On the investigation of oblique shock‐wave/turbulent boundary‐layer interactions with a high‐order discontinuous Galerkin method

Abstract

Shock-wave/turbulent boundary-layer interactions are still a challenge for numerical simulation. The shock capturing needs dissipation to avoid spurious oscillations while turbulence will be falsified by introducing dissipation. Especially, an accurate prediction of quantities such as the skin-friction coefficient inside the interaction area of shock wave and turbulent flow is a critical point. In this article, we investigate a wall-resolved large eddy simulation of oblique shock-wave/turbulent boundary-layer interactions by a high-order discontinuous Galerkin scheme. The high-order scheme handles the turbulent flow very well. The shock-capturing is confined to the near shock region by switching locally to a finite volume second-order TVD scheme on subcells. This strategy is completed with the application of a shock indicator to a filtered flow field. A global spanwise filter is applied to avoid switching on the shock-capturing procedure in regions of under-resolved turbulent structures. We validate our numerical results first at shock-wave/laminar boundary-layer interaction. The main simulation under consideration is a Mach 2 turbulent boundary-layer with an inlet momentum-thickness Reynolds number of 1628, interacting with an oblique shock that deflects the incoming flow by 8°. We employ a reformulated synthetic eddy method at the inlet to avoid the influence of recycling-based turbulence generating schemes on the low-frequency unsteadiness. The anisotropic linear forcing technique is adopted to further reduce the turbulence recovery length. Through the spectral analysis of wall pressure probes, a typical Strouhal number of around 0.03 is observed. We attribute the discrepancies between an experimental scaling law and our computation to the three-dimensional sidewall effects in the experiment. With the assistance of numerical results from this article and other authors, a new scaling law for the spanwise-periodic computations is suggested to quantify the difference between experimental and computed data.