Hydrodynamics of Newtonian fluid flow through assemblages of rigid spherical particles in intermediate Reynolds number regime

Abstract

The complete Navier-Stokes equations describing the flow of incompressible Newtonian fluids relative to beds of particles have been solved numerically using the finite element technique in terms of the primitive variables, i.e. u-p-v. The interparticle interactions are incorporated into the analysis using the well known free surface cell model due to Happel. Information on the detailed structure of the flow field in terms of the variation of the angular velocity, surface pressure and shear stress distributions, streamline plots as well as the values of the integrated quantities such as drag coefficient (total, pressure and friction) have been obtained under wide ranges of kinematic and physical conditions as follows: 0.001 ≤ Re ≤ 100; 0.3 ≤ ε ≤ 0.9. The numerical results presented herein have been validated using the appropriate theoretical and experimental results available in the literature. The range of applicability of the free surface cell model has been identified, and its performance has been contrasted with that of its rival model, namely, the zero vorticity cell model. Typical streamline patterns are presented to elucidate qualitatively the salient features of the flow field.