Linear stability of a compressible channel flow with compliant walls

Modal stability analysis is carried out for a compressible channel flow past compliant walls. The base flow is a steady fully developed flow driven in a plane channel by a constant body acceleration. The normal displacement of the compliant walls are modeled by the spring-backed plate model. From numerical solution of the stability equations, three classes of instabilities are identified—the Tollmien–Schlichting mode, the Flow-induced Surface Instability (FSI), and the compressible higher modes. These instabilities are studied with respect to the variations in the flow compressibility, quantified by the Mach number, and variations in wall compliance, quantified by the ratio of the free oscillation timescale of the surface to the flow timescale. It is observed that increasing flow compressibility and wall compliance both have a stabilizing effect on the Tollmien–Schlichting mode. Increasing the flow compressibility has a stabilizing effect on the FSI modes and increasing the wall compliance has a stabilizing effect on the compressible higher modes. Wall dissipation has been observed to have a destabilizing effect on the Tollmien–Schlichting and compressible modes and a stabilizing effect for the FSI modes.