Power law fluid flow through beds of spheres at intermediate Reynolds numbers: Pressure drop in fixed and distended beds

Abstract

Extensive numerical predictions of friction, pressure and total drag coefficients for the steady incompressible flow of power law liquids through assemblages of spherical particles are presented in this paper. The governing equations (continuity and momentum) have been solved numerically for the unknown pressure and velocity components which, in turn, have been used to infer the values of the derived variables like vorticity, stream function, pressure and frictional components of the overall drag coefficient. The inter-particle hydrodynamic interactions have been mimicked by the two commonly used concentric spherein-sphere cell models. The numerical results presented herein span the following ranges of kinematic and physical conditions: power law index, 0.5, 0.6, 0.8, 1, 1.2, 1.4, 1.6, 1.8, thereby including both shear-thinning and shear-thickening flow behaviour; the particle Reynolds number, 1-500; and bed voidages of 0.4, 0.5 and 0.6, thereby covering packed and distended bed conditions. The accuracy of the numerical solution procedure has been validated by carrying out extensive comparisons with the previously available analytical and scant numerical results, mainly limited to the creeping flow conditions. The utility of such a simple approach is demonstrated by presenting detailed comparisons with the experimental results available in the literature.