mgr Jarosław Gołembiewski

Power exponential velocity distributions in disordered porous media

Velocity distribution function (vdf) link the micro- and macro-level theories of fluid flow through porous media. Several reports, by different research groups, about vdf in porous media are already available. The findings, however, appear to be inconsistent with each other. On the one hand, theoretical [1], experimental [1] and numerical [2] results suggest that the vdf can be approximated by a Gaussian. On the other hand exponential [3, 4] or even stretched exponential [5] functions were also reported. To reconcile these contradictions, we propose that the velocity distribution functions follow the power exponential distribution. Using the Lattice Boltzmann Method we verify our hypothesis in a stochastically generated porous media. To this end we study distributions of the fluid absolute velocity and its longitudinal and lateral components relative to the macroscopic flow direction in various configurations, porosities and boundary conditions. We claim that all these velocity distributions follow the power exponential law controlled by an exponent and a shift parameter and find how these parameters depend on the porosity [6].