Uncertainty Quantification on the Cooling Performance of a Transonic Turbine Vane With Upstream Endwall Misalignment

Abstract

With increasing aerodynamic and thermal loads, film cooling has been a popular technology integrated into the design of the modern gas turbine vane endwall, especially for the first-stage vane endwall. A staggering amount of research has been completed to quantify the effect of operating conditions and cooling hole geometrical properties. However, most of these investigations did not address the influence of the manufacturing tolerances, assembly errors, and operation degradations on the endwall misalignment. In this paper, uncertainty quantification (UQ) analysis was performed to quantify the impacts of upstream endwall misalignment uncertainties on the endwall film cooling performance and vane surface phantom cooling performance. The upstream endwall misalignment, step geometry with various step heights, commonly exists between the combustor exit and the first-stage vane endwall. Based on the non-intrusive polynomial chaos expansion (NIPC) and the uniform probability distribution assumption, the deviation (step height) uncertainties of the upstream endwall misalignment were quantified. To predict the endwall secondary flow and film cooling effectiveness in the transonic linear vane passage, the commercial computational fluid dynamic solver ANSYS FLUENT was used to numerically solve the three-dimensional steady-state Reynolds-Averaged Navier–Stokes (RANS) equations. The robustness analysis of endwall film cooling performance and phantom cooling performance to the upstream endwall misalignment was conducted for three design upstream step heights (ΔH): a baseline configuration (ΔH = 0 mm), two misaligned configurations with forward step (ΔH = −5 mm) and backward step (ΔH = 5 mm), respectively. Results show that the actual cooling performance has a high probability of deviating from the nominal value for the baseline configuration. The critical regions that are most sensitive to the upstream step misalignment are also identified by variances. The UQ results also show that the design geometry with a forward step has a more robust film cooling performance on endwall and phantom cooling performance on the vane pressure side surface, which means a smaller variance and a better expectation than the no-step configuration. In contrast, the design geometry with a backward step induces the reductions in the expectation of the film cooling effectiveness and coolant coverage and the amplification of performance fluctuations. This work provides a certain guiding direction for the optimization design for the upstream step geometry.