Influence of Permeability and Shear-Thinning Behavior On the Hydrodynamics Flow Features Around Porous Square Cylinders

Abstract

This article investigates the laminar flow of power-law fluids through two identical porous square cylinders in a side-by-side configuration within a channel. The effects of three critical parameters, power-law index (n), Darcy number (Da), and gap ratio (g/W) on the flow behavior are explored for ranges of g/W=0.5-5, n=0.4-0.8, and Da=10-6-10-2, respectively. Two flow conditions are considered: first, for a creeping flow (unseparated flow) at Re=1 where only Darcy's law is applicable; second, for a viscous dominant flow at Re=100, where Darcy-Forchheimer extended model is exercised. The flow patterns behind the porous square cylinders are analyzed using streamlines, velocity profiles, pressure distribution curves, and vorticity structural parameters (Г). In low permeability levels, the flow exhibits an irregular non-periodic vortex shedding characterized by a single large vortex street far-off the downstream for g/W=0.5. However, synchronized wake patterns were observed in either anti-phase or in-phase modes for higher gap ratios. The presence of a jet-like flow in the square cylinders' gap section significantly influences unsteady wake patterns. The impact of g/W, power-law index, and permeability on drag is also examined. The study findings provide valuable insights into flow behavior and offer a potential approach for improving the design of fluidic systems that involve porous cylinders.