Chemical Engineering Science 80 (2012) 365–379

Contents lists available at SciVerse ScienceDirect

Chemical Engineering Science

0009-25

http://d

n Corr

E-m

journal homepage: www.elsevier.com/locate/ces

CFD simulation of hydrodynamic characteristics in a multiple-spouted bed

Yongchao Li, Defu Che n, Yinhe Liu

State Key Laboratory of Multiphase Flow in Power Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

H I G H L I G H T S

c Two-fluid model with kinetic theory of granular flow is adopted for simulation.c Effect of gas flow rates on the multiple-spouted bed hydrodynamics is studied.c Effect of different particle sizes is investigated.c Spout diameter and fountain height increases initially and then decreases.c Static bed thickness has an obvious influence on the flow behavior in the bed.

a r t i c l e i n f o

Article history:

Received 21 February 2012

Received in revised form

3 May 2012

Accepted 5 June 2012Available online 15 June 2012

Keywords:

Multiple-spouted bed

Hydrodynamics

Simulation

Voidage

Momentum transfer

Fountain height

09/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.ces.2012.06.003

esponding author. Tel.: þ86 29 82665185; fa

ail address: dfche@mail.xjtu.edu.cn (D. Che).

a b s t r a c t

In present work, the gas-solid two-phase flow in the multiple-spouted bed is simulated by the

Eulerian–Eulerian approach, the Gidaspow drag model is chosen to describe the interface momentum

exchange. The simulated results agree well with the experimental results from the literature. Then the

detailed flow behavior in the multiple-spouted bed is investigated for 1.0 mm, 1.4 mm and 1.8 mm

glass beads. The effect of the ratio of central/auxiliary and auxiliary/central gas flow on the

hydrodynamic characteristics in the multiple-spouted bed is studied. The high velocity spouting gas

dominates the flow pattern in the bed and restricts the development of the low velocity spouting gas.

The distribution of voidage, the profile of particle velocity and the variation of particle volume

concentration are obtained. The fountain height and spout diameter increases with increasing gas flow

rate initially and then decreases. The increasing bed thickness has an obvious influence on the

hydrodynamics in the bed. For Multi-spouting, the spout diameter increases with increasing bed height,

however the bed becomes unstable when the bed thickness is increased to 200 mm. For Single-

spouting, the fountain height decreases with increasing bed thickness, but the fountain width and the

solid volume concentration in the fountain increases. The results of this study provide important

information on the flow behavior within the multiple-spouted bed and may be helpful for better

application of this type of spouted bed to the industrial process.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Spouted beds can achieve an intensive gas solid contact andcan operate stably in a broad range of gas flow rate due to thedistinguished heat and mass transfer properties and the ability toprocess coarse, sticky, irregularly shaped and heat-sensitivematerials. In recent years spouted beds have been widely usedin various industrial and physical operations such as drying ofbiomaterials, foods and pharmaceutical powders (Devahastinet al., 1998); coating application on hard and soft capsules(Oliveira et al., 2005; Pissinati and Oliveira, 2003); granulation;combustion of coals, sawdust and waste biomass (Konduri et al.,

ll rights reserved.

x: þ86 29 82668703.

1999); coal gasification (Tsuji and Uemaki, 1994); thermal cata-lytic process (Kechagiopoulos et al., 2009; San Jose et al., 2009);pyrolysis of plastics (Artetxe et al., 2010; Elordi et al., 2011) andflash pyrolysis of biomass (Amutio et al., 2011, 2012). Researchershave used and developed various measuring techniques to studythe flow behavior in the spouted bed, such as non-intrusivemeasuring technique (Mohs et al., 2009), particle trackingmethod, microwave heating and infrared thermal imaging tech-nology (Zhong et al., 2010) etc. Meanwhile, some experimentalworks have been done to investigate the combustion behavior(Pimchuai et al., 2010; Shen et al., 2009) and the gasificationperformance (Spiegl et al., 2010) in the spouted bed reactor.

In order to satisfy different purposes for using the spoutedbeds and achieve the optimum performance in various industrialapplications, numerous modifications have been carried out toovercome some limitations of the conventional spouted beds.

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379366

Such as conical spouted bed (Barrozo et al., 2010; Bettega et al.,2009; San Jose et al., 2008), spout-fluid bed (Littman et al., 2009;Patterson et al., 2010), spouted bed with draft tube (Freitas andFreire, 2002; Olazar et al., 2012; Shirvanian and Calo, 2004),rotating spouted bed (Devahastin et al., 1999), slot rectangularspouted bed (Freitas et al., 2004) and multiple-spouted bed etc.However, the scaling-up problem has not been solved well, andthis limits the application of spouted bed technique in industrialprocesses, especially on large-scale. The multiple-spouted bedseems to be a valuable modification in industrial application.Several papers (Albina, 2003; Ren et al., 2010; Saidutta andMurthy, 2000) about the characteristics and applications ofmultiple-spouted bed have been published.

To investigate the particle and gas flow characteristics inspouted beds, one can choose the experimental approach ornumerical method. In recent years, numerical simulation withcomputational fluid dynamics becomes very popular to obtaindetailed information of the flow characteristics in spouted bedsdue to the rapid development of numerical computational tech-niques and computer performances over past decades.

The approaches most commonly used in CFD models for thesimulation of gas solid flow are mainly divided into two groups,the Lagrangian approach (discrete models) and the Eulerianapproach (continuum models). Both approaches consider the fluidphase as continuum. The main difference between them is how todeal with the dispersed phase. The Lagrangian approach whichtreats particles individually has two branches, the stochastictrajectory method and discrete element method. The trajectorymethod is often applied to dilute systems. The discrete elementmethod can deal with the dense system with high particleconcentration and shows a good performance (Link et al., 2009;Takeuchi et al., 2004, 2008). However, the computation workloadincreases very quickly with the increase of particle number.Consequently, the particle number is too huge to do calculationby this model for large scale industrial spouted bed.

The Eulerian description considers the dispersed phase as acontinuum. In this approach, the gas phase and solid phase aremathematically treated as interpenetrating continuum. Thus,supplementary closure equations are required for particle inter-actions. Subsequently an extension of the classical kinetic gastheory called the kinetic theory of granular flow has beendeveloped for the closure and is widely accepted (Ding andGidaspow, 1990; Gidaspow, 1994; Lun et al., 1984). Comparedto the discrete element method, the Eulerian approach makes thescheme of the mathematical solutions relatively easier andcomputational cost less expensive, since the dispersed phase istreated with the same discretization and similar numericaltechniques as those used for the continuous phase, and thusgreatly benefits the practical applications of this approach.Numerical studies (Cunha et al., 2009; da Rosa and Freire, 2009;Gryczka et al., 2009; Reuge et al., 2008; Sobieski, 2010) haveshown the capability of the continuum model incorporated withthe kinetic theory approach for modeling gas solid flow and havedemonstrated its superiority for hydrodynamic simulations.

The two-fluid model based on Eulerian approach assumes thatboth the carrier fluid and the particles comprise two separate, butintermixed, continua. For simulating the gas solid flow in spoutedbed, the motion of particles depends on the proper description ofthe interphase momentum exchange. The interphase momentumtransfer which has the primary effect on the hydrodynamicbehavior between the phases is one of the most significant termsin the momentum equation, and this momentum exchange isrepresented by drag force. Firstly, the drag force is based on asingle spherical particle, but people seldom do the simulation ofjust one particle. Secondly, some correlations have been obtained,such as Ergun (1952) equation and Wen and Yu (1966) equation.

However, their validity is limited to the given range of solidconcentration. In order to overcome this problem and constitute adrag equation which can cover a broad range of solid concentra-tion, Gidaspow combined the Ergun equation and Wen and Yuequation, then propose a Gidaspow (1994) model to calculate thedrag force. This Gidaspow model seems to be more attractive andactive. It has been widely used and achieved good agreement withthe experimental findings.

In this paper, we adopt the two-fluid Eulerian model tosimulate the complex gas solid two phase flow in a spoutedbed. The Gidaspow drag model is chosen to describe the inter-phase momentum exchange. Among the various types of spoutedbeds, we consider a rectangular multiple-spouted bed with acentral inlet jet and two auxiliary spouting nozzles. The gas solidflow patterns in this spouted bed is simulated and compared withthe recent experimental data. The results show that the overallflow behavior and the total bed pressure drop within the spoutedbed can be predicted well by the aforementioned model. Then,the detailed characteristics of the gas solid flow in the multiple-spouted bed are examined. The effects of the hydrodynamicparameters on the flow patterns in the bed under differentoperational conditions are analyzed, and some interesting anduseful results are obtained.

2. Mathematical model

The two-fluid model based on Eulerian approach is used forsimulating the gas solid flow in the spouted bed, both phases aretreated as interpenetrating continua, identified by their volumefraction and exchanging properties between the phases. Theequations of mass conservation and momentum conservationare used to describe each of these continua. These governingequations are summarily given below.

2.1. Continuity equations

The continuity equations for gas and solid phase are

@

@tegrg

� �þr � egrgug

� �¼ 0 ð1Þ

@

@tesrs

� �þr � esrsus

� �¼ 0 ð2Þ

where eg ,rg ,ugare the volume fraction, density, velocity vector ofgas phase, respectively, and es,rs,us is the volume fraction,density, velocity vector of solid phase, respectively. The additionalcondition for the volume fraction is

egþes ¼ 1 ð3Þ

2.2. Momentum equations

The gas phase momentum equation has the following form

@

@tegrgug

� �þr � egrgugug

� �¼�egrpþegrggþ

r � sgþb us�ug

� �ð4Þ

where p stands for the pressure, g stands for the gravitationalacceleration, sgstands for the gas phase stress tensor, b denotesthe drag coefficient. The gas phase is treated as Newtonian fluidand the viscous stress tensor is calculated according to Newton’slaw.

sg ¼�2

3egmg r � ug

� �Iþegmg rugþr

T ug

h ið5Þ

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379 367

where mg stands for gas phase viscosity, I stands for identitymatrix.

The solid phase momentum equation has a similar form to thatfor the gas phase.

@

@tesrsus

� �þr � esrsusus

� �¼�esrpþesrsgþr

� ssþb ug�us

� �ð6Þ

where ss denotes the solid phase stress tensor, and it will be givenin the following section.

2.3. Kinetic theory of granular flow

For the solid phase, the constitutive equations based on thekinetic theory of granular flow are popularly used. This theory isderived from the kinetic theory of gas, and a new concept, namelygranular temperature, is proposed. Compared to the thermody-namic temperature, the latter represents the fluctuating energy ofthe molecules on the micro-scale; the former expresses thekinetic energy of the particle random motion on the macro-scale.The meanings of the two concepts are very similar. Thus, the fluiddynamic properties of the solid phase, such as the solid pressureand viscous force, can be described as a function of the granulartemperature. The granular temperature y is defined by thefollowing equation (Gidaspow, 1994).

y¼1

3c2� �

ð7Þ

where c is the particle fluctuating velocity, the brackets denoteensemble averaging. The transport equation of the granulartemperature derived from the kinetic theory of granular flow is

3

2

@

@tesrsy� �

þr � esrsusy� ��

¼ �psIþss

� �: rusþr � ksryð Þ�gsþfsþDgs ð8Þ

where �psIþss

� �: rus is the generation of energy by the solid

stress tensor, ps, is the granular pressure, ksry is the diffusion ofenergy, ks is the conductivity of the particle fluctuating energy, gs,is the collisional dissipation of energy, fs is the energy exchangebetween the gas and solid phase, and Dgs is the rate of energydissipation per unit volume. The conductivity of the particlefluctuating energy based on the effective coefficient of restitutionis calculated by the expression of Gidaspow et al. (1992) asfollows.

ks ¼150rsds

ffiffiffiffiffiffipyp

384g0 1þesð Þ1þ

6

5esg0 1þesð Þ

� 2

þ2rses2dsð1þesÞg0

ffiffiffiffiyp

rð9Þ

where es is the coefficient of restitution for particle collisions, ds isthe particle diameter, and g0 is the radial distribution function.The radial distribution function is used for measuring the prob-ability of particle collisions, it can be expressed by Ogawa et al.(1980)

g0 ¼ 1�es

es,max

� �1=3" #�1

ð10Þ

where es,max is the maximum packing volume fraction of particle.For granular flow, the particle pressure is calculated by the

following equation (Lun et al., 1984) which contains the radialdistribution function. The volume fraction of solid phase is limitedby its allowed maximum value. When the solid volume fractionreaches the packing limit, the particle pressure becomes infinity,which implies that the unphysical phenomenon happens.

ps ¼ esrsyþ2es2rs 1þesð Þg0y ð11Þ

The solid phase stress tensor can be calculated by the followingequation

ss ¼ es ls�2

3ms

� �r � usð Þ

� Iþesms rusþr

T us

h ið12Þ

where ls stands for granular bulk viscosity, ms stands for solidphase shear viscosity. The granular bulk viscosity which accountsfor the resistance to compression and expansion of the granularparticles is calculated by the following correlation of Lun et al.(1984).

ls ¼4

3esrsdsg0 1þesð Þ

yp

� �1=2

ð13Þ

The shear viscosity of solid phase contains two parts, acollisional shear viscosity and a kinetic shear viscosity, as shownin the following equation (Gidaspow, 1994).

ms ¼ ms,colþms,kin ð14Þ

The collisional shear viscosity is calculated by the followingequation (Gidaspow et al., 1992)

ms,col ¼4

5esrsdsg0 1þesð Þ

yp

� �1=2

ð15Þ

and the kinetic shear viscosity is expressed by Gidaspow et al.(1992)

ms,kin ¼10rsds

ffiffiffiffiffiffipyp

96esg0 1þesð Þ1þ

4

5esg0 1þesð Þ

� 2

ð16Þ

The collisional dissipation of energy represents the rate ofenergy dissipation due to collisions between particles. It isrepresented by the following equation (Lun et al., 1984).

gs ¼12 1�e2

s

� �e2

s

dsffiffiffiffipp rsg0y

3=2ð17Þ

The transfer of the kinetic energy of random fluctuationbetween the gas and solid phase is calculated by the followingequation (Gidaspow et al., 1992).

fs ¼�3by ð18Þ

The last term in the transport equation of the granular tempera-ture is calculated using the Koch’s expression (Koch, 1990).

Dgs ¼dsrs

4ffiffiffiffiffiffipyp

18mg

ds2rs

!2

ug�us

2 ð19Þ

2.4. The coefficient of interface momentum exchange

The interface momentum transfer, as mentioned above, isrepresented by the drag force. Since its essential effect on thehydrodynamic behavior of gas-solid flow, a lot of work has beendone on this subject and various drag models have been pro-posed. As described above, different models including Schiller andNaumann drag model, Ergun model, Wen &Yu model and Gidas-pow model have been put forward. In these models, the Gidaspowmodel has proved to be effective for modeling the interfacemomentum exchange, and has been widely used for simulatingthe solid-fluid systems. Researchers have done some modificationbased on the Gidaspow theory in recent years, one example is theGidaspow model with a switch function (Lathouwers and Bellan,2001; Sobieski, 2009; Zhonghua and Mujumdar, 2007). We adoptthe Gidaspow model in present work and it has the followingexpression (Gidaspow, 1994).

b¼3

4

eg 1�eg

� �ds

rg ug�us

CD0eg�2:65 eg Z0:8 ð20aÞ

Table 1Parameters and simulation settings in present work.

Parameters Description Value

rs (kg/m3) Solid density 2400

rg (kg/m3) Gas density 1.225

mg (Pa s) Gas viscosity 1.7894E�5

ds (mm) Particle diameter 1.0,1.4,1.8

es,max Maximum solid volume fraction 0.59

es Particle restitution coefficient 0.9

D0 (mm) Spout nozzle width 10

Dt (mm) Bed width 300

H0 (mm) Static bed height 100,150,200

Ht (mm) Bed height 1200

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379368

b¼ 1501�eg

� �2mg

egds2þ1:75

1�eg

� �rg ug�us

ds

eg o0:8 ð20bÞ

where

CD0 ¼24

Re1þ0:15Re0:687� �

Reo1000 ð21aÞ

CD0 ¼ 0:44 ReZ1000 ð21bÞ

Re¼egrgds ug�us

mg

ð22Þ

Parti

cle

velo

city

(m/s

)Coarse grids(25×80)Mid grids(48×120)Fine grids(96×160)

Ug= 0.825m/sds= 1.4mmρs= 2400kg/m3

-0.2

0.3

0.8

1.3

0.3

0.5

0.7

0.9

Coarse grids(25×80)Mid grids(48×120)Fine grids(96×160)

Ug= 0.825m/sds= 1.4mmρs= 2400kg/m3

Poro

sity

3. Numerical procedure

The experimental results obtained by Ren et al. (2010) areadopted to validate the model. The structure of the multiple-spout vessel is schematically shown in Fig. 1. The vessel has awidth of 300 mm, a depth of 30mm and a height of 1200 mm. Thedetailed description of the experimental parameters can be foundin the paper of Ren et al. (2010). Then, the flow characteristics inthe multiple-spouted bed under different operation conditionshave been studied. The parameters used in the present simulationare listed in Table 1. We adopt a two-dimensional computationalgrid to simulate the multiple-spouted bed. The effect of the frontand back walls on the flow behavior in the bed is not considered.

0 0.05 0.1 0.15 0.2 0.25 0.3x(m)

Fig. 2. Comparison of the simulated voidages and particle velocities at three

different grid sizes.

3.1. Solution method of equations

The set of governing equations presented in the previoussections are solved numerically using a CFD code called MFIX(Multiphase Flow with Interphase eXchanges) (Syamlal et al.,1993) which is developed earlier at the National Energy

H0

1200

mm

300mm

Outlet

Gas inlet

10mm

Spout nozzle

Fig. 1. Schematic diagram of the multiple-spouted bed.

Technology Laboratory (NETL) of USA and is available on theinternet at http://www.mfix.org.

The code uses a finite volume method to solve the governingequations. The coupling between the pressure and the velocity isobtained using Patankar and Spalding’s SIMPLE algorithm(Patankar, 1980). We employed a staggered grid to partition thecomputational domain. The time step is 1�10�4 s. For eachresidual component, a convergence criterion of 10�3 is fixed forthe relative error between two iterations. All simulations are runfor 30 s, and data in the last 20 s are used to calculate the time-averaged variables.

The effect of grid partition on the simulation results isexamined by comparing the simulation results from three differ-ent grid sizes. As shown in Fig. 2, the predictions from the midgrids and fine grids are the same along horizontal direction. Thus,we choose the grid partition with the mid grid size for the currentsimulations.

3.2. Initial and boundary conditions

Initially, the whole bed is assumed to hold still at atmosphericpressure, both of the gas velocity and solid velocity are set to zero.The particles are filled in the bed below the given static bedheight and the volume fraction of particles is limited to the loosepacking volume fraction.

For the boundary conditions, the gas is injected into the bedfrom the three spout nozzles, and the gas velocity is specified atthe spout inlets. The solid velocity is set to zero at the inlets; Zeronormal gradient condition and the atmospheric pressure are usedfor the outlet at the top of the bed; The no-slip boundarycondition is used for gas phase at the left and right walls, and

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379 369

the boundary condition of Johnson and Jackson (1987) is used forthe solid phase.

0

0.3

0.6

0.9

1.2

0 5 10 15 20 25 30Uc(m/s)

ΔP (k

Pa)

SimulationExperimental

Ua= 12m/sds= 2.8mmρs= 900kg/m3

H0/Dt0 = 1.0

Fig. 4. Comparison between experimental and simulated total bed pressure drops

against central injected gas velocity at the static bed height of H0=Dt0 ¼ 1:0.

4. Results and discussion

4.1. Validation of the model

Fig. 3 presents the snapshots of the simulated three typicalflow patterns, compared with the experimental images photo-graphed by Ren et al. (2010) using a CCD imaging system. Theyare the internal jet with bubble (IJB), single spouting (SS), andmulti-spouting (MS), respectively. Reasonable agreementsbetween simulations and experiments are found. Fig. 3a showsthe flow pattern of internal jet with bubble. This is an unstableflow pattern, which occurs at high gas spouting flow rates and atrelatively high static bed heights as in the multiple-spouted coalgasifier. In this flow pattern, small bubbles lift off from the jetsand agglomerate to form a large bubble at the lower part of thebed, then the large bubble grows bigger and bigger. When thebubble grows big enough to occupy almost the whole width of thebed, periodic slugging occurs, which is an awful disaster thatshould be avoided in industrial process. Therefore, the properoperation parameters are very important. Simulation results andexperimental results in Fig. 3b both indicate that the spout isstable and non-pulsating, and the movement of particles issmooth. The same characteristics as the conventional spoutedbed can be obviously observed. Fig. 3c also shows the goodagreement between simulation and experiment. In this case, theauxiliary gas spouting velocity is larger than the central gasspouting velocity, and two distinct annular fountains can beobserved, the central fountain is not formed because the annularspouts suppress the development of the central spout.

Fig. 4 compares the simulated and the experimental total bedpressure drops versus the central gas spouting velocity at theconstant auxiliary gas flow rate. Both the simulation and experi-mental values appear to have the same tendency. The total bedpressure drop increases at first, and then decreases gradually afterit reaches a maximum value.

From the above comparisons and discussions, it can be seenthat the simulated results have reasonable agreements with theexperimental results qualitatively. This indicates that the presentmodels are suitable to simulate the gas-solid two phase flow inspouted bed and predict a reasonable tendency.

Fig. 3. Comparison between experimental and simulated flow patterns under variou

snapshots. (a) H0=Dt0 ¼ 3:0, Qc=Qmf ¼ 3:06, Qa=Qmf ¼ 1:83; (b) H0=Dt0 ¼ 1:5, Qc=Qmf ¼

4.2. Flow behaviors at different central/auxiliary and auxiliary/

central spouting gas proportions

The basic aim of present modeling about the hydrodynamicbehavior in the multi-spouted bed is to obtain the detailedinformation on flow structure.

4.2.1. Effect of central spouting gas flow rate

Fig. 5 shows the voidage distributions within the spouted bedfor the central injected gas flow rates of 0.2Qa–0.8Qa at theconstant auxiliary spouting gas flow rate for the particle size of1.4 mm, and the constant Qa is equal to 1.1Qmf, where Qmf is theminimum fluidizing flow rate. The flow patterns are remarkablydifferent for different central spouting gas flow rates.

The picture in Fig. 5a shows the voidage distributions for thecentral injected gas flow rate of 0.2Qa. It can be seen that there isnot a spout or fountain in the center at this time, because thecentral gas flow rate is very low. The two fountains formed by thehigh auxiliary spouting gases expand through the surface of thebed, and throw the particles to the central part of the bed,therefore, restricts the growth of the central spouting gas, thena dense zone with the particles moving downward is formed andleads to a big flow resistance for the gas in the central region.Consequently the gas disperses to the bed in all directions as soonas it leaves the central spout nozzle, and it is hard to form a jet. Inthis case, particles accelerated by the auxiliary spouting gas travelat relatively high speed, while particles in the central region forma packed bed and flow downwards at relatively low speed,feeding into the spouts along their entire height.

s operational conditions. The left is experimental images, the right is simulated

3:6, Qa=Qmf ¼ 1:65; (c) H0=Dt0 ¼ 1:0, Qc=Qmf ¼ 1:2, Qa=Qmf ¼ 3:03.

Fig. 5. Snapshots of the gas phase voidage distributions with increased central injected gas velocity for 1.4 mm glass beads. (a) Qc=Q a ¼ 0:2; (b) Qc=Qa ¼ 0:3;

(c) Qc=Qa ¼ 0:4; (d) Qc=Qa ¼ 0:5; (e) Qc=Qa ¼ 0:6; (f) Qc=Qa ¼ 0:7; (g) Qc=Qa ¼ 0:8.

-1

-0.5

0

0.5

1

1.5

x(m)

Parti

cle

velo

city

(m/s

) 0.1 0.2 0.3 0.50.7 0.8 0.9

-1

-0.5

0

0.5

1

1.5

x(m)

Parti

cle

velo

city

(m/s

) 0.1 0.2 0.3 0.50.7 0.8 0.9

-1

-0.5

0

0.5

1

1.5

x(m)

Parti

cle

velo

city

(m/s

)

0.1 0.2 0.3 0.50.7 0.8 0.9

-1

-0.5

0

0.5

1

1.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

x(m)

Parti

cle

velo

city

(m/s

)

0.1 0.2 0.3 0.50.7 0.8 0.9

z/H0 z/H0

z/H0z/H0

Fig. 6. Profiles of time-averaged particle velocities with increased central injected gas velocity at various bed levels for 1.0 mm glass beads. (a) Qc=Qa ¼ 0:2;

(b) Qc=Qa ¼ 0:4; (c) Qc=Qa ¼ 0:6 and (d) Qc=Qa ¼ 0:8.

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379370

As shown in Fig. 5b, when the central spouting gas velocity is alittle higher than that in Fig. 5a, a void zone is generated only in thelower region along the direction of the central spout nozzle.However, the central jet is very small and hardly to reach thebed surface since the central gas velocity is not high enough, thusthe turbulence intensity on the upper central region of the bed isweak, therefore, the central region of the bed surface is almost flat.

From Fig. 5c–g, we can see that, at first, the central gas dispersesto the bed and some pass the packed region, and then enter theauxiliary spouts since the gas has the preference to go through thesmall resistance path. As the central spouting gas velocity increases,the central spout growth higher and higher. For the effect of thegradually strong central spout, the auxiliary spouts tilt slightlytowards the wall. For the effect of the wall, the fountains aresqueezed out of shape, and expand to the center. When the centralspout is high enough to reach the surface of the bed, at last the

central fountain is formed. However, the central fountain height isnot very high due to the influence of the auxiliary spouting gas.

It is the flowing gas in the bed that drives the particle to move,so particle performance is different under different operationalgas conditions. The distribution of particle velocity in the bedunder various operational conditions is analyzed as follows.

Profiles of time-averaged particle velocity appear in Figs. 6 and 7for the particle sizes of 1.0 mm and 1.8 mm used in this work atvarious bed levels. For each particle diameter, the auxiliary spoutinggas flow was held constant, and the proportion of central flow wasvaried from 0.2Qa to 0.8Qa. The profiles of particle velocity showdifferent variation tendencies with the changing gas spoutingconditions. San Jose et al. (1998) indicated that the particle velocityprofiles change with the geometry of the spout and, consequently,with the operating variables that affect this geometry. Olazaret al.(1998) determined that the radial profile of the vertical

-1

-0.5

0

0.5

1

1.5

0 0.05 0.1 0.15 0.2 0.25 0.3x(m)

Parti

cle

velo

city

(m/s

)

-1

-0.5

0

0.5

1

1.5

0 0.05 0.1 0.15 0.2 0.25 0.3x(m)

Parti

cle

velo

city

(m/s

) -1

-0.5

0

0.5

1

1.5

0 0.05 0.1 0.15 0.2 0.25 0.3x(m)

Parti

cle

velo

city

(m/s

)

-1

-0.5

0

0.5

1

1.5

0 0.05 0.1 0.15 0.2 0.25 0.3x(m)

Parti

cle

velo

city

(m/s

)

Fig. 7. Profiles of time-averaged particle velocities with increased central injected gas velocity at various bed levels for 1.8 mm glass beads.(a) Qc=Q a ¼ 0:2;

(b) Qc=Qa ¼ 0:4; (c) Qc=Qa ¼ 0:6 and (d) Q c=Qa ¼ 0:8.

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379 371

component of particle velocity changes with the longitudinalposition. These phenomena also exist in the present spouted bed.

It is noteworthy that the particles are accelerated moreintensively by the spouting gas in vertical direction in the jetzone and, consequently, a distinct peak value of particle velocityis reached close to the spout axis. At the bottom of the bed, thevelocity of particle is almost zero in the region between thespouts and in the region near the wall, because the particles movein horizontal direction until they enter the spout regions.

It can be seen that, when at the lowest ratio of central gas flowto auxiliary gas flow as shown in Figs. 6a and 7a, the profiles ofparticle velocity have two maximum values above the auxiliaryorifices, and then decreases with the increasing distance from thespout axis. In the lower part of the bed, the profiles of particlevelocity are almost flat in the middle region of the bed alongthe horizontal orientation. Near the bed surface, there are tworegions of negative particle velocity. It is because that, the gasconveys a mass of particles to the bed surface due to the highvelocity of auxiliary gas spouting, and the particles reach theirmaximum value of velocity, then the particles move towards thecenter of the bed. When arriving at the region close to the top ofthe central spout, the particles change their direction and movedownwards.

From Figs. 6 and 7 it can be noted that increasing theproportion of central gas increases the local particle velocity inthe central region of the bed due to the higher spouting gas flowrate. In the spout region, the particle velocities increase ratherdramatically with increasing height. In addition, the difference inparticle velocity between the top and bottom of the bed decreaseswith increasing Qc/Qa. The particles move downwards in theregion among the spouts and near the wall. In the upper packedsection of the bed, the particle velocities decrease with decreasingheight due to cross-flow of solids from the packed region to thespouts. In the lower packed section of the bed, the particlevelocities show the same trend. The cross-flow is greater in the

lower portion of the bed, probably because of the higher shear atthe interface between the spouts and the packed region.

The gas spouting velocity plays a dominant role in the motionof particle, and then the movement of particle has an importantinfluence on the particle distribution, consequently, while the gasspouting velocity is increased, the effect on the particle volumeconcentration distribution becomes pronounced, as presented inFigs. 8 and 9.

At the bottom of the bed, it is observed that the particles in thepacked region are dense, and the particles in the spout region aredilute. In the dense region, the particle volume fraction almostapproaches 0.59, and the variation of particle volume concentrationis too small to be observed. In the diluted spout channel, theparticle volume concentration is very low since the position isoccupied by the gas. Throughout the whole curve of particle volumeconcentration at lower level, it can be seen that the curve is almostflat like a straight line in the packed region, and then decreases verysharply to a minimum value close to the axis of the spouts.

It can be noted that increasing the proportion of central gas, thecentral spout becomes stronger and stronger, and occupies moreand more space. Finally, it grows almost the same as the other two.As shown in Figs. 8 and 9, the particle concentration in the spoutsincreases with increasing height, while the trend is reverse for thepacked region. The increase of particle concentration in spouts isdue to entrainment of particles from the packed region and loss ofgas to the packed region along the height of the bed.

For all particle sizes, the particle concentration in the centralregion of the bed decreases with increasing Qc/Qa. The effect ofcentral gas on particle concentration is more pronounced in thecentral region of the bed. The area of packed region decreaseswith the increasing central gas flow rate, since more gas enterinto the bed, and loosen the particles in the packed region,facilitating their entrainment into the spouts. In Figs. 8 and 9,one can also observe the gap in particle concentration at the axisof the spout between the upper and lower sections of the bed.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9z/H0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9z/H0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9z/H0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9z/H0

Fig. 8. Profiles of time-averaged particle volume concentration with increased central injected gas velocity at various bed levels for 1.0 mm glass beads. (a) Qc=Qa ¼ 0:2;

(b) Qc=Qa ¼ 0:4; (c) Qc=Qa ¼ 0:6 and (d) Qc=Qa ¼ 0:8.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9z/H0z/H0

z/H0 z/H0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9

Fig. 9. Profiles of time-averaged particle volume concentration with increased central injected gas velocity at various bed levels for 1.8 mm glass beads.(a) Qc=Qa ¼ 0:2;

(b) Qc=Qa ¼ 0:4; (c) Qc=Qa ¼ 0:6 and (d) Qc=Qa ¼ 0:8.

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379372

This indicates that the momentum of spouting gas is limited, andthe particles are entrained into the spout mostly in the lowersection by the high speed gas along the height of the spouts.

The particle concentration in the packed region varies fromthe bottom to the top of the bed, with the greatest variationoccurring with the largest particles. Probably because the largest

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379 373

particles is hardest to be entrained by spouting gas in verticaldirection, meanwhile, the loss of gas to the packed region ismore than the small particles. By comparing the results of thethree different particle sizes, it seems that the particle diametersdose not have a significant influence on the trend of thetime-averaged profiles of particle concentration in the rangeinvestigated.

4.2.2. Effect of auxiliary spouting gas flow rate

Fig. 10 shows the voidage distributions within the spouted bedfor the auxiliary injected gas flow rates of 0.2Qc–0.8Qc at theconstant central spouting gas flow rate for the particle size of1.4 mm, and the constant Qc is equal to 1.1Qmf. The flow patternsare remarkably different for different auxiliary spouting gasflow rates.

Fig. 10. Snapshots of the gas phase voidage distributions with increased auxiliary

(c) Qa=Qc ¼ 0:4; (d) Qa=Qc ¼ 0:5; (e) Qa=Qc ¼ 0:6; (f) Qa=Qc ¼ 0:7; (g) Qa=Qc ¼ 0:8.

-1

-0.5

0

0.5

1

1.5

x(m)

Parti

cle

velo

city

(m/s

)

0.1 0.2 0.3 0.50.7 0.8 0.9

-1

-0.5

0

0.5

1

1.5

x(m)

Parti

cle

velo

city

(m/s

)

0.1 0.2 0.3 0.50.7 0.8 0.9

z/H0

z/H0

0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3

Fig. 11. Profiles of time-averaged particle velocities with increased auxiliary inject

(b) Qa=Qc ¼ 0:4; (c) Qa=Qc ¼ 0:6 and (d) Q a=Qc ¼ 0:8.

As shown in Fig. 10a, when the auxiliary gas flow rate is nothigh enough, the bed resembles a slot-rectangle spouted bed. Thetypical three regions can be observed clearly, the spout, thefountain and the packed region. As the auxiliary gas velocity isincreased, the height of the void zone along the auxiliary nozzlesincreases. The void eventually reaches the bed surface at a certainthreshold auxiliary gas flow rate and the fountain is formed. Thethreshold gas flow rate is about 0.4Qc, it is a little lower than thatin Fig. 5. From Fig. 10, it can be seen that the spouts formed by theauxiliary gas tilt towards the axis of the bed, but the fountains arepushed aside to the wall under the complex influence of thecentral spouting gas and the bed wall. From Fig. 10, it can also beseen that near the top of the spout, there is a dense zonesurrounding the spout axis, and such dense zone also exists inthe fountain. This is consistent with the experimental work ofGrace and Mathur (1978).

injected gas velocity for 1.4 mm glass beads. (a) Qa=Qc ¼ 0:2; (b) Qa=Qc ¼ 0:3;

-1

-0.5

0

0.5

1

1.5

x(m)

Parti

cle

velo

city

(m/s

)

0.1 0.2 0.3 0.50.7 0.8 0.9

z/H0

z/H0

-1

-0.5

0

0.5

1

1.5

0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3

x(m)

Parti

cle

velo

city

(m/s

)

0.1 0.2 0.3 0.50.7 0.8 0.9

ed gas velocity at various bed levels for 1.0 mm glass beads.(a) Qa=Qc ¼ 0:2;

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379374

According to Fig. 10, we can see that, the height of the centralfountain increases with the increasing auxiliary spouting gasfirstly until the auxiliary gas flow rate is more than 0.4Qc, thenthe height of central fountain decreases with the increasingauxiliary gas. It can be interpreted that the auxiliary gas hardlymove upwards in vertical direction at low gas flow rates, part ofauxiliary gas is diverted into the central spout for reducing flowresistance. The central spout is enhanced and has more power toform higher fountain. As the auxiliary gas flow rate is sufficientlyhigh to reach the bed surface, the loss of gas to central spoutgradually decreases, and the fountains formed by the auxiliary gashave some influence on the central fountain, then the height ofthe central fountain decreases.

When the auxiliary gas velocity is low, its influence on thecentral spout is very weak. But as the auxiliary gas velocityincreases, the influence on the central spout is graduallyenhanced, and this influence can change the shape of the centralspout and disturb the flow pattern of the central fountain.Compared with Fig. 5, we can see that the influence of auxiliarygas on central gas is stronger than the influence of central gas onauxiliary gas.

Profiles of time-averaged particle velocity are presented inFigs. 11 and 12 for the particle sizes of 1.0 mm and 1.8 mm usedin this work at various bed levels. For each particle diameter, thecentral spouting gas flow rate was held constant, and the proportionof auxiliary gas flow rate was varied from 0.2Qc to 0.8Qc.

The simulation results show that, when the auxiliary gas flowrate is very low, the particles move upwards fast in the centralspout zone, the particle velocity decreases with the horizontaldistance from the central spout axis, then the particles movedownwards and reach a negative peak velocity near the interfaceof the spout and the packed region. Finally, the particle velocity isalmost zero near the wall, they do not move anywhere. Along thespout axis, the particle velocity increases firstly, and thendecreases with the increasing height for the two large particles.

-1

-0.5

0

0.5

1

1.5

x(m)

Parti

cle

velo

city

(m/s

)

0.1 0.2 0.3 0.50.7 0.8 0.9

-1

-0.5

0

0.5

1

1.5

x(m)

Parti

cle

velo

city

(m/s

)

0.1 0.2 0.3 0.50.7 0.8 0.9

0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3

z/H0

z/H0

Fig. 12. Profiles of time-averaged particle velocities with increased auxiliary inject

(b) Qa=Qc ¼ 0:4; (c) Qa=Qc ¼ 0:6 and (d) Qa=Qc ¼ 0:8.

This characteristic trend is the same as those reported in conicalspouted beds (He et al., 1994a, b). But the particle velocityincreases monotonically with height for the smallest particle.

According to Figs. 11 and 12, it can be seen that the particlevelocity increases with the increased auxiliary gas velocity in theregion above the auxiliary nozzles. But, in the central spout, theparticle velocity increases firstly, then decreases when the aux-iliary gas flow rate greater than 0.4Qc. As the auxiliary gas flowrate increases further, it is clear that the particles move upwardsfast in the spouts and move downwards in the entire regionexcept the spouts. When the auxiliary gas flow rate is increasedtoo high to loosen the great mass of the particles in the bed, thespouts become unstable and oscillate with time. From Figs. 11and 12, we can also see that the particle velocity in the centralspout is lower than that in the other two spouts when theauxiliary gas flow rate is higher than 0.8Qc. It can be interpretedas follows: the auxiliary gas accelerates and brings more andmore particles to the freeboard of the bed by increasing theauxiliary gas spouting velocity, then, most of these particles fallback to the central region of the bed and move downward. Theflow resistance in the central region increases, and the velocity ofup particles is reduced.

Profiles of time-averaged particle volume concentration areshown in Figs. 13 and 14 with increased auxiliary gas flow rate atconstant central spouting gas flow rate for the particle sizes of1.0 mm and 1.8 mm used in this work at various bed levels.

According to Figs. 13 and 14, the particle concentrationincreases with bed height in the spout region, and decreases fromthe bottom to the top of the bed in the packed region. The presentsimulation results share a similar characteristic with the experi-mental work on the spout-fluid bed by the previous researchers(Pianarosa et al., 2000).

From Figs. 13 and 14, it can be seen that the particleconcentration increases with increasing auxiliary spouting gasflow rate in the upper part of the central spout. This indicates that

-1

-0.5

0

0.5

1

1.5

x(m)

Parti

cle

velo

city

(m/s

)

0.1 0.2 0.3 0.50.7 0.8 0.9

-1

-0.5

0

0.5

1

1.5

0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3

x(m)

Parti

cle

velo

city

(m/s

)

0.1 0.2 0.3 0.50.7 0.8 0.9

z/H0

z/H0

ed gas velocity at various bed levels for 1.8 mm glass beads. (a) Qa=Qc ¼ 0:2;

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9z/H0

z/H0z/H0

z/H0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9

Fig. 13. Profiles of time-averaged particle volume concentration with increased auxiliary injected gas velocity at various bed levels for 1.0 mm glass beads. (a) Qa=Qc ¼ 0:2;

(b) Qa=Qc ¼ 0:4; (c) Qa=Qc ¼ 0:6 and (d) Q a=Qc ¼ 0:8.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9z/H0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9z/H0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9z/H0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3

x(m)

Parti

cle

conc

entra

tion

0.1 0.2 0.3 0.5 0.7 0.8 0.9z/H0

Fig. 14. Profiles of time-averaged particle volume concentration with increased auxiliary injected gas velocity at various bed levels for 1.8 mm glass beads. (a) Qa=Qc ¼ 0:2;

(b) Qa=Qc ¼ 0:4; (c) Qa=Qc ¼ 0:6 and (d) Q a=Qc ¼ 0:8.

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379 375

the auxiliary spouting gas launches a cluster of particles into thefreeboard and subsequently rain down the central region of thebed when the auxiliary gas velocity is sufficiently high.

It is clearly depicted in the two figures that the profiles ofparticle concentration spread out with increasing bed height. Inthe upper part of the bed, the variation of particle concentration is

0

0.1

0.2

Qc/Qa

Foun

tain

hei

ght(m

)0

0.1

0.2

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1Qa/Qc

Foun

tain

hei

ght(m

)

ds = 1.0mmds = 1.4mmds = 1.8mm

ds = 1.0mmds = 1.4mmds = 1.8mm

Fig. 15. Fountain height vs. injected gas flow rate for all three particles. (a) Qa ¼ 1:1Qmf , Qc ¼ 0�0:9Qa; (b) Qc ¼ 1:1Qmf , Qa ¼ 0�0:9Qc .

0

0.2

0.4

0.6

0.8

1

1.2

Dimensionless radius

Dim

ensi

onle

ss h

eigh

t

0.00.10.20.30.40.50.60.70.8

Qc/Qa

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0 0.1 0.2 0.3Dimensionless radius

Dim

ensi

onle

ss h

eigh

t

0.00.10.20.30.40.50.60.70.8

Qa/Qc

Fig. 16. Dimensionless spout diameters as a function of dimensionless height for

1.4 mm glass beads. (a) Qa ¼ 1:1Qmf , Qc ¼ 0�0:8Qa; (b) Qc ¼ 1:1Qmf , Qa ¼ 0�0:8Qc .

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379376

less obvious along the bed surface and the fluctuation of the curveis moderate, nevertheless they are not flat.

4.3. Fountain height

Simulated fountain heights for three different particles arepresented in Fig. 15. The fountain height is the distance from thebottom of the bed to the fountain top.

Fountain height is a significant characteristic of spouted bed.Sobieski (2008) has analyzed sensitivity of Eulerian multiphasemodel for a spouted-bed grain dryer, and the fountain height waschosen to be the basic value characterizing the bed. He found that,besides the inlet gas velocity, the particle diameter was a keyparameter influencing the fountain height. Even a small modifica-tion of that value resulted in a significant and clearly noticeablechange in the fountain height.

From Fig. 15, it is observed that fountain heights increase withincreasing spouting gas until the ratio of gas flow rate is greaterthan 0.4, then decrease with increasing spouting gas. This may beprimarily due to redistribution of fluid between spout and packedregions, more fluid flows through the spout when the ratio of gasflow rate is lower than 0.4. Because of higher fluid flow through thespout, the particle velocity in the spout is also increased, resultingin a high fountain height. It is also observed that the fountainheight fluctuates with the increasing gas flow rate around twotimes the static bed height under the conditions studied.

At steady spouting, all observed fountain shapes are nearlyparabolic. But the shape and structure of the fountain has somedifference from that observed for pure spouting. The fountain inpure spouting is extremely dilute, but the fountain in this study isobserved to have a greater solid concentration. The fountain isformed by particle clusters periodically ejected by the burstingbubbles. A maximum height is achieved with the expansion of thespout when the rising bubbles burst upon the bed surface, and thena minimum value is present thereafter. Therefore, the fountainheight oscillates between a minimum and a maximum value withthe bubble eruption. Fountain height and shape as well as particlevelocity and concentration within the fountain has great significanceto certain applications of spouted bed such as granulators andcoating units. In view of this, more studies are required to examinethe effects of operation conditions on fountain characteristics.

4.4. Spout diameter and shape

Simulated dimensionless spout diameter as a function of dimen-sionless height are presented in Fig. 16 for 1.4 mm glass beads undervarying operating conditions. Dimensionless spout diameter meansspout diameter normalized by the bed width, and dimensionlessheight means bed height normalized by the static bed height.Knowledge of the spout diameter and shape has fundamentalimportance for understanding the hydrodynamics of spouted bedsand for spouted bed modeling and design. Several researchers (Heet al., 1998; Mathur and Epstein, 1974; McNab, 1972) have observed

the spout shape and studied the dependence of spout diameter bydifferent experiments with different materials, particle sizes, beddimensions, column geometries and fluid velocities et al.

From Fig. 16, it can be seen that the simulated diameter ofspout expands sharply in the region immediately above the inletorifice where the spout diameter is considerably greater than theinlet diameter, and then converges slightly near the bed surface.The spout shape is related to the interaction between the gas andparticles at the interface of the spout and packed region. At thespout inlet, the gas shears the particle layer at the interface inaxial orientation and pushes the solids tightly in the horizontaldirection, then the spout region is enlarged. Ongoing interactionbetween the two phases, the gas carries more and more particlesas it travels upward in the spout, and then the gas gradually losesenergy by friction with solids. Therefore, at the upper part of thebed, the expanding of the spout begins to decrease, consequently,it narrows back. As shown in Fig. 16a, spout diameter decreasesslightly then remains nearly constant along the height in theupper part of the bed. But in Fig. 16b, the decrease of spoutdiameter is considerable.

The inlet gas spouting velocity has an important effect on thespout diameter and shape. The influence of gas flow rate is alsoshown in Fig. 16. It is seen that the spout shape remained the same,but the spout diameter increases with increasing gas flow rate untilthe proportion is great than 0.5, then spout diameter decreaseswith increasing gas flow rate. The influence of gas flow rate is moreobvious in the upper part of the bed than in the lower part.

4.5. Effect of static bed thickness

Static bed height is a significant factor affecting the flowpattern in the spouted bed, such as spout shape and diameter,

H0=100mm H0=150mm H0=200mm H0=100mm H0=150mm H0=200mm

Fig. 17. Snapshots of the gas phase voidage distributions with increased static bed thickness for 1.4 mm glass beads. (a) Qc ¼ 0, Qa ¼ 1:1Qmf ; (b) Qc ¼ 1:1Qmf , Qa ¼ 0.

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379 377

fountain height and shape et al. The variation of the voidage in thebed with bed height is presented in Fig. 17.

As shown in Fig. 17a, it appears that the spout diameterincreases with increasing bed height. However, further increasein static bed thickness induces the spouting jet to be submerged bythe particles below the bed surface, and discharge bubbles peri-odically. When the static bed thickness is increased to 200 mm, thespouting characteristics are quite different from those observed atlower bed thickness. Stable spouting becomes unachievable, sub-sequently the flow pattern in the bed changes to pulsed spouting.The fountain collapses, the permanent spout disappears andbubbling ensues. The whole bed becomes unsteady and the mixingand turbulence of particles in the bed are intensive.

According to Fig. 17b, with the increasing bed thickness, thespout diameter is found to narrow at the middle section butexpand slightly at the bed surface. As predicted in the equationproposed by Grace and Mathur (1978), the fountain height isproportional to the square of the particle velocity in the spout atthe bed surface, therefore higher fountain height will be formed byhigher gas velocity since higher gas velocity produces higherparticle velocity. However, the gas velocity in the spout at thebed surface decreases with increasing bed height, then for thelarger bed height, the resulting fountain height is relatively lowerthan for the smaller bed height, but the fountain shape becomeswider. In addition, the solid volume concentration in the fountainbecomes higher and higher with the increasing bed height,especially for the central region of the fountain. By ComparingFig. 17a with Fig. 17b, it is found that the effect of static bedthickness on multi-spouting is more obvious than single-spouting.

4.6. Scaling up

Scale-up of spouted beds is an interesting and important taskfor the implementation of this type of fluid-particle contactors atindustrial scale. Many scholars have already dealt with this topic.Glicksman (1984) proposed a scaling relationship for fluidized bed,the controlling non-dimensional parameters were identified as

gds

U2 , rsdsUm ,

rg

rs, H0

ds, Dt

ds, fs,

dimensionless particle size distribution, dimensionless bed geometry:

8<:

ð23Þ

He et al. (1997) modified Glicksman’s (1984) relationship toprovide a full set of scaling parameters for spout bed scaling up.They considered the difference between spouted bed and flui-dized bed, then added two dimensionless parameters, the internalfriction angle (j) and the loose packed voidage (e0) to Glicksman’s(1984) relationship by analyzing the force balance for particlesin the annulus region of spouted bed. The non-dimensional

parameters were identified as

gds

U2 , rsdsUm ,

rg

rs, H0

ds, Dt

ds, fs, j, e0

dimensionless particle size distribution, dimensionless bed geometry:

8<:

ð24Þ

He et al. (1997) has performed the experimental verifications oftheir scaling parameters, and the modified parameters were validfor conventional spouted beds. Although conventional spouted bedsand multiple-spouted beds share many common features, there arealso significant differences between them. The flow characteristic inthe multiple-spouted bed is more complex than conventionalspouted bed. The multiple spouts interact significantly with eachother in multiple-spouted bed. Therefore, before the non-dimen-sional scaling parameters proposed by He et al. (1997) can be usedto scale up multiple-spouted bed, the detailed validation should beconducted. We will do this work in our future study.

5. Conclusions

In this paper, the numerical computational technique is used toinvestigate the characteristics of gas solid flow in a multiple-spoutedbed. Several typical flow patterns are simulated and validated by theexperimental results carried out by Ren et al. (2010) The simu-lated results show a reasonable agreement with experimental results.Then further investigation has been done when the operationalconditions are changed. Some significant conclusions are drawn.

When the central gas flow rate is low, the high auxiliaryspouting gas completely dominates the flow pattern in the bedand restricts the growth of the central spouting gas. With theincrease of Qc/Qa, the particle velocity increases, but the particlevolume concentration decreases. The height of central spoutingjet increases, and the central fountain is formed finally. However,the central fountain height is not very high because of theinfluence of the auxiliary spouting gas. The auxiliary gas isaffected by the gradually strong central spout and deflectedslightly towards the wall. In addition, the difference in particlevelocity between the top and bottom of the bed decreases withincreasing Qc/Qa. On the contrary, the central spouting gascontrols the whole flow behavior in the bed, and the developmentof the auxiliary gas is suppressed by the central gas. The influenceof particle size on the flow pattern is unobvious.

The central fountain height increases with increasing auxiliaryspouting gas flow rate initially and then decreases. The fountainshape is nearly parabolic. The solid concentration in the fountainfor the current conditions is greater than that for pure spouting.The spout diameter expands sharply in the region above the inletorifice and then converges slightly near the bed surface. The spoutdiameter increases with increasing gas flow rate firstly, and thendecreases. This is similar to the variation of the fountain height.

Y. Li et al. / Chemical Engineering Science 80 (2012) 365–379378

For the multi-spouting, the spout diameter increases withincreasing bed height, but the bed becomes unstable when thebed thickness is increased to 200 mm, The fountain collapses, thespout swings sharply and discharges bubbles. For single-spouting,the spout diameter narrows at the middle section but expandslightly at the bed surface with the increasing bed thickness. Thefountain height decreases with the bed thickness, but the solidconcentration in the fountain increases.

The hydrodynamic characteristics in multiple-spouted bed withmono-dispersed particles has been investigated in this study. How-ever, the hydrodynamics of spouted beds with poly-dispersed parti-cles is important in many industrial applications, such as segregationand mixing processes. Olazar et al. (1993) and San Jose et al. (1994)have done some significant works about the stability and segregationof conical spouted beds with binary and tertiary mixtures. For furtherstudy, the investigation on hydrodynamics in multiple-spouted bedwhen handling solid mixtures will be an interesting topic.

Nomenclature

c particle fluctuating velocity, (m/s)CD0 drag coefficient, dimensionlessds particle diameter, (mm)D0 spout nozzle width, (mm)Dt bed width, (mm)Dt0 bed width of each cell, (mm)es particle–particle restitution coefficient, dimensionlessg acceleration of gravity, (m/s2)g0 radial distribution function, dimensionlessH0 static bed height, (mm)Ht bed height, (mm)I identity matrixp pressure, (Pa)Qc central spouting gas flow rate, (m3/s)Qa auxiliary spouting gas flow rate, (m3/s)Qmf minimum fluidizing gas flow rate for a cell, (m3/s)Re Reynolds number, dimensionlesst time, (s)u velocity, (m/s)ums spouted-nozzle-based minimum spouting velocity, (m/s)U superficial gas velocity, (m/s)Ua spouted-nozzle-based auxiliary spouting velocity, (m/s)Uc spouted-nozzle-based central spouting velocity, (m/s)

Greek letters

e volume fraction, dimensionlesse0 loose packed voidagees,max the maximum of particle volume fractiongs the collisional dissipation term of granular energyy granular temperature, (m2/s2)ls granular bulk viscosityks granular energy conductivityb the momentum exchange coefficient, (kg/m3 s)r density, (kg/m3)s stress tensorm viscosity, (Pa s)fs sphericity of particlesj internal friction angle of particle phase, (deg)

Subscripts

col collisiong gas phase

kin kineticmax maximums solid phase

Acknowledgement

The financial supports from the Natural Science Fund of China(50806058) and the Natural Science Fund of Shaanxi (SJ08E213)are gratefully acknowledged.

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