Investigations on Turbulence Model Uncertainty for Hypersonic Shock-Wave/Boundary-Layer Interaction Flows

Shock-wave/boundary-layer interaction (SWBLI) is a fundamental scientific problem that restricts the breakthrough of high-speed flight technology. Owing to the complex shock structure and boundary-layer separation in the interaction region, the widely used eddy-viscosity turbulence models have large uncertainties and model errors in the simulation of such flows. To make more reasonable aerodynamic/aerothermal predictions and identify the critical parameters affecting the prediction results, Bayesian uncertainty quantification and sensitivity analysis are conducted for the three turbulence models [Spalart–Allmaras (SA), SA with quadratic constitutive relation (SA-QCR), and shear-stress transport (SST) models] and the hypersonic SWBLI cases. First, the prior variances and Sobol indices are calculated to obtain a preliminary understanding of the parameter variability for turbulence models. Then, the posterior distributions of the model closure coefficients and posterior uncertainties of the wall pressure and thermal flux are systematically analyzed and compared. The results indicate that the prediction performances of the three models can be effectively enhanced by Bayesian estimation. The peak of the posterior uncertainty of the SST model is the largest among the three models, whereas that of the SA-QCR model is the smallest. The results of the Bayesian model evaluation demonstrate that the SA-QCR model has the highest reliability.