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Stabilité et perturbations optimales globales d'écoulements compressibles pariétaux

Abstract : Parietal compressible flows have been studied by means of optimal forcing computations in order to characterize the noise amplifier nature of these flows. This approach is able to take into account the non-modal growth of linear perturbations induced by the non-normality of the linearized Navier-Stokes equations. The numerical strategy is based on the computation of the global resolvent matrix and an eigenvalue problem stemming from an optimization problem. Optimal forcing and response energy densities of a supersonic boundary layer have been linked to the experimental neutral curve obtained by Laufer et Vrebalovich, provided that the forcing localization is constrained upstream from the lower branch. Afterwards, a parametric study with respect to the Mach number of the 2D receptivity of the laminar shock wave/boundary layer interaction flow has allowed to analyze the growth of Kelvin-Helmholtz and Tollmien-Schlichting instabilities (TS) occurring at high frequencies. At low frequencies, the receptivity of the system has been linked to the resonance of a stable global mode. Furthermore, the 2D numerical method has been extended to allow the computation of 3D perturbations. This approach has been applied to a supersonic boundary layer flow at M=4.5 in which the 3D non-modal growth of streaks has been identified, as well as the development of oblique TS waves, whose growth is larger than the one associated to 2D waves in compressible regime. This study has also allowed to detect the growth of Mack mode at higher frequencies.
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Benjamin Bugeat. Stabilité et perturbations optimales globales d'écoulements compressibles pariétaux. Mécanique des fluides [physics.class-ph]. Université Pierre et Marie Curie - Paris VI, 2017. Français. ⟨NNT : 2017PA066504⟩. ⟨tel-01814275⟩

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