Uncertainty research on effects of position deviation on aerodynamic performance of rotor
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摘要:
为探究位置度偏差对动叶气动性能的影响，以Rotor 37为研究对象，基于二维非嵌入式混沌多项式方法，量化研究了位置度偏差对动叶气动性能和流场结构的不确定性影响。结果表明：在等背压条件下，位置度偏差对动叶气动性能的平均水平几乎不会造成影响，各工况的气动性能近似为正态分布；动叶气动性能受轴向位置度偏差的影响更显著，且两者之间存在高度相关的线性关系。当位置度偏差沿着轴向增大时，会使性能曲线整体向流量减小的方向偏移，改变了压气机稳定工作的流量范围；在参考峰值效率工况下，轴向位置度偏差会影响叶顶激波位置和激波强度，对动叶的做功能力产生影响，进而影响总压比，同时会影响波阻损失和激波-附面层干扰损失，进而影响等熵效率。
Abstract:In order to study the influence of position deviation on the aerodynamic performance of rotor, Rotor 37 was taken as the research object and the non-intrusive polynomial chaos method was used as uncertainty quantification to evaluate the uncertainty effect of position deviation on rotor aerodynamic performance and flow field structure. Results showed that: the position deviation had almost no effect on the average level of aerodynamic performance of rotor under the condition of equal backpressure, and the aerodynamic performance of each working condition was approximately normally distributed; the aerodynamic performance of rotor was more significantly affected by the axial position deviation, and there was a highly correlated linear relationship between them. When the position deviation increased along the axial direction, it made the performance curve shift towards the direction of flow rate decrease, changing the flow range of compressor stable operation; under the condition of reference peak efficiency, the axial position deviation could affect the position and intensity of the shock wave at the tip of the blade, which may affect the working ability of the blade, then affect the total pressure ratio and the wave resistance loss and shock wave-boundary layer interaction loss, and then affect the isentropic efficiency.
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图 2 数值模拟结果的性能曲线与实验数据的对比
Figure 2. Comparison between experimental and simulation results
图 3 近似速工况下转子基元级性能
Figure 3. Elementary stage performance of rotor under near stall condition
图 4 近失速工况下95%叶高截面的相对马赫数分布
Figure 4. Relative Mach number distribution at 95% span at near stall condition
图 5 各样本叶根剖面积叠点的相对位置分布
Figure 5. Relative positional distribution of leaf-root profile superposition points for each sample
图 6 叶片改型前后20%和80%叶高截面型线对比
Figure 6. Comparison of 20% and 80% span profile before and after blade reshaping
图 12 出口周向平均总压比的无量纲标准差沿叶高分布
Figure 12. Dimensionless standard deviation of the circumferential mean total pressure ratio at the outlet
图 13 参考峰值效率工况95%叶高静压系数均值沿无量纲弦长的分布
Figure 13. Mean value of static pressure coefficient distribution along 95% span in reference peak efficiency condition
图 14 参考峰值效率工况95%叶高静压系数标准差沿无量纲弦长的分布
Figure 14. Standard deviation of static pressure coefficient distribution along 95% span in reference peak efficiency condition
图 15 出口周向平均熵的无量纲标准差沿叶高分布
Figure 15. Dimensionless standard deviation of the circumferential mean entropy at the outlet
图 16 参考峰值效率工况下出口截面熵的面积平均的均值分布
Figure 16. Mean value distribution of the area average of the outlet section of the entropy under the reference peak efficiency condition
图 17 参考峰值效率工况下40%叶高熵标准差云图
Figure 17. Standard deviation of the entropy at 40% span under reference peak efficiency condition
表 1 Rotor 37的部分参数
Table 1. Partial parameters of Rotor 37
参数 数值 叶片数 36 设计质量流量/（kg/s） 20.19 堵塞质量流量/（kg/s） 20.93$ \pm $0.14 设计总压比 2.106 等熵效率 0.889 设计总温比 1.270 设计转速/（r/min） 17188 叶顶间隙/mm 0.356 
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表 2 W0和KW选值表
Table 2. Optional value table of W0 and KW
参数 组别编号 Ⅰ类 Ⅱ类 ${W_0}$ 1 0.10 0.10 2 0.20 0.20 3 0.30 0.40 4 0.40 0.60 5 0.60 1.00 ${K_{{\mathrm{W}}}}$ 1 0.002 0 2 0.004 0 3 0.006 0 4 0.008 0 5 0.01 0
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表 3 二元非线性试验函数试验结果
Table 3. Results of the binary nonlinear test function test
参数 m N μ σ ${e^2}$ MC 2$ \text{×} $107 1.387375 7.160191 NIPC 3 16 1.387403 7.161575 4.83$ \text{×} $10−5 4 25 1.387402 7.161602 7.43$ \text{×} $10−7 5 36 1.387402 7.161601 7.34$ \text{×} $10−8
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表 4 多元线性回归结果
Table 4. Multiple linear regression results
工况 气动性能参数 变量/mm 权重因子 显著性 WP2 质量流量 $ \tau_{{Z}} $ −24 0 $ \tau_{{Y}} $ −1.3 0 WP4 等熵效率 $ \tau_{{Z}} $ −0.40 0 $ \tau_{{Y}} $ −0.066 0 WP6 总压比 $ \tau_{{Z}} $ −0.78 0 $ \tau_{{Y}} $ 0.037 0
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