J. J., A. Z. Ch. E . Journal 6, 460 (1960). P. L., Appl. Sci. Research A6, 96 (1956). P. L., Acrivos, A., J . Appl. Phys. 27, 11 (1956). apman, D. R., Rubesin, M. W., J . Aeron. Sci. 16, 547 (1949). (9) Chung, P. M., Anderson, A. D.: A R S Journal 30, 3 (1960). (10 Cohen, C. B., et al., GMTR 268, Contract AF 18(600)1190, duided Missile Research Division, Ram0 Wooldrige Corp., Los Angela, Calif. (11) Friedlander, S. K., A. I. Ch. E. Journal 3,43 (1957). (12) Garner, F. H., Keey, R. B., Chem. Eng. Sci. 9 , 119 (1958). (13) Gordon, K. F., “ A Cell Model for Mass and Heat Transfer in a Fixed Bed.” Deuartment of Chemical and Metalluraical Engineering, Univer’sity of Michigan, Ann Arbor, MTch., A. I. Ch. E. Washington meeting, 1960. (14) Griffith, R. M., Chem. Eng. Scz. Sci. 12, 198 (1960). (15) Happel, J., A. I. Ch. E . Journal 2, 197 (1958). (15) (16) Hokischer, Zbtd., 4, 300 (1958). Hoelscher, H. E., Zbid., (17) HouFen. 0. A.. Watson. K. M.. “Chemical Process Kinetics.” ’ Part IIf, Chap. 18, Wiley,’New York, 1959. (18) Zbid., Chap. 20. (19) Hsu, H., Bird, R. B., A . Z. Ch. E. Journal 6, 516 (1960). (20) Jensen, V. G., Proc. Roy. Sac. (London) A249, 346 (1959). (21) Lighthill, M. J., Zbid., A202, 359 (1950). (22) Linton, M., Sutherland, K. L., Chem. Eng. Sci. 12, 214 (1960). (23) Meksyn, D., J . Aeron. Space Sci.25, 631-4, 664 (1958). (24) Merk, H. J., Appl. Sci. Research AS, 237 (1959). (25) Zbid., p. 261. ,
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(26 Mickley, H. S., et al., Natl. Advisory Comm. Aeronaut., k c h . Note 3208 (1954). (27) Milne-Thomson. L. M., “Theoretical Hydrodynamics,” ’ ‘ 4th ed., p. 499, Macmillan, New York, 1960. (28) Mixon, F. O., Carberry, J. J., Chem. Eng. Sci. 13, 30 (1960). (29) Morduchow, M., Natl. Advisory Comm. Aeronaut., Rept. 1245 (1955). (30) Morris, D. N., Smith, J. W., J . Aeron. 9i.20, 805 (1953). (31) Potter, O., Trans. Znst. Chem. Engrs. 36, 415 (1958). (32) Ruckenstein, E., Chem. Eng. Sci. 10, 22 (1959). (33) Rosner, D. E., Aero Chem. Lab., Princeton. N. J., Tech. Pub. 14, (1958). (34) Zbid., 16, (1960). (35) Rosner, D. E., Aero Chem. Lab., Princeton, N. J., TM-12
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36) Rosner, D. E., A R S Journal 30, 114 (1960). 37) Rosner, D. E., Jet Propulsion 28, 445 (1951). (38) Schlichting, H., “Boundary Layer Theory,” Pergamon Press, New York, 1955. (39) Sherwood, T. K., Pigford, R. L., “Absorption and Extraction,” McGraw-Hill, New York, 1952. (40) Taneda, S., J . Phys. SOC.Japan 2, 10 (1956). (41) Tomotika, S., London, Aero Research Committee Rept. 8r Memo. 1678 (July !‘935). (42) Treybal, R. E., Mass Transfer Operations,” Chap. 2, McGraw Hill, New York, 1955. RECEIVED for review November 17, 1961 ACCEPTEDJune 4, 1962
PROPELLER PUMPING AND SOLIDS FLUIDIZATION IN STIRRED TANKS JOSEPH V. PORCELLI, JR.,’
AND G E O R G E R . M A R R , JR.*
Columbia University, New York, N . Y.
Data characterizing propeller pumping, fluid entrainment, and solids fluidization in stirred tanks are presented. It is shown that propeller pumping is given b y the product ND13, independent of Reynolds number and tank geometry in the turbulent range of operation, but that entrainment flow is a function of tank geometry. Particle nuidization is correlated in terms of the settling velocity for a single particle and the total circulation rate of the tank fluid.
N THE CHEMICAL PROCESS INDUSTRIES
the most frequently used
I method for the achievement of solid-liquid contacting is the stirred tank. Despite the widespread use of agitated vessels through the years, little is known concerning the effects of many important variables on the resultant behavior of stirred tank systems. The type of impeller, the geometry of the tank-impeller system, the presence of auxiliary equipment such as baffles or stator rings, and the properties of the liquid and solid phases all influence the behavior of such systems. There are two requirements for satisfactory operation in most solid-liquid contacting systems: adequate suspension of the solid particles and adequate turbulence in the liquid phase. Adequate suspension infers suspension to that degree which ensures uniform process conditions leading to predictable results. Adequate turbulence is that degree of turbulence
Present address, Scientific Design Co., Inc., New York, N. Y.
* Present address, Electronic Associates, Inc., Princeton, N. J. 172
l&EC FUNDAMENTALS
which minimizes mass transfer resistances and maintains the various mass transport processes at acceptable levels. Past research in the field of solids suspension has taken two directions. In many studies, the suspension process was isolated from the mass transfer processes by the utilization of inert (nondissolcing, nonreacting) solids, such as silica sand, in various liquids. Other experimenters have directed their efforts towards the mass transfer aspects, the suspension phenomena being described qualitatively as a secondary study. Neither of the above approaches assumes the barest knowledge of the flow characteristics of stirred tanks. The suspension characteristics of any given stirred tank design are empirically determined, aided at best by the results of dimensional analysis on the system. I t was felt that an approach to the solids suspension problem which includes the understanding of the fluid mechanical characteristics of the stirred tank system and the “laws of settling” could yield simple and general relationships among the physical properties of solid-liquid systems, the impeller-tank geometry, and the solid suspension
characteristics of any stirred tank. The present research was undertaken to evaluate such a n approach, and the first phase (5) was devoted to studies of the fluid mechanical characteristics of propeller-driven baffled tanks in the absence of a solid phase. Equipment
The agitator used throughout the present work was the experimental agitator, hlodel ELB (Chemineer, Inc., Dayton, Ohio). The basic kit of the ELB includes a large number of components designed I O give high flexibility in research. The major components utilized in the present study are listed below. Motor, 0.25 hp., 3450 r.p.m., 1-60-115/230, a.c., totally enclosed. Variable speed transmission, 0 to 1100 r.p.m., micrometer controlled. Shaft, 0.5-inch diameter. TvDe 303 stainless steel. Propellers, 2 . 5 , 3-, 4-,.
