Numerical simulations of fluid flow though model geometries of porous media - at low to high Reynolds number -

Abstract

Paper presented at the 6th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 30 June - 2 July, 2008.

When modeling fluid flow through porous media it is necessary to know when to switch from a creeping flow formulation to a more elaborate laminar description or to a fully turbulent one. This is of importance in a large number of industrial processes such as flow through embankment dams, composites manufacturing, filtering and in the refinement of iron ore pellets. Regarding the creeping flow regime the Darcy law is sufficient while when inertia-effects become significant it is necessary to use the full Navier-Stokes equations or at least add a non-linear term to Darcy’s law as done in the empirically derived Ergun equation, which has also turned out to be valid for some turbulent flows. It is however not obvious which equation to use at a certain Reynolds number and on what velocities and length scales Reynolds number should be based on. In order to shed some light on this Computational Fluid Dynamics is here applied to simple model geometries of porous media. In particular the flow through quadratic and hexagonal arrays of cylinders is studied. The main quantities of interest are the apparent permeability, the Blake-type friction factor as well as the forces acting on the cylinders. The simulations are carried out for a wide range of Reynolds number ranging from the creeping region to rather high Reynolds number flow, considering flow in porous media. The simulations are based on as well a laminar flow formulation as a turbulent one where the turbulence model chosen is the Shear Stress Transport model, and the CFD-software used is ANSYS CFX with extra care regarding grid resolution and numerical iteration in order to secure that the numerical errors are sufficiently small. One result is that inertia-effects become significant already at Reynolds number of about 10, for the quadratic packing, but around 50 for the hexagonal arrangement and the region where the laminar simulations differ considerably from the turbulent calculations is dependent on the different array arrangements.