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

• Interaction effect of coolant and hot mainstream on impinging-film cooling under three interaction modes TF, TBL and WJ are quantitatively evaluated via active subspace. • 1-D active subspaces are sufficient to map cooling effectiveness in TF and TBL modes while multi-dimensional ones are warranted for WJ mode. • Cooling effectiveness is the most sensitive to blowing ratio and turbulent effects are more significant in near fields for TF and TBL modes. • Twofold impacts of blowing ratio and turbulence on cooling are identified in WJ mode by the “parabolic law” of cooling effectiveness versus active variables. • Propagations of input uncertainties to cooling effectiveness are space- and operational condition-dependent. 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 η with respect to coolant mass flow rate M c and model parameters ( C μ , C ε 1 , C ε 2 , P r tw ) are estimated. Results show that 1-D active subspaces are sufficient to map η 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. η 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 η in TF and TBL modes while initially increases η then reduces it for WJ mode. Further analysis of flow characteristics of WJ mode demonstrates that the reduction in η results from the strengthened impingement-induced streamwise vortexes and thereby, enhanced mixing between the coolant and mainstream. The propagation of the input uncertainty to η is space- and operational condition-dependent, consistent with the evolution of active subspaces.