We present wall-modelled large-eddy simulations (WLES) of oblique shock waves interacting with the turbulent boundary layers (TBLs) (nominal $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\delta _{99}=5.4\ \mathrm{mm}$ and ${\mathit{Re}}_{\theta }\approx 1.4\times 10^4$) developed inside a duct with an almost-square cross-section ($45\ \mathrm{mm}\times 47.5\ \mathrm{mm}$) to investigate three-dimensional effects imposed by the lateral confinement of the flow. Three increasing strengths of the incident shock are considered, for a constant Mach number of the incoming air stream $M\approx 2$, by varying the height (1.1, 3 and 5 mm) of a compression wedge located at a constant streamwise location that spans the top wall of the duct at a 20° angle. Simulation results are first validated with particle image velocimetry (PIV) experimental data obtained at several vertical planes (one near the centre of the duct and three near one of the sidewalls) for the 1.1 and 3 mm-high wedge cases. The instantaneous and time-averaged structure of the flow for the stronger-interaction case (5 mm-high wedge), which shows mean flow reversal, is then investigated. Additional spanwise-periodic simulations are performed to elucidate the influence of the sidewalls, and it is found that the structure and location of the shock system, as well as the size of the separation bubble, are significantly modified by the lateral confinement. A Mach stem at the first reflected interaction is present in the simulation with sidewalls, whereas a regular shock intersection results for the spanwise-periodic case. Low-frequency unsteadiness is observed in all interactions, being stronger for the secondary shock reflections of the shock train developed inside the duct. The downstream evolution of secondary turbulent flows developed near the corners of the duct as they traverse the shock system is also studied.

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Experimental data acquired using high resolution two-component particle image velocimetry (PIV) are presented for shock boundary layer interactions (SBLIs) generated by a compression-expansion ramp geometry. The incident oblique shock wave is generated by a sub-boundary layer height ramp inclined 20 • to the M ∞ = 2.05 inflow. Results are presented for two different ramp sizes (h ramp /δ 0 = 0.56 and h ramp /δ 0 = 0.93), and compared to a previously documented h ramp /δ 0 = 0.20 case. For each case, mean velocitiy and turbulent statistics for both the SBLI at the foot of the compression ramp and the incident/reflected SBLI on the opposite wall are analyzed. Data are acquired in several streamwise-vertical planes across the span of the low aspect ratio duct in order to document spanwise non-uniformities and confinement effects, with the specific goal of producing a high quality experimental database for CFD validation. The angles of the incident and reflected shock waves become steeper as the side wall is approached, due to the lower velocities within the side wall boundary layer. Mean flow reversal is observed near the spanwise centerline of the duct, but only instantaneous flow reversal is seen closer to the side walls. These spanwise non-uniformities are more prominent for the stronger interactions caused by the larger ramp geometry. For this case there is no nominally two-dimensional region of the flow, and a Mach stem occurs in the core of the flow, causing a significant subsonic wake. The shock excursion length scale relative to the incoming boundary layer thickness, L ex /δ 0 , is measured for all of the shock features and found to be significantly lower than values reported in the literature for similar flows. Furthermore, L ex /δ 0 for the reflected shock does not depend on the strength of the incident shock or the size of the separated zone.

The sensitivity of two shock boundary layer interactions (SBLIs) -a compression corner interaction and an incident shock interaction -to small geometric perturbations (h < 0.2δ0) was investigated using particle image velocimetry (PIV) measurements. Tests were performed in a continuously operated Mach 2.1 wind tunnel with a low aspect ratio test section. The primary oblique shock was generated by a 1.1mm high 20 • degree compression wedge on the top wall of the tunnel, and small bumps were introduced upstream on the opposite wall. A total of 100 perturbed cases were tested; 45 for the compression corner interaction and 55 for the incident shock interaction. This dataset is well suited to be used for the validation of CFD codes which are intended to be used in design and analysis of systems with stochastic inputs. Both the compression corner and incident shock interactions were very sensitive to perturbations in a given region (-69mm < xp < -54mm), and insensitive to perturbations outside of it. Depending upon the location of the perturbations, the compression corner interaction could be strengthened or weakened significantly. Areas of high wall-normal velocity in the incident SBLI were intensified as larger perturbations were added in the sensitive region. For all perturbations, the incident shock interaction either moved upstream or stayed in the same location. The deviation in the position of this SBLI from its unperturbed location was a strong function of both the location and size of the perturbations. NomenclatureM Mach number P 0 Upstream stagnation pressure, kPa gauge T 0 Upstream stagnation temperature, K x Streamwise coordinate, mm y Wall-normal coordinate, mm U Mean streamwise velocity, m/s V Mean wall-normal velocity, m/s δ 0 Incoming boundary layer thickness, mm h Perturbation height, mm