Validatable Shock-Wave/Turbulent Boundary-Layer Interaction over a Compliant Panel

Abstract

Shock-Wave/Turbulent-Boundary Layer Interactions (SWTBLI) often occur in applications of technological interest. The associated inherent low-frequency unsteadiness dictates the use of Large-Eddy Simulation (LES) approaches to resolve the interaction, which unavoidably implies a very high computational cost. For this reason, no well-resolved long-integration time LES of an experimentally validatable setup has yet been conducted. Therefore, a new numerical set-up for LES, which is reproducible in the ST-15 supersonic blowdown windtunnel, is identified using analytical and inviscid two-dimensional methods. First of all, a state-of-the-art analytical model for shock-panel interactions was implemented. It was observed that ignoring the transverse steady pressure difference over the panel and the subsequent mean panel deformation led to an erroneous prediction of the flutter dynamic pressure. Incorporating both resulted in a correct stiffening of the panel for low shock strengths, but the destabilisation of the panel for stronger shocks, as shown by high fidelity methods, was not obtained. This was attributed to the linearity of the stability analysis and the absence of certain nonlinear flow features in the model, such as a passive adaptation of the reflected shock to the local panel slope. Thus, to include these nonlinearities, the Euler equations were loosely coupled to a FEM model of a clamped two-dimensional panel, which were solved using INCA and CalculiX respectively. The frequency, amplitude and modal content of the panel response were found to be highly sensitive to shock impingement location. A sensitivity study of the obtained Limit Cycle Oscillation (LCO) with respect to panel thickness and settling chamber total pressure allowed to identify parameters which maximize panel unsteady motion. It must be noted that in the viscous case, spreading of the shock-system pressure jump is expected to occur, which depends strongly on Reynolds number, shock-strength, relative positioning of the shock-generator trailing edge expansion fan, and panel unsteadiness. Given the selected conditions and an interaction length estimate based on literature, the most promising impingement point was found to be located at the panel midpoint, which should place the separated shock foot in an unsteady region identified near the panel leading edge. Based on an initial estimation of the grid distribution and the required integration time, it can be stated that a computationally feasible set-up has been obtained, which is also reproducible in the ST-15 and which should induce a strong LCO, independent of initial conditions. Furthermore, it was found that the nondimensional dynamic pressure, a parameter typically used to characterize classic panel flutter, is not valid for panel flutter with shock impingement.