Exploiting Active Subspace for Modeling Uncertainty and Optimization in Fan-Shaped Film Cooling Simulation

Abstract The numerical studies for film cooling performance have gained considerable interest for the development of advanced gas turbines and aero-engines. However, the accuracy of Reynolds-Averaged Navier–Stokes simulations is significantly influenced by the uncertainties associated with turbulence modeling closure coefficients. The traditional Monte Carlo (MC) methods for uncertainty quantification (UQ) are computationally prohibitive as the cost of constructing an accurate response surface increases exponentially with the number of input parameters. The active subspace (AS) method, developed recently as a means of dimension reduction, incurs a moderate cost when dealing with high-dimensional uncertain inputs. In this study, the AS method is applied to quantify the modeling uncertainties related to turbulent Prandtl number and Shear Stress Tensor (SST) turbulence modeling parameters in a fan-shaped film cooling simulation. The results reveal that the quantified modeling uncertainties exhibit distinct characteristics across different blowing ratios, and the response functions are constructed based on the primary control parameters. Subsequently, the turbulence model parameters are optimized to minimize the computational error based on the response functions. In the optimized test point, the average relative errors decrease to 1.3% and 0.3%, respectively, under blowing ratios of 0.5 and 2.5 after optimization. Furthermore, a set of unified model parameters is optimized and applied across different blowing ratios (0.5, 1.5, 2.5), resulting in average relative error of 4.3%, 3.7%, and 3.1%, respectively, demonstrating the advantages of the AS method for modeling uncertainty quantification and optimization in film cooling simulation.