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The scaling of cluster velocity at the wall of circulating fluidized bed risers
PII:
Chemical Engineering Science, Vol. 53, No. 13, pp. 2475—2477, 1998 ( 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0009–2509(98)00038–4 0009—2509/98 $19.00#0.00
The scaling of cluster velocity at the wall of circulating fluidized bed risers (Received 8 July 1997; in revised form 31 October 1997)
Recent models of heat transfer to the wall of circulating fluidized bed risers have underlined the central role played by particle clusters (Lints and Glicksman, 1993). In this flow regime, the suspension consists of an ascending dilute core surrounded by a descending annulus near the wall. In the annulus, the suspension partly condenses into denser clusters separated from the wall by a thin gas film of order the mean particle diameter (Glicksman, 1997). The clusters generally dominate the convective heat exchange with the wall because of their relatively high solid volume fractions and heat capacity. Accordingly, Lints and Glicksman (1993) suggested that the rate of heat transfer to the wall scales with the mean time spent by individual clusters there. They calculated this transit time from the average descending cluster velocity and the mean contact length with the wall. Although descending cluster velocities are reported in several studies, their scaling with riser conditions and suspension parameters has remained unclear. For simplicity, Lints and Glicksman (1993) assumed that cluster velocity is constant in order to calculate the cluster contact time with the wall, while Glicksman (1997) scaled the cluster residence time using the superficial gas velocity. In this shorter communication, inspection of earlier studies implies a different scaling. Table 1 summarizes descending cluster velocities recorded by several authors under a wide variety of flow conditions. The data are collected primarily in the upper region of the
riser where the flow is likely to be fully developed. We exclude data recorded in the bottom acceleration zone or under unusual circumstances. For example, we do not consider the descending wall velocities of single clusters injected in an otherwise empty tube (Glicksman, 1988). Although these velocities have similar magnitudes to those observed in a more conventional riser suspension, such a flow with negligible vertical pressure gradient is not likely governed by similar physics. Perhaps as a consequence, cluster velocities in that unusual flow are relatively independent of particle size. The cluster velocities in the table span a range of approximately a factor of two. As Fig. 1 indicates, they appear to scale with the square root of the particle diameter and the gravitational acceleration, º +36Jgd. This trend #is remarkably robust, considering the broad variations in solid flux, superficial gas velocity, riser diameter, riser geometry and solid density among those experiments. The measurements of Glicksman and Noymer (1996) and Wu et al. (1991) confirm that the cluster velocity is relatively insensitive to the solid flux and superficial gas velocity. The high temperature tests of Golriz and Leckner (1992) further suggest that the gas density and viscosity also fail to influence the trend. Rhodes et al. (1992) exploit the high temporal and spatial resolution of a high-speed video camera to distinguish two families of clusters. The first consists of occasional, relatively
Table 1. Descending cluster velocities at the wall Authors Glicksman and Noymer (1996) Bader et al. (1988) Golriz and Leckner (1992) Horio et al. (1988) Nowak et al. (1991) Hartge et al. (1988) Wu et al. (1991) Wu et al. (1991) Wirth et al. (1991) Rhodes et al. (1992) wall strands bulk downflow
Measurement technique
º #(m/s)
º 0 (m/s)
z/H
G (kg/m2 s)
¹ (°C)
D (cm)
o 4 (kg/m3)
d (km)
Thermal imaging Pitot tube
1.1$0.1 1.0$0.2
2.3—3.6 3.7
0.21 0.75
8—28 98
20 20
16* 31
6980 1714
69 76
Thermocouples Optical fibers Optical fibers Optical fibers Heat transfer probe Video Video
1.8$0.4 0.8$0.1 0.8$0.2 1.2$0.2 1.6$0.5 1.3$0.5 1.3$0.2
3.6—6.7 1.2 4.0 2.9 7.0 7.0 1.2—1.9
0.81 0.58 0.28 0.56 0.43 0.43 0.73
&10 11.7 55.7 49 15—47 15—47 —
850 20 20 20 20 20 20
170* 5 21 40 15 15 17*
2600 1000 2300 1500 2650 2650 3950
260 60 46 85 171 171 50
High-speed video
0.3 to 0.4 &1
3—5
0.53
2—80
20
31
2456
75
* Square cross-section. 2475
2476
Shorter Communications
Fig. 1. Suggested scaling of descending cluster velocity at the wall with particle diameter and gravitational acceleration. The symbols are data from the investigators shown; the line is º +36Jgd). #slow strands in close proximity or contact with the wall. The second is a more prominent bulk downflow slightly farther from the wall; it exhibits a faster velocity in agreement with the trends summarized in the table. Because the other authors do not distinguish between the two families, their measurements are likely dominated by the uninterrupted, faster bulk downflow. Remarkably, the downward velocity of neither class appears to be affected by the superficial gas velocity or overall solid flux. The velocity difference between the two classes may reflect the downward shearing of the particle phase at the wall. For completeness, the table provides cluster velocities measured by Rhodes et al. for both classes. Because the cluster velocity is seemingly unaffected by overall flow conditions, it is likely that it is set by a local force balance at the wall. Its apparent insensitivity to the properties and velocity of the gas further suggests that interactions in the particle phase dominate the balance. In this case, the only parameters relevant to the velocity scaling would include the material density and mean diameter of the particles, the gravitational acceleration and, if the particles are engaged in collisional interactions, the parameters characterizing the impacts. Because in this formulation the particle material density is the only parameter involving mass, it cannot appear in the velocity scaling. In addition, because collisional parameters often belong to a relatively narrow range of values (Massah et al., 1995; Lorenz, et al., 1997), we expect that cluster velocities from a wide range of experiments would indeed scale as Jgd. Acknowledgments The authors gratefully acknowledge M. Golriz, B. Leckner, K. Wirth and O. Molerus, who provided further details of operational conditions for their experiments, and L. Glicksman and P. Noymer for helpful discussions. This work was funded by the University Coal Research Program of the US Department of Energy, Pittsburgh Energy Technology Center under grants DE-FG22-93PC93216 and DE-FG2295PC95228, and by the International Fine Particle Research Institute. This material is also based upon work supported by National Science Foundation Graduate Research Fellowship Number GER-9253848. A. ELIZABETH GRIFFITH MICHEL Y. LOUGE* Sibley School of Mechanical and Aerospace Engineering Cornell University Ithaca, NY 14853 U.S.A
* Corresponding author.
NOTATION
d D g G ¹ º 0 º #o s z/H
mean particle diameter, km riser diameter, m gravitational acceleration, m/s2 cross-sectional solids flux, kg/m2 s mean suspension temperature, °C superficial gas velocity, m/s average particle cluster velocity at the wall, m/s material density of the particles, kg/m3 elevation of velocity measurement relative to riser height REFERENCES
Bader, R., Findlay, J. and Knowlton, T. M. (1988) Gas/solid flow patterns in a 30.5-cm-diameter circulating fluidized bed. In Circulating Fluidized Bed ¹echnology II, eds P. Basu and J. F. Large, pp. 123—137. Pergamon Press, Oxford, U.K. Glicksman, L. R. (1988) Circulating fluidized bed heat transfer. In Circulating Fluidized Bed ¹echnology II, eds P. Basu and J. F. Large, pp. 13—29. Pergamon Press, New York, U.S.A. Glicksman, L. R. (1997) Heat transfer in circulating fluidized beds. In Circulating Fluidized Beds, eds J. R. Grace, A. A. Avidan and T. M. Knowlton, pp. 261—311. Blackie Academic and Professional, London, U.K. Glicksman, L. R. and Noymer, P. D. (1996) Measurements of the velocity and acceleration of clusters at the wall of a circulating fluidized bed. In Preprints: Fluidization and Fluid—Particle Systems, eds H. Arastoopour, Y.-M. Chen and T. Guttilla, pp. 45—52. AIChE, New York, U.S.A. Golriz, M. and Leckner, B. (1992) Experimental studies of heat transfer in a circulating fluidized bed boiler. In Proceedings International Conference on Engineering Applications of Mechanics, Vol. 3. Sharif University of Technology, Teheran, Iran, pp. 167—174. Hartge, E.-U., Rensner, D. and Werther, J. (1988) Solids concentration and velocity patterns in circulating fluidized beds. In Circulating Fluidized Bed ¹echnology II, eds P. Basu and J. F. Large, pp. 165—180. Pergamon Press, Oxford, U.K. Horio, M., Morishita, K., Tachibana, O. and Murata, N. (1988) Solid distribution and movement in circulating fluidized beds. In Circulating Fluidized Bed ¹echnology II, eds P. Basu and J. F. Large, pp. 147—154. Pergamon Press, Oxford, U.K. Lints, M. and Glicksman, L. R. (1993) Parameters governing particle-to-wall heat transfer in a circulating fluidized bed. In Circulating Fluidized Bed ¹echnology I», eds by A. A. Avidan, Proceedings of the 4th International Conference on Circulating Fluidized Beds, AIChE, New York, U.S.A., pp. 297—304.
Shorter Communications Lorenz, A., Tuozzolo, C. and Louge, M. Y. (1997) Measurements of impact properties of small, nearly spherical particles. Exp. Mech. 37, 3, 292—298. Massah, H., Shaffer, F., Sinclair, J. and Shahnam, M. (1995) Measurements of specular and diffuse particle-wall collision properties. In Fluidization »III, eds C. Lague´rie and J.-F. Large, Proceedings of the 8th International Conference on Fluidization. The Engineering Foundation, New York, U.S.A., pp. 641—648. Nowak, W., Mineo, H., Yamazaki, R. and Yoshida, K. (1991) Behavior of particles in a circulating fluidized bed of a mixture of two different sized particles. In Circulating Fluidized Bed ¹echnology III, eds P. Basu, M. Horio,
2477
and M. Hasatani, pp. 219—224. Pergamon Press, Oxford, U.K. Rhodes, M., Mineo, H. and Hirama, T. (1992) Particle motion at the wall of a circulating fluidized bed. Powder ¹echnol. 70, 207—214. Wirth, K.-E., Seiter, M. and Molerus, O. (1991) Concentration and velocities of solids in areas close to the walls in circulating fluidized bed systems. »GB Kraftwerkstechnik 10, 824—828. Wu, R. L., Lim, C. J., Grace J. R. and Brereton C. M. H., (1991) Instantaneous local heat transfer and hydrodynamics in a circulating fluidized bed. Int. J. Heat Mass ¹ransfer 34, 2019—2027.
Chemical Engineering Science, Vol. 53, No. 13, pp. 2475—2477, 1998 ( 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0009–2509(98)00038–4 0009—2509/98 $19.00#0.00
The scaling of cluster velocity at the wall of circulating fluidized bed risers (Received 8 July 1997; in revised form 31 October 1997)
Recent models of heat transfer to the wall of circulating fluidized bed risers have underlined the central role played by particle clusters (Lints and Glicksman, 1993). In this flow regime, the suspension consists of an ascending dilute core surrounded by a descending annulus near the wall. In the annulus, the suspension partly condenses into denser clusters separated from the wall by a thin gas film of order the mean particle diameter (Glicksman, 1997). The clusters generally dominate the convective heat exchange with the wall because of their relatively high solid volume fractions and heat capacity. Accordingly, Lints and Glicksman (1993) suggested that the rate of heat transfer to the wall scales with the mean time spent by individual clusters there. They calculated this transit time from the average descending cluster velocity and the mean contact length with the wall. Although descending cluster velocities are reported in several studies, their scaling with riser conditions and suspension parameters has remained unclear. For simplicity, Lints and Glicksman (1993) assumed that cluster velocity is constant in order to calculate the cluster contact time with the wall, while Glicksman (1997) scaled the cluster residence time using the superficial gas velocity. In this shorter communication, inspection of earlier studies implies a different scaling. Table 1 summarizes descending cluster velocities recorded by several authors under a wide variety of flow conditions. The data are collected primarily in the upper region of the
riser where the flow is likely to be fully developed. We exclude data recorded in the bottom acceleration zone or under unusual circumstances. For example, we do not consider the descending wall velocities of single clusters injected in an otherwise empty tube (Glicksman, 1988). Although these velocities have similar magnitudes to those observed in a more conventional riser suspension, such a flow with negligible vertical pressure gradient is not likely governed by similar physics. Perhaps as a consequence, cluster velocities in that unusual flow are relatively independent of particle size. The cluster velocities in the table span a range of approximately a factor of two. As Fig. 1 indicates, they appear to scale with the square root of the particle diameter and the gravitational acceleration, º +36Jgd. This trend #is remarkably robust, considering the broad variations in solid flux, superficial gas velocity, riser diameter, riser geometry and solid density among those experiments. The measurements of Glicksman and Noymer (1996) and Wu et al. (1991) confirm that the cluster velocity is relatively insensitive to the solid flux and superficial gas velocity. The high temperature tests of Golriz and Leckner (1992) further suggest that the gas density and viscosity also fail to influence the trend. Rhodes et al. (1992) exploit the high temporal and spatial resolution of a high-speed video camera to distinguish two families of clusters. The first consists of occasional, relatively
Table 1. Descending cluster velocities at the wall Authors Glicksman and Noymer (1996) Bader et al. (1988) Golriz and Leckner (1992) Horio et al. (1988) Nowak et al. (1991) Hartge et al. (1988) Wu et al. (1991) Wu et al. (1991) Wirth et al. (1991) Rhodes et al. (1992) wall strands bulk downflow
Measurement technique
º #(m/s)
º 0 (m/s)
z/H
G (kg/m2 s)
¹ (°C)
D (cm)
o 4 (kg/m3)
d (km)
Thermal imaging Pitot tube
1.1$0.1 1.0$0.2
2.3—3.6 3.7
0.21 0.75
8—28 98
20 20
16* 31
6980 1714
69 76
Thermocouples Optical fibers Optical fibers Optical fibers Heat transfer probe Video Video
1.8$0.4 0.8$0.1 0.8$0.2 1.2$0.2 1.6$0.5 1.3$0.5 1.3$0.2
3.6—6.7 1.2 4.0 2.9 7.0 7.0 1.2—1.9
0.81 0.58 0.28 0.56 0.43 0.43 0.73
&10 11.7 55.7 49 15—47 15—47 —
850 20 20 20 20 20 20
170* 5 21 40 15 15 17*
2600 1000 2300 1500 2650 2650 3950
260 60 46 85 171 171 50
High-speed video
0.3 to 0.4 &1
3—5
0.53
2—80
20
31
2456
75
* Square cross-section. 2475
2476
Shorter Communications
Fig. 1. Suggested scaling of descending cluster velocity at the wall with particle diameter and gravitational acceleration. The symbols are data from the investigators shown; the line is º +36Jgd). #slow strands in close proximity or contact with the wall. The second is a more prominent bulk downflow slightly farther from the wall; it exhibits a faster velocity in agreement with the trends summarized in the table. Because the other authors do not distinguish between the two families, their measurements are likely dominated by the uninterrupted, faster bulk downflow. Remarkably, the downward velocity of neither class appears to be affected by the superficial gas velocity or overall solid flux. The velocity difference between the two classes may reflect the downward shearing of the particle phase at the wall. For completeness, the table provides cluster velocities measured by Rhodes et al. for both classes. Because the cluster velocity is seemingly unaffected by overall flow conditions, it is likely that it is set by a local force balance at the wall. Its apparent insensitivity to the properties and velocity of the gas further suggests that interactions in the particle phase dominate the balance. In this case, the only parameters relevant to the velocity scaling would include the material density and mean diameter of the particles, the gravitational acceleration and, if the particles are engaged in collisional interactions, the parameters characterizing the impacts. Because in this formulation the particle material density is the only parameter involving mass, it cannot appear in the velocity scaling. In addition, because collisional parameters often belong to a relatively narrow range of values (Massah et al., 1995; Lorenz, et al., 1997), we expect that cluster velocities from a wide range of experiments would indeed scale as Jgd. Acknowledgments The authors gratefully acknowledge M. Golriz, B. Leckner, K. Wirth and O. Molerus, who provided further details of operational conditions for their experiments, and L. Glicksman and P. Noymer for helpful discussions. This work was funded by the University Coal Research Program of the US Department of Energy, Pittsburgh Energy Technology Center under grants DE-FG22-93PC93216 and DE-FG2295PC95228, and by the International Fine Particle Research Institute. This material is also based upon work supported by National Science Foundation Graduate Research Fellowship Number GER-9253848. A. ELIZABETH GRIFFITH MICHEL Y. LOUGE* Sibley School of Mechanical and Aerospace Engineering Cornell University Ithaca, NY 14853 U.S.A
* Corresponding author.
NOTATION
d D g G ¹ º 0 º #o s z/H
mean particle diameter, km riser diameter, m gravitational acceleration, m/s2 cross-sectional solids flux, kg/m2 s mean suspension temperature, °C superficial gas velocity, m/s average particle cluster velocity at the wall, m/s material density of the particles, kg/m3 elevation of velocity measurement relative to riser height REFERENCES
Bader, R., Findlay, J. and Knowlton, T. M. (1988) Gas/solid flow patterns in a 30.5-cm-diameter circulating fluidized bed. In Circulating Fluidized Bed ¹echnology II, eds P. Basu and J. F. Large, pp. 123—137. Pergamon Press, Oxford, U.K. Glicksman, L. R. (1988) Circulating fluidized bed heat transfer. In Circulating Fluidized Bed ¹echnology II, eds P. Basu and J. F. Large, pp. 13—29. Pergamon Press, New York, U.S.A. Glicksman, L. R. (1997) Heat transfer in circulating fluidized beds. In Circulating Fluidized Beds, eds J. R. Grace, A. A. Avidan and T. M. Knowlton, pp. 261—311. Blackie Academic and Professional, London, U.K. Glicksman, L. R. and Noymer, P. D. (1996) Measurements of the velocity and acceleration of clusters at the wall of a circulating fluidized bed. In Preprints: Fluidization and Fluid—Particle Systems, eds H. Arastoopour, Y.-M. Chen and T. Guttilla, pp. 45—52. AIChE, New York, U.S.A. Golriz, M. and Leckner, B. (1992) Experimental studies of heat transfer in a circulating fluidized bed boiler. In Proceedings International Conference on Engineering Applications of Mechanics, Vol. 3. Sharif University of Technology, Teheran, Iran, pp. 167—174. Hartge, E.-U., Rensner, D. and Werther, J. (1988) Solids concentration and velocity patterns in circulating fluidized beds. In Circulating Fluidized Bed ¹echnology II, eds P. Basu and J. F. Large, pp. 165—180. Pergamon Press, Oxford, U.K. Horio, M., Morishita, K., Tachibana, O. and Murata, N. (1988) Solid distribution and movement in circulating fluidized beds. In Circulating Fluidized Bed ¹echnology II, eds P. Basu and J. F. Large, pp. 147—154. Pergamon Press, Oxford, U.K. Lints, M. and Glicksman, L. R. (1993) Parameters governing particle-to-wall heat transfer in a circulating fluidized bed. In Circulating Fluidized Bed ¹echnology I», eds by A. A. Avidan, Proceedings of the 4th International Conference on Circulating Fluidized Beds, AIChE, New York, U.S.A., pp. 297—304.
Shorter Communications Lorenz, A., Tuozzolo, C. and Louge, M. Y. (1997) Measurements of impact properties of small, nearly spherical particles. Exp. Mech. 37, 3, 292—298. Massah, H., Shaffer, F., Sinclair, J. and Shahnam, M. (1995) Measurements of specular and diffuse particle-wall collision properties. In Fluidization »III, eds C. Lague´rie and J.-F. Large, Proceedings of the 8th International Conference on Fluidization. The Engineering Foundation, New York, U.S.A., pp. 641—648. Nowak, W., Mineo, H., Yamazaki, R. and Yoshida, K. (1991) Behavior of particles in a circulating fluidized bed of a mixture of two different sized particles. In Circulating Fluidized Bed ¹echnology III, eds P. Basu, M. Horio,
2477
and M. Hasatani, pp. 219—224. Pergamon Press, Oxford, U.K. Rhodes, M., Mineo, H. and Hirama, T. (1992) Particle motion at the wall of a circulating fluidized bed. Powder ¹echnol. 70, 207—214. Wirth, K.-E., Seiter, M. and Molerus, O. (1991) Concentration and velocities of solids in areas close to the walls in circulating fluidized bed systems. »GB Kraftwerkstechnik 10, 824—828. Wu, R. L., Lim, C. J., Grace J. R. and Brereton C. M. H., (1991) Instantaneous local heat transfer and hydrodynamics in a circulating fluidized bed. Int. J. Heat Mass ¹ransfer 34, 2019—2027.