Uncertainty Quantification and Sensitivity Analysis of Closure Parameters of Transition Models

The closure parameters introduced in transition models can compromise the accuracy of prediction results. This paper investigated the uncertainty caused by the closure parameters in transition models ($\gamma$ and $k-\omega -\gamma$), and identified the key parameters that have the greatest impact on quantities of interest. The uncertainty was propagated by the point-collocation no-intrusive polynomial chaos method, and the relative contribution of each parameter to uncertainty was assessed by the Sobol index. The natural transition flow (Schubauer–Klebanoff flat plate) and low-velocity airfoil flow (NLF0416 airfoil) were chosen for computational cases. The results, which are highly dependent on the closure parameters, validate the necessity of uncertainty research. The parameters of the $k-\omega -\gamma$ model are more sensitive than those of the $\gamma$ model. In the $\gamma$ model, the most critical parameter is $C_{TU2}$, which is negatively related to the transition position, i.e., the transition delays when $C_{TU2}$ increases and advances when $C_{TU2}$ decreases. In the $k-\omega -\gamma$ model, the most critical parameter is $C_2$, which is positively related to the transition position.