Sensitivity analysis and modeling uncertainties quantification for impinging-film cooling via active subspaces

Within the context of exploiting efficient cooling methods for advanced gas turbine combustors, understanding the fundamental physics for impinging-film cooling under various operational conditions is of significance. In this paper, impacts of different interaction modes between coolant and hot mainstream on the impinging-film cooling are quantitatively evaluated via active subspace (AS) method. Three interaction modes are considered, i.e., a transitional flow (TF), a turbulent boundary layer (TBL) and a wall jet (WJ). Sensitivities and uncertainties of cooling effectiveness $\eta$ with respect to coolant mass flow rate $M_c$ and model parameters ($C_{\mu },C_{\epsilon 1},C_{\epsilon 2},P{r}_{\mathrm{tw}}$) are estimated. Results show that 1-D active subspaces are sufficient to map $\eta$ in TF and TBL modes while high-dimensional active subspaces are warranted for WJ mode, indicating its more complicated interaction between cold and hot flows. $\eta$ is the most sensitive to and dominated by $M_c$ especially in the slot and far fields, and turbulent effects are more significant in the near field than other places. Specifically, an increase in $M_c$ or a decrease in turbulent level monotonously improves $\eta$ in TF and TBL modes while initially increases $\eta$ then reduces it for WJ mode. Further analysis of flow characteristics of WJ mode demonstrates that the reduction in $\eta$ results from the strengthened impingement-induced streamwise vortexes and thereby, enhanced mixing between the coolant and mainstream. The propagation of the input uncertainty to $\eta$ is space- and operational condition-dependent, consistent with the evolution of active subspaces.