CFD modeling of a spouted bed with a porous draft tube

Page 1

C

Sa

b

c

a

ARRA

KSPHKC

1

Gctrosw

kspsipbtitadt

1d

Particuology 8 (2010) 415–424

Contents lists available at ScienceDirect

Particuology

journa l homepage: www.e lsev ier .com/ locate /par t ic

FD modeling of a spouted bed with a porous draft tube

alar Azizi a,∗, Seyyed Hossein Hosseinib, M. Moraveji a, Goodarz Ahmadic

Chemical Engineering Department, Faculty of Engineering, Arak University, Sardasht, Arak 38156-875, IranDepartment of Chemical Engineering, Faculty of Engineering, Ilam University, Ilam, IranDepartment of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725, USA

r t i c l e i n f o

rticle history:eceived 26 February 2009eceived in revised form 30 August 2009ccepted 16 December 2009

a b s t r a c t

Spouted bed with a porous draft tube is used for drying of grains and chemical products and thermaldisinfestations process. This work provides a computational fluid dynamics (CFD) simulation of binarymixtures of glass particles in a spouted bed with a porous draft tube. The simulation used the multi-fluid

eywords:pouted bedorous draft tubeydrodynamicsinetic theory

Eulerian–Eulerian approach based on kinetic theory of granular flows, incorporating a kinetic-frictionalconstitutive model for dense assemblies of particulate solids and Gidaspow’s drag model for the inter-action between gas and particles. Influences of solids mass fraction and inlet gas flow rate on pressuredistribution, gas and particle velocities were studied. The modeling results were compared with the exper-imental work of Ishikura, Nagashima, and Ide (2003) for the flow condition along the axis of the spoutedbed. Good agreement between the modeling results and experimental data was observed.

ciety

thcptppi

ftii

ciffEi

FD © 2010 Chinese So

. Introduction

Spouted beds, originally invented in Canada by Mathur andishler (1955) as an alternative to fluidized beds for handlingoarse particles, are now widely applied in various physical opera-ions such as drying, coating, and granulation, as well as chemicaleactors in coal gasification, catalytic partial oxidation, catalyticxidative coupling reaction, catalytic polymerization, and pyroly-is. The advantages of spouted beds for various chemical processesere reported by Mathur and Epstein (1974).

Conventional spouted beds with simple structures are wellnown. According to Claflin and Fane (1983) the conventionalpouted beds have a drawback, that is, the need for control ofarticle trajectory history, for otherwise the particles enter thepout area from the annulus from all levels, resulting essentiallyn random behavior of these particles. The insertion of an axiallyositioned non-porous draft tube into the conventional spouteded has shown potential advantages in stability and flexibility ofhe system (Ishikura et al., 2003). There is, however, a potential lim-tation in using a spouted bed with a non-porous draft tube when

he gas has an active role, such as drying or reaction, inasmuchs the non-porous draft tube prevents gas percolation from theraft tube into the annulus, thus reducing the net gas–solid con-acting and therefore particle–gas mass and heat transfer in both

∗ Corresponding author. Tel.: +98 871 4173446–9.E-mail address: sa [email protected] (S. Azizi).

spb

2

g

674-2001/$ – see front matter © 2010 Chinese Society of Particuology and Institute of Process Eoi:10.1016/j.partic.2009.12.004

of Particuology and Institute of Process Engineering, Chinese Academy ofSciences. Published by Elsevier B.V. All rights reserved.

he spout and the annulus areas. Insertion of a porous draft tube,owever, reduces this drawback, while still providing a means ofontrolling particle trajectory history (Ishikura et al., 2003). Com-aring spouted beds with porous and non-porous draft tube showshat the pressure drop and minimum spouting velocity for non-orous draft tube spouted beds are lower than spouted beds withorous draft tube. Increase in efficiency of heat and mass transfer

s however the advantage of using a porous draft tube.Annulus gas flow rate and solids circulation rate are important

actors from the viewpoint of gas–solids contact and in predictinghe spouted bed performance with a draft tube. Hence, understand-ng the hydrodynamics of gas and particle flow is important for bothndustrial application and fundamental research.

Most previous computational fluid dynamics (CFD) models foronventional spouted beds (Szafran & Kmiec, 2004) have providedmportant information on the flow field within the spouted bedsor process design, scale up, optimization and reducing the needor experimentations. The present work uses the two-dimensionalulerian two-fluid model (TFM) to study the hydrodynamic behav-or of spouted beds with porous draft tube to give transientolutions under isothermal conditions. Modeling results are com-ared with the experiments of Ishikura et al. (2003) for spoutededs with porous draft tube.

. Model equations

Two methods have been improved for CFD modeling ofas–solid flows, the Eulerian–Lagrangian discrete element model

ngineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

Page 2

416 S. Azizi et al. / Particuology

Nomenclature

CDs single particle drag functionCflm coefficient of friction for solids phases l and mCs finer particle mass fraction

Dg rate of strain tensor, fluid phase (s−1)

Dms rate of strain tensor, solids phase (s−1)dpm diameter of the particles constituting the mth solids

phase (m)elm coefficient of restitution for the collisions of mth and

lth solids phasesFgm coefficient for the interphase force between the

fluid phase and the mth solids phase (kg/(m3 s))Fslm coefficient for the interphase force between the lth

and the mth solids phase (kg/(m3 s))�g acceleration due to gravity (m/s2)g0lm radial distribution function at contactH solids bed height (m)�Igm momentum transfer from fluid phase to mth solids

phase (N/m3)�Iml momentum transfer from mth to lth solids phase

(N/m3)Nsm total number of solids phase-m chemical speciesPm pressure of mth phaseRe Reynolds number

Sg gas-phase stress tensor (Pa)

Ssm solids phase-m stress tensor (Pa)�Vg gas-phase velocity vector (m/s)�Vsm mth solids phase velocity vector (m/s)

Greek letters˛g volume fraction of the fluid phase˛sm volume fraction of the mth solids phaseˇ fluid particle interaction coefficient (kg/(m3 s))�gm granular energy transfer to fluid phase (J/(m3 s))�lm granular energy transfer between solids phases

(J/(m3 s))��m granular energy dissipation due to inelastic colli-

sions (J/(m3 s))

(Deaiacp

a1iuwtpemm(

tbtlwT2u

2

a

u

2

cdittt

�

m

wt�ttpdfl

q

w

�g molecular viscosity of the fluid phase (kg/(m s))�m granular temperature of phase-m (m2/s2)

DEM) and the Eulerian–Eulerian two-fluid model (TFM). In theEM gas phase is described by locally averaged Navier–Stokesquations. Lagrangian equations of motion for individual particlesre then solved and individual particle trajectories are traced, tak-ng into account the effects of particle collisions and the forcescting on the particle by the flowing gas. In this approach, theomputational demand rises sharply with the number of tracedarticles, which limits its applicability to high concentration flows.

In the TFM model, the two phases are mathematically treateds interpenetrating continua (Ahmadi & Ma, 1990; Ma & Ahmadi,990). The success of TFM depends on proper description of the

nterfacial forces and the solids stress. The interfacial forces aresed to describe the momentum transfer between the two phases,hich has the primary effect on the hydrodynamic behavior. In

he TFM models, the conservation equations for each of the two

hases are derived, resulting in two sets of coupled hydrodynamicquations with similar mathematical structure. As a result, theanipulation of the system and development of the computerodel become somewhat easier thus reducing computation cost

Wu & Mujumdar, 2008).�

8 (2010) 415–424

The DEM approach provides a direct physical interpretation ofhe fluid–particle, particle–particle and particle–wall interactions,ut computational demand rises significantly with the number ofraced particles. Therefore, the applications of DEM models are stillimited to systems much smaller than industrial. In the present

ork, because of advantages of TFM, and earlier successes in usingFM-based CFD works on spouted beds (Du, Bao, Xu, & Wei, 2006a,006b; Lu et al., 2004), the two-fluid model (TFM) approach wassed.

.1. Conservation of mass

The continuity equation for the gas and mth solid phase is givens

∂

∂t(˛g�g) + ∇ · (˛g�g �Vg) = 0, (1)

∂

∂t(˛sm�sm) + ∇ · (˛sm�sm �Vsm) = 0. (2)

The first term accounts for the rate of mass accumulation pernit volume, and the second term is the net convective mass flux.

.2. Granular energy conservation

The kinetics for flow of smooth, slightly inelastic and spheri-al particles is used in the derivation of the constitutive relation forescribing the stress tensor in the mth solids phase, Ssm. The result-

ng constitutive relations contain the granular temperature, �m, ofhe mth solids phase. The granular temperature is proportional tohe specific kinetic energy of the random fluctuating component ofhe particle velocity (Cm). That is,

m = 13

〈C2m〉. (3)

The transport of granular temperature (kinetic energy) for theth solids phase is governed by

32

∂

∂t˛sm�sm�m + 3

2∇ · ˛sm�sm�m �Vsm

=

⎡⎢⎣Ssm : ∇ �Vsm − ∇ · �q�m − ��m + �gm +

M∑l=1

l /= m

�lm

⎤⎥⎦ . (4)

here ��m is the rate of granular energy dissipation due to inelas-ic collisions, and q�m is the flux of granular energy; the termgm = − 3ˇ�m accounts for the transfer of granular energy between

he gas phase and the mth solids phase, whereas �lm accounts forhe transfer of granular energy between the mth and lth solidshases; ˇ is the fluid–particle interaction coefficient which isescribed in the next section. The constitutive law for the energyux q�m and energy dissipation ��m are given as

��m = −k�m∇�m, (5)

here k�m = 15dp sm�sm˛sm√

��m4(41−33)

[1 + 12

5 2(4 − 3)˛smg0 mm]

+ 16

15� (41 − 33)˛smg0 mm & = 1+emm2 ,

�m = 12(1 − emm)�smg0 mm˛sm

√�3

m

dp sm√

�. (6)

Page 3

uology

2

wfas

wtito

2

a

�I

wabˇ

�f

bsitfit⎧⎪⎨⎪⎩w

C

R

2

kw

�I

t

F

wbrs

g

2

S

wt

wt

D

2

i

S

ws

wnftcfAt(aswibpf

rTwt(a

S. Azizi et al. / Partic

.3. Conservation of momentum

The gas-phase momentum balance is expressed as

∂

∂t(˛g�g �Vg) + ∇ · (˛g�g �Vg �Vg) = ∇ · Sg + ˛g�g�g −

M∑m=1

�Igm, (7)

here Sg is the gas-phase stress tensor and �Igm is an interactionorce representing the momentum transfer between the gas phasend the mth solids phase. The momentum equation for the mtholids phase is given as

∂

∂t(˛sm�sm �Vsm) + ∇ · (˛sm�ms �Vsm �Vsm)

= ∇ · Ssm + ˛sm�sm�g + �Igm −M∑l=1

l /= m

�Iml, (8)

here Ssm is the stress tensor for the mth solids phase. The firsterm on the left hand side represents the net rate of momentumncrease. The second term on LHS represents the net rate of momen-um transfer by convection. In these equations, g is the accelerationf gravity.

.3.1. Fluid–solids momentum transferThe interaction force, or momentum transfer between the gas

nd the mth solids phase, is modeled as

gm = −˛sm∇Pg − �fdrag, (9)

here the first term on the right side describes the buoyancy forcend the second term describes the drag force which generally cane represented by the product of momentum transfer coefficient,, and the slip velocity, ( �Vsm − �Vg) between the two phases, that is

drag = ˇ( �Vsm − �Vg). (10)

The drag force acting on a particle in fluid–solid systems cane represented by several models, of which that for conventionalpouted bed studied by Du et al. (2006a, 2006b) significantlympacts the computational model predictions of dense gas–solidswo-phase flows encountered in spouted beds, such as voidage pro-les, particle velocity and solid flow patterns. In the present work,he Gidaspow drag model (1994) was used as given below

ˇErgun = 150˛sm�g

˛gd2psm

+ 1.75˛sm�g

dpsm| �Vsm − �Vg|, ˛g < 0.8,

ˇWen-Yu = 34

CD˛sm�g

dpsm| �Vsm − �Vg|˛−2.65

g , ˛g ≥ 0.8,

(11)

here drag coefficient CD was expressed by

D =

⎧⎨⎩

24˛gRep

[1 + 0.15(˛gRep)0.687], Rep < 1000,

0.44, Rep ≥ 1000,

(12)

ep = �g| �Vsm − �Vg|dpsm

�g. (13)

.3.2. Solids–solids momentum transfer

Compared to fluid–solids momentum transfer, much less is

nown about solids–solids momentum transfer. In the presentork solids–solids momentum transfer, �Iml , is represented as

ml = −Fsml( �Vsl − �Vsm). (14)

8 (2010) 415–424 417

Syamlal (1987) used a simplified version of the kinetic theoryo derive an expression for the drag coefficient, Fsml, as follows

sml = 3(1 + elm)(�/2 + Cflm�2/8)˛sl˛sm�s(dpsl + dpsm)2g0lm| �Vsl − �Vsm|2�(d3

psl+ d3

psm), (15)

here elm and Cflm are the coefficients of restitution and frictionetween the lth and mth solids phase particles, respectively. Theadial distribution function at contact, g0lm for mixtures of hardpheres is used (Lebowitz, 1964):

0lm = 1˛g

+ 3dpldpm

˛2g(dpl + dpm)

M∑�=1

˛s�

dp�. (16)

.3.3. Fluid-phase stress tensorThe stress tensor for the fluid phase is given by

g = −PgI + g, (17)

here Pg is the pressure. The viscous stress tensor, g, is assumedo be of the Newtonian form

g = 2˛g�gDg + ˛g�gtr(Dg)I, (18)

here I is the identity tensor and Dg is the strain-rate tensor forhe fluid phase, which is given by

g = 12

[∇ �Vg + (∇ �Vg)

T]

. (19)

.3.4. Solids-phase stress tensorRelated equation for calculating solids-phase stress tensor given

s

sm = PsmI − sm, (20)

here Psm is the pressure and sm is the viscous stress in the mtholids phase.

In spouted beds particle concentration in the annulus is highhere particles are enduring frictional contact with multipleeighbors. Particle stresses in this zone are mainly caused by

rictional interaction between particles at points of sustained con-act. In the fountain region, however, both collision and frictionontribute to particle stresses. Lu et al. (2004) discussed the kinetic-rictional stress model of granular flow in spouted beds. Earlierbu-Zaid and Ahmadi (1990) developed a kinetic model including

he frictional energy loss. More recently, Srivastava and Sundaresan2003) suggested frictional flow that is easier to implement in

CFD code (Benyahia, 2008). A critical comparison of frictionaltress models applied to the simulation of bubbling fluidized bedsas reported by Passalacqua and Marmo (2009). Accordingly, the

ntroduction of a frictional stress model improves the prediction ofubble diameter in a bubbling fluidized bed with a central jet andositively affects the bubbles diameter distribution in a uniformlyed bubbling fluidized bed.

As noted earlier, frictional interactions play a very importantole in many dense phase gas–solid flows such as spouted beds.he frictional-kinetic closure for the particle phase stress thatas presented by Srivastava and Sundaresan (2003) is outlined in

his section. This model assumes that the kinetic-collision stressesevaluated based on granular kinetic theory) and frictional stressesre additive, that is,

sm = k-csm +

fsm,

Psm = Pk-csm + Pf

sm,

�sm = �k-csm + �f

sm,

�sm = �k-csm + �f

sm.

(21)

Page 4

4 uology

esidto

f2v

e

P

P

�

wtic

n

Cc

P

�

w

g

�

2

stt

S

wmiElpg

2

�

sp

˛

3

qfltp(robam(

rFig. 1 shows the experimental apparatus for batch operation understeady-state conditions, inclusive of the computational grid. Theaxisymmetric computational domain was divided into 2726 com-putation cells. The mesh size is 2.5 mm near the wall and 1.5 mmat the center of the spout section, and varies along the bed height

Table 1CFD domain scales.

Computational domain Unit Value

Diameter of column m 0.10Height of column m 1.0Diameter of nozzle m 0.012

18 S. Azizi et al. / Partic

Savage (1998) argued that even in purely quasi-static flow therexist fluctuations in the strain rate associated with the formation ofhear layers, and that these fluctuations will lower the shear stressn the assembly. These shear layers are typically tens of particleiameters in thickness. Therefore, the length scales associated withhe microscale (particle diameter dp) and the macroscale (thicknessf the shear layer) are not much different.

In this work, a modification of the Savage model that accountsor strain-rate fluctuations was used (Srivastava & Sundaresan,003). The frictional model influences the flow behavior at solidsolume fractions below maximum packing (˛sm,min = 0.5).

The resulting frictional solids pressure and viscosity arexpressed as

fsm = Pc

(1 − ∇ · �Vsm

n√

2 sin �√

Ssm : Ssm + �m/d2psm

)n−1˛sm∑M

m=1˛sm

,

(22)

c =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

1024(˛sm − ˛sm,max)10 ˛sm > ˛sm,max

Fr(˛sm − ˛sm,min)r

(˛sm,max − ˛sm)s ˛sm,max ≥ ˛sm > ˛sm,min

0 ˛sm ≤ ˛sm,min

, (23)

fsm =

√2 sin � Pf

2(√

Ssm : Ssm + (�m/d2psm)

)

×(

n − (n − 1)(

Pf

Pc

)1/(n−1))

˛sm∑Mm=1˛sm

, (24)

here Fr, r and s are empirical material constants which are takeno be 0.05, 2.0, and 5.0. The coefficient n is set differently depend-ng on whether the granular assembly experiences dilatation orompaction:

={ √

32 sin �

∇ · �Vsm ≥ 0

1.03 ∇ · �Vsm < 0. (25)

According to the kinetic model of Lun, Savage, Jeffrey, andhepurniy (1984), the kinetic-collisional solids pressure and vis-osity are given as

k-csm = ˛sm�sm�m[1 + 2˛smg0mm(1 + emm)], (26)

k-csm = dpsm�sm˛sm

√�m

2

{(5/48)

√�

(1 + emm)g0 mm

×[

1 + 45

˛smg0 mm(1 + emm)]2

+ 8˛smg0 mm(1 + emm)5√

�

},

(27)

here

0 mm = 1˛g

+ 3dpsm

2˛2g

M∑�=1

˛s�

dps�. (28)

The corresponding bulk viscosities are given as

k-csm = 4dpsm�sm(1 + emm)˛smg0 mm

3√

�˛sm

√�m − 2

3�k-c

sm and

�fsm = −2

3�f

sm. (29)

8 (2010) 415–424

.4. Porous media equation

Porous media are modeled by the addition of a momentumource term to the standard gas flow equation. The source termhat is added to Eq. (7) is composed of two parts: a viscous losserm and an inertial loss term:

� = −(

�g

˛p�Vg + C2

�g

2| �Vg| �Vg

), (30)

here �S is the source term in the momentum equation, | �Vg| is theagnitude of the velocity and ˛p is the permeability and C2 is the

nertial resistance factor. The first term on the right-hand side ofq. (30) is the viscous effect and the second term is due to inertialoss. This momentum sink contributes to the pressure losses in theorous region, creating a pressure drop that is proportional to theas velocity (or velocity squared).

.5. Equation of state

The fluid phase is modeled as an ideal gas, that is,

g = PgMw

RTg. (31)

Volume fractions are assumed to be continuous functions ofpace and time. By definition, the volume fractions of all of thehases must sum to one:

g +M∑

m=1

˛sm = 1. (32)

. Results and discussion

Lettieri, Micale, Cammarata, and Colman (2002) reported goodualitative agreement between 2D and 3D simulations of gas-uidized beds, and indicated that 2D models could be usedo reduce computational time. Simulation of full 3D problemsrovides greater accuracy, though extremely time-consumingBertola, Vanni, & Baldi, 2003). To keep the computational costeasonable, and in agreement with a number of earlier CFD worksf spouted beds, an axisymmetric computation model of spoutededs, instead of full 3D in the cylindrical physical domain, isssumed in the present simulation. Axisymmetric and 2D planeodels were also used earlier by Du et al. (2006a, 2006b), Lu et al.

2004), and Wu and Mujumdar (2008).Simulations of the flow conditions in the spouted beds are car-

ied out using the input data that are listed in Tables 1 and 2.

Cone angle ◦ 60Draft tube inside diameter m 0.014Draft tube length m 0.3Distance of tube inlet from gas nozzle m 0.03Permeability of draft tube, ˛p m2 1.944 × 10−11

Resistance of draft tube, C2 1/m 16,510,400Initial bed height from nozzle m 0.3

Page 5

S. Azizi et al. / Particuology 8 (2010) 415–424 419

Table 2Gas and particle properties for case studies.

Property Unit Case 1 Case 2 Case 3

N Number of solids phase – 1 2 2dpm Particle diameter �m 1351 477, 1351 477, 1351Cs Mass fraction of finer particles kg/kg 0.0 0.05 0.0, 0.05, 0.10, 0.25, 0.5, 1.0Psm Solids density kg/m3 2480 2480 2480emm Coefficient of restitution – 0.9 0.9 0.9� Angle of internal friction ◦ 28.5 28.5 28.5˛∗

g Packed bed void fraction – 0.39 0.39 0.39, 0.39, 0.388, 0.385, 0.38, 0.373

.5, 0.6

fas2attbcs

ttasi

�g Gas-phase density kg/m 1.185�g Gas-phase viscosity Pa s 1.14 × 10−5

U Superficial inlet gas velocity m/s 0.362, 0.414, 0

rom 2.5 to 8.5 mm. Computation cells are more refined in the spoutnd conical sections because of sharp variation of variables in theseections, as was noted in the earlier CFD works of Du et al. (2006a,006b), Lu et al. (2004), Wu and Mujumdar (2008), and Zhao, Yao,nd Li (2006). Du et al. (2006a, 2006b) also showed that increasinghe number of grids beyond certain limit had no obvious effect on

he simulation results. Here the grid independence has been testedy varying the density of computation domain. Grid refining wasontinued until the solution parameters, such as voidage, gas andolids velocity, showed no variations.

taia

Fig. 1. Experimental setup

1.185 1.1851.14 × 10−5 1.14 × 10−5

, 0.7 0.362, 0.414, 0.5, 0.6, 0.7 0.362

Our simulation showed that 5 s were needed for the spouted bedo reach steady-state. All simulations were continued for 10 s, andhe last 5 s of simulations were used to compute the time aver-ged variables. The computation model uses an automatic timetep adjustment to reduce the run time, by making small increas-ng or decreasing adjustments in time steps and monitoring the

otal number of iterations for several time steps. The adjustmentsre continued, if there is a favorable reduction in the number ofterations. Otherwise, adjustments in the opposite direction arettempted. Whenever the simulation fails to converge, the time

and numerical grid.

Page 6

4 uology 8 (2010) 415–424

st

t

12

3

4

e

1

2

3

45

3

UDweaDtzttl

bf

iUatms

20 S. Azizi et al. / Partic

tep is decreased till convergence is obtained. Typically an initialime step of 10−4 s is used.

The following boundary conditions were applied to all simula-ions performed:

The walls were treated as nonslip for all phases.Uniform velocity profile boundary condition was imposed at theinlet.Constant pressure boundary condition was considered at the out-let.Axisymmetric boundary condition was applied along the axis ofsymmetry.

The following assumptions were applied throughout the mod-ling:

Temperature, density and viscosity of the gas and solids areassumed constant.Mass transfer between phases is ignored and the gas phase isassumed to be air.Permeability and resistance of porous draft tube were selectedfrom the experimental work.Axisymmetric model was used.Aggregation and breakage of particles are ignored.

.1. Gas volume fractions and particle segregation

Fig. 2 shows the computed voidage contours for Case 1 at= 0.414 m/s (Fig. 2A and B), and Case 2 at U = 0.362 m/s (Fig. 2C and), indicating that voidage through the porous draft tube increasesith increasing the bed height. Formations of spout and annulus are

stablished as shown in Fig. 2. For establishing fountain, in Fig. 2And C scale of color bar has been changed. As shown in Fig. 2B and, particle concentration is low in spout, while the particle concen-

ration reaches the particle maximum packing limit in the annularone. Particles are carried up by gas in the spout to reach the top ofhe bed to form a fountain in which particle concentration is lowerhan that in the spout and the annular zones. The particles circu-ate between the spout, annulus and the fountain in the bed. As can

4taef

Fig. 2. Voidage contours at different fine particle mass fractio

Fig. 3. Computed volume fraction contours of fine particles.

e seen in Fig. 2A and C, finer particles lead to dragged fountainormation.

Segregation behavior in conventional spouted beds contain-ng binary mixtures of particles of different sizes was studied byemaki, Yamada, and Kugo (1983), who found noticeable radialnd axial segregation even for high gas velocities, particularly whenhe particle sizes were highly different. The present study uses a

ixture of 477 and 1351 �m particles, showing pronounced axialegregation in a spouted bed with a porous draft tube when the fine77 �m particles reach 5% (Cs = 0.05). Fig. 3 shows that the finer par-icles act as flotsam, collecting above the annulus section, and both

xial and radial segregations in the annulus section are not muchnhanced by increasing the inlet gas velocity, as will be discussedurther in Figs. 7 and 10.

ns (Cs) in fountain (A and C), and bed zones (B and D).

Page 7

S. Azizi et al. / Particuology 8 (2010) 415–424 421

er par

3

ihflwttpfl

mfi0

sigrdbIQtt

Fig. 4. Gas velocity contours for fin

.2. Gas velocity pattern

Velocity contours are shown in Fig. 4, with more refined formsn Fig. 4A and C. As seen from Fig. 4B and D, the gas velocity isigh in the spout, and low in the annular zone. In addition, gasow increases with height in the annulus section but decreasesith height in the spout section, because of the presence of porous

ube wall through which gas permeates outward (see Fig. 5). Inhe fountain zone, gas flow is divergent slightly because of fallingarticles into the annulus. In the upper level of the fountain, gasow diverges uniformly.

Fig. 5 shows the variation of computed as well as experi-ental gas flow rate through annulus against vertical distance y,

ne particle concentration Cs and radial coordinate (r = 0.015 and.045 m).

e

fr

Fig. 5. Gas flow rate through annulus as a function of vertical dista

ticle mass fractions of 0.05 and 0.0.

Figs. 4 and 5 show that the gas flow rate through the annulusection increases in the vertical direction and reaches some max-mum value. Gas flow increased because of the existing pressureradient and after this pressure gradient had consumed gas floweached a constant value. Increasing gas flow through the porousraft tube in the horizontal direction is an advantage of spouteded with a porous draft tube. According to experimental work of

shikura et al. (2003), in spouted beds with a non-porous draft tubeA/QT profile is flat, while in spouted bed with a porous draft tube

his profile is not flat due to gas percolation into the annulus regionhrough the porous wall of the draft tube, as shown in Fig. 5 for both

xperimental and computational results.

Figs. 6 and 7 show respectively the effect of finer particle massraction (Cs) and inlet gas flow rate (QT) on the annulus gas flowate. Similar to the numerical results of Hosseini, Zivdar, and Rahimi

nce y, fine particle mass fraction Cs , and radial coordinate r.

Page 8

422 S. Azizi et al. / Particuology 8 (2010) 415–424

Fig. 6. Effect of fine particle mass fraction on annulus section gas velocity for con-stant inlet gas velocity (U = 0.362).

Fp

(tfio(bi

3

ssbsps

ig. 7. Effect of gas inlet flow rate on annulus section gas flow rate for constant finearticle mass fraction (Cs = 0.05).

2009) for a spouted bed with a non-porous draft tube, Fig. 6 showshat for constant inlet gas velocity (U = 0.362 m/s), with increasingne particle mass fraction, annulus gas velocity decreases becausef decreasing voidage. For constant fine particle mass fractionCs = 0.05), Fig. 7 shows that QA/QT increases with decreasing QTecause of gas jet expanding into the porous draft tube in the con-

cal section of spouted bed.

.3. Pressure

The modeling results on variation of reduced longitudinal pres-ure versus reduced bed level (y/H) for the different radius in thepouted bed are shown in Fig. 8. Adding fine solids to the spouted

ed reduces the pressure in the bed. Gas pressure through the spoutection is greater than the annulus section. In the annulus section,ressure variation with the horizontal distance is negligible. Fig. 8hows that the experimentally measured pressure of Ishikura et

Fig. 8. Longitudinal pressure distribution within annulus and spout region.

Page 9

S. Azizi et al. / Particuology

abhtlr

wod

tssws

Fs

pecd

3

tRtiitsVmei

4

buoiptgiiidmfl

Fig. 9. Variation of total bed pressure drop with superficial gas velocity.

l. (2003) is higher than the model prediction this is considered toe due to the lower gas–solid drag coefficient and higher particleold up in spout region. Higher particle hold up might be attributedo inclusion of lower rolling friction, since the rolling friction canower the flow rheology of granular media in the dense annulusesulting in reduction of solid hold up in spout zone.

Fig. 9 shows the variation of the total bed pressure drop (�PS)ith superficial gas velocity (U) for the case that the mass fraction

f fine particles is Cs = 0.05. Similar to the trend of experimentalata, the pressure drop increases with inlet gas velocity.

Average value of experimental solids hold up in the spout sec-ion for U = 0.364 m/s and C = 0.05 is 0.05, while because of higher

s

pills of particles in conical section the predicted average value ofolids hold up is 0.085, though modeled results are in agreementith the experimental data in terms of QA/QT. Because of higher

olids hold up in the model predictions, the predicted pressure and

ig. 10. Particle local velocity in the center axis of the draft tube at the middleection.

R

A

A

B

B

C

D

D

G

H

I

L

L

8 (2010) 415–424 423

ressure drop in both spout and annulus sections are lower thanxperimental value. Large gas pressure differences occurs in theonical section and after the conical section the slope of pressurerop in the annulus section is close to the experimental value.

.4. Solids velocity

The behavior of both gas and solid particles within the draftube is important for reaction and drying of grain (Tulasidas, Kudra,aghavan, & Mujumdar, 1992). The local velocity of particles withinhe draft tube (Vps) was measured by an optical fiber probe methodn experimental work of Ishikura et al. (2003). Fig. 10 shows Vps

n the axis of the draft tube at the middle section for the caseshat the average mass fractions of fine particles are 0 and 0.05. Theolids velocity for Cs = 0.05 is slightly higher than Vps for Cs = 0.0.ps increases with increasing inlet gas velocity in both the experi-ent and numerical results. With increasing U, difference between

xperiment and model prediction increases, maybe due to thencrease of solids hold up deviation.

. Conclusion and future works

In this work a CFD model was used for simulating the spouteded with a porous draft tube for binary particle mixtures. The sim-lation results showed an agreement with the experimental dataf Ishikura et al. (2003). This study also shows that the gas veloc-ty in the annulus section increases longitudinally because of theresence of porous draft tube. Effect of the fine particle fraction ofhe particle mixture Cs on behavior of the system was also investi-ated, showing gas velocity in annulus section UA decreases withncreasing the Cs. It was observed that the total gas pressure dropncreases and the annulus gas velocity decreases with increasingnlet gas velocity. Particle segregation in spouted bed with porousraft tube was analyzed, showing that the solid segregation is notuch enhanced by increasing gas velocity and fine particles act as

otsam.

eferences

bu-Zaid, S., & Ahmadi, G. (1990). Simple kinetic model for rapid granular flowsincluding frictional losses. Journal of Engineering Mechanics, 116, 379–389.

hmadi, G., & Ma, D. (1990). A thermodynamical formulation for dispersed multi-phase turbulent flows-I: Basic theory. International Journal of Multiphase Flows,16, 323–340.

enyahia, S. (2008). Validation study of two continuum granular frictional flowtheories. Industrial & Engineering Chemistry Research, 47(22), 8926–8932.

ertola, F., Vanni, M., & Baldi, G. (2003). Application of computational fluid dynamicsto multiphase flow in bubble columns. International Journal of Chemical RectorEngineering, 1, A3.

laflin, J. K., & Fane, A. G. (1983). Spouting with a porous draft-tube. The CanadianJournal of Chemical Engineering, 61, 356–363.

u, W., Bao, X., Xu, J., & Wei, W. (2006a). Computational fluid dynamics (CFD)modeling of spouted bed: Assessment of drag coefficient correlations. ChemicalEngineering Science, 61, 1401–1420.

u, W., Bao, X., Xu, J., & Wei, W. (2006b). Computational fluid dynamics (CFD)modeling of spouted bed: Influence of frictional stress, maximum packinglimit and coefficient of restitution of particles. Chemical Engineering Science, 61,4558–4570.

idaspow, D. (1994). Multiphase flow and fluidization, continuum and kinetic theorydescriptions. Boston: Academic Press.

osseini, S. H., Zivdar, M., & Rahimi, R. (2009). CFD simulation of gas–solid flow ina spouted bed with a non-porous draft tube. Chemical Engineering & Processing,48, 1539–1548.

shikura, T., Nagashima, H., & Ide, M. (2003). Hydrodynamics of a spouted bed witha porous draft tube containing a small amount of finer particles. Powder Tech-nology, 131, 56–65.

ebowitz, J. L. (1964). Exact solution of generalized percus-yevick equation for amixture of hard spheres. Physical Review, A133, 895–899.

ettieri, P., Micale, G., Cammarata, L., & Colman, D. (2002, April). Computationalfluid-dynamics simulations of gas-fluidized beds: A preliminary investigation ofdifferent modelling approaches. In Proceedings of the10th workshop on two-phaseflow predictions, vol. 1 Merseburg, Germany, (pp. 300–309).

Page 10

4 uology

L

L

M

MM

P

S

S

S

S

T

U

24 S. Azizi et al. / Partic

u, H. L., He, Y. H., Liu, W. L., Ding, J., Gidaspow, D., & Bouillard, J. (2004).Computer simulations of gas–solid flow in spouted beds using kinetic-frictional stress model of granular flow. Chemical Engineering Science, 59, 865–878.

un, C. K. K., Savage, S. B., Jeffrey, D. J., & Chepurniy, N. (1984). Kinetic theories forgranular flow: Inelastic particles in couette flow and slightly inelastic particlesin a general flow field. Journal of Fluid Mechanics, 140, 223–256.

a, D., & Ahmadi, G. (1990). A thermodynamical formulation for dispersed multi-phase turbulent flows—II: Simple shear flows for dense mixtures. InternationalJournal of Multiphase Flow, 16, 341–351.

athur, K. B., & Epstein, N. (1974). Spouted beds. New York: Academic Press.athur, K. B., & Gishler, P. E. (1955). A technique for contacting gases with coarse

solid particles. AIChE Journal, 1(1), 157–164.assalacqua, A., & Marmo, L. (2009). A critical comparison of frictional stress mod-

els applied to the simulation of bubbling fluidized beds. Chemical EngineeringScience, 64, 2795–2806.

avage, S. B. (1998). Analysis of slow high concentration flows of granular materials.The Journal of Fluid Mechanics, 377, 1–26.

W

Z

8 (2010) 415–424

rivastava, A., & Sundaresan, S. (2003). Analysis of a frictional-kinetic model forgas-particle flow. Powder Technology, 129, 72–85.

yamlal, M. (1987). The particle–particle drag term in a multiparticle model of flu-idization topical report, DOE/MC/21353-2373, NTIS/DE87006500. Springfield, VA:National Technical Information Service.

zafran, R. G., & Kmiec, A. (2004). CFD modeling of heat and mass transfer in aspouted bed dryer. Industrial & Engineering Chemistry Research, 43, 1113–1124.

ulasidas, T. N., Kudra, T., Raghavan, G. S. V., & Mujumdar, A. S. (1992, August).Effect of bed height on drying of shelled corn in a two-dimensional spouted bedequipped with draft plates. In Proceedings of 15th international symposium ondrying Budapest, Hungary, (pp. 1564–1570).

emaki, O., Yamada, R., & Kugo, M. (1983). Particle segregation in a spouted bed of

binary mixtures of particles. The Canadian Journal of Chemical Engineering, 61,303–307.

u, Z., & Mujumdar, A. S. (2008). CFD modeling of the gas–particle flow behavior inspouted beds. Powder Technology, 183, 260–272.

hao, X. L., Yao, Q., & Li, S. Q. (2006). Effects of draft tubes on particle velocity profilesin spouted beds. Chemical Engineering Technology, 29, 875–881.