244 0.25 0.28 0.34 0.31 1.295 0.28 0.29 0.36 0.32 1.346 0.35 0.30 0.36 0.33 1.37

eering Journal 171 (2011) 301–313

The simulation with this interphase exchange coefficient model isexpected to match well with the experimental data according to theabove discussion (Section 3.2). Fig. 3(a) displays a contour plot ofthe solid volume fraction for the EMMS interphase exchange coef-ficient model using a grid number of 44 (in x-direction) × 100 (iny-direction) and a superficial gas velocity of 0.35 m/s. The time-averaged solid volume fraction versus the system height with twotime-averaged ranges is illustrated in Fig. 3(b). When the simula-tion time was increased to 20 s, only a slight change in the resultswas seen, supporting that the numerical simulation had reachedthe quasi-steady state condition since 10 s of simulation time. Thus,the 10–20 s time-averaged range result was selected to use to repre-sent the system in all subsequent simulations. In the figures, the bedheight or bed expansion ratio was recorded at the position wherethe solid volume fraction is equal to 0.20. It can be seen that theresult shows the bed over-expansion and hence any change to theEMMS interphase exchange coefficient model would not improvethe predictions of FCC particles in a bubbling fluidized bed system.Also, the result exhibits a significant loss of solid particles throughthe system outlet over time, as observed by Ferschneider and Mege[54].

From the above data, it can be inferred that in the real sys-tem, there are other significant forces besides cohesive interparticleforces that are still to be taken into account. Indeed, Colver [55]and Hendrickson [56] stated that the commonly accepted numeri-cal model for FCC particles in the fluidized bed system does not takeall the forces into account, such as van der Waals and electrostaticforces. Along these lines, Kim and Arastoopour [57] modified thekinetic theory of granular flow by introducing a very complex addi-tional force model, but their model is limited in its use due to therequirement for many empirical input variables. Wang et al. [33]reported a model that can predict the correct bed expansion with-out any modification simply by using a sufficiently fine grid sizeand small time step size. However, their method is not appropriatefor a large-scale fluidized bed system. Here, we used the conceptby Grace and Sun [31] and McKeen and Pugsley [32]. To take theother forces into account, they introduced a new scale factor, C, toan interphase exchange coefficient model. This scaling factor forthe interphase exchange coefficient model represents only an adhoc way for repairing the deficiencies of the model.

The modified EMMS interphase exchange coefficient model isformulated as follows:

ˇgs,new = Cˇgs (19)

However, there is no specific approach for determining this scalefactor since it is dependent upon the system conditions. As alreadystated, this is possibly due to the simplification of the interphaseexchange coefficient model which excludes the slip velocity effect.Grace and Sun [31] suggested that a scale factor of C = 0.15–0.30gives a good representation of bed expansion, while McKeen andPugsley [32] found that the best value of C for their experimentalcondition was narrower between 0.20 and 0.30. In this study, thisparameter was varied over a range of 0.10–1.00 and checked for thematch of the simulated bed expansion ratio with the experimentaldata.

Fig. 4 displays a contour plot of the solid volume fraction for themodified EMMS interphase exchange coefficient model with differ-ent scale factors at 15 s, a grid number of 44 × 100 and a superficialgas velocity of 0.35 m/s. The time-averaged solid volume fractionversus the system height with different scale factors for varioussuperficial gas velocities is illustrated in Fig. 5. The scale factor low-ers the resistance force, allowing the movement of solid in the bed

through a gas stream. Therefore, the bed expansion ratio decreaseswhen decreasing the scale factor.

Comparison of the bed expansion ratio data for the modifiedEMMS interphase exchange coefficient model with different scale

B. Chalermsinsuwan et al. / Chemical Engineering Journal 171 (2011) 301–313 307

F ange0 with

fwciictioffrfi

F4

ig. 3. (a) Contour plot of the solid volume fraction for the EMMS interphase exch.35 m/s and (b) The time-averaged solid volume fraction versus the system height

actors, using a grid number of 44 × 100, is shown in Fig. 6, alongith experimental data from this study. All simulations show a

onsistent increase in the bed expansion ratio with an increasen the superficial gas velocity, except for when the scale factors equal to one, where a net decrease is seen due to a signifi-ant loss of solid particles, as already discussed. The scale factorhat is the most consistent with the experimentally derived datas 0.10 for a superficial gas velocity of 0.25 m/s and a scale factorf 0.15 for superficial gas velocities of 0.28 and 0.35 m/s. There-

ore, a scale factor between 0.10 and 0.15 is seemingly optimalor the superficial gas velocity range used in this simulation. Theesult supports that the modified EMMS interphase exchange coef-cient model can be used to predict the results of FCC particles

ig. 4. Contour plot of the solid volume fraction for the modified EMMS interphase exch4 × 100 and superficial gas velocity of 0.35 m/s.

coefficient model using a grid number of 44 × 100 and a superficial gas velocity oftwo time-averaged ranges.

in a bubbling fluidized bed system with the appropriate scalefactor.

The effect of the grid numbers used in the system, which canalso influence the simulation results as discussed in this section,was evaluated. Ideally, the grid number should be sufficiently fineso that further refinement does not change the results. Taking oneexample case, with a superficial gas velocity of 0.35 m/s and a scalefactor of 0.15, the effect of different grids (see Table 1 for thoseused) was evaluated. The contour plot of the solid volume frac-

tion at 15 s and the time-averaged solid volume fraction versusthe system height with three different grid numbers are displayedin Fig. 7(a) and (b), respectively. These figures show that the bedheight is reduced with the finer grids. A grid number equal to

ange coefficient model with different scale factors at 15 s using a grid number of

308 B. Chalermsinsuwan et al. / Chemical Engineering Journal 171 (2011) 301–313

Fig. 5. Time-averaged solid volume fraction versus the system height for the modifi

Fig. 6. Bed expansion ratio data for the modified EMMS interphase exchange coef-ficient model with different scale factors using a grid number of 44 × 100.

Fig. 7. (a) Contour plot of the solid volume fraction at 15 s and (b) the time-averaged soli

ed EMMS interphase exchange coefficient model with different scale factors.

22 × 50 over-predicts the bed expansion; and as the grid numberis increased to 33 × 75 and then to 44 × 100, the bed expansionis much lower than the former but shows only a slight differencebetween them and matches with the experimental data. This meansthat the grid number is essentially independent if it is higher than33 × 75.

4.2. Computation and comparison of two- and three-dimensionalcomputational domains

In this section, the modified EMMS model was used to simulatethe system hydrodynamics, which are the solid volume fractionand the turbulence and dispersion coefficients from both 2-D and3-D computational domains. For brevity, from all the data, onlythe system conditions with a superficial gas velocity of 0.35 m/s

and a scale factor of 0.15 are illustrated. For the 2-D computationaldomain, a grid number equal to 44 × 100 was employed while forthe 3-D computational domain, the grid number used was 44 (inx-direction) × 100 (in y-direction) × 10 (in z-direction).

d volume fraction versus the system height with three different grid numbers.

B. Chalermsinsuwan et al. / Chemical Engineering Journal 171 (2011) 301–313 309

F ase ev .

4

ts3cdhdsx

Ft

ig. 8. (a) Contour plot of the solid volume fraction for the modified EMMS interphersus the system height with two- and three-dimensional computational domains

.2.1. Solid volume fractionThe derived contour plot of the solid volume fraction for

he modified EMMS drag model, along with the time-averagedolid volume fraction versus the system height, with 2-D and-D computational domains at 15 s is shown in Fig. 8. The 3-Domputational domain results are averaged both over the x- and z-irections as the mean value across each central plane. Similar bed

eights were obtained from both the 2-D and 3-D computationalomains. For the 3-D computational domain, the time-averagedolid volume fraction in the z-direction was lower than that in the-direction due to the wall effect in the third direction. This is con-

ig. 9. The time-averaged solid volume fraction versus the radial direction at the heighthe x-direction and (b) three-dimensional computational domain averaged in the z-direc

xchange coefficient model at 15 s and (b) the time-averaged solid volume fraction

sistent with the previous observation of Briongos and Guardiola[58]. The time-averaged solid volume fraction versus the radialdirection with 2-D and 3-D computational domains at a heightof 0.20 m is shown in Fig. 9, with a flow structure as observed inthe typical bubbling fluidized bed experiment. The results derivedfrom the 2-D computational domain agree well with the resultsin the x-direction from the 3-D computational domain (Fig. 9(a)),

except for the slightly non-symmetrical behavior compared to thatseen in the 3-D one. This is because of the effect of third systemdimension which can handle more solid particles and so reducessuch behavior. The time-averaged solid volume fraction in the z-

of 0.20 m with (a) two- and three-dimensional computational domain averaged intion.

310 B. Chalermsinsuwan et al. / Chemical Engineering Journal 171 (2011) 301–313

F the pac ion.

dtphitur

4

tfpp

ig. 10. Comparison of the computed time-averaged granular temperatures due to) three-dimensional computational domains averaged in the (b) x- and (c) z-direct

irection for the 3-D computational domain is also lower than inhe x-direction (Fig. 9(b)), being consistent with the result in therevious figure. Therefore, a satisfactory agreement in the systemydrodynamics between the 2-D and 3-D computational domains

s observed. The results support those of Xie et al. [49], who reportedhat the 2-D computational domain can be successfully used to sim-late the hydrodynamics of FCC particles in bubbling fluidized bedegimes.

.2.2. Granular temperaturesAs already reviewed in the introduction section, this study used

he same methodology employed by Chalermsinsuwan et al. [15]or computation of the turbulence or granular temperature. To com-ute the granular temperatures, the related equations have to berogrammed into the CFD models. The code itself computes the

rticle oscillation and the bubble or particle cluster oscillation with (a) two- and (b,

classical or laminar granular temperature (�). The turbulent granu-lar temperature (�t), defined as the average of the normal Reynoldsstresses, is the average of the three squares of the velocity compo-nents in the three directions and is computed by using the followingdefinition:

�t ∼= 13

v′xv′

x + 13

v′yv′

y + 13

v′zv′

z (20)

Fig. 10 shows a comparison of the computed time-averagedgranular temperatures due to the particle oscillation and the bub-ble or particle cluster oscillation with 2-D and 3-D computationaldomains. The sum of the granular temperatures due to the particle

oscillations and due to the bubble or particle cluster oscillationsis the total granular temperature. All the computation domainsresults are similar. In the lower section of the system, the computedgranular temperature due to the bubble or particle cluster oscilla-

B. Chalermsinsuwan et al. / Chemical Engin

Fa

tmhoftbfl3pm

dFwmHac

are in the same broad range as the reported experimentally derived

ig. 11. A comparison of the theoretical granular temperatures derived in this studynd those experimentally derived in the literature.

ion is higher than that due to particle oscillation. This is becauseost of the gas moves as bubbles or the solids move as clusters,

ence, the turbulent granular temperature should dominate thescillations. In the upper section of the system, the solid volumeraction decreases and causes the particle oscillation to dominatehe system. At the top section, the granular temperatures are zero,eing consistent with the solid volume fraction profile in bubblinguidized bed system. When comparing the results from the 2-D and-D computational domains, those derived from the 3-D domainossess lower values than those from the 2-D domain since it hasore solid particles and space available.A comparison of the total granular temperatures with the

erived experimental data in the literature [59–61] is displayed inig. 11. There is a good agreement between the simulation resultsith 2-D and 3-D computational domains and with the experi-ental results from the literature at low solid volume fractions.

owever, in the dense section (high solid volume), the results showsimilar trend but the values are slightly deviated with a lower

omputed total granular temperature than the experimentally

eering Journal 171 (2011) 301–313 311

derived values. This is likely to be because the literature experi-ments were conducted in fast fluidization regime risers which havehigher superficial gas velocities.

4.2.3. Dispersion coefficientsAs already stated in Section 1, there are two kinds of mixing

in fluidization: a “laminar” type due to individual particle oscil-lations and a “turbulent” type due to bubble or particle clusteroscillations. A broad (within an order of magnitude) estimate of thedispersion coefficients due to individual particle’s oscillations canbe obtained from the laminar granular temperature [15]. In order tocompare the solid and gas dispersion coefficients in this dense sys-tem, we focus on the dispersion coefficient due to bubble or particlecluster oscillations. The turbulent dispersion coefficient (Di) can beobtained as a function of the normal Reynolds stress (v′

iv′

i) and the

Lagrangian integral time scale (TL) as expressed below:

Di = v′iv′

iTL (21)

Where the Lagrangian integral time scale of the solid particlemotion is defined by:

TL =∫ ∞

0

v′(t)v′(t + t′)

v′2dt′ (22)

The subscript “i” is to represent the direction of the flow and dis-persion. The radial and axial solid and gas dispersion coefficientswith 2-D and 3-D computational domains at the height of 0.20 mare summarized in Table 4. In the system, there is a slip velocitybetween the phases. The gas phase has a slightly higher velocitythan the solid phase and so the solid dispersions are lower than thegas dispersions, similar to the published experimental and com-putational results for bubbling fluidized bed systems [2,10,62]. Inaddition, the axial dispersions are higher than the radial disper-sions, which is because the axial direction is the main flow direction.Only the radial dispersions in the x-direction for the 3-D compu-tational domain averaged in the z-direction are comparable withthe axial dispersions, but are lower in the z-direction than in thex-direction due to restriction of the movable space. The simula-tions also show that, for 2-D and 3-D computational domains, theaxial dispersion coefficients are close to each other while the radialdispersion coefficients are significantly different. The value of theradial dispersion coefficient for the 2-D computational domain isin between the values of radial dispersion coefficient for the 3-Dcomputational domain averaged in the x- and z-directions. Whenaveraged in the x-direction, the effect of the system wall becomesapparent when compared with the ones in the z-direction. In addi-tion, the thin available space and flow structure in the z-directionwill change the velocity or oscillation and so decrease and increasethe radial dispersion coefficients in the x- and z-directions, respec-tively.

To compare the dispersion coefficients evaluated here withthose reported in the literature, the dispersions were collected fromboth bubbling and fast fluidization conditions, operated in the gasvelocity range. The comparisons between the computed solid dis-persion coefficients for both axial and radial directions and thosereported in the literature [2,10,15,62] are shown in Fig. 12(a) and(b), respectively. The computations show that the solid dispersioncoefficients evaluated here are slightly lower than those in the lit-erature, which is likely to be because this system is a thin bubblingfluidized bed system. Fig. 12(c) and (d) display the comparisonsof the computed axial and radial gas dispersion coefficients, takenfrom the same literature. The calculated gas dispersion coefficients

data in the literature. Therefore, the dispersion coefficients derivedfrom the 2-D computational domain, and especially the axial ones,can be used as an approximation or order of magnitude estimation

312 B. Chalermsinsuwan et al. / Chemical Engineering Journal 171 (2011) 301–313

Table 4Radial and axial solid and gas dispersion coefficients with two- and three-dimensional computational domains at a height of 0.20 m.

Computational domain Dispersion coefficient (m2/s)

Phase Axial Radial (x-dispersion) Radial (z-dispersion)

Two-dimensional Solid 0.0355 0.0090 –Gas 0.0818 0.0094 –

Three-dimensional (averaged in x-direction) Solid 0.0271 0.0257 0.0015Gas 0.1005 0.0361 0.0040

Three-dimensional (averaged in z-direction) Solid 0.0264 0.0551 0.0007Gas 0.0904 0.1050 0.0046

xial so

ots

5

mcgidhd

t

Fig. 12. Effect of the gas velocity on the experimental and computed (a) a

f the system dispersion coefficient. Besides, from all the results,he simulation with the 2-D computational domain is sufficient toimulate the bubbling fluidized bed system.

. Conclusion

The kinetic theory of granular flow based CFD model, with aodified interphase exchange coefficient, was successfully used to

ompute the bed height, bed expansion ratio, solid volume fraction,ranular temperature and dispersion coefficients of FCC particlesn a thin bubbling fluidized bed with 2-D and 3-D computationalomains. The scaling of the drag correlation represents only an ad

oc way for repairing the deficiencies of the model and a moreetailed study is required into the origin of the failure.

For the bed height, bed expansion ratio and solid volume frac-ion, similar results from both the 2-D and 3-D computational

lid, (b) radial solid, (c) axial gas and (d) radial gas dispersion coefficients.

domains were obtained. The time-averaged solid volume fraction inthe z-direction for the 3-D computational domain is lower than thatin the x-direction due to the wall effect. For the granular temper-ature, all the computational results showed similar trends. In thelower section, the turbulent granular temperature was higher thanthe laminar granular temperature but by the upper section, the lam-inar granular temperature has changed to dominate the system. Thegranular temperatures derived from the 3-D computational resultswere lower than those from the 2-D ones due to the available spacein the system. For dispersion coefficients, the computations showedthat the dispersion coefficients were in good agreement with theexperimentally measured values and suggested that the 2-D com-

putational domain can be used to simulate the bubbling fluidizedbed system. In addition, the radial dispersion coefficient in the z-direction for the 3-D computational domain was lower than thecorresponding ones in the x-direction.

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B. Chalermsinsuwan et al. / Chemica

cknowledgements

This study was financially supported by the Research Strategiclan (A1B1), Research Funds from the Faculty of Science, Chula-ongkorn University. This study also was partially supported by therants for Development of New Faculty Staff (Ratchadaphisek Som-hot Endowment Fund) of Chulalongkorn University and the Grantrom the Center for Petroleum, Petrochemicals, and Advanced

aterials, Chulalongkorn University.

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