Relative performance of body fitted and fictitious domain simulations of flow through fixed packed beds of spheres

Abstract

The relative performance of two numerical approaches involving body conforming and non-conforming grids for simulating porescale flow in complex configurations of fixed packed beds of spheres at moderate pore Reynolds numbers (12⩽Re⩽600) is examined. In the first approach, an unstructured solver is used with tetrahedral meshes which conform to the boundaries of the porespace. In the second approach, a fictitious domain formulation is used which employs non-body conforming Cartesian grids and enforces the no-slip conditions on the pore boundaries implicitly through a rigidity constraint force. Sphere to sphere contact points, where the fluid gap between solid boundaries becomes infinitesimal, are not resolved by either approach, but this is shown to have a negligible effect on the local flow field at the Reynolds numbers considered. Detailed grid convergence studies of both steady and unsteady flow through simple cubic packings indicate that for a fixed level of uncertainty, significantly lower grid densities may be used with the fictitious domain approach which also does not require complex grid generation techniques. This translates into large savings for simulation of flow through realistic packed beds, which is shown by both analytic estimates and actual CPU timings. The applicability of the fictitious domain approach is demonstrated by simulating unsteady flow through a randomly packed bed of 51 spheres at a pore Reynolds number of 600. The results are used to examine the dominance of helical vortices in the porescale flow field.