Hydrodynamics of Slot-Rectangular SpoutedBeds: Effect of Slot Configuration on theLocal Flow StructureZ. Chen, C. J. Lim* and J. R. Grace

Department of Chemical & Biological Engineering, University of the British Columbia, 2360 East Mall, Vancouver,BC, Canada V6T 1Z3

The local flow structure in a slot-rectangular spouted bed column of 300 mm × 100 mm cross-section was investigated with slots of equal areabut different length-to-width ratios. Dead-zones, spout shapes, and distributions of pressure, particle velocity, and voidage were explored. Thelocal flow structure of the slot-rectangular spouted bed became similar to conventional spouted beds as the height increased, with spouts fromslots of different length-to-width ratios approaching similarity in the upper part of the bed. Static bed height was found to have little influenceon the flow in the spout at a given level.

On a etudie la structure d’ecoulement local dans une colonne a lit jaillissant rectangulaire a fentes d’une section transversale de 300 mm × 100 mm,les fentes etant de surface egale mais les rapports longueur sur largeur differents. Les zones mortes, les formes de bec et les distributions de pressionet de vitesse des particules ainsi que le degre de vide ont ete explores. La structure d’ecoulement local du lit jaillissant a fentes rectangulairesdevient semblable a celle des lits jaillissants conventionnels lorsque la hauteur augmente, les jets des fentes de differents rapports longueur surlargeur approchant une similarite dans la partie superieure du lit. On a trouve que la hauteur de lit statique avait peu d’influence sur l’ecoulementdans le jet a un niveau donne.

Keywords: spouted bed, slot configuration, hydrodynamics, spout shape

INTRODUCTION

Since their development by Mathur and Gishler (1955), con-ventional spouted beds have been used in a number ofapplications (Mathur and Epstein, 1974; Epstein and Grace,

1997). Conventional axisymmetric spouted beds of small scalehave proven to be effective for gas/particle contacting. However,the spouted bed technique has seldom been applied in large-scale industrial processes due to scale-up difficulties (Dogan et al.,2000), such as the inability to achieve good quality spouting inlarge vessels, and difficulties in predicting the performance ofspouted beds larger than about 0.3 m in diameter. To address thescale-up issue, a modified geometry, denoted “two-dimensionalspouted bed”, was proposed by Mujumdar (1984), who noted itspotential for avoiding scaling-up difficulties. This configurationwas renamed “slot-rectangular spouted bed” (SRSB) by Doganet al. (2000) and Freitas et al. (2000) because of the significantthree-dimensional effects found experimentally as the columnthickness was increased for constant width.

SRSB hydrodynamics, stability and scale-up have been inves-tigated (Kalwar et al., 1989, 1992, 1993; Passos et al., 1991,

1993, 1994; Dogan et al., 2000, 2004; Freitas et al., 2000,2004a,b). However, most previous work has focused on globalflow properties, e.g. minimum spouting velocity, maximumpressure drop and maximum spoutable bed height. The localflow structure of SRSBs has received little notice. Becauseof insufficient research, little work has been reported on theapplication of SRSBs, although coating of particles has receivedsome attention (Taranto et al., 1997; Donida and Rocha, 2002;Wiriyaumpaiwong et al., 2003, 2004).

In the present work, experiments were carried out on the localflow structure of a SRSB column with slots of equal area, butdifferent length/width ratios. Results are reported on spout anddead-zone shape, local profiles of pressure, particle velocity andvoidage.

∗Author to whom correspondence may be addressed.E-mail address: cjlim@chml.ubc.caCan. J. Chem. Eng. 86:598–604, 2008© 2008 Canadian Society for Chemical EngineeringDOI 10.1002/cjce.20043

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Figure 1. Schematic of spouted bed column: (1) Rectangular column,(2) slot (gas inlet), (3) pressure relief valve, (4) wind box, (5) orifice flowmeter, (6) main valve, �P: differential pressure transducer, P: absolutepressure transducer.

EXPERIMENTALExperiments were carried out in a plexiglas rectangular columnof width ˛ = 300 mm, thickness ˇ = 100 mm, and overall height1000 mm, shown in Figure 1. Glass beads of 1.33 mm diameterand 2500 kg/m3 density were contacted with compressed air atroom temperature, with the top of the column open to the atmo-sphere. A fine wire mesh underneath the slot prevented solidsfrom falling into the entry pipe. The air flow rates were measuredby an orifice flow meter.

Three air entry slots were tested having the same cross-sectionalarea, 400 mm2, but three different length/width ratios: 4, 2 and1. The dimensions of these slots are listed in Table 1. As shown inFigure 1, the slot length, Ls, is the dimension in the direction ofthe column thickness, and slot width, Ws, in the direction of thecolumn width. A calming chamber of the same cross-section asthe column and 250 mm height was installed below the air entryslots to streamline the airflow.

Pressure was measured by pressure transducers of OMEGAPX140 series connected to a stainless steel pressure probe insertedinto the column. The pressure signal was collected by a DAS-08A/D data acquisition board. The local particle velocity and localvoidage in the spouted beds were determined by an optical probeusing a Particle Velocity Analyzer version 4 (PV4A) manufacturedby the Institute of Process Engineering of the Chinese Academyof Sciences. The location of the spout–annulus interface wasdetermined based on where the frequency of the voidage probesignal changed abruptly, the same method as employed by He(1995). Dead-zone boundaries were identified from signals show-ing where there were no fluctuation in the voidage optical signals.

Table 1. Dimensions of slots

Slot length/width 4 2 1

Length (mm) 40 28 20Width (mm) 10 14 20Perimeter (mm) 100 84 80Cross-sectional area (mm2) 400 392 400

Measurements were only carried out for conditions where theflow was steady, i.e., the position and size of the spout and foun-tain were seen to be invariant with time, and the pressure dropacross the bed was statistically steady. Local flow properties weremeasured one point at a time. In this work, the flow propertieswere only measured at two vertical surfaces, orthogonal to eachother, intersecting at the vertical axis of the column, one directionparallel, and the other normal, to the length of the slot. Y and Xindicate the distance from the centre in these two directions. Thecolumn was flat-bottomed for convenience in measuring from dif-ferent sides to allow determination of the position of the spout anddead-zone boundaries. Axial profiles in this work are measuredfrom the axis of the column.

RESULTS AND DISCUSSION

Spout Shape and Dead-ZoneAs summarized by Mathur and Epstein (1974), a variety of spoutshapes can be identified in conventional axisymmetric spoutedbeds. As shown in Figure 2, two of these shapes were foundin this work: (a) “continuously diverging,” normally observednormal to the slot; and (b) “expanding, necking and expanding,”normally appearing in the direction along the slot length. Atlow gas velocities, the second shape could also be observednormal to the slot length. Consistent with the previous findings

Figure 2. Spout shapes for different superficial gas velocities for slotlength = 40 mm, width = 10 mm, and Hs = 300 mm.

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Figure 3. Annulus/dead-zone interfaces for different superficial gasvelocities for slot length = 40 mm, width = 10 mm, and Hs = 300 mm.

of Freitas et al. (2004b), with increasing height, the spout shapeseems to forget the original slot shape and, instead, to approacha nearly circular shape. However, in the current work, it wasalso found that there is overshoot, with the dimension in thedirection that started smaller ultimately exceeding the dimensionin the orthogonal direction, before beginning to shrink. Withincreasing height, the spout oscillated in the two orthogonaldirections around a circular shape, needing more height to reacha fully developed circular shape.

Because the experiments were carried out in a flat-bottomedcolumn, there were significant dead-zones, where particles did notmove at all. Dead-zones could only be observed in the X direction,i.e., in the direction normal to the slot length. No dead-zone couldbe seen in the orthogonal direction. At a higher gas velocity thedead-zone was found to be smaller. However, gas velocity hadlittle influence on the shape of the annulus/dead-zone interface,as shown in Figure 3.

Local PressureLefroy and Davidson (1969) found that the longitudinal pressuredistribution in a flat-bottomed axisymmetric cylindrical spoutedbed could be fitted by a cosine function:

�PZ

�Ps= cos

(�Z

2Hs

)(1)

where Z is the vertical coordinate measured from the bottom, Hs

the static bed height, �PZ the gauge pressure at Z, and �Ps thepressure drop across the whole bed. In the current work, �Ps

and �PZ were measured at the wall near one end of the slots. Asshown in Figure 4, the longitudinal pressure distribution is fittedwell by Equation (1), suggesting that the cosine correlation canbe applied to the SRSBs of different slot configurations. However,the pressure at the centre of the column was not well representedby this equation. Instead, a pressure-ascending region appearedat the bottom, likely due to the high entry velocity and Venturieffect at the slot outlet. After reaching a maximum, the pressurethen decreased with increasing height. As expected, the pressurewas higher for a deeper bed and lower for higher gas velocities.

Particle Velocity and VoidageProfiles of the vertical particle velocity and voidage along the axisof the column appear in Figures 5 and 6, respectively. This evolu-

Figure 4. Axial pressure distributions at the wall compared with cosinerelationship, Equation (1).

Figure 5. Effect of superficial gas velocity on axial particle velocity profilefor slot length = 40 mm, width = 10 mm and Hs = 300 mm.

tion of velocity showed a pattern similar to previous findings foraxisymmetric spouting (Mathur and Epstein, 1974), with particlesrapidly accelerated at the bottom and then gradually deceleratinguntil they reached the bed surface. The voidage along the axis ofthe column varied in a manner similar to the pressure and theparticle velocity along the centre line. The voidage was low at thebottom, then increased with height, and finally decreased. Thiscan be explained by the evolution of particle velocity. When parti-cles are accelerated at the bottom, the distance between particlesincreases, causing an increase in voidage. After a maximum isreached, the voidage decreases due to the velocity decreasing andparticles being drawn into the spout from the side. As shown inFigures 5 and 6, a higher Ug led to higher voidages and particlevelocities, also producing a longer acceleration zone.

Lateral profiles of vertical particle velocity in the spout at thebed surface, Z = Hs, were also measured from the two orthogonaldirections at different superficial gas velocities. Results are shownin Figure 7. Increasing the superficial gas velocity caused the par-ticle velocity at the bed surface to be higher, although there is anexception in Figure 7(a).

The radial distribution of particle velocity in the spout of con-ventional axisymmetric spouted beds was summarized by Mathur

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Figure 6. Effect of superficial gas velocity on axial voidage profile for slotlength = 40 mm, width = 10 mm and Hs = 300 mm.

Figure 7. Effect of superficial gas velocity on lateral profile of particlevelocity for slot length = 40 mm, width = 10 mm, Hs = 300 mm andZ = Hs.

and Epstein (1974), who noted that the velocity profile could bedescribed by a parabolic equation:

vr

v0= 1 −

(r

rs

)2

(2)

where vr is the particle velocity at radial position r, v0 is the parti-cle velocity at the centre of spout, and rs is the spout radius. In thecurrent work, the flow was asymmetric and the spout dimensionswere unequal in different directions. Hence, the particle velocitiesat different lateral positions were correlated to a best-fit parabolicequation of the form:

vx

v0= 1 −

(X − X0

Xs

)2

,vy

v0= 1 −

(Y − Y0

Ys

)2

(3)

for (X − X0) ≤ xs and (Y − Y0) ≤ Ys, where Xs and Ys are the half-widths of the spout in the two orthogonal directions, X0 and Y0

are the positions of the spout centre in these two directions, andvx and vy are the vertical component of particle velocities at (X, 0)and (0, Y) and height Z, respectively. The lines plotted in Figure 10are least-square fits based on this form of equation. Agreementwith this form of correlation is favourable, indicating that the lat-eral particle velocity profile in SRSBs can also be represented byparabolic relationships, although the centre of the spout did notcoincide with the axis of the column.

Influence of Bed DepthAs shown in Figures 8, spout shapes were similar for differentstatic bed heights. At any specific level, the dimensions did notvary significantly with static bed height.

Figure 8. Shape of spout for different static bed depth with slotlength = 40 mm, width = 10 mm, and Ug = 0.7 m/s.

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Figure 9. Effect of static bed height on axial particle velocity profile forslot length = 40 mm, width = 10 mm, and Ug = 0.7 m/s.

Figure 10. Annulus/dead-zone interface for different static bed heightswith slot length = 40 mm, width = 10 mm, and Ug = 0.7 m/s.

As shown in Figure 9, particle velocities for different static bedheights were similar, with the velocity in the spout at a given levelnot affected significantly by the static bed height. The voidageswere also found to be similar at the same level for different staticbed heights, although there were small differences at the bottom(Chen, 2008).

Although the static bed height seems to have little effect on theflow in the spout, there was a noticeable effect on the includedangle of the dead-zones. As shown in Figure 10, deeper beds led tosmaller angles. To prevent dead-zones for deeper beds, divergingbases of smaller included angle seem to be necessary.

Effect of Slot Length/Width RatioSpout shapes and dead-zones for slots of different length/widthratio appear in Figures 11 and 12. The slot of the highestlength/width ratio had the widest spout at the bottom. However,for the same superficial gas velocity, the spouts for all three slotsof different shape all approached a similar size towards the bedsurface in the direction parallel to the slot length. In the directionnormal to the slot length, spouts for different slots were not atthe same position because of asymmetry caused by the effect ofthe column wall. However, the widths of the spouts were nearly

Figure 11. Spout shapes for different slot configuration for Hs = 300mm, and Ug = 0.7 m/s. All dimensions in mm.

Figure 12. Annulus/dead-zone interfaces for different slot configurationfor Hs = 300 mm, and Ug = 0.7 m/s. All dimensions in mm.

the same for a specific vertical position near the bed surface. Theposition of the dead-zone also showed little dependence on theslot configuration.

Trends were similar for the other flow properties, with differ-ences due to slot configurations occurring mainly at the lower partof the column near the slot. For example, Figure 13 shows that

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Figure 13. Influence of slot geometry on axial profile of pressure forHs = 300 mm, and Ug = 0.8 m/s. All dimensions in mm.

Figure 14. Effect of slot geometry on lateral profile of particle velocityfor Hs = 300 mm, Z = Hs, and Ug = 0.8 m/s. All dimensions in mm.

axial pressure profiles differed near different slots, but becamevery similar as the bed surface was approached. Axial profilesof particle velocities and voidage for different slot configurationsshowed similar trends (Chen, 2008). Lateral distributions of par-ticle velocity measured at Z = Hs for different slot configurations,

portrayed in Figure 14, show some asymmetry, but again confirmthat the local flow structure tends to be nearly independent of theoriginal shape of the slot. As a result, the slot configuration hadlittle effect on the local flow properties in the upper part of thecolumn, the local flow then depending primarily on the gas veloc-ity. However, because of the increased perimeters, slots of largerlength/width ratio led to slightly higher solids volume fractions inthe spout, as well as higher solids circulation rates (Chen, 2008).

CONCLUSIONSFor a slot entrance, the spout shape evolves to approach circu-lar with increasing height, with local flow properties seeming to“forget” the shape of the slot towards the bed surface. As a result,the local flow structure of SRSBs shows considerable similarityto the flow pattern of conventional axisymmetric spouted beds.For example, correlations for conventional spouted bed can beadapted to cover axial pressure distributions and lateral profilesof particle velocities.

Another consequence is that the effect of slot geometry is smallin the upper part of the bed. Spouts from slots of equal area,but different length-to-width ratios approach similarity in spoutshape, local pressure, and local particle velocities with increasingheight.

Local flow properties show little dependence on the static bedheight. For different static bed heights, the flow properties, includ-ing the spout size and particle velocity, are nearly the same at aspecified level.

ACKNOWLEDGEMENTSThe authors are grateful to the Natural Sciences and EngineeringResearch Council for Canada for supporting the research pre-sented in the paper.

NOMENCLATUREHs static bed height (mm)Ls slot length (mm)r radial position of measurement point (mm)rs radius of spout in conventional spouted bed (mm)Ug superficial gas velocity (m/s)vo particle velocity at spout centre (m/s)vr particle velocity at radial position r (m/s)Ws slot width (mm)X coordinate normal to slot length (mm)X0 centre of spout in X-direction (mm)Xs spout half-width normal to slot length (mm)Y coordinate parallel to slot length (mm)Y0 centre of spout in Y-direction (mm)Ys spout half-width parallel to slot length (mm)Z vertical coordinate (mm)

Greek Symbols˛ width of column (mm)ˇ thickness of column (mm)�Ps Mean spouting pressure drop from bottom to bed surface

(kPa)�PZ Mean pressure drop from vertical level Z to bed surface

(kPa)

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Manuscript received January 9, 2008; revised manuscriptreceived February 13, 2008; accepted for publication February 21,2008.

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