Spout velocity

As in the case of fluidization, there is a gas velocity below which spouting does not occur. The earliest and best known relationship to predict the minimum spouting velocity u s is that due to Mathur and Gishler (1955)... 

The design of the jet spouted bed requires the rigorous definition of the gas flow pattern in order for the residence time distribution to be considered. In previous papers, the regime of jet spouted bed and its hydrodynamics correlations have been defined [2-8]. The minimum jet spouting velocity is calculated by the following correlation [7]. 

The minimum spouting velocity is determined, as a function of the geometrical parameters of the particle-reactor system [8] ... 

Reynolds number at the minimum spouting velocity time and average cycle time (s) gas velocity and gas velocity at the minimum spouting (ms-1)... 

Spouting cannot be maintained once the bed height exceeds a certain level, coim monly known as maximum spoutable bed depth, Hm. At Hm, the spout starts to collapse and the bed starts to change from a spouted bed to a fluidized bed. As indicated in Eq. (9.67), the minimum spouting velocity increases with an increase in the bed height. Consequently, (7msp achieves its maximum at Hm. The maximum value of the minimum spouting velocity can be related to the minimum fluidization velocity by... 

Minimum Spouting Velocity and Pressure Drop in Spouted Beds. Can. J. Chem. Eng.,... 

Serious deviations from Eq. (3) were reported by Smith and Reddy (S2), who worked with solid materials having a wide spread of particle size (up to sixfold) and used the weight-mean diameter [dp = Xi(dp) i]. When recalculated in terms of the reciprocal mean diameter (S3), these data show much better agreement with the equation (see Table IB). Hence, Eq. (3) appears to predict the spouting velocity for materials having a wide range of particle size if the reciprocal mean diameter is used. 

Thus, the minimum spouting velocity for a given material, column size, inlet size, and bed depth can be obtained by combining Eqs. (7)-(10). Calculation by this method is valid for H/D greater than 1, Rem of 10-100, and Di/Dc less than 0.1. 

Minimum Spouting Velocity Correlations for Conical Vessels (Spouting Fluid-Air)... 

In summaxy, then, the simplest and most reliable method for estimating the minimum spouting velocity for common materials over a wide range of practical conditions is by use of Eq. (3), provided that in the case of mixed-size particles the reciprocal mean diameter is employed. The equation has been validated for column diameters up to 2 ft, not only for wheat but also for a coarse grade of ammonium nitrate (12), but industrial data for larger units have unfortunately not been released. 

It should be noted further that Eq. (37) does not enable one to predict theoretically the gas-distribution profile for a given bed since the value of U H must be independently known. The figures in Table IV show that and the ratio it bears to C/, (superficial spouting velocity, corresponding to total flow through the column) are dependent on bed geometry. Hence... 

Note The spouting velocities used in the above experiments are roughly 10% above UmB except for the last two results of Thorley et al. (M and 30% above). 

The maximum spoutable bed depth was found to decrease with increasing particle size by Malek and Lu (M3), who experimented with four different sizes of wheat (1.2-3.7 mm) in a 6-in. column. On the other hand, Reddy et al. (Rl), who worked with mixed-size materials (alimdum, glass spheres, and polystyrene), also in a 6-in. column, reported that Hm first increases with particle size and then decreases, a peak value being attained at a mean particle size of 1.0-1.5 mm. The observed variation of Hm, correlated by Reddy et al. with mean particle size, is likely to be also influenced by size distribution, which cannot be fully characterized by any particular mean diameter. Nevertheless, the existence of a peak Hm with respect to particle size alone is theoretically predictable from a comparison of the effect of particle size on the gas velocities required for spouting and for fluidizing a given material (Rl). From Eq. (3), the effect of particle size and bed depth on spouting velocity, with all other variables held constant, is as follows ... 

For spouting velocity, they used Eq. (3). The values of Hm obtained by substituting Um, calculated from Eq. (80) for Um. in Eq. (3) agreed well with experimental results for several closely sized materials. 

Manurung has pointed out a basic similarity between the equations of Thorley et al. and of Becker, quoted above. Equation (80), used by the former workers for calculating spouting velocity at m (Um Ums), can be rearranged to the form... 

With a constant value of voidage substituted in the above equation, it becomes similar to Becker s empirical relation, Eq. (8). A similarity also exists in the second equation used for relating Um to Hm [i.e., between Eqs. (3) and (10)]. In the limiting case oi H = Hm, Eq. (3) for spouting velocity (used by Thorley et al.) becomes... 

Yet another method for calculating H , based on the same approach is given by Reddy et al. Their experimental data were mainly for beds of mixed-size particles. For this reason, these workers chose the Smith and Reddy equation for spouting velocity, Eq. (13), using it in conjunction with the minimum fluidization velocity equation of Wen and Yu (Wl),... 

Investigator Type of correlation Phases involved Mathur and Gishler [21] Minimum spouting velocity prediction Gas-solid... 

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