Uncertainty Quantification of Heat Transfer for a Highly Loaded Gas Turbine Blade Endwall Using Polynomial Chaos

The durability of highly loaded gas turbine blade is significantly impacted by high heat transfer. The heat transfer performance of the gas turbine endwall can be varied significantly due to the impacts of uncertainties in the manufacturing process and operation conditions. In this work, an uncertainty quantification (UQ) method is proposed by integrating generalized polynomial chaos expansions, non-intrusive spectral projection and Smolyak sparse grids. Then coupled with three dimensional (3D) Reynolds-Averaged Navier-Stokes (RANS) solutions, an uncertainty quantification procedure is carried out for heat transfer performance of highly loaded blade endwall. Wherein, the effects of the variation of geometric parameters and operation conditions are taken into account. Specifically, the endwall heat transfer performance of a typical highly loaded turbine blade named Pack-B is numerically investigated. The turbulence intensity Tuinlet and Reynolds number Reinlet of inlet flow are considered as flow condition uncertainty parameters. As geometrical uncertainty parameters, the radius r and minimum angle α of blade root fillet are considered. These uncertainty factors have important influence on the secondary flow structure, resulting in significant variation of heat transfer performance of the endwall. Non-intrusive Polynomial Chaos (NIPC) is used to build a surrogate to reduce the quantity of the time consuming CFD simulation. A total of 137 sparse-grid-based design-of-experiment computations were carried out to build the high-fidelity surrogate. Using above method, the probability density function of the Nusselt number ( Nu ) of the endwall is obtained. The overall variation of Nu can be more than 10% due to the effect of the uncertainty factors. Finally, the sensitivity analysis shows that Reinlet has the most important influence on heat transfer performance of the whole endwall and other uncertainty factors also have significant effect on heat transfer performance at some local regions of the endwall such as wake region and middle part of blade passage.