Receptivity of Compressible Boundary Layers on Flat and Concave Porous Surfaces

  • Fossa, Ludovico (University of Sheffield)
  • Ricco, Pierre (University of Sheffield)

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The effect of wall permeability on the response of pre-transitional compressible boundary layers perturbed by free-stream vortical disturbances is investigated via asymptotic methods and numerically by solving the unsteady boundary-region equations. A porous wall with regularly-spaced cylindrical pores couples the pressure and wall-normal velocity fluctuations at the wall. The growth of the excited low-frequency, streamwise-elongated laminar streaks, known as Klebanoff modes, is reduced when the spanwise diffusion is negligible. The curvature of the wall forces the Klebanoff modes to evolve into streamwise-aligned, spanwise-counterrotating Gortler vortices. As the flow evolves dowmstream, the growth of the Gortler vortices is first slightly damped, then enhanced and eventually reduced. For a range of frequencies and spanwise 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 by a permeable wall, while the growth rate increases, thus confirming previous experimental results. The underlying physical mechanism is explained by a triple-deck analysis, which shows that the onset of Tollmien-Schlichting waves shifts upstream over a permeable wall. The triple-deck results show excellent quantitative agreement with the numerical solution of the boundary-region equations.