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Description
Unstable acoustic modes in high Mach number boundary layer flows contribute to the laminar-turbulent transition and play an important role in boundary layer noise emission. Therefore, we investigate the influence of porous wall linings on the acoustic modes in high-velocity boundary layers. These porous walls, which are characterized by their porosity and porous layer thickness, are commonly used for flow stabilization. However, Fedorov et al. (2003) showed an amplification of the first mode instabilities for certain porous wall configurations.
The aim of the current work is to deepen the understanding of the destabilization mechanism and to get a complete picture of which wall configurations lead to different types of instabilities. For the inviscid problem, we find unstable modes depending on the porous layer thickness, which do not persist in the case of rigid walls. It should be noted that the amplification induced by thin porous layers is significantly different from that observed in the literature for thick layers.
For an exponential mean flow profile with a shape factor $H\approx 1.3$, the compressible Rayleigh equation, i.e. the linearized Euler equations for compressible shear flows, is solved exactly in terms of Heun functions. With the impedance wall boundary condition, the stability problem is reduced to an algebraic eigenvalue equation, which allows us to compute the complete inviscid eigenvalue spectrum without spurious modes.
Based on the knowledge that modes supersonic with respect to the far field can radiate into the far field (Tam \& Burton, 1984), we classify the newly appearing instabilities with respect to their sound radiating character. Furthermore, for subsonic boundary layers, we identify those wall parameter ranges that lead to the onset of inviscid instabilities.
