Power-law fluid flow across an array of infinite circular cylinders: a numerical study

Abstract

The steady flow of power-law liquids normal to arrays of long circular cylinders has been studied theoretically. The governing equations (continuity and momentum) have been solved numerically using the finite difference method. The hydrodynamic interactions between cylinders have been accounted for by employing the so-called zero vorticity cell model which assumes each cylinder in the array to be surrounded by a hypothetical concentric envelope of fluid. Extensive results on the detailed kinematics of the flow in terms of the variation of the surface vorticity and the power-law viscosity on the cylinder surface, streamline and iso-vorticity plots as well as on gross fluid dynamic parameters in terms of the friction and pressure drag coefficients under wide ranges of conditions (0.01 ≤ Re ≤ 10; 1 ≥ n ≥ 0.5 and 0.95 ≥ ε ≥ 0.4) have been presented and discussed herein. The paper is concluded by performing comparisons between the present predictions and the scant analytical and experimental results available in the literature.