High velocity flow through fractured and porous media: the role of flow non-periodicity

In the present paper we examine the evolution of the macroscopic flow law in a crenellated channel, representing an element of fractured or porous medium and in function of the Reynolds number Re. A numerical analysis based on the Navier–Stokes equations is applied. We focus on the influence of the flow periodicity or non-periodicity upon the macroscopic law. The physical explanation of the non-linear deviation from Darcy's law is still an issue, as the Ergun–Forchheimer law admitted for high Reynolds numbers comes up against some theoretical problems. In the periodic case, three non-linear flow regimes were revealed: a cubic flow with respect to velocity at low Re, an intermediate non-quadratic law, and a self-similar mode independent of Re at very high Re. The Forchheimer law is not confirmed. The case of a non-periodic flow clearly highlights the link between the flow non-periodicity and the quadratic law. The quadratic deviation becomes all the more important as the non-periodicity degree is high.