Spouting spout diameter

The spout diameter varies along the bed height. The average spout diameter Ds can be estimated by [McNab, 1972]... 

McNab, G. S. (1972). Prediction of Spouted Diameter. Brit. Chem. Eng. Proc. Technol., 17, 532. 

Mamuro and Hattori (M6) dismissed their annulus data and used only the local air-velocity results obtained in the spout to calculate the air distribution between the spout and the annulus. The calculation, however, requires separate knowledge of spout diameter and of the vertical voidage profile in the spout. While the former could be directly measured, for the latter they had to rely on the values estimated by Mathur and Gishler for a wheat bed 25 in, deep and 6 in. in diameter with the further assumption that the same profile (voidage versus reduced bed level) is valid, not only for wheat beds of different depths, but also for soma sand. This assumption is speculative and weakens the reliability of their calculated air-distribution results as a means for verifying Eq, (37). The earlier experimental results based on pressure-drop measurements (iMlO, Tl), on the other hand, are free from the above objection, and these provide some support for the theoretical derivation of Mamuro and Hattori (Fig. 12), especially for Eq. (36), although less so for its arbitrary extension to Eq. (37). 

From a comparison of the theoretical spout diameters required to satisfy the above equation against experimentally measured values, Lefroy and Davidson conclude that a constant spout diameter is possible for the upper half of the bed, but that in the lower half, the spout must taper downward to less than half its upper diameter, as for example in Fig. 23a and b. 

By combining the force balance Eq. (66) with the spout momentum balance Eqs. (43) and (44) and the particle entrainment Eq. (59), Lefroy and Davidson were able to derive the following expression for spout diameter ... 

The coeflicient they gave is 1.06, but the arithmetic they used corresponds more closely to the shown value of 1.07.) The above equation, though based in part on first principles, is really semiempirical, since certain approximations based on experimental observations had to be made in its derivation, the range of variables covered being dp = 1.7-9.0 mm and Dc = 7.6 and 30.5 cm. Because of oversimplification, spout diameters... 

Semicircular 24 4 60 72 Wheat With wheat, maximum spout diameter attained at z OAH T2... 

However, in these experiments upper spout diameter exceeded >i, as in spout type a. 

Under most three-dimensional conditions, the major adjustment in the spout diameter occurs in the region immediately above the inlet orifice, variation in diameter further up the bed being relatively small. Malek et al. (M4) found that in 4- and 6-in. semicircular columns, spout diameters measured at various levels starting from 1 in. above the orifice were generally within 10% of the mean value. iMean spout diameters observed by these workers for eight different solid materials, using different orifice sizes and air-flow rates, as well as the results reported by Thorley et al. (T2) for 24-in. diameter wheat beds, w ere correlated by the following empirical equation ... 

Semiempirical expressions for Tfm have been developed by Lefroy and Davidson from their theoretical analysis discussed in Section IV,B and V,A. From measurements of spout diameter made in beds of kale seeds, polyethylene, and peas at maximum spoutable depths, they determined the value of the left-hand side of their force-balance equation q. (66) ] and found it to be about 0.36 in all cases. Therefore... 

Db Diameter of upper surface of bed Do Column diameter Di Fluid inlet diameter D, Spout diameter dp Particle diameter, or characteristic dimension of particle (dp)t Particle diameter of size fraction Xi... 

The spout diameter for a wide range of maferials, column diameter, orifice diamefer, and bed depfh, can be estimated by... 

Figure 21 CDimensionless spout diameters as a function of dimensionless height for small columns. Case A, test case Case B, all dimensionless parameters matched, bed diameter halved Case C, particle Reynolds number mismatched Case D, Froude number mismatched Case E, density ratio, Reynolds number mismatched Case F, bed Reynolds number mismatched Case G, internal friction angle, loose packed voidage mismatched. (From He et al. 1995.)...

The average spout diameter has been correlated empirically by McNab (1972) with the equation... 

Equation (9) is a dimensional equation where SI imits should be used. Equation (9) is good to 5.6% at room temperature. He et al. (1998a) employed a fiber-optic probe to measure the spout diameter in a semicylindrical and a full cylindrical spouted bed and found that the presence of the flat front plate in the semicylindrical bed considerably distorted the spout shape. They found that the McNab equation underestimated the spout diameter in a full cylindrical bed by an average of 35.5%. Under pressure, the McNab equation can also introduce error up to 65.5% at a pressure of 343 kPa (He et al., 1998b). Spout diameter tends to increase with increasing pressure. 

He YL, Lim CJ, Qin SZ, Grace JR. Spout diameters in full and half spouted beds. Can J Chem Eng 76 702-706, 1998a. 

McNab GS. Prediction of spout diameter. Brit Chem Eng Proc Tech 17 532, 1972. 

On the basis of experimental studies, Mathur and Gishler derived an empirical correlation to describe the minimum fluid flow necessaiy for spouting, in 3- to 12-in-diameter columns ... 

Increasing bed diameter increases spoutable depth. By employing a bed-orifice diameter ratio of 12 for air spouting, a 9-in-diameter bed was spouted at a depth of 65 in while a 12-in-diameter bed was spouted at 95 in. 

As indicated by Eq. (12-62) the superficial fluid velocity required for spouting increases with bed depth and orifice diameter and decreases as the bed diameter is increased. 

Employing wood chips, Cowan s drying studies indicated that the volumetric heat-transfer coefficient obtainable in a spouted bed is at least twice that in a direct-heat rotaiy diyer. By using 20- to 30-mesh Ottawa sand, fluidized and spouted beds were compared. The volumetric coefficients in the fluid bed were 4 times those obtained in a spouted bed. Mathur dried wheat continuously in a 12-in-diameter spouted bed, followed by a 9-in-diameter spouted-bed cooler. A diy-ing rate of roughly 100 Ib/h of water was obtained by using 450 K inlet air. Six hundred pounds per hour of wheat was reduced from 16 to 26 percent to 4 percent moisture. Evaporation occurred also in the cooler by using sensible heat present in the wheat. The maximum diy-ing-bed temperature was 118°F, and the overall thermal efficiency of the system was roughly 65 percent. Some aspec ts of the spouted-bed technique are covered by patent (U.S. Patent 2,786,280). 

Down spouts (or up spouts) are best set flush with the plate from which they lead, with no weir as in gas-hquid contact. The velocity of the continuous phase in the down spout V, which sets the down-spout cross section, should be set at a value lower than the terminal velocity of some arbitrarily small droplet of dispersed phase, say, 0.08 or 0.16 cm i M or Mfi in) in diameter otherwise, recirculation of entrained dispersed phase around a plate will result in flooding. The down spouts should extend beyond the accumulated layer of dispersed phase on the plate. 

Stirring rods. These are made from glass rod 3-5 mm in diameter, cut into suitable lengths. Both ends should be rounded by heating in the Bunsen or blowpipe flame. The length of the stirring rod should be suitable for the size and the shape of the vessel for which it is employed, e.g. for use with a beaker provided with a spout, it should project 3-5 cm beyond the lip when in a resting position. 

A conical funnel is full of liquid. The diameter of the top (mouth) is Dj, that of the bottom (spout) is D2 (where D2 <time required for the fluid to drain by gravity to a level of H0/2, assuming frictionless flow. 

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