Bayesian parameter estimation of SST model for shock wave-boundary layer interaction flows with different strengths

Abstract

The Shock Wave-Boundary Layer Interaction (SWBLI) flow generated by compression corner widely occurs in engineering. As one of the primary methods in engineering, the Reynolds Averaged Navier-Stokes (RANS) methods usually cannot correctly predict strong SWBLI flows. In addition to the defects of the eddy viscosity assumption, the uncertainty of the closure coefficients in RANS models often significantly impacts the simulation results. This study performs parametric sensitivity analysis and Bayesian calibration on the closure coefficients of the Menter k-ω Shear-Stress Transport (SST) model based on the SWBLI with different strengths. Firstly, the parametric sensitivity on prediction results is analyzed using the Sobol index. The results indicate that the Sobol indices of wall pressure and skin friction exhibited opposite fluctuation trends with the increase of SWBLI strength. Then, the Bayesian uncertainty quantification method is adopted to obtain the posterior probability distributions and Maximum A Posteriori (MAP) estimates of the closure coefficients and the posterior uncertainty of the Quantities of Interests (QoIs). The results indicate that the prediction ability for strong SWBLI of the SST model is significantly improved by using the MAP estimates, and the relative errors of QoIs are reduced dramatically.