A revised mono-dimensional particle bed model for fluidized beds

Abstract

The formulation of the equations of change proposed by Foscolo and Gibilaro in their original mono-dimensional particle bed model (PBM) for the prediction of the fluid-bed stability of Geldart's group A powders has been revisited along with the relevant closure relationships. The buoyancy has been expressed in accordance with its “ classical” definition, which regards it as being equal to the weight of the fluidizing fluid displaced by the particle phase. A new constitutive equation has been developed for the drag force; this proves more accurate than the expression used in the original PMB particularly in the intermediate flow regimes comprised between the viscous and inertial ones. The “ elastic” force has been estimated by employing a rigorous approach which needs not resort to equilibrium-based relations. The result, enhanced in accuracy and breadth of validity, considers “ elastic” force and drag force proportional. The equations of change themselves have been partly revised. The pressure gradient is no longer shared by the two phases in proportion to their volume fractions, but has been accounted for only in the continuous one. Conversely, the “ elastic” force has been included, with opposite signs, in the linear momentum equations pertaining to both phases, so that the principle of action and reaction, to which the force is subjected, is fulfilled. The revised model has been validated by performing a fluid-bed stability analysis on a wide range of Geldart's group A powders at different operating temperatures. Predicted values for the minimum bubbling voidage estimated by means of the revised model have been compared with experimental values and with predictions from both the original Foscolo and Gibilaro model and that previously revised by Jean and Fan. The latter has been found to be always in good agreement with the model proposed here, whereas the former has seemed to somewhat underestimate the bed minimum bubbling voidage thus anticipating the transition between homogeneous and bubbling fluidization. All of the models have proved to yield predictions whose validity is strongly dependent on the particular powder in hand and on the operating conditions considered.