Characterization of a porous medium employing numerical tools: Permeability and pressure-drop from Darcy to turbulence

A large set of microscopic flow simulations in the Representative Elementary Volume (REV) of a porous medium formed by staggered square cylinders is presented. For each Reynolds number selected, 10 different porosities are simulated in the 5-95% range. The Reynolds number is varied from Re = 10 ^-3 to Re = 10⁵, covering the Stokes flow regime, the laminar flow regime and the turbulence flow regime. Low and moderate Reynolds number flow solutions (Re ≤ 200) are achieved by numerically solving the 2D Navier-Stokes equations. Reynolds Averaged Navier-Stokes equations are employed to simulate the turbulence regime. Numerical results allow the investigation of the microscopic features of the flow as a function of the porosity and Reynolds number. Based on these microscopic results, the permeability of the porous medium is computed and a porosity-dependent correlation is developed for this macroscopic parameter. The Darcy-Forchheimer term or, equivalently, the friction factor, is also computed to characterize the porous medium for the complete range of porosity and Reynolds number simulated. The Forchheimer coefficient is found to be weakly dependent on the Reynolds number and strongly dependent on the porosity if the flow is fully turbulent. A porosity-dependent correlation is proposed for this quantity for high Reynolds numbers.