Fluid–structural coupling of an impinging shock–turbulent boundary layer interaction at Mach 3 over a flexible panel

We present high-fidelity numerical simulations of the interaction of an oblique shock impinging on the turbulent boundary layer developed over a rectangular flexible panel, replicating wind tunnel experiments by Daub et al. (AIAA Journal, vol. 54, 2016, pp. 670–678). The incoming free-stream Mach and unit Reynolds numbers are $M_{\infty } = 3$ and $Re_{\infty }=49.4\times 10^6 {\rm m}^{-1}$ , respectively. The reference boundary layer thickness upstream of the interaction with the shock is $\delta _0 = 4$ mm. The oblique shock is generated with a rotating wedge initially parallel to the flow that increases the deflection angle up to $\theta _{{max}} = 17.5^{\circ }$ within approximately $15$ ms. A loosely coupled partitioned flow–structure interaction simulation methodology is used, combining a finite-volume flow solver of the compressible wall-modelled large-eddy simulation equations, an isoparametric finite-element solid mechanics solver and a spring-system-based mesh deformation solver. Simulations are conducted with rigid and flexible panels, and the results compared to elucidate the effects of panel flexibility on the interaction. Three-dimensional effects are evaluated by conducting simulations with both full ( $50 \delta _0$ ) and reduced ( $5\delta _0$ ) spanwise panel width, the latter enforcing spanwise periodicity. Panel flexibility is found to increase the separation bubble size and modify its spectral dynamics. Time- and spanwise-averaged streamwise profiles of the wall pressure exhibit a drop over the flexible panel prior to the interaction and a reduced peak pressure in comparison with the rigid case. Spectral analyses of wall pressure data indicate that the low-frequency motions have a similar spectral distribution for the rigid and flexible cases, but the flexible case shows a wider region dominated by low-frequency motions and traces of the panel vibration on the wall pressure signal. The sensitivity of the interaction to small variations in the wedge extent and incoming boundary layer thickness is evaluated. Predictions obtained from lower-fidelity modelling simplifications are also assessed.