Darcy-Forchheimer law for porous media flows in the highly-nonlinear regime for passive flow control

The original Darcy-Forchheimer (DF) law was tuned for low to moderate Reynolds number porous media flows, where the non-linear effects are not dominant. With the emergence of new high-porosity materials for passive flow control where the interstitial Reynolds number can reach relatively high values, understanding and possibly re-tuning the DF law is necessary for capturing the associated nonlinear effects in these flows. We have examined two-dimensional flows within highly-porous media, differing in inclusions shape and arrangement, over a wide range of interstitial Reynolds numbers and flow angles. It is found that, irrespective of the inclusion shapes and arrangement, the original DF law remains accurate for low Reynolds number flows. However, its accuracy is significantly contingent upon the appearance of effects such as flow separation and vortex shedding within the porous media in the nonlinear regime. New resistance laws are proposed and tested in configurations designed for passive control of boundary layer separation.