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A two-dimensional analysis of the resolvent spectrum of a Mach 1.6 transitional boundary layer impacted by an oblique shock wave is carried out. The investigation is based on a two-dimensional mean flow obtained by a RANS model that includes a transition criterion. The goal is to evaluate whether such a low cost RANS based resolvent approach is capable of describing the frequencies and physics involved in this transitional boundary layer/shock-wave interaction. Data from an experiment and a companion large eddy simulation (LES) are utilized as reference for the validation of the method. The flow is characterized by a laminar boundary layer upstream, a laminar separation bubble (LSB) in the interaction region and a turbulent boundary layer downstream. The flow exhibits low amplitude unsteadiness in the LSB and at the reflected shock wave with three particular oscillation frequencies, qualified as low, medium and high in reference to their range in Strouhal number, here based on free stream velocity and LSB length ($S_{t}=0.03{-}0.11$, 0.3–0.4 and 2–3 respectively). Through the resolvent analysis this dynamics is found to correspond to an amplifier behaviour of the flow. The resolvent responses match the averaged Fourier mode of the time dependent flow field, here described by the LES, with a close agreement in frequency and spatial distribution, thereby validating the resolvent approach. The low frequency dynamics relates to a pseudo-resonance process that sequentially implies the amplification in the separated shear layer of the LSB, an excitation of the shock foot and a backward travelling density wave. As this wave hits back the separation point the amplification in the shear layer starts again and loops. The medium and high frequency modes relate to the periodic expansion/reduction of the bubble and to the turbulent fluctuations at the reattachment point of the bubble, respectively.

This paper presents an overview of the work performed recently at ONERA on the control of the buffet phenomenon. This aerodynamic instability induces strong wall pressure fluctuations and as such limits aircraft envelope; consequently, it is interesting to try to delay its onset, in order to enlarge aircraft flight envelop, but also to provide more flexibility during the design phase. Several types of flow control have been investigated, either passive (mechanical vortex generators) or active (fluidic VGs, fluidic trailing-edge device (TED)). It is shown than mechanical and fluidic VGs are able to delay buffet onset in the angle-of-attack domain by suppressing the separation downstream of the shock. The effect of the fluidic TED is different, the separation is not suppressed, but the rear wing loading is increased and consequently the buffet onset is not delayed to higher angles of attack, but only to higher lift coefficient. Then, a closed loop control methodology based on a quasi-static approach is defined and several architectures are tested for various parameters such as the input signal, the objective function or, the tuning of the feedback gain. All closed loop methods are implemented on a dSPACE device calculating in real time the fluidic actuators command from the unsteady pressure sensors data.