Flow field statistics and scaling in random 2D porous media*

Pore-scale simulations and analysis of fluid flow in a two-dimensional channel filled with a random array of cylinders are presented. Numerical calculations are obtained by solution of the Navier-Stokes equations using an unstructured finite-volume solver. The geometry of the random configurations are characterized by means of the Voronoi tessellation using cylinder center points. To investigate features such as large-scale coherence of the flow field, the Eulerian and Lagrangian statistics of the fluid velocity are computed and presented for a range of Reynolds numbers, spanning from the Darcy to the inertial and turbulent regimes. Additionally, the dependences of these statistics on the porosity and pore-length distributions of the random array of cylinders are presented, aiming to further the fundamental understanding of how the local pore structure controls large-scale flow features. These results have relevance in the characterization of properties such as tracer dispersion, pressure drop, and interphase convective heat transfer in porous media.