Linear Stability Analysis of Compressible Channel Flow with Porous Walls

We have investigated the effects of permeable walls, modeled by linear acoustic impedance with zero reactance, on compressible channel flow via linear stability analysis (LSA). Base flow profiles are taken from impermeable isothermal-wall laminar and turbulent channel flow simulations at bulk Reynolds number, $Re_b$= 6900 and Mach numbers, $M_b$ = 0.2, 0.5, 0.85. For a sufficiently high value of permeability, two dominant modes are excited: a bulk pressure mode, causing symmetric expulsion and suction of mass from the porous walls (Mode 0); a standing-wave-like mode, with a pressure node at the centerline (Mode 1). In the case of turbulent mean flow profiles, both modes generate additional Reynolds shear stresses augmenting the (base) turbulent ones, but concentrated in the viscous sublayer region; the trajectories of the two modes in the complex phase velocity space follow each other very closely for values of wall permeability spanning two orders of magnitude, suggesting their coexistence. The transition from subcritical to supercritical permeability does not alter significantly the structure of the two modes for the range of wavenumbers investigated, suggesting that wall permeability simply accentuates pre-existing otherwise stable modes. Results from the present investigation will inform the design of new control strategies for compressible turbulent boundary layers based on more general impedance boundary conditions and high-fidelity numerical simulation.