Uncertainty Analysis of Laser Drilling Imperfection and Impacts on the Cooling Performance of a Transonic Turbine Vane

Abstract To ensure the durability and reliability of gas turbine, film cooling has been integrated into the design of the modern gas turbine vane endwall, especially for the first-stage vane endwall. Percussion laser drilling has been a very attractive technique used to drill holes in aero-engine hot components, due to its capability of drilling on a thermal barrier coated-superalloy in milliseconds. It should be noticed that micro-geometric deviations often exist in the resulting holes manufactured by laser drilling. However, most of the investigations in the literature treated the aleatory geometric imperfections as deterministic or ideal cases, which imported an uncertainty bias to life prediction. Therefore, a detailed uncertainty quantification analysis is performed to quantify the impacts of laser drilling imperfections on the endwall cooling performance in this article. This article conducted a dual non-deterministic analysis to analyze the cooling performance robustness of a double-row film holes scheme employed in a high-pressure turbine nozzle guide vane, subjecting to the variability of film hole geometric parameters set by manufacturing deviation range. First, to evaluate the impact of laser drilling imperfections on the endwall cooling performance, a conical nozzle film hole imperfection model is proposed to parameterize the real laser drilled hole. Then, a fundamental uncertainty quantification framework, which combines the conical nozzle parameterized model, non-intrusion Polynomial Chaos UQ methodology, and k-Nearest Neighbor clustering algorithm, is built to quantify the cooling performance while geometric parameters of all film holes are consistent. The UQ results show that the likelihood of all holes being on the edge of their tolerance range increases dramatically. Large variations in mass flow ratio and film cooling effectiveness were observed. Mass flow ratios ranged from 0.51% to 2.31% (μ ± 3σ), where the baseline MFR was 1.27%. The standard deviation of adiabatic effectiveness was up to 0.2. An additional consideration to be made is that for a more real-life scenario, the geometric parameters of all film holes are not identical. A flow parameter dimensionality reduction UQ approach (FPDR), which transforms the deviations of multiple geometric parameters into the fluctuations of several key flow parameters, is proposed to address the curse of dimensionality phenomenon in predicting the cooling performance under uncertain conditions of inconsistent film hole imperfection characteristic parameters. The results show that the fluctuation ranges of MFR and adiabatic cooling effectiveness under uncertain conditions of inconsistent film hole parameters are significantly reduced, less than one-fourth and one-fifth of the fluctuation ranges under conditions of consistent film hole parameters. The developed uncertainty quantification platform can provide a useful tool to evaluate the cooling performance robustness of advanced cooling systems with multi-row cylindrical cooling holes, considering laser drill imperfection.