Film cooling and shock interaction: An uncertainty quantification analysis with transonic flows

This work shows an Uncertainty Quantification (UQ) study of film cooling with shock impingement. A numerical method is proposed to use high order polynomials for the reconstruction of the stochastic output, without the instabilities characteristic of UQ with shock dominated flows. At the same time it is shown that the region with highest uncertainty is driven by a complex flow physics involving shock-boundary layer interaction and the generation of tornado vortices that merge with kidney ones. High-pressure turbine stages are characterized by transonic conditions with the suction side of the nozzle affected by the shock shed by the trailing edge of the adjacent aerofoil. Due to manufacturing deviations and in service degradation the geometrical parameters, such as trailing edge thickness and hole diameter, are subjected to random variations, changing the shock location and the heat transfer loading on the stator nozzle. For these reasons an UQ methodology has been used in this study to model the interaction between the impinging shock and film cooling. The variability of the geometrical parameters has been represented with uniform probability distributions and the stochastic output is obtained using Probabilistic Collocation Method with Padè's polynomials. Transonic flows are challenging in Uncertainty Quantification because a better reconstruction of the stochastic output can be achieved increasing the order of polynomials but higher order polynomials become unstable for the Runge's phenomenon. This work proposes a method that allows the application of high order Padè's polynomial without having instabilities in the stochastic output. The proposed methodology can be applied to other transonic configurations in gas turbines, requiring only a limited number of simulations to reconstruct the stochastic output. The results show that the maximum level of uncertainty is located downstream the region of interaction between shock and boundary layer. In particular the shock generates complex flow structures that develop into tornado vortices, highly dependent on the uncertainty input.