Receptivity of compressible boundary layers over porous surfaces

TL;DR

This study investigates how porous surfaces affect the growth and attenuation of disturbances in supersonic boundary layers, revealing that porosity can suppress certain instabilities and influence wave evolution.

Contribution

It provides a combined numerical and asymptotic analysis of compressible boundary layer receptivity over porous surfaces, highlighting the effects of porosity and curvature on disturbance growth.

Findings

Porous surfaces negligibly affect Klebanoff modes with small spanwise wavelengths.

Larger spanwise wavelengths are effectively attenuated by the porous surface.

Porosity increases growth rates of Tollmien-Schlichting waves, confirming experimental observations.

Abstract

Supersonic pre-transitional boundary layers flowing over porous flat and concave surfaces are studied using numerical and asymptotic methods. The porous wall is composed of thin equally-spaced cylindrical microcavities. The flow is perturbed by small-amplitude, free-stream vortical disturbances of the convected gust type. From the proximity of the leading edge, these external agents generate the compressible Klebanoff modes, i.e. low-frequency disturbances of the kinematic and thermal kind that grow algebraically downstream. For Klebanoff modes with a spanwise wavelength comparable with the boundary-layer thickness, the porous surface has a negligible effect on their growth. When the spanwise wavelength is instead larger than the boundary-layer thickness, these disturbances are effectively attenuated by the porous surface. For a specified set of frequency and wavelengths, the Klebanoff modes evolve into oblique Tollmien-Schlichting waves through a leading-edge-adjustment receptivity mechanism. The wavenumber of these waves is only slightly modified over the porous surface, while the growth rate increases, thus confirming previous experimental results. An asymptotic analysis based on the triple-deck theory confirms these numerical findings. When the wall is concave, the amplitude of the Klebanoff modes is enhanced by the wall curvature and is attenuated by the wall porosity during the initial development.