Compressible boundary layers over isotropic porous surfaces

TL;DR

This paper investigates compressible laminar boundary layers over isotropic porous surfaces using asymptotic and numerical methods, revealing effects of porosity, grain size, and Mach number on flow and temperature profiles.

Contribution

It extends a self-similar solution to include compressibility, heat conduction, and nonlinear drag for porous substrates, providing new insights into boundary layer behavior.

Findings

Velocity profile shows an inflection point at the interface.

High porosity and Mach number reduce adiabatic recovery temperature.

Temperature at the substrate bottom has negligible effect on shear stresses.

Abstract

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. The momentum and enthalpy balance equations are derived by volume averaging. The self-similar solution proposed by Tsiberkin (2018) [Transp. Porous Media 121(1):109-120] for streamwise-growing permeability is extended to include compressibility, heat conduction and a nonlinear drag. The velocity profile shows an inflection point at the free fluid-porous interfacial layer, below which it decreases to zero. A marked reduction of the adiabatic recovery temperature of the fluid and the velocity gradient at the interface is observed for high porosity, large grains and relatively high Mach numbers. The temperature imposed at the bottom of the porous substrate has a negligible influence on the shear stresses.