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S.
H. BRANSOM and S. PENDSE
Department of Chemical Engineering, The University of Birmingham, Edgbaston, Birmingham 15, England
Dynamics of Liquid-Solid Fluidization For design of fluidized beds, a simple and direct method is given for determining void fraction and minimum fluidizing velocity
CORRELATIONS
of the mechanical factors involved in liquid-solid fluidization were undertaken as part of the studies on continuous crystallizers. A reliable method for determining the void fraction as a function of the liquid velocity was required as well as a method for predicting the minimum fluidizing velocity. Since the mechanics of fluid flow have an important influence on heat and mass transfer, it was considered that the mechanical correlation would provide modified Reynolds numbers and friction factors relevant to heat and mass transfer in fluidized systems. The apparatus consisted of a vertical glass pipe, 3 inches by 4 feet which served as the fluidizing chamber. This pipe was separated a t the bottom from a calming section by a wire mesh. The upper end of the pipe enlarged to 8 inches in diameter in order to retain the solids when the liquid velocity approahed the terminal falling velocity of the particles. The liquid was pumped from a thermostatic tank through an orifice meter to the bottom of the calming section. From here the liquid passed through the mesh to the bottom of the fluidized bed. Water at room temperature was used as the liquid in most experiments and a solution of Cellofas B was used to give results at higher viscosities. The solids were glass ballotini and rounded and irregular sands of various sizes. The void fraction of the bed was determined from the measured height of a bed of known mass and absolute volume. The solid particles were treated as spheres throughout and their equivalent diameters were computed by a number of methods for comparison. The results of the fluidization experiments were extrapolated to give VOcorresponding to E = 1.0 where the liquid velocity is the terminal velocity, V,, of the particles. An equivalent diameter can then be calculated through the appropriate settling law, or with the help of Heywood's tables (2) of the drag coefficients of single motionless spheres in a liquid stream. Thus the properties of the system and V , give the value of the modified drag coefficient
which Heywood has tabulated as a function of Re,, as defined below. The appropriate value of Re, therefore yields d directly. The present authors also measured equivalent diameters independently in a photo-extinction sedimentometer ( I ) . In later experiments on the minimum fluidizing velocity, there was some doubt about the relevance to the case of incipient fluidization of diameters measured through values of V$. I t was found that slightly different values of d were obtained, which gave better agreement in these particular cases, by measuring the specific surface, S, of a fixed bed of the particles by means of the pressure drop across it. The fluidization apparatus was adapted for this purpose by inserting a valve in the liquid feed line so that the flow could be arrested suddenly. A second valve to drain, inserted at the bottom of the calming section, enabled the liquid flow to reverse and so collapse the bed to a randomly packed state. The rate of liquid flow through the fixed bed and the corresponding pressure drop gave the value of the specific surface, S, and the equivalent diameter of the particles is given by
In addition to the tables which appear in this condensed version, the unabridged manuscript (see coupon) contains:
A study of systems of solid particles fluidized in liquid stream to provide a general correlation of mechanical factors governed b y the flow A correlation of variables in liquidsolid fluidized systems b y simple extension of the Carman-Kozeny equation for fixed beds Minimum fluidizing velocity Particle diameters b y fixed b e d measurements
for fluidized systems with the same coefficient for isolated, motionless spheres in a liquid stream (2). Regarding all fluidized systems as being in the same corresponding state when V , + V , ( E + I), a "reduced equation of state" containing the reduced velocity V,/V, was deduced. By plotting the data, it was shown that K(V&",/) = +&e,
d = 6/S
Table 1 compares values of d measured by these various methods. I n column 4, diameter has been calculated from correlating equations (Equation 2 ) with measured conditions Vmr and emf for minimum fluidization. The relevant variables were correlated by comparing the friction coefficient
K = R'.Re:/p V,"
where
(1)
Re, = d . E V,/EM
is practically identical with the function IC = $ Re for single m o t ~ o n ~ e sspheres. s The experimental results together with results calculated from other-data (3, 4 ) showed
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AVAILABLE FOR ONE DOLLAR The complete manuscript, including equations and derivations, figures, tables, additional text, and bibliography, by Bransom and Pendse.
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After one year this material can be obtained from the AD1 Auxiliary Pub. lications Project, Library of Congress, Washington 25, D. C., as Document
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The price is $2.25 for microfilm $5.00 for photostat copies.
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No. 6737.
Clip and mail coupon on reverse side VOL. 53, NO. 7
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JULY 1961
575
Comparison of Selected d ( c m . ) Values Measured by Various Methods
Table 1.
PhotoExtinct
Intermediate
He\ n ood's
Law and Vt
Tables (2)
Equation 2
Piess Drop
0.088 0.060 0.043
0.094 0.064 0.053
0.093 0.057 0.050
0.11 0.07
0.11 0.08
0.06Ih
0.069
0.064
0.037 0.24
0.047" 0.097
...
Round sand.
...
...
* Iriegular sand.
that Equation 1 could be simplified for practical applications to K ( V , / V , ) = 7.5Re:.4 (1
> Re,
