Compressible laminar boundary layers over isotropic porous substrates

A compressible laminar boundary layer developing over an isotropic porous substrate is investigated by asymptotic and numerical methods. The substrate is modeled as an array of cubes of high porosity, the momentum and enthalpy balance equations are derived by volume averaging, and the properties of the substrate are assumed to vary smoothly across a thin interfacial layer. The solid matrix is rigid and in thermal equilibrium with the fluid phase. For the first time, the self-similar solution proposed by Tsiberkin (2017, 2018) for streamwise-growing permeability is extended to include a Forchheimer term, compressibility, and heat conduction effects. The velocity and temperature profiles show an inflection point in the interfacial layer, where the velocity decreases exponentially to zero because of the Darcy-Forchheimer drag. The static temperature recovers a quasi-adiabatic value at the interface regardless of the boundary condition imposed at the bottom of the porous substrate, and a sharp reduction of the velocity gradient is observed. The effect of the grain diameter, volume porosity, and the Mach number are discussed.