Voidage at minimum fluidisation

The fluid velocity at which the particles become suspended is the minimum fluidisation velocity, um. For spherical particles, the velocity at minimum fluidisation can be predicted by combining Equations (25) and (30), given that the values of the bed voidage at minimum fluidisation, smf, are known a priori ... 

This formulation assumes values of the voidage at minimum fluidisation of around 0.38. 

The results show that the values calculated using the Ergun equation are very sensitive to the value used for the voidage at minimum fluidisation. The value obtained from the Wen-Yu equation corresponds to that obtained from the Ergun Equation (25) with a voidage of approximately 0.38, as reported in Section 7.3.2. 

Obtain a relationship for the ratio of the terminal falling velocity of a particle to the minimum fluidising velocity for a bed of similar particles. It may be assumed that Stokes Law and the Carman-Kozeny equation are applicable. What is the value of the ratio if the bed voidage at the minimum fluidising velocity is 0.4 ... 

Wen and Yu(6) have examined the relationship between voidage at the minimum fluidising velocity, emf, and particle shape, (ps, which is defined as the ratio of the diameter of the sphere of the same specific as the particle d, as used in the Ergun equation to the diameter of the sphere with the same volume as the particle dp. 

The minimum fluidising velocity, umf, may be expressed in terms of the free-falling velocity o of the particles in the fluid. The Ergun equation (equation 6.11) relates the Galileo number Ga to the Reynolds number Re mj in terms of the voidage < , / at the incipient fluidisation point. 

An alternative method of calculating the value of Re mf (and hence //,/) is to substitute for Re 0 from equation 6.21 into equation 6.35, and to put the voidage e equal to its value emf at the minimum fluidising velocity. 

Thus, the bubbling region, which is an important feature of beds operating at gas velocities in excess of the minimum fluidising velocity, is usually characterised by two phases — a continuous emulsion phase with a voidage approximately equal to that of a bed at its minimum fluidising velocity, and a discontinous or bubble phase that accounts for most of the excess flow of gas. This is sometimes referred to as the two-phase theory of fluidisation. 

A bed consists of uniform glass spheres of size 3.57mm diameter (density = 2500 kg/m ). What will be the minimum fluidising velocity in a polymer solution of density, 1000kg/m, with power-law constants n = 0.6 and m = 0.25 Pa-s" Assume the bed voidage to be 0.4 at the point of incipient fluidisation. 

Now assume that the dense (and wake) phase voidage remains constant at its minimum fluidisation value. If the voidage does not change then the permeability is unlikely to change and the interstitial gas velocity must be maintained at U if the bed is to remain fluidised without a net force lifting particles out of... 

For cracker catalyst (d = 55 (im, density = 950 kg/m3) fluidised by air, values of umb/umf of up to 2.8 have been found by Davies and Richardson(45). During the course of this work it was found that there is a minimum size of bubble which is stable. Small bubbles injected into a non-bubbling bed tend to become assimilated in the dense phase, whilst, on the other hand, larger bubbles tend to grow at the expense of the gas flow in the dense phase. If a bubble larger than the critical size is injected into an expanded bed, the bed will initially expand by an amount equal to the volume of the injected bubble. When, however, the bubble breaks the surface, the bed will fall back below the level existing before injection and will therefore have acquired a reduced voidage. 

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