Receptivity of inviscid modes in supersonic boundary layers to wall perturbations
نویسندگان
چکیده
Abstract The present paper investigates the receptivity of inviscid first and second modes in a supersonic boundary layer to time-periodic wall disturbances form local blowing/suction, streamwise velocity perturbation temperature perturbation, all introduced via small forcing slot on flat plate. is studied using direct numerical simulations (DNS), finite- high-Reynolds-number approaches, which complement each other. finite-Reynolds-number formulation predicts as accurately DNS, but does not give much insight detailed excitation process, nor can it explain significantly weaker efficiency perturbations relative blowing/suction. In order shed light these issues, an asymptotic analysis was performed limit large Reynolds number. It shows that three forms reduced same mathematical form: Rayleigh equation subject equivalent suction/blowing velocity, be expressed explicitly terms physical perturbations. Estimates magnitude excited eigenmode made priori for case. Furthermore, efficiencies are quantitatively related blowing/suction by simple ratios, $$O(R^{-1/2})$$ O ( R - 1 / 2 ) have expressions, where R number based boundary-layer thickness at centre slot. leading-order theory instability characteristics sufficiently numbers (about $$10^4$$ 10 4 ), appreciable error exists moderate numbers. An improved developed appropriate impedance condition accounts transverse induced viscous motion Stokes adjacent wall. both ( $$R=O(10^3)$$ = 3 ) with satisfactory accuracy. particular, captures well effects, including Reynolds-number dependence strong occurring near so-called synchronisation point.
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ژورنال
عنوان ژورنال: Journal of Engineering Mathematics
سال: 2021
ISSN: ['1573-2703', '0022-0833']
DOI: https://doi.org/10.1007/s10665-021-10124-4