Volume Filtered Large Eddy Simulation of Flow Over a Permeable Bed of Particles: A priori and A posteriori analysis

A volume filtered formulation (Whitaker 1996) for large eddy simulation of flow over a bed of randomly packed particles with bed-normal porosity variation is investigated. A variable filter width bound by a unit Lipschitz constant that is proportional to the grid size in the freestream, rapidly increases in the interface region, and reaches a constant value proportional to the particle size inside the bed is devised to obtain a better representation of the velocity in the bed while avoiding non-physical oscillations in porosity. The variable filter width together with the assumption of an exponential Brinkman velocity solution in the interface region are used to develop a correction scheme for the drag force closure model based on the Ergun equation with correlations for permeability and Forchheimer tensor. The developed darg force closure is evaluated in a posteriori analysis for a range of Reynolds numbers in the laminar and turbulent flow regime to show very good predictive capability.