Direct numerical simulation of inertial flows in porous media

At modest flow rates (10 ≤ Re ≤ 300) through porous media and packed beds, fluid inertia can result in complex steady and unsteady recirculation regions, dependent on the local pore geometry. Body fitted CFD is a broadly used design and analysis tool for flows in porous media and packed bed type reactors. Unfortunately, the inherent complexities of porous media make unstructured mesh generation a difficult and time consuming step in the simulation process. To accurately capture the inertial dynamics using high-fidelity direct simulations, body fitted meshes must be high quality and sufficiently refined. We present methods to parameterize and simplify mesh generation for packed beds, with an eye toward obtaining efficient mesh independence for Reynolds numbers in the inertial and unsteady regimes. The crux of mesh generation for packed beds is dealing with sphere-sphere or sphere-wall contact points, where a geometric singularity exists. To handle the sphere-sphere and sphere-wall contact points, we use a fillet bridge model, in which every pair of contacting entities are bridged by a fillet, eliminating a small fluid region near the contact point. This results in a continuous surface mesh which does not require resizing of the spheres and can accommodate prism cells for improved boundary layer resolution. A second order accurate, parallel, incompressible flow solver [Moin and Apte, AIAA J. 2006] is used to simulate flow through three different sphere packings: a periodic simple cubic packing, a wall bounded hexagonal close packing, and a randomly packed tube. Mesh independence is assessed using several measures including Ergun pressure drop coefficients, viscous and pressure components of drag force, kinetic energy, kinetic energy dissipation and interstitial velocity profiles. The results of these test cases are used to determine the feasibility of accurate and very large scale simulations of flow through a randomly packed bed of 10³ pores. Preliminary results of these simulations will be presented.