Direct numerical simulation of the pressure drop through structured porous media

Abstract

This paper presents direct numerical simulations for the flow through regular porous media composed of equal size staggered square cylinders obtained with a compact finite differences immersed boundary method. Different moderate Reynolds numbers are simulated in order to capture the dependence of the pressure drop with the Reynolds number in the Forchheimer regime. The pressure drop predictions agree well with the Hazen-Dupuit-Darcy model; however, when compared to a widely used semi-empirical correlation, the modified Ergun equation, the agreement is poor. A better agreement is found if the particle diameter is taken to be equal to the cylinder diameter. From the intrinsic-averaged pressure calculated along the flow direction, it can be seen that, for the porous media studied, the bulk pressure drop dominates and the entrance and exit effects are negligible.