(45d) A study of the Dynamics of Homogeneous and Bubbling Fluidized Beds by means of Computational Fluid Dynamics

In the present work, the equations of change and the closure relationships featuring in the original mono-dimensional Particle Bed Model (PBM) proposed by Foscolo & Gibilaro (1984) have been revised. The model, initially intended for analyzing the stability of homogeneous fluidized beds, has been extended to a multi-dimensional formulation so as to render it suitable for the study of the dynamics of both particulate and aggregative regimes of fluidization. In the equations of change, the pressure gradient is no longer shared by the two phases in proportion to their volume fractions, but features only in the continuous phase. Conversely, the ?elastic? force is included, with opposite signs, in both fluid and solid linear momentum equations, so that the principle of action and reaction, to which the force is subjected, is fulfilled. Finally, the contributions of the fluid viscous stress tensor and of the solid stress tensor to the linear momentum conservation equations for the continuous and dispersed phases respectively are accounted for and no longer neglected. As for the closure relationships, the buoyancy is related to the weight of the fluidizing fluid displaced by the particle phase and to the local fluid acceleration, hence no longer being regarded as proportional to the fluid pressure gradient as proposed in the original PBM. Furthermore, a new constitutive equation is advanced for the drag force; this is expressed as the product of the drag force exerted on an unhindered particle, subject to the same volumetric flux of fluid, and a ?corrective? function dependent on both bed voidage and particle Reynolds number. This revised equation is deemed more accurate than the original one proposed by Foscolo & Gibilaro particularly with reference to the intermediate flow regimes comprised between the viscous and the inertial ones. Finally, the ?elastic? force is estimated by employing a rigorous approach which does not resort to equilibrium-based relations; the result, enhanced in accuracy and breadth of validity, considers ?elastic? force and drag force proportional. The Revised Particle Bed Model has been first used to investigate the stability of homogeneous fluidized beds by means of linear analysis; moreover, it has been employed to simulate the fluidization dynamics of a gas-fluidized Geldart's Group B powder. The multi-dimensional model has been solved using the commercial CFD code CFX 4.4.