Nonlinear interactions in the hypersonic boundary layer on the permeable wall

Abstract

Instability evolution and nonlinear interactions in a hypersonic boundary layer on the permeable wall are investigated over a flared cone. Permeable material is used here as an ultrasonically absorptive coating. Calculations are performed based on both Floquet theory and parabolized stability equations. Relative to the case of the smooth wall, the second mode grows faster in the linear stage and lasts over a longer distance along the flow direction on the permeable wall. Stability calculations based on the acoustic model show that the permeable wall partially promotes the second mode, which is in good agreement with the experimental measurements. For the smooth wall, the fundamental resonance is much stronger than the subharmonic and detuned resonance. The main part of the energy transfers is below the sonic line. However, the suppression of the near-wall disturbances by the permeable wall changes the spatial distribution of perturbations in the fundamental resonance, which disrupts the phase-locked relationship and prevents the growth of fundamental oblique waves.