Uncertainty analysis of impact of blade thickness deviation on rotor performance
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摘要:
为研究叶片厚度偏差对转子性能的影响，以Rotor37为研究对象，采用非嵌入式混沌多项式作为不确定性量化方法，量化评估了叶片厚度偏差对转子气动性能和流场结构的不确定性影响。研究发现：对于厚度偏差概率分布为对称分布且均值为0的叶片组，其气动性能的平均水平较原型叶片变化不大，气动参数的波动程度则与厚度偏差分布的标准差呈正相关；加工精度较高时转子性能改变量与厚度偏差之间为强线性相关。同时，叶片吸、压力面厚度偏差对转子气动性能产生的影响存在明显差异，叶片吸力面厚度偏差对叶片等熵效率以及质量流量的影响程度更大，而压力面厚度偏差对转子总压比特性影响更明显，两者对转子性能单独造成的不确定性影响在其共同作用时会部分相互抵消。
Abstract:In order to study the impact of blade thickness deviation on rotor performance, the Rotor37 was taken as the research object and non-intrusive polynomial chaos was used as uncertainty quantification method to evaluate the uncertainty impact of blade thickness deviation on rotor aerodynamic performance and flow field structure. The results showed that for the blade group with symmetric probability distribution of thickness deviation and mean value of 0, the average level of aerodynamic performance almost unchanged compared with the prototype blade, and the fluctuation degree of aerodynamic parameters was positively correlated with the standard deviation of the thickness deviation probability distribution. The linear correlation between rotor performance change and thickness deviation was strong when machining accuracy was higher. In the meantime, the impact of thickness deviation of blade suction and pressure surface on rotor aerodynamic performance was obviously different. The suction surface thickness deviation had a greater impact on isentropic efficiency and mass flow rate, while the thickness deviation of pressure surface had a more obvious impact on the total pressure ratio characteristics of rotor, and the uncertain impacts of these two on rotor performance alone were partially cancelled out when they worked together.
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图 3 流场参数的径向分布计算结果与实验数据对比
Figure 3. Comparison between experimental and simulation results of radial distribution of flow field parameters
图 6 厚度改变前后50%叶高截面对比
Figure 6. Comparison of 50% blade height section before and after thickness change
图 8 NIPC模型预测值与CFD计算结果对比
Figure 8. Comparison between NIPC model prediction and CFD calculation results
图 10 气动性能无量纲标准差对比
Figure 10. Comparison of dimensionless standard deviations of aerodynamic performance
图 12 80%叶高截面
${\mu _{{C_p}}}$ 及${\sigma _{\mu , {C_p}}}$ 分布Figure 12. Distribution of
${\mu _{{C_p}}}$ and${\sigma _{\mu , {C_p}}}$ at 80% span
图 13 原型叶片80%叶高截面相对马赫数分布
Figure 13. Relative Mach number distribution at 80% span of prototype blade
图 14 95%叶高截面相对马赫数无量纲标准差分布
Figure 14. Distribution of dimensionless standard deviations of relative Mach number at 95% span
图 15 原型叶片95%叶高截面相对马赫数分布
Figure 15. Relative Mach number distribution at 95% span of prototype blade
图 16 各叶片组气动性能均值曲线
Figure 16. Average aerodynamic performance curve of each blade group
图 17 气动性能无量纲标准差对比
Figure 17. Comparison of dimensionless standard deviations of aerodynamic performance
图 18 总压比无量纲标准差分布对比
Figure 18. Comparison of dimensionless standard deviation distribution of total pressure ratio
图 19 95%叶高截面相对马赫数无量纲标准差分布
Figure 19. Distribution of dimensionless standard deviations of relative Mach number at 95% span
表 1 Rotor37主要设计参数
Table 1. Main design parameters of Rotor37
参数 数值 转速/（r/min） 17188.7 堵塞点流量/（kg/s） 20.93 设计流量/（kg/s） 20.188 设计点总压比 2.106 设计点总温比 1.270 设计点等熵效率 0.877 叶片数 36 展弦比 1.19 
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弦长公称
尺寸/mm精度等级 压气机叶片/mm 边缘 叶中 40～64 1 0.06 0.10 2 0.08 0.13 3 0.10 0.16 4 0.13 0.20
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表 3 不同叶片组厚度偏差的概率分布
Table 3. Probability distribution of thickness deviation of different blade groups
叶片组 吸力面厚度偏差
概率分布压力面厚度偏差
概率分布相关
系数G1 $N （0,{\text{ 0}}{\text{.03}}{{\text{3}}^2}） $ $N （0,{\text{ 0}}{\text{.03}}{{\text{3}}^2}） $ 1 G2 $ N （0,{\text{ 0}}{\text{.05}}{{\text{3}}^2}） $ $ N （0,{\text{ 0}}{\text{.05}}{{\text{3}}^2}） $ 1 G3 $ U （ - 0.16,{\text{ 0}}{\text{.16}}） $ $ U （ - 0.16,{\text{ 0}}{\text{.16}}） $ 1 G4 $ N （0,{\text{ 0}}{\text{.05}}{{\text{3}}^2}） $ $ N （0,{\text{ 0}}{\text{.05}}{{\text{3}}^2}） $ 0 G5 $ N （0,{\text{ 0}}{\text{.05}}{{\text{3}}^2}） $ 0 0 G6 0 $ N （0,{\text{ 0}}{\text{.05}}{{\text{3}}^2}） $ 0
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表 4 正交多项式基与概率分布的对应关系
Table 4. Relation between orthogonal polynomial basis and probability distribution
分布形式 正交多项式基 定义域 高斯分布 Hermite （$ - \infty $,$ + \infty $） 均匀分布 Legendre [a, b] $\varGamma $分布 Laguerre [0,$ + \infty $） $\beta $分布 Jacobi [a, b]
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表 5 非线性函数实验结果
Table 5. Results of non-linear function experiment
抽样方法 ${f_1} （x） $ $ {f}_{2} （{x}_{1},{x}_{2}） $ r ${N_1}$ $\mu $ $\sigma $ ${e_{{\mathrm{ave}}}}$ ${e_{{\mathrm{rms}}}}$ ${N_1}$ $\mu $ $\sigma $ ${e_{{\mathrm{ave}}}}$ ${e_{{\mathrm{rms}}}}$ MCS ${10^7}$ 3.8540 0.1028 1010 $2.487 \times {10^{ - 4}}$ 15.01717 NIPC 4 5 3.8540251 0.102830 $8.326 \times {10^{ - 4}}$ $1.019 \times {10^{ - 3}}$ 25 $ - 2.920 \times {10^{ - 12}}$ 15.017637 $3.914 \times {10^{ - 12}}$ $4.909 \times {10^{ - 12}}$ 5 6 3.8540246 0.102860 $1.834 \times {10^{ - 4}}$ $3.109 \times {10^{ - 4}}$ 36 $ - 1.501 \times {10^{ - 13}}$ 15.017637 $1.218 \times {10^{ - 13}}$ $ 1.474 \times {10^{ - 13}} $ 6 7 3.8540246 0.102859 $1.786 \times {10^{ - 4}}$ $2.720 \times {10^{ - 4}}$ 49 $ - 1.998 \times {10^{ - 13}}$ 15.017637 $9.760 \times {10^{ - 14}}$ $1.138 \times {10^{ - 13}}$
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表 6 相关系数计算结果
Table 6. Calculation result of correlation coefficient
气动性能 G1 G2 G3 $\rho $ r $\rho $ r $\rho $ r 峰值效率工况 等熵效率 −1 − 0.9996521 −1 − 0.9987765 −1 − 0.9984424 总压比 −1 − 0.9999987 −1 − 0.9999985 −1 − 0.9999981 质量流量 −1 − 0.9998717 −1 − 0.9996336 −1 − 0.9995207 近失速工况 等熵效率 1 0.9928828 1 0.9707880 1 0.9710273 总压比 −1 − 0.9998778 −1 − 0.9995079 −1 − 0.9994595 质量流量 −1 − 0.9961136 − 0.9995744 − 0.9828225 − 0.9961844 − 0.9798240
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