Quantifying and Modeling the Force Variation Within Random Arrays of Spheres

In this study, we perform fully-resolved direct numerical simulations (DNS) of a flow past random arrays of spheres using immersed boundary methods (IBM). These simulations are used to quantify the error arising from point-particle (PP) force models which assumes equal drag and zero lateral forces on all particles. The results show that the rms drag and lateral force fluctuation can be as high as 26% and 15% of the mean drag value, respectively. For each sphere, the hydrodynamic forces are shown to be dependent on the exact location of few neighboring spheres. A pairwise interaction extended point-particle (PIEP) model is then presented. The model can approximate the drag and lateral forces on each sphere by systematically accounting for the location of few of its neighbors. The perturbation from each neighbor is considered separately then linearly superposed to obtain the total variation of the drag and lateral force. Significant error reduction is observed when using PIEP model instead of mean drag models upon comparing to exact forces acquired from the DNS IBM simulations.