Uncertainty quantification of film cooling performance of an industrial gas turbine vane

Computational Fluid Dynamics (CFD) results are often presented in a deterministic way despite the uncertainties related to boundary conditions, numerical modelling, and discretization error. Uncertainty quantification is the field studying how these phenomena affiect the numerical result. With these methods, the results obtained are directly comparable with the experimental ones, for which the uncertainty related to the measurement is always shown. This work presents an uncertainty quantification approach applied to CFD: the test case consists of an industrial prismatic gas turbine vane with standard film cooling shaped holes system on the suction side only. The vane was subject of a previous experimental test campaign which had the objective to evaluate the film cooling effectiveness through pressure-sensitive paint technique. CFD analyses are conducted coherently with the experiments: the analogy between heat and mass transfer is adopted to draw out the adiabatic film effectiveness, solving an additional transport equation to track the concentration of CO2 used as a coolant fluid. Both steady and unsteady simulations are carried out: the first one using a RANS approach with k-ω SST turbulence model the latter using a hybrid LES-RANS approach. Regarding uncertainty quantification, three geometrical input parameters are chosen: the hole dimension, the streamwise inclination angle of the holes, and the inlet fillet radius of the holes. Polynomial-chaos approach in conjunction with the probabilistic collocation method is used for the analysis: a first-order polynomial approximation was adopted which required eight evaluations only. RANS approach is used for the uncertainty quantification analysis in order to reduce the computational cost. Results show the confidence interval for the analysis as well as the probabilistic output. Moreover, a sensitivity analysis through Sobol's indices was carried out which prove how these input parameters contribute to the film cooling effectiveness, in particular, when dealing with the additive manufacturing process.