Wake Prediction in 3D Porous–Fluid Flows: A Numerical Study Using a Brinkman Penalization LBM Approach

The simulation of the wake past porous obstacles is numerically challenging because since it requires both an accurate model of the porous medium and a good grid resolution in the fluid domain. In this study a single-domain Brinkman penalization technique in a LBM framework is employed to investigate wake prediction in 3D porous–fluid flows. First we assess the ability of the Brinkman model to predict porous flow features with different permeability values (Darcy numbers). In particular the flow over a porous bed is studied to characterize the ability of this approach to predict the thickness of the porous boundary layer (called Brinkman boundary layer) and the slip velocity at the porous/fluid interface. The porous boundary layer is well described with this model and a finer grid resolution at the wall is needed for low permeability values (low Darcy numbers). Then the impact of these quantities on the wake prediction of a 3D porous sphere is studied for various Darcy and Reynolds numbers. It is shown that wake transitions are well recovered and some further studies are made in terms of grid resolution. Some preliminary results are presented for higher Reynolds numbers.