Uncertainty quantification of Menter SST turbulence model coefficients in hypersonic flow simulations

The precision of numerical simulations for hypersonic flows is significantly influenced by the uncertainties in the closure coefficients of the Menter SST turbulence model. This study conducts a quantitative assessment of these uncertainties across three canonical hypersonic models: the two-dimensional compression corner, the two-dimensional cylinder, and the three-dimensional double ellipsoid. Firstly, the non-intrusive polynomial chaos method is used to quantify the uncertainty in the numerical simulations of aerodynamic forces and heating caused by the uncertain closure coefficients of the Menter SST turbulence model. The sensitivities of the closure coefficients are then ranked based on the Sobol sensitivity index to identify the key factors contributing to the uncertainty. The results show that uncertainties in aerodynamic heating generally exceed those in aerodynamic forces. Among all the nine closure coefficients examined in this paper, ${\sigma }_{\omega 1}$、 ${\beta }^{\ast }$、 $\kappa$、 $a_1$ are the key model parameters that contribute significantly to the uncertainty of the simulation results. And the sensitivities of which are related to local flow characteristics. In most flow areas, the coefficients of production term ${\sigma }_{\omega 1}$ and $\kappa$ are the main factors contributing to the uncertainty of the numerical simulation results. While in regions of flow separation or behind shock waves, the simulation results are more significantly influenced the dissipation term coefficient ${\beta }^{\ast }$ and the shear stress limiter $a_1$.