Numerical Investigation of a Turbulent High-Speed Flow Separating from a Deforming Cantilever Plate

Deep understanding of multiscale nonlinear phenomena, such as shocks, turbulent flow, and separation, is critical for the accurate and efficient treatment of high-speed fluid-structural interactions. To better characterize the principal issues, a numerical investigation is performed of the response of a Mach 2.0 flow to prescribed motion of a cantilever plate. The main features of the flow are separation at the end of the plate and re-attachment on the downstream floor, which are modulated by shear layer instabilities and interactions with the cavity beneath the plate. The influence of structural motions on the fluid dynamics is investigated through forced simple harmonic oscillations of the cantilever in three different dynamic modal states of a plate. The potential impact of flow resolution on energy transfer is assessed by comparing unsteady Reynolds-averaged Navier-Stokes (URANS) and large-eddy simulation (LES). Spectral and modal analyses are conducted to baseline the multiscale dynamics of the rigid configuration, revealing low-frequency fluid dynamics on the order of typical structural response scales. First examined is the oscillation of the cantilever in the first streamwise bending mode at the same frequency as the baseline low-frequency fluid dynamics. Second, the flow response to two-dimensional structural oscillations is studied by forcing the cantilever in a combination of the first streamwise bending and first spanwise torsional modes. For these, the URANS method compares reasonably well with the LES result for asymptotic time-averaged flow features. However, the associated integrated aeroelastic forces are underpredicted by the URANS by approximately 15% due to a longer separation length prediction. In the third motion, the potential for energy transfer through the broadband scales in the incoming boundary layer to high-frequency structural modes to the shear layer is examined by forcing the cantilever with a low-amplitude oscillation at a frequency on the order of the shear layer scales. This is observed as a mechanism to enhance the turbulence level of the shear layer scales and alter the time-averaged separation length. However, the mean integrated aeroelastic force is only marginally impacted for the amplitudes considered, with increases of 5% or less.