Uncertainty analysis of measured geometric variations in turbine blades and impact on aerodynamic performance

Inevitable geometric variations significantly affect the performance of turbines or even that of entire engines; thus, it is necessary to determine their actual characteristics and accurately estimate their impact on performance. In this study, based on 1781 measured profiles of a typical turbine blade, the statistical characteristics of the geometric variations and the uncertainty impact are analyzed, and some commonly used uncertainty modelling methods based on Principal-Component Analysis (PCA) are verified. The geometric variations are found to be evident, asymmetric, and non-uniform, and the non-normality of the random distributions is non-negligible. The performance is notably affected, which is manifested as an overall offset, a notable scattering, and significant deterioration in several extreme cases. Additionally, it is demonstrated that the PCA reconstruction model is effective in characterizing major uncertainty characteristics of the geometric variations and their impact on the performance with almost the first 10 PCA modes. Based on a reasonable profile error and mean geometric deviation, the Gaussian assumption and stochastic-process-based model are also found to be effective in predicting the mean values and standard deviations of the performance variations. However, they fail to predict the probability of some extreme cases with high loss. Finally, a Chi-square-based correction model is proposed to compensate for this deficiency. The present work can provide a useful reference for uncertainty analysis of the impact of geometric variations, and the corresponding uncertainty design of turbine blades.