Flow stability and regime transitions on periodic open foams

This study aims to link critical Reynolds numbers associated with either steady-state or temporal bifurcations to fluid flow regimes described by macroscopic laws (Darcy, Forchheimer) in a periodic 3D Kelvin foam, using direct numerical simulations. We first identify the permeability and inertial coefficient of the Darcy's law and the Forchheimer's one. We explicit the different flow regimes that are accounted for in the Forchheimer's framework (Darcian, weak inertia and strong inertia regimes, respectively). We present an original systematic way to determine the critical Reynolds number associated with both regime transitions. We calculate them over a wide range of porosities and present two power-law correlations that locate these regime transitions for engineering purposes. We have performed pore-scale resolved calculations for various porosities with the Asymptotic Numerical Method (ANM) to find steady-state bifurcations, if any, along with a Linear Stability Analysis (LSA) to find temporal (Hopf) bifurcations from steady-state base flows. All the computed bifurcations occur at Reynolds numbers in the vicinity of the transition from weak to strong inertia regimes, where a change of behavior takes place. On the other hand, no bifurcation has been found in the transition between Darcian and weak inertia regimes.