整级环境下涡轮叶片型面加工几何偏差影响的不确定性分析

加工等过程中产生的几何偏差会导致涡轮叶片气动性能及工作状态发生显著变化，对该影响的准确评估与合理分析具有重要意义。本文提出了一种考虑三维型面几何偏差对气动性能影响的不确定性计算分析方法，包括随机叶型几何建模、不确定性量化计算和敏感性分析等，并结合某一单级高压涡轮进行分析。基于随机过程理论和主成分分析法，参考现有叶片加工公差标准，并结合正态性假设，完成实际叶型几何的不确定性建模。选用基于多项式混沌展开的Kriging代理模型进行不确定性计算，结果表明，几何偏差对所研究涡轮的气动性能和工作状态存在较为显著的影响：相较设计值，实际等熵效率的标准差为 0.33%，下 3%分位值减小 0.65%；实际质量流量和膨胀比的相对标准差分别为 1.24%、0.19%，下 3%分位值分别相对减小 2.37%、0.37%，上 3%分位值分别相对增加 2.38%、 0.36%。采用Spearman秩相关性分析法进行敏感性分析，结果表明，对于所研究的单级涡轮，不同几何参数间存在较大的相关性；导叶几何偏差的影响明显大于动叶；导叶尾缘区域几何对气动性能影响较为显著，该区域的加工偏差应严格控制。

Uncertainty Analysis of Impact of Profile Geometric Manufacture Variations on Turbine Blade Performance in Stage Environment

Geometric variations in the manufacturing process will lead to variations of aerodynamic performance and working status of turbine, and accurate evaluation and reasonable analysis of the impact are of great significance. A method to quantify and analyze the uncertainty impact of 3D blade geometric variations on aerodynamic performance was proposed in this paper, including uncertainty modeling of blade geometric variations, uncertainty quantification and sensitivity analysis. And a single-stage high-pressure turbine was taken as an example for analysis. Based on the manufacturing tolerance and Gaussian hypothesis, random process and Principal-component analysis (PCA) were used for the uncertainty modeling. The Kriging surrogate model based on polynomial chaos expansions (PC-Kriging) was applied for the uncertainty calculation. The results showed that, for the turbine under study, the aerodynamic performance and working status were significantly influenced by the geometric variations. Compared with the nominal value, the standard deviation of the actual isentropic efficiency is 0.33%, and the lower 3% quantile value decrease by 0.65%; the relative standard deviations of the actual mass flux and expansion ratio are 1.24% and 0.19%, the lower 3% quantile values decrease by 2.37% and 0.37%, and the upper 3% quantile values increase by 2.38% and 0.36%, respectively. Spearman Rank Correlation (SRC) analysis was adopted for the sensitivity analysis. According to the results, for the single-stage turbine studied, there is a large correlation between these geometric parameters, and the influence of geometric variations of the stator is significantly greater than those of the rotor. Those geometric variations in the trailing edge region of the stator have a significant impact, which should be restricted in the manufacturing process.