Inertial Effects on Fluid Flow through Disordered Media

TL;DR

This study uses numerical simulations to explore how inertial effects cause deviations from Darcy's law in fluid flow through disordered porous media, highlighting a transition to non-linear behavior at high Reynolds numbers.

Contribution

It introduces a statistical characterization of the transition from linear to non-linear flow regimes based on kinetic energy distribution.

Findings

Transition from linear to non-linear flow at high Reynolds numbers

Inertia effects cause deviations from Darcy law

Kinetic energy distribution correlates with flow behavior

Abstract

We investigate the origin of the deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional disordered porous media. We apply the Forchheimer equation as a phenomenological model to correlate the variations of the friction factor for different porosities and flow conditions. At sufficiently high Reynolds numbers, when inertia becomes relevant, we observe a transition from linear to non-linear behavior which is typical of experiments. We find that such a transition can be understood and statistically characterized in terms of the spatial distribution of kinetic energy in the system.