Scaling of permeabilities and friction factors of homogeneously expanding gas-solids fluidized beds: Geldart’s A powders and magnetically stabilized beds

Abstract

The concept of a variable friction factor of fluid-driven de form able powder beds undergoing fluidization is discussed. The special problem discussed addresses the friction factor and bed permeability relationships of Geldart?s A powders and magnetically stabilized beds in axial fields. Governing equations and scaling relation ships are developed through three approaches (1) Minimization of the pressure drop with respect to the fluid velocity employing the Darcy-Forchheimer equation together with the Richardson-Zaki scaling law, (2) Minimization of the pres sure drop across an equivalent-channel replacing the actual packed beds by a straight pipe with bed-equivalent obstacle of a simple geometry, and (3) Entropy minimization method applied in cases of the Darcy-Forchheimer equation and the equivalent-channel model. Bed-to-surface heat transfer coefficients are commented in the context of the porosity/length scale relationships developed. Both the pressure drop curves developments and phase diagram de signs are illustrated by applications of the intersection of asymptotes technique to beds exhibiting certain degree of cohesion.