An Efficient Immersed Boundary Method Based on Penalized Direct Forcing for Simulating Flows Through Real Porous Media

Abstract

A computationally efficient Immersed Boundary Method (IBM) based on penalized direct forcing was employed to determine the permeability of a real porous medium. The porous medium was composed of about 9000 glass beads with an average particle diameter of 1.93 mm and a porosity of 0.367. The forcing of the IBM depends on the local solid volume fraction within a computational grid cell. The latter could be obtained from a high-resolution X-ray Computed Tomography (CT) scan of the packing. An experimental facility was built to determine the permeability of the packing experimentally. Numerical simulations were performed for the same packing based on the data from the CT scan. For a scan resolution of 0.1 mm the numerical value for the permeability was nearly 70% larger than the experimental value. An error analysis indicated that the scan resolution of 0.1 mm was too coarse for this packing.