Inertial-Flow Anisotropy in Oblique Flow through Porous Media

Abstract

The extension of the Darcean momentum equation to the inertial-flow is considered using the results of direct numerical simulation of flow through two-dimensional ordered porous media. Using oblique flows, the inertial-flow regime is examined for Reynolds numbers (based on the unit-cell length) up to 300. The results show that the inertial-flow regime is marked at the very beginning by a low-Reynolds number subregime (0 ≤ R _e ≤ 10), where the deviation from the Darcean-flow pressure drop is quadratic in R _e (cubic in the Darcean velocity). After a relatively extended intermediate-Reynolds number subregime (10 ≤ R _e ≤ 50), a high-Reynolds subregime is observed (for R _e > 50) which seems to be linear in R _e (quadratic in the velocity). It is shown that for ordered arrangements the Darcean-isotropic structures become inertially anisotropic, i.e., the pressure gradient and the Darcean velocity vectors are not parallel in the inertial-flow regime, even though they are in the Darcean regime. The Darcean-anisotropic structures remain anisotropic in the inertial-flow regime. For strongly inertial flows, we study the transition to unsteady periodic solutions. The values of the critical Reynolds number depend on the angle θ that the incoming flow makes with the x-axis. The critical reynolds number increases with the angle of the flow. The R _e dependence of the angle a that the drag force makes with the x-axis don’t confirm the new results of [5] The authors claim that for high Reynolds numbers, for low angle oblique flows (< 12°), the angle α reaches a maximum and the drag force becomes horizontal, and that for high angle oblique flows (> 12°, < 45°), the drag force makes a 45° angle with the x-axis. Concerning the Darcean-anisotropic structures, we present results which contradict their conclusions.