Homogenized Flux-Body Force Treatment of Compressible Viscous Porous Wall Boundary Conditions

A homogenization approach is proposed for the treatment of porous wall boundary conditions in the computation of compressible viscous flows. Like any other homogenization approach, it eliminates the need for pore-resolved fluid meshes and therefore enables practical flow simulations in computational fluid domains with porous wall boundaries. Unlike alternative approaches however, it does not require prescribing a mass flow rate and does not introduce in the computational model a heuristic discharge coefficient. Instead, it models the inviscid flux through a porous wall surrounded by the flow as a weighted average of the inviscid flux at an impermeable surface and that through pores. It also introduces a body force term in the governing equations to account for friction loss along the pore boundaries. The source term depends on the thickness of the porous wall and the concept of an equivalent single pore. The feasibility of the latter concept is demonstrated using low-speed permeability test data for the fabric of the Mars Science Laboratory parachute canopy. The overall homogenization approach is illustrated with a series of supersonic flow computations through the same fabric and verified using supersonic, pore-resolved numerical simulations.