Drag Coefficient for Arrays of Cylinders in Flows of Power-Law Fluids

Numerical simulations are presented of flows of power-law fluids through periodic arrays of aligned cylinders, both creeping flows and flows with finite inertia. Results are presented for the drag coefficient of the cylinders and are compared against asymptotically valid analytical results. Square and hexagonal arrays are considered, both for flow in the plane perpendicular to the alignment vector of the cylinders (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) for creeping flows can be described at all solid area fractions by scaling the drag on a cylinder with appropriate velocity and length scales. For flows with finite inertia a similar scaling is found