Uncertainty Quantification of Non-Dimensional Parameters for a Film Cooling Configuration in Supersonic Conditions

In transonic high-pressure turbine stages, oblique shocks originating from vane trailing edges impact the suction side of each adjacent vane. High-pressure vanes are cooled to tolerate the combustor exit-temperature levels, then it is highly probable that shock impingement will occur in proximity to a row of cooling holes. The presence of such a shock, together with the inevitable manufacturing deviations, alters the location of the shock impingement and of the performance parameters of each cooling hole. The present work provides a general description of the aero-thermal field that occurs on the rear suction side of a cooled vane. Computational Fluid Dynamics (CFD) is used to evaluate the deterministic response of the selected configurations in terms of adiabatic effectiveness, discharge coefficient, blowing ratio, density ratio, and momentum ratio. Turbulence is modelled by using both the Shear Stress Transport method (SST) and the Reynolds Stress Model (RSM) implemented in ANSYS® FLUENT®. The obtained results are compared with the experimental data obtained by the Institut für Thermische Strömungsmaschinen in Karlsruhe. Two uncertainty quantification methodologies based on Hermite polynomials and Padè–Legendre approximants are used to consider the probability distribution of the geometrical parameters and to evaluate the response surfaces for the system response quantities. Trailing-edge and cooling-hole diameters have been considered to be aleatory unknowns. Uncertainty quantification analysis allows for the assessment of the mutual effects on global and local parameters of the cooling device. Obtained results demonstrate that most of the parameters are independent by the variation of the aleatory unknowns while the standard deviation of the blowing ratio associated with the hole diameter uncertainty is around 12%, with no impact by the trailing-edge thickness. No relevant advantages are found using either SST model or RSM in combination with Hermite polynomials and Padè–Legendre approximants.