Wall-resolved large-eddy simulations are performed to study the interaction between a supersonic turbulent boundary layer and an impinging shock over a wall. The freestream conditions used were Mach 2 and a moderate friction Reynolds number of 𝑅𝑒𝜏 = 950. A passive control method was implemented using perforations in the interaction region of influence of the reference case (flat plate), with the addition of two separated cavities beneath the perforations. The cavities were designed to work as Helmholtz-like resonators at a separation length-based Strouhal number of 𝑆𝑡_𝐿𝑠𝑒𝑝 ≈ 0.03. For the reference case results consistent with the literature were obtained and a time analysis, based on the cross-correlations between dynamic properties allowed to suggest a sequence of events driving the unsteadiness of the interaction. The controlled case, resulted in a larger region of influence of the interaction, with the blowing-suction mechanism inside the cavities allowing a reduction of the separation length. Large oscillations were found close to the wall for thermodynamic properties, but also skin friction and wall-normal velocity. The topology of the recirculation bubble changed to become less symmetric resulting in a stronger reattachment compression fan. Regarding the unsteadiness of the controlled interaction, a tonal behaviour was found (at 𝑆𝑡_𝐿𝑠𝑒𝑝 ≈ 0.3) for the reflected shock motion associated with the resonant frequency found inside the cavities and also for the bubble volume variation. In general, the resonance within the cavities seemed to be able to affect the dynamics of the interaction, despite maintaining its global topology.

An experimental investigation on shock-shock interactions has been conducted with the aim of studying the transition between Regular (RI) and Mach interactions (MI) under the condition of variable inflow Mach number. The RI contains only oblique shocks while the MI has a quasi-normal shock segment, known as the Mach stem. MI configurations generate larger total pressure losses, which is specially relevant for the design of supersonic inlets and rocket nozzles. The study was conducted in the TST-27 transonic-supersonic wind tunnel at Delft University of Technology, which allows a variation of the Mach number during a run through a flexible nozzle system. The wind tunnel model was built using two full span wedges that deflected the freestream flow to generate a shock-shock interaction. The minimum vertical distance between the wedges was kept constant throughout the runs. The Mach number was determined through continuous pressure readings in both the settling chamber and the test section. Schlieren and Focusing Schlieren systems were used to visualize the shock wave pattern. For all cases, the wind tunnel runs were initialized in the RI domain after which the Mach number was slowly decreased to the MI domain, thereby traversing the whole dual solution domain. The process was then inverted to reach again the RI domain in order to investigate a possible transition hysteresis. The Focusing Schlieren setup was capable of eliminating three-dimensional effects that contaminated the images obtained with the Schlieren visualization system. It also revealed that the main three-dimensional effect in the setup was a boundary layer detachment at the sidewalls. Schlieren visualization was used as the main quantitative flow diagnostics tool, allowing a clear view of the shock pattern and revealing the absence of any hysteresis effect. A custom built image processing software was used to obtain accurate measurements of the Mach stem height (MSH) evolution and detect transition. The MSH measurements confirmed the nonexistence of the hysteresis loop and an increase of the rate of change of the MSH with the Mach number as the deflection angle was decreased. The detected transition points between RI and MI showed a very good experimental repeatability and revealed that transition always occurred at the von Neumann condition regardless of the initial shock configuration. These results suggest that flow perturbations present in the TST-27 wind tunnel may prevent a RI from existing within the theoretical dual solution domain and thus suppressing any hysteresis loop. Further experiments and simulations are required to characterize these perturbations and fully understand the physical mechanism that triggers premature transition.

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