Uncertainty analysis of compressor aerodynamic performance with impact of global profile errors on blade
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摘要:
为了研究全局轮廓度误差对跨声速轴流压气机性能及稳定性的影响，基于高斯过程和主成分分析法构建了表征叶表全局轮廓度误差的五维几何不确定性模型。同时，基于非嵌入式混沌多项式法量化了全局轮廓度误差对压气机气动性能的影响，并采用了损失源模型对两类极端性能叶型进行了流动机理分析。研究结果表明：在全局轮廓度误差的影响下压气机峰值效率工况下的总性能参数略微偏离正态分布，并且转子的性能会倾向于恶化；各性能参数对叶顶前缘部位的轮廓度误差最敏感，并且将其适当减薄能够有利于性能的提升；其中的原因是，叶顶前缘轮廓变薄有利于削弱激波强度，因而会减弱激波-泄漏涡相互作用的强度，从而减小流动损失。
Abstract:To investigate the effects of global profile errors on the aerodynamic performance of a transonic compressor, a five-dimensional geometric variability model characterizing blade surface global profile errors was established based on Gaussian process and principal component analysis. Combined with the non-intrusive polynomial chaos expansion based on Gaussian distribution, a surrogate mode of compressor performance was proposed. The effects of the performance were quantified using non-intrusive polynomial chaos methodology, complemented by loss source analysis to investigate the critical flow mechanisms in two extreme-performance blade profiles. Key findings indicated that the performance parameters at peak efficiency condition exhibited slight deviations from normal distributions under the effects of random profile errors, with the performance showing degradation. And the performance was most sensitive to the error at blade tip leading edges. The thinner leading edge can reduce shock intensity and weaken shock-leakage vortex interactions, with the loss decrease.
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图 2 压气机近失速流量的网格无关性验证
Figure 2. Grid independence verification of near-stall mass flow of the compressor
图 4 近失速工况下静子进口的径向总压分布
Figure 4. Radial total pressure distribution at stator leading edge under near-stall conditions
图 5 不同参数对近失速工况98%叶高截面流场损失的刻画
Figure 5. Description of flow field losses at 98% span under near-stall conditions based on different parameters
图 6 特征值与累计方差贡献率分布
Figure 6. Distribution of eigenvalues and cumulative variance contribution rate
图 9 性能参数相对偏移的概率密度分布
Figure 9. Probability density distribution of the performance relative deviation
图 11 总性能参数对全局轮廓度误差的敏感性分布
Figure 11. Sensitivity analysis of performance parameters to global profile errors
图 12 $ {{M}{a}}_{\text{r}} $标准差的周向平均分布
Figure 12. Standard deviation of $ {{M}{a}}_{\text{r}} $ in meridional patches
图 14 95%叶高下$ { {M} {a}}_{\text{r}} $的标准差分布
Figure 14. Standard deviation of $ { {M} {a}}_{\text{r}} $ at 95% span
图 16 极端性能叶型全局轮廓度误差的均值分布
Figure 16. Average of the global profile errors on extreme-performance blades
图 17 极端性能叶型全局轮廓度误差的相对标准差分布
Figure 17. Relative standard deviation of the global profile errors on extreme-performance blades
图 18 两类极端性能叶型中0%～S%叶高范围的累积损失分布
Figure 18. Cumulative loss distribution in the zone from 0% to S% span-wise for two extreme-performance blades
图 19 两类极端性能叶型中不同叶高区间内的损失分布
Figure 19. Loss distribution in different span-wise intervals for two extreme-performance blades
图 20 两类极端性能叶型中各类损失的分布
Figure 20. Different kinds of loss distribution for two extreme-performance blades
图 21 两类极端性能叶型99%叶高$ { {M} {a}}_{\text{r}} $分布
Figure 21. $ { {M} {a}}_{\text{r}} $ distribution at 99% span for two extreme-performance blades
图 22 两类极端性能叶型99%叶高损Φ分布
Figure 22. Φ distribution at 99% span for two extreme-performance blades
图 23 两类极端性能叶型90%叶高Φ分布
Figure 23. Φ distribution at 90% span for two extreme-performance blades
表 1 Wennerstrom跨声速风扇的几何参数
Table 1. Geometric features of Wennerstrom transonic fan
参数 数值 设计点转速/（r/min） 20152.4 叶顶间隙/mm 0.41 转子平均展弦比 1.320 静子平均展弦比 1.255 转子叶片数 20 静子叶片数 31 
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表 2 两类极端性能叶型性能较原型的相对偏移
Table 2. Relative deviation of the performance based on nominal blade for two extreme-performance blades
% 叶型 效率 总压比 总温比 熵增 S1 0.42 1.04 0.18 −2.71 S2 −0.74 −1.56 −0.26 5.14
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