Hydrodynamics of slot-rectangular spouted beds: effect of slot configuration on the local flow structure.

Chen, Z. ; Lim, C.J. ; Grace, J.R. 等

INTRODUCTION

Since their development by Mathur and Gishler (1955), conventional spouted beds have been used in a number of applications (Mathur and Epstein, 1974; Epstein and Grace, 1997). Conventional axisymmetric spouted beds of small scale have proven to be effective for gas/particle contacting. However, the spouted bed technique has seldom been applied in largescale industrial processes due to scale-up difficulties (Dogan et al., 2000), such as the inability to achieve good quality spouting in large vessels, and difficulties in predicting the performance of spouted beds larger than about 0.3 m in diameter. To address the scale-up issue, a modified geometry, denoted "two-dimensional spouted bed", was proposed by Mujumdar (1984), who noted its potential for avoiding scaling-up difficulties. This configuration was renamed "slot-rectangular spouted bed" (SRSB) by Dogan et al. (2000) and Freitas et al. (2000) because of the significant three-dimensional effects found experimentally as the column thickness was increased for constant width.

SRSB hydrodynamics, stability and scale-up have been investigated (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 global flow properties, e.g. minimum spouting velocity, maximum pressure drop and maximum spoutable bed height. The local flow structure of SRSBs has received little notice. Because of insufficient research, little work has been reported on the application of SRSBs, although coating of particles has received some attention (Taranto et al., 1997; Donida and Rocha, 2002; Wiriyaumpaiwong et al., 2003, 2004).

In the present work, experiments were carried out on the local flow structure of a SRSB column with slots of equal area, but different length/width ratios. Results are reported on spout and dead-zone shape, local profiles of pressure, particle velocity and voidage.

[FIGURE 1 OMITTED]

EXPERIMENTAL

Experiments were carried out in a plexiglas rectangular column of width [alpha] = 300 mm, thickness [beta] =100 mm, and overall height 1000 mm, shown in Figure 1. Glass beads of 1.33 mm diameter and 2500 kg/[m.sup.3] density were contacted with compressed air at room temperature, with the top of the column open to the atmosphere. A fine wire mesh underneath the slot prevented solids from falling into the entry pipe. The air flow rates were measured by an orifice flow meter.

Three air entry slots were tested having the same cross-sectional area, 400 [mm.sup.2], but three different length/width ratios: 4, 2 and 1. The dimensions of these slots are listed in Table 1. As shown in Figure 1, the slot length, [L.sub.s], is the dimension in the direction of the column thickness, and slot width, [W.sub.s], in the direction of the column width. A calming chamber of the same cross-section as the column and 250 mm height was installed below the air entry slots to streamline the airflow.

Pressure was measured by pressure transducers of OMEGA PX140 series connected to a stainless steel pressure probe inserted into the column. The pressure signal was collected by a DAS-08 A/D data acquisition board. The local particle velocity and local voidage in the spouted beds were determined by an optical probe using a Particle Velocity Analyzer version 4 (PV4A) manufactured by the Institute of Process Engineering of the Chinese Academy of Sciences. The location of the spout-annulus interface was determined based on where the frequency of the voidage probe signal changed abruptly, the same method as employed by He (1995). Dead-zone boundaries were identified from signals showing where there were no fluctuation in the voidage optical signals.

Measurements were only carried out for conditions where the flow was steady, i.e., the position and size of the spout and fountain were seen to be invariant with time, and the pressure drop across the bed was statistically steady. Local flow properties were measured one point at a time. In this work, the flow properties were only measured at two vertical surfaces, orthogonal to each other, intersecting at the vertical axis of the column, one direction parallel, and the other normal, to the length of the slot. Y and X indicate the distance from the centre in these two directions. The column was flat-bottomed for convenience in measuring from different sides to allow determination of the position of the spout and dead-zone boundaries. Axial profiles in this work are measured from the axis of the column.

RESULTS AND DISCUSSION

Spout Shape and Dead-Zone

As summarized by Mathur and Epstein (1974), a variety of spout shapes can be identified in conventional axisymmetric spouted beds. As shown in Figure 2, two of these shapes were found in this work: (a) "continuously diverging," normally observed normal to the slot; and (b) "expanding, necking and expanding," normally appearing in the direction along the slot length. At low gas velocities, the second shape could also be observed normal to the slot length. Consistent with the previous findings of Freitas et al. (2004b), with increasing height, the spout shape seems to forget the original slot shape and, instead, to approach a nearly circular shape. However, in the current work, it was also found that there is overshoot, with the dimension in the direction that started smaller ultimately exceeding the dimension in the orthogonal direction, before beginning to shrink. With increasing height, the spout oscillated in the two orthogonal directions around a circular shape, needing more height to reach a fully developed circular shape.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Because the experiments were carried out in a flat-bottomed column, there were significant dead-zones, where particles did not move 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 could be seen in the orthogonal direction. At a higher gas velocity the dead-zone was found to be smaller. However, gas velocity had little influence on the shape of the annulus/dead-zone interface, as shown in Figure 3.

Local Pressure

Lefroy and Davidson (1969) found that the longitudinal pressure distribution in a flat-bottomed axisymmetric cylindrical spouted bed could be fitted by a cosine function:

[DELTA][P.sub.z]/[DELTA][P.sub.s] = cos ([pi]Z/[2H.sub.s]) (1)

where Z is the vertical coordinate measured from the bottom, [H.sub.s] the static bed height, [DELTA][P.sub.z] the gauge pressure at Z, and [DELTA][P.sub.s] the pressure drop across the whole bed. In the current work, [DELTA][P.sub.s] and [DELTA][P.sub.z] were measured at the wall near one end of the slots. As shown in Figure 4, the longitudinal pressure distribution is fitted well by Equation (1), suggesting that the cosine correlation can be applied to the SRSBs of different slot configurations. However, the pressure at the centre of the column was not well represented by this equation. Instead, a pressure-ascending region appeared at the bottom, likely due to the high entry velocity and Venturi effect at the slot outlet. After reaching a maximum, the pressure then decreased with increasing height. As expected, the pressure was higher for a deeper bed and lower for higher gas velocities.

Particle Velocity and Voidage

Profiles of the vertical particle velocity and voidage along the axis of the column appear in Figures 5 and 6, respectively. This evolution of velocity showed a pattern similar to previous findings for axisymmetric spouting (Mathur and Epstein, 1974), with particles rapidly accelerated at the bottom and then gradually decelerating until they reached the bed surface. The voidage along the axis of the column varied in a manner similar to the pressure and the particle velocity along the centre line. The voidage was low at the bottom, then increased with height, and finally decreased. This can be explained by the evolution of particle velocity. When particles are accelerated at the bottom, the distance between particles increases, causing an increase in voidage. After a maximum is reached, the voidage decreases due to the velocity decreasing and particles being drawn into the spout from the side. As shown in Figures 5 and 6, a higher [U.sub.g] led to higher voidages and particle velocities, also producing a longer acceleration zone.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Lateral profiles of vertical particle velocity in the spout at the bed surface, Z = [H.sub.s], were also measured from the two orthogonal directions at different superficial gas velocities. Results are shown in Figure 7. Increasing the superficial gas velocity caused the particle velocity at the bed surface to be higher, although there is an exception in Figure 7(a).

The radial distribution of particle velocity in the spout of conventional axisymmetric spouted beds was summarized by Mathur and Epstein (1974), who noted that the velocity profile could be described by a parabolic equation:

[v.sub.r]/[v.sub.0] = 1- [(r/[r.sub.s]).sup.2] (2)

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

where [v.sub.r] is the particle velocity at radial position r, [v.sub.0] is the particle velocity at the centre of spout, and [r.sub.s] is the spout radius. In the current work, the flow was asymmetric and the spout dimensions were unequal in different directions. Hence, the particle velocities at different lateral positions were correlated to a best-fit parabolic equation of the form:

[v.sub.x]/[v.sub.0] = 1- [(X -[X.sub.0])/[X.sub.s]).sup.2], [v.sub.y]/[v.sub.0] = 1- [(Y -[Y.sub.0])/[Y.sub.s]).sup.2] (3)

for (X-[X.sub.0]) [less than or equal to] [x.sub.s] and (Y-[Y.sub.0]) [less than or equal to] [Y.sub.s], where [X.sub.s] and [Y.sub.s] are the half-widths of the spout in the two orthogonal directions, [X.sub.0] and [Y.sub.0] are the positions of the spout centre in these two directions, and [v.sub.x] and [v.sub.y] are the vertical component of particle velocities at (X, 0) and (0, Y) and height Z, respectively. The lines plotted in Figure 10 are least-square fits based on this form of equation. Agreement with this form of correlation is favourable, indicating that the lateral particle velocity profile in SRSBs can also be represented by parabolic relationships, although the centre of the spout did not coincide with the axis of the column.

Influence of Bed Depth

As shown in Figures 8, spout shapes were similar for different static bed heights. At any specific level, the dimensions did not vary significantly with static bed height.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

As shown in Figure 9, particle velocities for different static bed heights were similar, with the velocity in the spout at a given level not affected significantly by the static bed height. The voidages were also found to be similar at the same level for different static bed heights, although there were small differences at the bottom (Chen, 2008).

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

Effect of Slot Length/Width Ratio

Spout shapes and dead-zones for slots of different length/width ratio appear in Figures 11 and 12. The slot of the highest length/width ratio had the widest spout at the bottom. However, for the same superficial gas velocity, the spouts for all three slots of different shape all approached a similar size towards the bed surface in the direction parallel to the slot length. In the direction normal to the slot length, spouts for different slots were not at the same position because of asymmetry caused by the effect of the column wall. However, the widths of the spouts were nearly the same for a specific vertical position near the bed surface. The position of the dead-zone also showed little dependence on the slot configuration.

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

Trends were similar for the other flow properties, with differences due to slot configurations occurring mainly at the lower part of the column near the slot. For example, Figure 13 shows that axial pressure profiles differed near different slots, but became very similar as the bed surface was approached. Axial profiles of particle velocities and voidage for different slot configurations showed similar trends (Chen, 2008). Lateral distributions of particle velocity measured at Z = [H.sub.s] for different slot configurations, portrayed in Figure 14, show some asymmetry, but again confirm that the local flow structure tends to be nearly independent of the original shape of the slot. As a result, the slot configuration had little effect on the local flow properties in the upper part of the column, the local flow then depending primarily on the gas velocity. However, because of the increased perimeters, slots of larger length/width ratio led to slightly higher solids volume fractions in the spout, as well as higher solids circulation rates (Chen, 2008).

[FIGURE 13 OMITTED]

[FIGURE 14 OMITTED]

CONCLUSIONS

For a slot entrance, the spout shape evolves to approach circular 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 similarity to the flow pattern of conventional axisymmetric spouted beds. For example, correlations for conventional spouted bed can be adapted to cover axial pressure distributions and lateral profiles of particle velocities.

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

Local flow properties show little dependence on the static bed height. For different static bed heights, the flow properties, including the spout size and particle velocity, are nearly the same at a specified level.

ACKNOWLEDGEMENTS

The authors are grateful to the Natural Sciences and Engineering Research Council for Canada for supporting the research presented in the paper.

NOMENCLATURE

[H.sub.s] static bed height (mm)
[L.sub.s] slot length (mm)
r radial position of measurement point (mm)
[r.sub.s] radius of spout in conventional spouted bed (mm)
[U.sub.g] superficial gas velocity (m/s)
[v.sub.0] particle velocity at spout centre (m/s)
[v.sub.r] particle velocity at radial position r (m/s)
[W.sub.s] slot width (mm)
X coordinate normal to slot length (mm)
[X.sub.0] centre of spout in X-direction (mm)
[X.sub.s] spout half-width normal to slot length (mm)
Y coordinate parallel to slot length (mm)
[Y.sub.0] centre of spout in Y-direction (mm)
[Y.sub.s] spout half-width parallel to slot length (mm)
Z vertical coordinate (mm)

Greek Symbols

[alpha] width of column (mm)
[beta] thickness of column (mm)
[DELTA][P.sub.s] Mean spouting pressure drop from bottom to bed
 surface (kPa)
[delta][P.sub.z] Mean pressure drop from vertical level Z to bed
 surface (kPa)

Mannscript received January 9, 2008; revised manuscript received February 13, 2008; accepted for publication February 21, 2008.

REFERENCES

Chen, Z., "Hydrodynamics, Stability and Scale-Up of Slot-Rectangular Spouted Beds," Ph.D. Thesis, University of British Columbia, Vancouver, BC (2008).

Dogan, O. M., L. A. P. Freitas, C. J. Lim, J. R. Grace and B. Luo, "Hydrodynamics and Stability of Slot-Rectangular Spouted Beds. Part I. Thin Bed," Chem. Eng. Commun. 181, 225-242 (2000).

Dogan, O. M., B. Z. Uysal and J. R. Grace, "Hydrodynamic Studies in a Half Slot-Rectangular Spouted Bed Column," Chem. Eng. Commun. 191, 566-579 (2004).

Donida, M. W and S. C. S. Rocha, "Coating of Urea with an Aqueous Polymeric Suspension in a Two-Dimensional Spouted Bed," Drying Technol 20, 685-704 (2002).

Epstein, N. and J. R. Grace, "Spouting of Particulate Solids," Chapter 10, in "Handbook of Powder Science and Technology," 2nd ed., M. E. Fayed and L. Otten, Eds., Chapman Hall/Academic Press, New York (1997).

Freitas, L. A. P., O. M. Dogan, C. J. Lim, J. R. Grace and B. Luo, "Hydrodynamics and Stability of Slot-Rectangular Spouted Beds. Part II. Increasing Bed Thickness," Chem. Eng. Commun. 181, 243-258 (2000).

Freitas, L. A. P., O. M. Dogan, C. J. Lim, J. R. Grace and D. Bai, "Identification of Flow Regimes In Slot-Rectangular Spouted Beds Using Pressure Fluctuations," Can. J. Chem. Eng. 82, 60-73 (2004a).

Freitas, L. A. P., K. Mitsutani, C. J. Lim, J. R. Grace and W Wei, "Voidage Profiles in a Slot-Rectangular Spouted Bed," Can. J. Chem. Eng. 82, 74-82 (2004b).

He, Y., "Hydrodynamic and Scale-up Studies of Spouted Beds," Ph.D. Thesis, University of British Columbia, Vancouver, BC (1995).

Kalwar, M. L, G. S. V Raghavan and A. S. Mujumdar, "Aerodynamics of Grains in a Large Scale Two-Dimensional Spouted Bed With Draft Plates," Drying '89, 433-439 (1989).

Kalwar, M. L, G. S. V Raghavan and A. S. Mujumdar, "Spouting of Two-Dimensional Beds With Draft Plates," Can. J. Chem. Eng. 70, 887-894 (1992).

Kalwar, M. L, G. S. V Raghavan and A. S. Mujumdar, "Circulation of Particles in Two-Dimensional Spouted Beds With Draft Plates," Powder Technol. 77, 233-242 (1993).

Lefroy, G. A. and J. F. Davidson, "The Mechanics of Spouted Beds," Trans. Instn. Chem. Eng. 47, T120-T128 (1969).

Mathur, K. B. and N. Epstein, "Spouted Beds," Academic Press, New York (1974).

Mathur, K. B. and P. E. Gishler, "A Technique for Contacting Gases With Coarse Solid Particles," AIChE J. 1, 157-164 (1955).

Mujumdar, A. "Spouted Bed Technology-A Brief Review," Drying '84 (1984).

Passos, M. L., A. S. Mujumdar and S. G. V Raghavan, "Design Parameters for a Two-Dimensional Spouted Bed," Presented at 3rd International Symposium on Spouted Beds, Vancouver, BC (1991).

Passos, M. L., A. S. Mujumdar and S. G. V Raghavan, "Prediction of the Maximum Spoutable Bed Height in Two-Dimensional Spouted Beds," Powder Technol. 74, 97-105 (1993).

Passos, M. L., A. S. Mujumdar and G. Massarani, "Scale-Up of Spouted Bed Dryers: Criteria and Applications," Drying Technol. 12, 351-391 (1994).

Taranto, O., S. Rocha and G. Raghavan, "Convective Heat Transfer During Coating of Particles in Two-Dimensional Spouted Beds," Powder Technol. 15, 1909-1918 (1997).

Wiriyaumpaiwong, S., S. Soponronnarit and S. Prachayawarakorn, "Soybean Drying by Two-Dimensional Spouted Bed," Drying Technol. 21, 1735-1757 (2003).

Wiriyaumpaiwong, S., S. Soponronnarit and S. Prachayawarakorn, "Drying and Urease Inactivation Models of Soybean Using Two-Dimensional Spouted Bed Technique," Drying Technol. 24, 1673-1681 (2004).

Z. 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

* Author to whom correspondence may be addressed.

E-mail address: cjlim@chml.ubc.ca

Table 1. Dimensions of slots

Slot length/width 4 2 1

Length (mm) 40 28 20
Width (mm) 10 14 20
Perimeter (mm) 100 84 80
Cross-sectional area ([mm.sup.2]) 400 392 400