The role of porosity in the transition to inertial regime in porous media flows

TL;DR

This paper explores how porosity influences the transition from Darcy to inertial flow regimes in porous media, focusing on vortex formation and tortuosity measures through numerical simulations.

Contribution

It introduces a detailed analysis of tortuosity definitions and their relation to vortex dynamics during flow regime transition, emphasizing porosity's role.

Findings

Tortuosity based on volume integrals behaves similarly in simple and complex systems.

Streamline-based tortuosity diverges at inertia onset in simple cubic systems.

Discrepancies in tortuosity relate to vortex growth dynamics governed by porosity.

Abstract

In this work, we investigate the fundamental physical mechanism of the transition from Darcy to inertial (Darcy-Forchheimer) regime in steady-state flows through porous media, with the focus on vortex formation. We investigate their influence on the tortuosity--Reynolds number relation during this transition for systems of various porosities. We do so by numerically solving the Navier-Stokes equations within the pore-scale of simple cubic systems and relating the observations made therein to stochastic systems of more complex geometry. We observe that the tortuosity defined by integrals over the whole fluid volume behaves similarly in both types of systems. At the same time, in simple cubic systems, the tortuosity based on averaging of the length of the streamlines diverges from the volume-integrated one when the inertia onset takes place. We show that the discrepancy between those two tortuosities at increasing Reynolds number carries information about the dynamics of the vortex growth in the system. We stipulate that those dynamics are directly governed by the porosity. Our results highlight the utility of various definitions of tortuosity as measures of inertia in porous media flows and explain the reasons for the differences between those definitions. This can lead to a more sensible choice of inertia indicators in more application-oriented problems.