Non-Newtonian single-phase flow through a two-dimensional porous medium

In this work, finite-element simulations are used to study statistically stationary single-phase non-Newtonian incompressible isothermal fluid flow through a non-deformable stationary porous medium. The fluids under observation are of shear-thinning and shear-thickening types. The porous medium considered consists of a square periodic array of rods with porosity ranging from 0.35 to 0.99. As a reference for comparison, a set of Newtonian flow cases is simulated under similar porous media and Reynolds number conditions. The results reveal that like the Newtonian case, non-Newtonian fluid transport is governed by a drag law associated with the Reynolds number (based on the apparent viscosity, rod diameter and superficial viscosity), and a dimensionless resistance parameter. In this study, it is observed that this resistance parameter is not only a function of the porous medium geometry and flow forces but rheology of the fluid. Additionally, the newly-observed phenomenological attributes of the resistance parameter indicate three main flow regimes with the most complex evolutions apparent in the shear-thickening fluid flow. An important conclusion of this work is a dimensionless parameter in terms of this resistance parameter with a scaling utility for a wide range of scientific evaluations.