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.
Highlights
Laminar-turbulent transition in the hypersonic boundary layer leads to a significant increase in heat transfer and skin friction
The wall admittance program is coupled in the stability analysis program. Both in the linear stability and nonlinear stability calculations, the admittance coefficients for waves of different frequencies are different. This provides us with an advantage that we can study the influence of permeable wall on disturbances of different frequencies under the same wall parameters, and makes it possible to use NPSE to study the nonlinear interactions of disturbances of different frequencies
The current results further indicate that the fundamental resonance on the permeable wall is weakened due to the suppression of the disturbances of the near wall by the permeable surface, which is consistent with the results of nonlinear parabolized stability equations (PSEs)
Summary
Laminar-turbulent transition in the hypersonic boundary layer leads to a significant increase in heat transfer and skin friction. The amount of experimental and nonlinear theoretical results available for the transition over porous surfaces in the hypersonic boundary layer is limited For this reason, new experiments and computations aimed at studying the influence of porous walls on the late stage of the transition have been performed on a flared cone. A flared cone can keep the thickness of the boundary layer constant, and the most unstable mode, the second mode, is limited to a narrow frequency range, resulting in a higher N factor This configuration is very suitable for the study of nonlinear transition processes.[33] The experiment of Lachwicz, Chokani, and Wikinson[34] in the Mach 6 quiet wind tunnel at the NASA Langley Research Center examined the primary mechanism of transition of a flared cone.
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