164
Ind. Eng. Chem. Fundam. 1984, 23, 164-170
C = concentration, kg/m3 d = characteristic dimension of the packing pieces, m
Gunn, D. J. Chem. Eng. Scl. 1980, 35,2405. Hochman, J. M.; Effron, E. Znd. Eng. Chem. Fundam. 1969, 8 , 63. Hoogendoorn, D. J.; Lips, J. Can. J . Chem. Eng. 1965,43, 125. Kramers, H.; Alberda, G. Chem. Eng. Sci. 1953, 2, 173. Kunugita, E.; Otake, T.; Yoshii, K. Kagaku Kogaku 1962,26, 672. Michell, R. W. PhD. Thesis. University of Sydney, Australia 1970. Michell, R. W.; Furzer, I. A. Chem, Eng. J. 1972a. 4, 53. Michell, R. W.; Furzer, I . A. Trans. Znst. Chem. Eng. l972b, 50,334. Otake, T.; Kunugita, E. Kagaku Kogaku 1958, 22, 144. Ostergaard, K.: Michelsen, M. L. Can. J . Chem. Eng. 1979,47, 107. Pavilca, R. T.; Olson. J. H. Znd. Eng. Chem. 1970, 62(12), 45. Polk, E. M.; Clements, W. C. Vanderbilt University Technical Report No. 10, 1966. Sater, V. E.: Levenspiei. 0.Znd. Eng. Chem. Fundam. 1966, 5,86. Schwartz, J. G. Dudukovic, M. P. AZChE J . 1978,22, 953. Stephens, G. K. Ph.D. Thesis University of Birmingham, England, 1968. Szonyi, L.: Furzer, I. A. AZChE J . 1983 (in press). Thompson, M., Furzer, I. A. AZChE J . 1983 (in press). Van Swaaij.; Charpender. J. C.; Villermaux, J. Chem. Eng. Sci. 1969,2 4 , 1083.
D = dispersion coefficient, m2/s Fr = Froude number Ga = Gallileo number H O P = liquid operating holdup, m3/m3of column space L = liquid flow rate, kg/m2 s M = mass tracer added, kg Pe = Peclet number Re = Reynolds number based on the interstitial liquid velocity ReL = Reynolds number based on the superficial liquid velocity ii = interstitial liquid velocity, m/s p = liquid density, kg/m3 ~r= liquid viscosity, kg/ms Literature Cited Dunn, W. E.: Vermeulen, T.; Wilke, C. A,; Word, T. T. University of California Radiation Laboratory Report 10394, 1962. Farid, M. M.; Gunn, D. J. Chem. Eng. Sci. 1979,34, 579. Furzer, I. A.; Micheil, R. W. AZChE J . 1970, 16, 380.
Received f o r review September 13, 1982 Revised manuscript received September 27, 1983 Accepted November 16, 1983
Effect of Electrostatic Field Direction on the Collection of Charged Aerosol by an Isolated Sphere Michael Shaplro and Gabrlel Laufer Faculty of Mechanical Engineering, Technlon -Israel
Institute of Technology, Haifa 32000, Israel
The collection of charged aerosol particles by an isolated collector sphere, under the influence of electric field, is investigated numerically. The limiting trajectories of inertial aerosol particles are calculated both when the electric field is aligned with the flow direction and when the field is transverse to the flow. The collection efficiencies associated with these field orientations are evaluated for a wide range of Stokes numbers and electric field intensities for the Stokes and potential flow approximations. Imposing either a field parallel to the flow direction or one perpendicular to the flow increases the collection efficiency. The relative merit of the two field orientations depends on the field strength and on the particle inertia.
Introduction Atmospheric submicron particles are usually considered as a health hazard. The emission of these particles by modern industrial plants is a major source for their presence in the atmosphere. Therefore, filtration devices capable of removing these particles must be designed. Although there is no scarcity of such devices, only a few can operate in the hostile environments of high temperature or corrosive gases normally present in industry. Among these are granular bed filters (Gutfinger et al., 1980). Granular bed filters offer high filtration efficiency at both extremes of the particle size spectrum (Tardos et al., 1978). For large particles (> 1 wm), inertia is the major deposition mechanism while a t the other extreme ( 1,and then using the Stokes flow approximation which is valid for Re, 0.2), the efficiency of the transverse configuration exceeds that of collinear configuration.
Nomenclature
+ 2c0) = collector polarization coefficient, dimensionless C = Cunningham's correction factor, dimensionless E = E,/Eo = dimensionless electrostatic field next to a collector E, = electrostatic field next to a collector, V/m Eo = external electrostatic field, V/m E,, E,,, E, = dimensionless electrostatic field around a collector in 2, y , z directions E,, Ecs = electrostatic field around a collector in r and 0 directions, V/m Te = external force experienced by the aerosol particle, N G = CqEo/6.rr~r,Uo = electric force parameter, dimensionless m = mass of an aerosol particle, kg q = aerosol particle electrostatic charge, Cb r = radial coordinate, m r, = aerosol particle radius, m r, = collector radius, m R = r / r , = dimensionless radial coordinate R, = r p / r c= interception parameter, dimensionless Re, = 2 r c U o p / = ~ collector Reynolds number, dimensionlass Re, = 2rpUOp/p= dust particle Reynolds number, dimensionless a, = ( E , - cO)/(cc
170
Ind. Eng. Chem. Fundam. 1 9 M 3 23, 170-174
2 s = capture area, m2 2s' = capture area projected on a plane perpendicular to
particle path, m2 S t = 2CppUorp2/9/*r,= Stokes number, dimensionless t = time, s T = t Uo/r, = dimensionless time g = gas velocity, m/s U = ii/Uo = dimensionless gas velocity gx,UJ.!U, = dimensionless gas velocity in x , y , z directions
Uo = filter face velocity, m/s = particle velocity, m/s V = ij/ Uo = dimensionless particle velocity V,, V,, V, = dimensionless particle velocity in x , y , z directions x , y , z = Cartesian coordinates, m X,Y , Z = x / r 0 y / r 0 z / r c = dimensionless coordinates X o , Yo,Zo = x o / r c ,y o / r c ,z o / r , = initial dimensionless coordinates & = coordinate of limiting trajectory, m Yo= jjo/rc= dimensionless coordinate of limiting trajectory Greek Letters to
= free space dielectric constant, f/m
tC
= collector dielectric constant, f/m = viscosity of the gas, kg/m s
/* p
= gas density, kg/m3
particle density, kg/m3 collection efficiency, dimensionless 9' = collection efficiency defined by Nielsen (1978) 4 = potential of electric field, V pp = 7 =
B = angular coordinate L i t e r a t u r e Cited Davies, C. N. "Air Filtration"; Academic Press: London, 1973. Fichman, M.; Pnueli, D. "Proceedings, 16 Israel Conference on Mechanical Engineering", Haifa, Technion, July 13-14, 1982. Gutfinger, C.; Degani, D.; Pnueli, D. "Proceedings, International Conference on Gas Cleaning at High Temperature and High Pressure", Julich. West Germany, May 6-7, 1980. Havlicek V. Int. J . Air Pollut. 1961, 4 , 225. Jackson, J. D. "Classical Electrodynamics"; Wiley: New York, 1975. Kallio, G. A.; Dietz, P. W.; Gutfinger, C. Proceedings, I 1 Symposium on the Transfer and Utllization of Particulate Control Technology, Denver, 1979. Lamb, G. E. R.; Costanza, P. A.: O'Meara, D. J. Text. Res. J. 1978 48, 566. Lamb, H. "Hydrodynamics"; 6th ed.; Dover Publications: New York, 1945. Melcher, J. R.; Sachar, K. S.;Warren, E. P. Proc. I€€€ 1977, 6 5 , 1659. Michael, D. H.; Norey, P. W. J . FiuidMech. 1969, 3 7 , 565. Mukherjee, S.; Nielsen, K. A,; Hill, J. C. J . Powder Bulk Solids Tech, 1978, 2 , 29. Nielsen, K. A. J . Colloid Interface Sci. 1978, 6 4 , 131, Nlelsen, K. A.; Hill, J. C. Ind. Eng. Chem. Fundam. 1976a, 15, 149. Nielsen, K. A.; Hill, J. C. Ind. Eng. Chem. Fundam. I976b, 15, 157. Nielsen, K. A.; Hill, J. C. Chem. Eng. Commun. 1981, 12, 171. Plumlee, H. R.; Semonin, R. G. Tellus 1965, XVII(3), 356. Semonin, R. G.; Plumlee, H. R. J . Geophys. Res. 1966, 71, 4271. Shapiro, M.; Laufer, G.; Gutfinger, C. Atmos. Environ. 1983, 17, 447. Tardos, G. I.;Abuaf, M.; Gutfinger, C. J . Air Poliut. Control Assoc. 1978, 2 8 , 354. Whipple. F. J. W.; Chalmer, J. A. Quart. J . Roy. Met. SOC.1944, 7 0 , 103. Zahedi, K.; Melcher, J. R. J . Air Pollut. Control Assoc. 1976, 2 6 , 345. Zebel, G. J. Colloid Interface Sci. 1968. 2 7 , 294.
Received for review October 18, 1982 Revised manuscript received October 31, 1983 Accepted December 6, 1983
Transient Axial Solid and Gas Temperature Profiles in the Grid Zone of a Gas-Solid Fluidized Bed J. C. Song,+N. Yutani,$ and L. T. Fan' Department of Chemical Engineering, Kansas State Universlty, Manhattan, Kansas 66506
The transient axial particle and gas temperature profiles in different regions near the distributor of a gas-solid fluidized bed at gas velocities near minimum fluidization were measured by means of highly sensitive thermocouple probes. Qualitative or semiquantitative accounts are presented of the thermal behavior of these regions where rapid heat transfer has been known to occur between the particles and fluidizing medium.
Introduction
In a gassolid fluidized bed with a perforated distributor, the gas enters the bed as high-speed jets which penetrate a certain distance before breaking up into bubbles; the portion of the bed within this distance is the so-called grid zone (Behie et al., 1975; Merry, 1975; Wen et al., 1978; Yang and Keairns, 1979, 1981; Hirsan, 1980). The solids concentrations in the jets and bubbles immediately above these jets within the grid zone are relatively low. For convenience, let us call the region of the grid zone dominated by these jets and bubbles the dilute phase. A relatively stagnant or dead region tends to form between adjacent vertical jets; the particles in this region tend to be immobile. Above the dead region there is a region of On leave from Chenguang Research Institute of Chemical Industry, Fushun County, Sichuan Province, China. 1On leave from the Department of Chemical Engineering, Tokyo University of Agriculture and Technology, Koganei, Tokyo, Japan 184.
sluggish particle motion, which we may call the quasi-dead region above which the so-called intermittently mixed region exists. For convenience, these three regions of high solid density in the grid zone, including the dead, quasidead, and intermittently mixed regions, may be termed the dense phase. The regions in the grid zone are sketched in Figure 1 (Wen et al., 1978; Rowe et al., 1978; Massimilla and Migliaccio, 1981). I t has been known (see, e.g., Behie et al., 1975; Grace and De Lasa, 1978; Wen et al., 1978) that the performance of a fluidized bed as a chemical reactor or heat transfer device is often governed by the hydrodynamic and thermal behavior of the bed near the distributor or in the so-called grid zone. Only a handful of investigators have published qualitative or semiquantitative accounts of the thermal behavior of the grid zone where rapid heat transfer has been known to occur between the particles and fluidizing medium (Ghaderi and Clift, 1980). The previous workers (Kettenring et al., 1950; Walton et ai., 1952; Frantz, 1961; Behie et al., 1975) have shown
0196-4313/84/1023-0170$01.50/00 1984 American Chemical Society
