Characterization of Solids Mixing Patterns in Bubbling-1

Journal Identification = CHERD Article Identification = 621 Date: May 17, 2011 Time: 5:48 am

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chemical engineering research and design 8 9 ( 2 0 1 1 ) 817–826

Contents lists available at ScienceDirect

Chemical Engineering Research and Design

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

haracterization of solids mixing patterns in bubblinguidized beds

.R. Norouzia, N. Mostoufia,∗, Z. Mansourpoura, R. Sotudeh-Gharebagha, J. Chaoukib

Process Design and Simulation Research Center, Oil and Gas Centre of Excellence, School of Chemical Engineering, College ofngineering, University of Tehran, PO Box 11155-4563, Tehran, IranDepartment of Chemical Engineering, Ecole Polytechnique de Montreal, Montreal, Canada

a b s t r a c t

Behavior of the solid phase in fluidized beds was studied by a 2D CFD-DEM approach to obtain more information

on the solid mixing and circulation. Hydrodynamic parameters, including solid diffusivity, and internal and gross

circulations were considered in this study. To validate the simulation, time-position data obtained by the Radioactive

Particle Tracking (RPT) technique were used. It was shown that the 2D model can satisfactorily predict the axial

diffusivity, while the radial diffusivity calculated based on the model is an order of magnitude smaller than the

experimental one in 3D. The influence of aspect ratio of the bed, type of distributor, and inlet gas velocity on solids

mixing pattern were also studied. The solids flow pattern in the bed changed considerably by increasing the aspect

ratio. Different solid circulations were captured by numerical model for the two types of distributors, namely porous

and injection types. The results suggested that increasing the superficial gas velocity caused rigorous internal and

gross circulations, which in return, improved solids mixing and decreased deviations from well mixed state.

© 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Fluidized bed; Discrete element method; Computational fluid dynamic; Solid mixing

is difficult, there have been very few researches on the solids

. Introduction

lthough the mechanisms of solid mixing are well understoodow, there is still much to be learned. Bubbles are mainlyesponsible for mixing in fluidized beds. When a bubble riseshrough the emulsion, it carries some particles to the bedurface in its wake. A down flow of solids in the regions sur-ounding the rising bubble results in the axial circulation ofarticles in the bed. At the same time, the lateral mixing ofolids occurs, which is caused by the lateral motion of bubblesdue to interaction and coalescence of neighboring bubbles)nd lateral dispersion of particles in the bubble’s wake at theed surface (due to the eruption of the bubble) (Rhodes et al.,001).

The clear observation of solid mixing inside a denseuidized bed is hardly possible through sophisticated exper-

mental techniques. Consequently, numerical simulation cane proposed and exploited to provide an insight into theolid mixing within the fluidized beds. Fortunately, the recent
rogress in the computational methods, especially computing
∗ Corresponding author. Fax: +98 21 6646 1024.E-mail address: [email protected] (N. Mostoufi).Received 3 July 2010; Received in revised form 21 September 2010; Acc

263-8762/$ – see front matter © 2010 The Institution of Chemical Engioi:10.1016/j.cherd.2010.10.014

resources, has allowed the carrying out of detailed simula-tions of many aspects of the complex phenomena occurringin the particulate systems. Available mathematical modelsfor gas–solid systems can be grouped into two main cate-gories: the continuum–continuum approach at a macroscopiclevel represented by the two-fluid models (TFM) (Andersonand Jackson, 1967) and the continuum-discrete approach ata microscopic level mainly represented by the combinedcomputational fluid dynamics and discrete element method(Cundall and Strack, 1979) (CFD-DEM). In the CFD-DEM, themotion of particles is modeled as a discrete phase, describedby Newton’s second law of motion for an individual particle,while the flow of fluid (gas or liquid) is treated as a continuumphase, described by the local averaged Navier-Stokes equationin a computational cell. It has been recognized as an effectivemethod to study the fundamentals of particle–fluid flow atvarious conditions, as briefly reviewed by Deen et al. (2007).

As the measurement of the solids velocity in fluidized beds

epted 12 October 2010

circulation in the fluidized beds. Among few works, Mostoufi

neers. Published by Elsevier B.V. All rights reserved.

http://www.sciencedirect.com/science/journal/02638762

mailto:[email protected]

dx.doi.org/10.1016/j.cherd.2010.10.014


818 chemical engineering research and design 8 9 ( 2 0 1 1 ) 817–826

Nomenclature

Ai area of particle i (m2)Acell area of fluid cell (m2)CD fluid drag coefficientD bed diameter (m)dpi particle diameter (�m)Dr radial solid diffusivity (m2 s−1)Dz axial solid diffusivity (m2 s−1)�fc,ij contact force between particle i and j (N)�fd,ij damping force (N)�ff,i particle–fluid interaction force (N)�ffp volumetric fluid–particle interaction force

(N m−3)�fg,i gravitational force (N)�g gravitational acceleration (m s−2)Ii moment of inertia (kg m2)H bed height (m)kc number of particles in a computational cellki number of particles in contact with particle ikn normal spring coefficient (N m−1)kt tangential spring coefficient (N m−1)mi mass of particle (kg)P fluid pressure (Pa)r radial position of tracer (m)�Ri radius vector (from particle center to contact

point) (m)�Ti,j torque (N m)t time (s)�U fluid velocity (m s−1)U0 superficial gas velocity (m s−1)Umf minimum fluidization velocity (m s−1)�vi particle velocity (m s−1)�vr,ij relative velocity of particle i and j (m s−1)Vc cell volume (m3)z axial position of tracer (m)

Greek symbols˛i

cellfractional area of particle i residing in the fluidcell

ˇ inter-phase momentum transfer coefficient(kg m−3 s−1)

ı deformation coefficient (m)ε porosity�i damping coefficient� inter-particle friction coefficient�f fluid viscosity (kg m−1 s−2)�f fluid density (kg m−3)�� fluid viscose stress tensor (N m−2)�ωi angular velocity of particle (s−1)

mii

dt= �ff,i + (�fc,i,j + �fd,i,j) + �ff,i (1)

and Chaouki (2001) studied the diffusivity of solid particles inboth bubbling and turbulent regimes. Their results show thatthe diffusivities increase with the superficial gas velocity, andthey are correlated linearly to the axial solid velocity gradient.They (Mostoufi and Chaouki, 2000) also studied solids behav-iors, including restricted and unrestricted axial movementof solids, by processing the data obtained by a RadioactiveParticle Tracking (RPT) technique. The nano-particles mixingbehavior in a nano-agglomerate fluidized bed was investigated
experimentally by Huang et al. (2008). Shen et al. (1995) used a
model that consisted of an upward moving wake phase and adownwards flowing emulsion phase, to investigate the radialand vertical mixing of solids. Kobayashi et al. (2000) proposeda novel bubble distribution model based on the populationbalance of bubbles to investigate the solids circulation in thebubbling fluidized beds, and verified the proposed model bycomparing its results with the experimental findings. Zhanget al. (2010) investigated the particle motion and mixing inthe flat-bottom spout-fluid bed by CFD-DEM method. Wu andZhan (2007) used a hard-sphere DEM model to study themixing behavior of particles for two kinds of inlet configura-tions, under specific superficial gas velocities. As Lagrangianapproaches (i.e. DEM) provide us with the trajectory of the indi-vidual particles, studding the mixing phenomena can be thepossible application of this method. Therefore, the objective ofthis paper is to investigate the use of discrete element method(DEM) simulation to study solid mixing in gas-fluidized beds.Simulated axial and radial dispersion coefficients were com-pared with the experimental ones to validate the model. Theinfluences of the bed geometry, type of distributor, and theinlet gas velocity on the axial and radial solid circulation werethen investigated numerically.

2. Experiments

The experiments were conducted in a Plexiglas fluidized bedwith a 152 mm internal diameter and a 1500 mm height. As thefluidizing gas, air at the room temperature and atmosphericpressure was blown into the bed through a bubble cap distrib-utor. An orifice plate was used to measure the gas flow rate.Air leaving the top of the column passed through a cycloneto return the entrained solid particles back to the bed. Thecolumn was initially filled with sand up to approximately 1.5times its diameter. The mean particle diameter and density ofsand were 650 �m and 2650 kg/m3, respectively. Experimentswere conducted at superficial gas velocity of 1 m/s.

Time-position data was obtained by the RPT technique. Inthe experiment, a single tracer was placed into the bed to movefreely with other particles. The tracer was made of a mixture ofgold powder and epoxy resin with a density of 2600 kg/m3. Thetracer was activated in the SLOWPOKE nuclear reactor of EcolePolytechnique before the experiment. The sampling periodwas 2 m s and 8.12 × 105 data were captured during 27 min.More information about the experiments are described byMostoufi et al. (2003) and Mostoufi and Chaouki (2004). Detailsof the system calibration and the inverse reconstruction strat-egy for tracer position rendition are described by Larachi et al.(1994, 1995).

3. Modeling

In the present work, the flow of spheres in a two-dimensionalgeometry was investigated. Newton’s second law of motionwas applied to describe the movement of individual particles.The translational and the rotational motions of the particlesat any time t, can be described by the following equations (Xuand Yu, 1997):

d�vkLi∑
j=1


chemical engineering research and design 8 9 ( 2 0 1 1 ) 817–826 819

Table 1 – Forces component and torque acting on particle i.

Forces or torque Symbol Equation

Normal forces Contact �fcn,ij −(knıc,ij)�ni

Damping �fdn,ij −(�i �vr,ij.�ni)�ni

Tangential forces Contact �fct,ij −(

min(�|�fcn,ij|, |ktıt,ij�ti|)

ıt,ij|ıt,ij |

)�ti

[5pt] Damping �fdt,ij −�i[(�vr,ij.�ti) + ( �ωi × �Ri − �ωj × �Rj)]

Torque Interparticle �Ti,j�Ri × �fc,ij

Gravity �fg,i mi �g

Fluid drag force �ff,i

ˇVpi1−ε ( �U − �vi)

ˇ =

⎧⎪⎨⎪⎩

150(1 − ε)2�f

ε2d2pi

+ 1.75�f (1 − ε)| �U − �vi|

εdpi, ε < 0.8

34

CD

�f (1 − ε)| �U − �vi|dpi

ε−2.65, ε ≥ 0.8

CD =

{24[1 + 0.15Re0.687

p,i]

Rep,i, Rep,i < 1000

0.44, Rep,i ≥ 1000

where �Ri = �xj − �xi, �ni = R̄i|R̄i |

, �vr,ij = �vi − �vj, Re�,i = �f dpiε| �U−�vt |�f

, �Ffp =i=kc∑i=1

�ff,iVc

.

a

I

pmpf

mb(

a

ttgipatwlotb

o

nd

id �ωi

dt=

ki∑j=1

�Ti,j (2)

The contact forces between the particles and between thearticle and wall were calculated according to the soft sphereethod (Cundall and Strack, 1979). Since the density of solid

article is much greater than that of gas phase, the buoyantorce acting on each particle was ignored.

The gas phase is treated as a continuous phase and itsotion is defined by equations of continuity and momentum

alance based on the local mean variables on the fluid cellAnderson and Jackson, 1967).

∂ε

∂t+ ∇ · (ε �U) = 0 (3)

nd

∂(�f ε �U)

∂t+ ∇ · (�f ε �U �U) = −∇P − �Ffp + ∇ · (ε��) + �f ε�g (4)

Eq. (4) is similar to the equation used in the TFM, referredo as Model B formulation (Feng and Yu, 2004) which assumeshat the pressure drop is applied to the gas phase only. Theas and the solid phases are coupled together through poros-ty and fluid–particle interaction force, �Ffp. Particle velocity, gashase velocity field and porosity are used to calculate the forcecting on each particle. Eq. (1) was then integrated over oneime step to obtain new position of particles. These positionsere used to calculate the porosity in each fluid cell and fol-

owed by the calculation of the gas phase velocity field basedn the new fluid–particle interaction force and porosity. Equa-ions used to calculate fluid–particle force and contact forcesetween particles are listed in Table 1.

In each fluid cell, porosity was calculated based on the areaccupied by the particles in the cell. The size of fluid cell was

smaller than the macroscopic motion of particles but largerthan the particle size (3 times the diameter of particles). The2D porosity in each cell was calculated by the following equa-tion:

ε2D = 1 − 1ACell

kC∑i=1

˛icellAi (5)

where ˛icell

is the fractional area of particle i presenting in eachcell and Ai is the area of that particle. The porosity calculatedby this method is based on the 2D analysis. Therefore, it isinconsistent with the drag force formula used in this worksince the drag force correlation is actually given for a 3D sys-tem. To overcome this inconsistency, the equation suggestedby Hoomans et al. (1996) was used for translating the porosityfrom 2D to 3D:

ε3D = 1 − 2√√

3(1 − ε2D)3/2 (6)

The SIMPLE (Semi-Implicit Method for Pressure-LinkedEquations) algorithm, introduced by Patankar (1980), was uti-lized to solve the gas phase equations. The first order up-windscheme was used for the convection terms. The cell size forthe calculation of gas flow was 2 mm × 2 mm. In the case of thefluid velocity, the no-slip boundary condition was applied tothe walls and the fully developed condition to the exit at thetop. The size of the particles in the simulations was 650 �mwhich is equal to the mean diameter of the particles used inthe experimental data. Initial aspect ratios were 0.5, 1.0, and1.5 for which approximately 34,000, 67,000 and 110,000 par-ticles were used respectively in the simulations. An initiallypacked bed of particles was fluidized at different superficialgas velocities from near the minimum fluidization velocity to1 m/s. All simulations continued up to 30 s. Table 2 summa-
rizes the computational conditions and parameters used inthe simulations. The minimum fluidization velocity of parti-



Table 2 – Computational conditions used in the present simulations.

Particles Gas

Particle shape Spherical Fluid air

Mean particle diameter (�m) 650 CFD cell Width (m) 2 × 10−3

Density (kg m−3) 2650 Height (m) 2 × 10−3

Spring constant (N m−1) 800 Bed geometry Width (m) 0.15Sliding friction coefficient 0.3 Height (m) 0.9Restitution coefficient 0.9 Viscosity (kg m−1 s−1) 1.7 × 10−5

Time step (s) 1 × 10−5 Umf (m s−1) 0.35−4

cles was calculated by the equation proposed by Lucas et al.(1986) for round particles.

4. Treatment of data

The mixing pattern in the bubbling fluidized bed was stud-ied by using the experimental data and numerical results.Because of Lagrangian approach in the solid phase, the samedata processing can be done for both RPT data and DEM sim-ulation. Hydrodynamic parameters such as solid diffusivity,and internal and gross solid circulations, which are represen-tative of solids mixing in the bed, were evaluated based ontime-position particle trajectory. To calculate these parame-ters, different programs based on the physical concept of eachabovementioned parameters were developed. The algorithmof these computer programs are described in the followingsections.

4.1. Solid diffusivity

In order to calculate axial and radial diffusivities, a large num-ber of solid tracers should be injected in a small cell in the bed.The principle of ergodicity is used to simulate a large num-ber of tracers in the cell while there is only one tracer in theexperiments. Details of this method have been described byMostoufi and Chaouki (2001). Using their proposed method, alarge number of tracers (1000 tracers) can be virtually injectedinto the imaginary compartment in the bed. According toMostoufi and Chaouki (2001), solid diffusivity can be evaluatedfrom the trajectory of tracers in the Lagrangian coordinates. Ifat the time t = 0, 1000 tracers are released from (r0, z0) insidethe injection cell, instantaneous excess axial displacement ofeach of the released traces can be defined as:

Z = z(t) − z0 (7)

Fig. 1 – Position of 1000 tra

Time step (s) 1 × 10

The average displacement at time can be calculated from:

Z̄ = 11000

1000∑i=1

Zi (8)

and mean-square displacement is given by:

Z̄2 = 11000

1000∑i=1

(Zi − Z̄)2

(9)

From which the axial solid diffusivity can be obtained:

Dz = 12

dZ̄2

dt(10)

If Z̄2 is plotted vs. time, a straight line is obtained fromslope of which the solid diffusivity in the radial direction canbe obtained by the same procedure described above. Similarmethod was considered for processing data obtained in thenumerical simulations. Fig. 1 shows 1000 tracers which areinitially in the injection cell. These tracers move in both axialand radial directions as time passes. The axial movement ofparticles is more rigorous compared to the radial displacementof particles. This dominant axial movement of particles can beattributed to the effect of the rising bubble and the wake justbelow it. Furthermore, the radial movement of particles nearthe bed surface (∼14 cm) is higher than that of the lower parts.This is mainly due to the bubble bursting which accelerates theradial movement of particles.

4.2. Solids circulation

In the bubbling fluidized beds, particles move mainly as a
result of the passage of bubbles through the bed. Particles areentrained in the wake of the rising bubbles at the scale of the
cer data versus time.



distributor zone

bed surface

Gross circulation Internal circulation

circulation length

Fig. 2 – Schematic of gross and internal circulations in theb

boptpaflt

tizzpraTiotc

sibllcb

rotwt

5

5

Ttccfoias

Fig. 3 – (a and b) Detection of circulations with differentlengths for sample trajectory of a tracer.

ed.

ed height. To maintain continuity, a downward, and a morer less continuous, flow of particles must exist in the densehase. The passage of a bubble also induces a drift effect inhe dense phase which results in a loop displacement of thearticles at the scale of the bubble diameter. These two mech-nisms are mainly responsible for solids mixing in bubblinguidized beds, which are called gross and internal circula-ions, respectively (Moslemian, 1987).

Fig. 2 demonstrates gross circulation and internal circula-ion of a sample tracer in the bed. According to this figure,n a gross circulation, the tracer moves from the distributorone toward the bed surface and returns to the distributorone while in an internal circulation the tracer travels shorterath in comparison with that in the gross circulation and theneturns to its original height. The circulation length is defineds the vertical displacement of the tracer in this circulation.he circulation length is nearly as long as the active bed height

n gross circulations while it is almost as long as the diameterf bubbles in internal circulations. A program was developedo detect these circulations according to the abovementionedoncepts.

Fig. 3a and b show 10-s axial trajectories of a tracer in theimulated and experimental bed, respectively. Both gross andnternal circulations which correspond to solids mixing in theed can be found in both figures. Circulations identified with

etter “A” are considered as internal circulations and circu-ations identified with letter “B” correspond to a typical grossirculation in the bed. Besides the circulation length, the num-er of circulations and their duration were also calculated.

In order to confirm that the selected particles are the rep-esentative of the whole flow pattern in the bed, the positionf these 1000 tracers is plotted in Fig. 4a and b at t = 2 s and= 12 s, respectively. Fig. 4b shows that the tracers explore thehole bed during 10 s and consequently, can represent well

he overall bed hydrodynamics.

. Results and discussion

.1. Simulation validation

o validate the simulation, predicted axial and radial diffusivi-ies, representative of the flow structure of fluidized beds, wereompared with the experimental diffusivities. Fig. 5 shows aomparison between the experimental and the calculated dif-usivities vs. dimensionless height at superficial gas velocityf 1 m s−1. To eliminate the entrance and exit effects, diffusiv-

ty was not calculated in the zones near the distributor plate
nd the bed surface. The axial diffusivity (values on the leftide vertical axis) obtained from the simulation agrees rea-
Fig. 4 – (a) initial position of 1000 injected tracers and (b)swept area of the bed by 1000 tracers during 10 s.



0.000

0.001

0.010

0.100

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.3 0.4 0.5 0.6 0.7 0.8

Dr(m

2/s

)

Dz(m

2/s

)

h/H

Dz-ModelDz-ExperimentDr-ModelDr-Experiment

Fig. 5 – A comparison between the experimental andcalculated axial and radial diffusivity at 1 m s−1superficialgas velocity.

flux vectors are in white color. The solids flux was determined

sonably well with the experimental results. In contrast, theradial diffusivity (values on the right side vertical axis) shows alarge deviation from the experimental results. This figure alsodemonstrates that the axial diffusivity is an order of magni-tude greater than the radial diffusivity. Particles in a fluidizedbed move as a result of the drag force caused by the passingof gas through bubbles and emulsion. In the bubbling regime,bubbles rise along a vertical line and deviate less in the lateraldirection. Therefore, the drag force exerted on particles, andconsequently the particles velocity, are dominant in the axialdirection.

The deviation between the simulated and the experimen-tal diffusivities can be attributed to the two-dimensionalapproach used in this study. It is the consequence of omit-ting one dimension in the simulation (from 3D to 2D), whichmainly affects the radial component. The effect of this omit-
ting on the axial component, which is an order of magnitude
Fig. 6 – (a–d) Void fraction contours and solid flux v

larger than the lateral one, is negligible. As a result, the axialdiffusivity predicted in the simulation is in general similarto those observed by experiments while the radial diffusiv-ity shows a considerable difference. It should be noted thataccording to Xie et al. (2008) a 2D Cartesian model agrees wellwith a 3D cylindrical experiment at low velocities due to thefact that the axial terms are dominant. Therefore, at the veloc-ity of ∼3Umf considered in this study (bubbling regime), the 2DCartesian simulation can be satisfactorily validated by the 3Dcylindrical experiment in the axial direction. However, a 2Dsimulation cannot be used to study the bed behavior in theradial direction. According to Fig. 5, diffusivity is mainly con-stant against height. This is due to the fact that in the bubblingfluidized beds, the bubbles with constant diameter rise at con-stant velocity above the coalescence zoon. As the bubbles playthe main role in the solid mixing, the axial diffusivity remainsconstant.

5.2. Qualitative study of solids mixing

Solid mixing in a freely bubbling fluidized bed is caused notonly by the vertical movement of the bubbles and the burstingof bubbles at the bed surface, but also by the lateral motion ofbubbles as a result of the interaction and coalescence betweenthe neighboring bubbles. According to Stein et al. (2000), bub-bles can be considered as kinetic energy sources for particles,and the emulsion phase as a kinetic energy sink, while thesource to sink energy transfer takes place through the driftregion. This energy transfer causes internal circulation at thescale of bubbles diameter in the drift regions. Consequently,the two general mechanisms internal circulation and grosscirculation control the solids mixing in the bed. All resultspresented in this section are obtained from simulation data.

Fig. 6 shows the void fraction contour and the solid fluxvectors at different times for a bed with H/D = 1.5 and porousplate distributor. Bubbles and the emulsion phase can be iden-tified by light gray and dark gray colors respectively, and solid

from the porosity and velocity of particles at each time step.

ectors of the bed with porous plate distributer.



IbacdcuitcttlctisllflwdivflTwcCtFodta

5

Imu(eflfiv1taladbtotsesupml

Fig. 7 – Solid flow pattern and void fraction contour ininjection type distributor, Uinjection = 3.3 m/s: (a) 12.0 s and (b)

n each fluid cell, the average particle velocity was multipliedy void fraction and particle density. The formation of bubblest the vicinity of the distributor, the growth of bubbles, theiroalescence and breakage can be seen in this figure. Threeistinct bubbles can be observed in Fig. 6a. These bubbles arelose to each other and each one is partly in the wake of thepper bubble. Since the bubbles are small enough in compar-

son to the bed diameter, the persistent upward movement ofhe particles is induced in the bed. This upward movement isompensated by the downward movement of the particles inhe emulsion and in the region close to the wall. In this condi-ion, gross circulation is formed through the bed. Major solidoops shown in this slide, represent the gross and internal solidirculations in the bed. In Fig. 6b, the lower bubble is pulledoward the upper bubble because there is a negative pressuren the wake region in comparison to the surrounding emul-ion. In Fig. 6c, the bubbles have coalesced completely and aarger bubble at the scale of the bed diameter is formed. Thisarge bubble has a rigorous wake which induces a large upwardow of the solid beneath the bubble while limits the down-ard solid flow through the bed. The unbalanced upward andownward solid flow around the bubble results in its breakage

n the last slide (Fig. 6d). That is, from the material point ofiew, bubble breakage occurs to compensate for the upwardow of the solid in the wake and drift of this rising bubble.he bubble breakage causes the internal particle circulation,hich results in the rapid local mixing of the particles. These

irculations are illustrated in Fig. 6d with bold white arrows.omparison between Fig. 6a and d reveals that in Fig. 6d,

he bubble diameter in distributor zone is larger than that ofig. 6a. This result can be attributed to the fact that the rig-rous wake and upward solids movement without sufficientownward solid movement causes a solid reduction in the dis-ributor zone. Thus, the void fraction increases in this regionnd bubbles with larger diameters are formed.

.3. Effect of distributor type on the mixing pattern

n order to investigate the effect of distributor type on theixing pattern of particles, an injection type distributor was

sed in the simulation. For this purpose, a two-hole distributor22 mm inner diameter and 60 mm pitch) at the bed center wasmployed. Fig. 7 shows the void fraction contour and solidsux vectors for the injection velocity of 3.3 m/s (equal to super-cial gas velocity U0 = 0.75 m/s). The two injection holes areisible in this figure. By following the bed dynamics from 12 s to2.12 s, it can be seen that a single bubble is formed just abovehe distributor plate, detaches from holes, and rises verticallyt the center of the bed. A small bubble is formed just below thearge bubble and rapidly coalesces into it. According to Fig. 6and Fig. 7b, it can be observed that in case of the injectionistributor, there is a larger time lag between the successiveubbles compared to the porous plate type distributor. Sincehe bubble size is small compared to the bed diameter in casef the injection distributor, wall effects are minimized and theendency of bubble breakup and coalescence is reduced. Theame flow pattern and bubble behavior were observed in 2Dxperiments (Utikar and Ranade, 2007). In addition, it can beeen in Fig. 6 that the bed is divided into three regions: anpward moving bubble phase free of solids, an upward solidshase moving approximate to the bubbles, and a downward
oving dense phase. This flow pattern causes the gross circu-
ation of particles.

12.12 s.

5.4. Effect of aspect ratio on the mixing pattern

It is well known that the rate of solids’ circulation and thedegree of mixing are primarily determined by the gas velocity.However, other parameters such as particle shape and theirsize distribution also play a part. Bed geometry is an importantparameter in solid mixing. To investigate this effect, three bedswith different aspect ratios (H/D = 0.5, 1.0 and 1.5) were simu-lated using a porous plate distributor. Fig. 8 shows solids flowpattern in the bed. The arrows at this figure demonstrate theoverall flow of particles. In the shallow bed (H/D = 0.5) the pre-dominant pattern is the down flow of solid at the centre whichdeflects the bubbles towards the walls and forms two bubblepaths in the bed. Increasing the aspect ratio to 1.0 changes thesolids flow pattern considerably. In this case, bubbles formedat the distributor plate rise vertically in the centre of the bedwhich induces solids up flow at the centre and continuoussolids down flow near the walls. In a deeper bed (H/D = 1.5)the flow pattern at the distributor region resembles the oneobserved in the shallow bed and changes into a central upflow-wall down flow pattern at higher elevations (Baeyens andGeldart, 1986).

5.5. Effect of velocity on circulation length, circulationtime and number of circulations

According to the procedure described in the data treatmentsection, the distributions of solids circulation lengths in thebed (at H/D = 1) with porous plate distributor at different super-ficial gas velocities were evaluated, and they are plotted inFig. 9. This figure shows that as the gas velocity increases,the maximum circulation length, and consequently the activebed height, increases. Moreover, Fig. 9 demonstrates that thereare two peaks in the circulation length distribution at each
superficial gas velocity. The sharp peak at the lower lengthscorresponds to the internal circulations and the wide peak



met
Fig. 8 – Effect of bed geo
at the higher lengths corresponds to the gross circulations.It can be seen that the both internal and gross circulationsare responsible for the solids mixing in the bubbling beds.Increasing the gas velocity increases the number of the bothinternal and gross circulations. As more gas passes throughthe bed, more energetic bubbles are formed, and the gross cir-culation, which is the main result of bubble passage, increases.The sharper peak which corresponds to the internal circula-tions suggests that increasing the gas velocity results in moregas entering into the bed, which increases the void fraction ofthe bubble wake. In return, the wake viscosity decreases andconsequently, the formation of internal circulations becomeeasier and their number grows higher. These phenomena weredescribed qualitatively in the previous section.

The situation is different when the gas velocity is closeto the minimum fluidization (U0 = 0.53 m/s). It can be seen in
Fig. 8 that the wide peak has completely vanished. At thisvelocity, the largest circulation length is limited to 2 cm and
0

500

1000

1500

2000

2500

3000

0 5 10 15 20

Nu

mb

er o

f C

ircu

lati

on

s (-

)

Circulation Length (cm)

Uo = 0.53 m/s

Uo = 0.70 m/s

Uo = 0.80 m/s

Uo = 1 m/s

Fig. 9 – Distribution of solid circulation lengths in the bedwith porous plate distributor at different superficial gasvelocities, H/D = 1.

ry on solid circulations.

there is a sharp peak around 0.4 cm. This structure indicatesthat at low superficial gas velocity, particles obtain energyfrom gas passing through the emulsion phase (that is justenough to keep particles suspended), in contrast to the bub-bling regime in which particles obtain energy from the risingbubbles. In this condition, the particles move randomly indifferent directions inside the emulsion at the scale of the par-ticle diameter. This confirms that bubbles in bubbling fluidizedbeds are the main cause of solids circulation and solid mixingmechanisms change considerably in the absence of bubbles.

A comparison between the sample experimental data andthe simulation results in terms of the circulation length dis-tribution is presented in Fig. 10. The superficial gas velocityand bed aspect ratio were, respectively, 1 m s−1 and 1.5 andthe porous plate distributes was used. Generally, the modelcould satisfactorily predict the overall trend of the circula-tion length distribution in the experiment. The shape of both
trends and the active bed height of the bed are the same. Inthe experiment in comparison with the simulation, the sharp
0

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3500

0 5 10 15 20 25 30 35 40

Nu

mb

er o

f C

ircu

lati

on

s (-

)


Experiment

Simulation

Fig. 10 – Distribution of circulations length for simulationand experiments, bed with porous plate distributor,H/D = 1.5 and U0 = 1 m/s.



0

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3500

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0 2 4 6 8

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ircu

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)

Circulation time (sec)

Uo = 0.70 m/s

Uo = 0.80 m/s

Uo = 1 m/s

Fig. 11 – Time and number of circulations at variouss

pnbb

ibwTatbihvt

egcft

Fg

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Uo = 0.60 m/s

Uo = 0.67 m/s

Uo =0.75 m/s

Uo = 0.82 m/s

Fig. 13 – Distribution of solid circulation lengths in the bedwith injection type distributor at different superficial gasvelocities, H/D = 1.5.

uperficial velocities, H/D = 1.

eak which corresponds to the internal circulations is more inumber, and it shifts from 4 cm to 7 cm. In addition, the num-er of circulations with greater lengths in the experiment is ait less than that of in the simulation.

Circulation time of tracers is also an important parametern mixing, especially when a reaction occurs in the fluidizeded. The distribution of circulation time of particles for a bedith H/D = 1 and porous plate distributor is shown in Fig. 11.his figure illustrates that there is a sharp peak at lower timest high superficial gas velocity. It can be concluded that inhis case, mixing has improved and the solid phase in theed tends to become well mixed. As the superficial gas veloc-

ty decreases, the peak becomes wider and shifts toward theigher residence times. In other words, at lower superficial gaselocities, the circulation time of particles alters in the bed andhe fluidized bed deviates from the well-mixed state.

It is known that the axial diffusivity decreases in the pres-nce of internal circulations while it increases by increasingross circulations (Moslemian, 1987). The axial diffusivity cal-ulated based on the simulations is shown in Fig. 12 as a
unction of the superficial gas velocity and compared withhe equation proposed by Mostoufi and Chaouki (2001). It
0.000

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0.4 0.6 0.8 1

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)

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Simulation

Mostoufi and Chaouki (2001)

ig. 12 – The axial diffusivity as a function of superficialas velocity for porous plate distributor, H/D = 1.

can be seen in this figure that a good agreement existsbetween the simulation results and the equation of Mostoufiand Chaouki (2001). Increasing the superficial gas velocity to0.8 m s−1 enhances the axial diffusivity sharply while by fur-ther increase in the superficial gas velocity beyond 0.8 m s−1,the axial diffusivity increases slowly. This can be attributed tothe solids circulation pattern in the bed. Increasing the super-ficial gas velocity results in increasing both internal and grosscirculations (see Fig. 9). At low superficial gas velocity (lessthan 0.8 m s−1) increasing gross circulations is dominant incomparison with internal circulations. But at higher superfi-cial gas velocities, the role of internal circulations becomesmore effective, which results in the reduction of the slope ofaxial diffusivity vs. superficial gas velocity.

Fig. 13 shows the distribution of circulation length at var-ious superficial gas velocities when using an injection typedistributor. As expected, at low superficial gas velocity (lessthan 0.67 m s−1), there is a wide peak which corresponds tothe gross circulations. This peak increases by increasing thesuperficial gas velocity. At superficial gas velocities beyond0.67 m s−1, the same trend that was observed in Fig. 9 canbe seen. That is, as the superficial gas velocity increases, thesharp peak, which corresponds to the internal circulation,increases while the number of gross circulations reduces. Sucha trend can be explained by the fact that by increasing thesuperficial gas velocity, the bubble size increases and the bub-bling regime tends to the slugging regime. Therefore, becauseof the wall effects, the possibility of the phenomena such asbubble breakage strengthens and the local circulation of solidsin the fluidized bed increases accordingly.

6. Conclusions

A CFD-DEM technique was used to investigate the solids cir-culation in gas–solid fluidized beds. The results of the modelwere compared with the experimental RPT data to validatethe model. Effect of gas velocity, distributor type, and bedaspect ratio on solids flow pattern and mixing properties werestudied. The results obtained in this study are summarized as
follows:



• The 2D model successfully captured the 3D experimentalsolid diffusivity in the axial direction while it overestimatesthe experimental results in the radial direction. The axialdiffusivity of particles remained constant along the bedheight, excluding distributor and surface zones.

• A qualitative understanding of solids flow pattern of thewhole bed was obtained by reviewing snapshots obtainedfrom the simulation results. Phenomena such as bubbleformation and bubble growth, the coalescence and thebreakage of bubbles and solids circulations were clearlyobserved.

• The influence of distributor type was investigated. Hydro-dynamics and solids flow pattern in the bed were altered byusing an injection type distributor instead of porous plate.Individual bubbles were formed at distributor zone and roseup vertically with higher time lags compared to the porousplate. Therefore, in the case of injection distributor, the ver-tical movement of bubbles is less affected by coalescenceand breakage and the solids flow pattern tends to the grosscirculation.

• By increasing the aspect ratio of the bed, the solids flow pat-tern changed considerably. At aspect ratio lower than one,the flow pattern was consistent with that of the shallowbeds. At aspect ratio equal to one, the flow changed into thecentral up flow-wall down flow pattern. By further increasein the aspect ratio to 1.5, a circulation pattern similar tothe shallow bed was formed above the distributor and acentral up flow-wall down flow above this region could berecognized.

• Both gross and internal circulations with positive and neg-ative impacts respectively, affect the axial diffusivity ofparticles. At higher superficial gas velocities, the role ofgross circulations becomes more effective than the internalcirculations and they result in enhancing the axial diffusiv-ity.

References

Anderson, T.B., Jackson, R., 1967. A fluid mechanical descriptionof fluidized beds: equations of motion. Ind. Eng. Chem.Fundam. 6, 527–539.

Baeyens, J., Geldart, D., 1986. Chapter 5 (Solid Mixing) of GasFluidization Technology. John Wiley & Sons Ltd, pp. 95–103.

Cundall, P.A., Strack, O.D.L., 1979. A discrete numerical model forgranular assemblies. Geotechnique 29, 47–65.

Deen, N.G., Sint Annaland, M.V., Van der Hoef, M.A., Kuipers,J.A.M., 2007. Review of discrete particle modeling of fluidizedbeds. Chem. Eng. Sci. 62, 28–44.

Feng, Y.Q., Yu, A.B., 2004. Assessment of model formulations in
the discrete particle simulations of gas–solid flow. Ind. Eng.Chem. Res. 43, 8378–8390.
Hoomans, B.P.B., Kuipers, J.A.M., Briels, W.J., van Swaaij, W.P.M.,1996. Discrete particle simulation of bubble and slugformation in a two-dimensional gas-fluidized bed: a hardsphere approach. Chem. Eng. Sci. 51 (1), 99–118.

Huang, C., Yao, W., Fei, W., 2008. Solids mixing behavior in anano-agglomerate fluidized bed. Powder Technol. 182,334–341.

Kobayashi, N., Yamazaki, R., Mori, S., 2000. A study on thebehavior of bubbles and solids in bubbling fluidized beds.Powder Technol. 113, 327–344.

Larachi, F., Chaouki, J., Kennedy, G., 1994. A g-ray detectionsystem for 3-D particle tracking in multiphase reactors. Nucl.Instrum. Methods A 338, 568–576.

Larachi, F., Chaouki, J., Kennedy, G., 1995. 3-D mapping of solidsflow fields in multiphase reactor with RPT. AIChE J. 41,439–443.

Lucas, A., Arnolds, J., Casa, J., Puigjaner, L., 1986. Improvedequation for the calculation of minimum fluidization velocity.Ind. Eng. Chem. Process Des. Dev. 25 (2), 426–429.

Moslemian, D., 1987. Study of solid motion, mixing and heattransfer in gas fluidized beds. PhD Thesis, University ofIllinios at Urbana-Champaign.

Mostoufi, N., Chaouki, J., 2000. On the axial movement of solids ingas–solid fluidized beds. Trans. IChemE 78, Part A (September2000).

Mostoufi, N., Chaouki, J., 2001. Local solid mixing in gas–solidfluidized beds. Powder Technol. 114, 23–31.

Mostoufi, N., Kennedy, G., Chaouki, J., 2003. Decreasing thesampling time interval in radioactive particle tracking. Can. J.Chem. Eng. 81 (1), 129–133.

Mostoufi, N., Chaouki, J., 2004. Flow structure of the solids ingas–solid fluidized beds. Chem. Eng. Sci. 59, 4217–4227.

Patankar, S.V., 1980. Numerical methods in heat transfer andfluid flow. Hemisphere.

Rhodes, M.J., Wang, X.S., Nguyen, M., Stewart, P., Liffman, K.,2001. Study of mixing in gas-fluidized beds using a DEMmodel. Chem. Eng. Sci. 56, 2859–2866.

Shen, L., Zhang, M., Xu, Y., 1995. Solids mixing in fluidized beds.Powder Technol. 84, 207–212.

Stein, M., Ding, Y.L., Seville, J.P.K., Parker, D.J., 2000. Solid motionin bubbling gas fluidized beds. Chem. Eng. Sci. 55, 5291–5300.

Utikar, R.P., Ranade, V.V., 2007. Single jet fluidized beds:experiments and CFD simulations with glass andpolypropylene particles. Chem. Eng. Sci. 62, 167–183.

Wu, C., Zhan, J., 2007. Numerical prediction of particle mixingbehavior in a bubbling fluidized bed. J. Hydrodyn. 19 (3),335–341.

Xie, N., Battaglia, F., Pannala, S., 2008. Effect of using two- versusthree- dimensional computational modeling of fluidized beds.Part I. Hydrodynamics. Powder Technol. 182, 1–13.

Xu, B.H., Yu, A.B., 1997. Numerical simulation of the gas–solidflow in a fluidized bed by combining discrete particle methodwith computational fluid dynamics. Chem. Eng. Sci. 52 (16),2785–2809.

Zhang, Y., Jin, B., Zhong, W., Ren, B., Xiao, R., 2010. DEM
simulation of particle mixing in flat-bottom spout-fluid bed.Chem. Eng. Res. Des. 88 (5–6), 757–771.

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