中文摘要：

受加工精度限制,叶片加工外形与设计外形存在一定偏差,该类偏差具有较强的随机性,对叶片气动性能造成不确定性影响。加工叶片外形偏差的不确定性影响为几何尺度上的小扰动问题。本文首先基于伴随方法建立了适用于加工叶片外形偏差气动灵敏度分析及气动性能偏差预估模型。之后,计算某二维涡轮叶片的气动参数伴随灵敏度,由此确定厚度均匀变化的测试叶片的气动性能偏差,并与数值模拟结果进行对比,验证伴随方法在叶片气动不确定性灵敏度分析中的精确性和有效性。最后,采用基于灵敏度分析的Monte Carlo方法研究满足正态分布的批量加工叶片的气动性能偏差,确定了相应的气动偏差统计模型。

英文摘要：

Due to the limited machine precision,there exist deviations between the nominal and the manufacturing aerodynamic shape of turbomachinery blades.The strong randomicity of manufacturing variations results in uncertainties to aerodynamic performance,which is essentially a small perturbation problem because the manufacturing variations are micro relative to the geometric parameters.In the paper,the evaluation of the resultant performance uncertainty is firstly introduced and completed with the adjoint sensitivity.Then the performance variations of two blades with uniformly thickened and thinned thickness,respectively reference to the nominal blade are predicted by the adjoint sensitivity,which are then compared with the computational ones to demonstrate the sufficient accuracy and practicability of the adjoint method in uncertainty studies.Finally,Monte Carlo simulations are performed on a group of blade samples,the manufacturing variations of which subject to normal distributions.By the adjoint method,the performance variations subject to normal distributions are successfully obtained.