Fluid flow in a fluidized bed

The fluid flow in a fluidized bed is related to a flow in a porous medium. The solid lattice constituted by the particles slows down the flow and produces a head loss. For the fluidized bed, the situation is more complex than for a settled bed. As the velocity of the fluid is increased, the thickness Hf of the bed grows and its porosity e increases. These two quantities are not geometrical data characterizing the bed they vary according to the fluid flow. The more the bed expands via the fluidization process, the greater its permeability becomes. Because of the increase in fluid velocity and the increase in the permeability k of the bed resulting from fluidization, the critical Reynolds nitmber Re = = 10 (which sets the 

JVcstokes is the expression of the Stokes fall velocity for small particles, and JVcNewton that of thc Newton fall velocity for large particles (see Table 15.1). Relation [15.39] shows that the porosity of the bed (and therefore its thickness) increases with velocity. The porosity and thickness of the bed also increase when the diameter of the particles diminishes. Relation [15.39] can be used to evaluate the minimum fluidization velocity U f theoretically. This only requires solving the second-degree equation constituted by [15.39], by taking the porosity equal to the porosity eq of the settled bed (derived from the mass balance [15.37] if the mass Mp of the bed and the thickness Hfo of the settled bed are known). 

T able 15.2. Correlations characterizing the fluidflow in a fluidized bed U is the mean streamwise velocity, D the diameter of the particles, U t the terminal entrainment velocity (equal to the fall velocity of the particle — see Table 15.1), and 0 the diameter of the column. Ret = UtD I v. 

Engineers often use the Lewis-Bowerman and Richardson-Zaki correlations to characterize fluidized beds by determining porosity as a function of the flow velocity. These correlations, empirical in nature, are recapitulated in Table 15.2. While the diameter of the column is taken into account by the Richardson-Zaki correlation, its effect remains very weak as long as the size of the particles is small compared to the diameter of the colunrn. Comparing the Lewis-Bowerman and Richardson-Zaki correlations with Ergun s relation, expressed in the form [15.39], 

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Zhu HP, Hou QF, Zhou ZY, Yu AB Averaging method of particulate systems and its application to particle-fluid flow in a fluidized bed. Chin Sci Bull 54 4309—4317, 2009. 

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