Flows of inelastic non-Newtonian fluids through arrays of aligned cylinders. Part 1. Creeping flows

Abstract

Numerical simulations are presented for flows of inelastic non-Newtonian fluids through periodic arrays of aligned cylinders, for cases in which fluid inertia can be neglected. The truncated power-law fluid model is used to define the relationship between the viscous stress and the rate-of-strain tensor. The flow is shown to be dominated by shear effects, not extension. Numerical simulation results are presented for the drag coefficient of the cylinders and the velocity variance components, and are compared against asymptotically valid analytical results. Square and hexagonal arrays are considered, both for crossflow in the plane perpendicular to the alignment vector of the cylinders (flows along the axes of the array as well as off-axis flows), and for flow along the cylinders. It is shown that the observed strong dependence of the drag coefficient on the power-law index (through which the stress tensor is related to the rate-of-strain tensor) can be described at all solid area fractions by scaling the drag on a cylinder with appropriate velocity and length scales. The velocity variance components show only a weak dependence on the power-law index. The results for steady-state drag and velocity variances are used in an approximate theory for flows accelerated from rest. The numerical simulation data for unsteady flows agree very well with the approximate theory.