Microscale flow bifurcation and its macroscale implications in periodic porous media

Finite volume/Euler-Newton continuation is made to study the microscale flow bifurcation and its macroscale implications in modeled 2D spatially-periodic porous media. The microscale flow bifurcation can occur if the inlet flow direction is isotropic with respect to two orthogonal principle axes. As the inlet flow rate increases, two asymmetric solution branches bifurcate from the primary symmetric (with respect to the inlet flow direction) branch through a symmetric-breaking bifurcation point. The location of this bifurcation point changes as the porosity of media. Such microscale flow bifurcation is preserved at macroscale. However, it has no effect on the Euler number-Reynolds number relation, further confirming the finding by Wang (2000) [1] that the Reynolds number is not a proper scalar characterizing the effect of microscale convective inertia.