Structural uncertainty quantification of Reynolds-Averaged Navier–Stokes closures for various shock-wave/boundary layer interaction flows

Abstract

Accurate prediction of Shock-Wave/Boundary Layer Interaction (SWBLI) flows has been a persistent challenge for linear eddy viscosity models. A major limitation lies in the isotropic representation of the Reynolds stress, as assumed under the Boussinesq approximation. Recent studies have shown promise in improving the prediction capability for incompressible separation flows by perturbing the Reynolds-stress anisotropy tensor. However, it remains uncertain whether this approach is effective for SWBLI flows, which involve compressibility and discontinuity. To address this issue, this study systematically quantifies the structural uncertainty of the anisotropy for oblique SWBLI flows. The eigenspace perturbation method is applied to perturb the anisotropy tensor predicted by the Menter Shear–Stress Transport (SST) model and reveal the impacts of anisotropy on the prediction of quantities of interest, such as separation and reattachment positions, wall static pressure, skin friction, and heat flux. The results demonstrate the potential and reveal the challenges of eigenspace perturbation in improving the SST model. Furthermore, a detailed analysis of turbulent characteristics is performed to identify the source of uncertainty. The findings indicate that eigenspace perturbation primarily affects turbulent shear stress, while the prediction error of the SST model is more related to turbulent kinetic energy.