Numerical investigation of hydrodynamics in porous media of two-dimensional rod packings: flow regimes from pre-Darcy to post-Darcy

Fluid flow through porous media of two-dimensional rod packings is studied by an approach that combines direct numerical simulation and techniques of Cartesian cut-cell and dynamic grid adaptation. The rod packings are generated from simulations using the discrete element method and have a wide range of porosity. The approach is comprehensively validated and then used to study the effect of porosity on the internal fluid flow and the hydrodynamics. Inertial flow structures are identified and related to local pore geometries. For the first time in direct numerical simulations, it is found the linear Darcy's law has both upper and lower limits of applicable Reynolds number. Based on the simulated data, a new equation spanning different flow regimes is formulated to calculate the friction factor. In terms of a Darcy-permeability-based characteristic length, the pressure drop of rod packings with different porosities can be unified. The directional permeability analysis demonstrates significant flow-orientation dependence in dense or sparse packings due to structural heterogeneity. The analysis of the forces acting on individual rods suggests that local non-uniformity of the packing structures may be related to the occurrence of pre-Darcy regime in rod packings.