Suppression of acoustic instabilities in boundary layer flows by heating / cooling of the wall and wall impedance

We address the problem of acoustic instabilities in compressible boundary layers with the aim of suppressing the instabilities and delaying the transition by means of cooled walls of impedance type.

Previous investigations, for example by Mack, 1993, showed that cooling a rigid wall can stabilize the first mode in a Mach 3 boundary layer. Combining wall cooling with impedance, we investigate to what extend the entire spectrum of all acoustic modes can be stabilized. Assuming an exponential boundary layer with a simplified temperature profile, the exact solution of the underlying linearized equations allows us to analyze all modes regarding the effects of wall coolingand impedance. The analytical results are combined with those of a numerical eigenvalue solver.

Thereby, we obtain the full spectrum of eigenvalues and eigenfunctions and identify optimal parameters for stabilization. However, due to the non-normality of the equations, transient growth can occur which we additionally investigate. We thus provide a comprehensive insight into the possibility of suppressing boundary layer instabilities.