Uncertainty Quantification and Robustness Optimization Methods for the Aero-Thermal Performance of Turbine Endwall Contour

Abstract

Abstract. Endwall contouring is a widely used technique for enhancing aerodynamic performance in turbine cascades. However, the manufacturing process of contoured endwalls inherently involves geometric errors, and thus, the performance of the contoured endwall always exhibits large uncertain deviations from design values. Currently, the uncertainty quantification method and robustness design criteria of contoured endwall performance are still insufficient, and the endwall contour is usually optimized under deterministic operation conditions instead of considering its robustness under operational uncertainties. Therefore, by using the Kriging surrogate model for global performance evaluation and polynomial chaos expansion (PCE) for uncertainty quantification, an uncertainty quantification and robustness optimization framework is established in this article. It is then implemented for the robust optimization of an endwall contour, with respect to both aerodynamic and cooling performance objectives. The robustly contour design is compared with traditional deterministic single-objective optimization results, and the advantages and necessity of robustness optimization superior to deterministic optimization of the endwall contour are revealed. The results show that the robustly designed endwall contour mainly enhances the pressure side and mid-pitch endwall cooling performance, showing an average η increase of 0.04. The contour in the upstream region causes greater uncertainties in endwall cooling parameters. The region near the leading edge on the pressure side endwall has the largest cooling effectiveness uncertainty with a standard deviation of 0.1, suggesting additional cooling designs for better protection. The robustly endwall contour design achieves a 0.7% reduction in pressure loss compared to a flat endwall, while its standard deviation of pressure loss is only 23% that of the deterministic optimization design. The robustly contour design enhances the aerodynamic robustness by accelerating the separation of the passage vortex from the endwall, thereby making it less influenced by downstream endwall contouring and near-endwall fluid. The endwall contouring at z/Cax = 0.143 and 0.71 dominates the cascade aerodynamic performance uncertainty.