Supersonic and transonic airfoil optimization design based on superimposing thickness on suction surface
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摘要:
为提高轴流压气机叶型优化设计水平，提出了一种基于吸力面叠加厚度分布的参数化造型方法，结合基于Kriging代理模型与差分进化的代理优化方法开发了一套优化设计平台，并将吸力面控制参数作为优化变量，对某跨声与超声叶型进行性能优化。结果表明：基于吸力面叠加厚度分布的叶片造型方法能对叶型进行较好的表达，并成功应用在优化设计平台中。跨声、超声优化叶型在设计点损失分别降低了10.66%与7.4%。分析表明：跨声优化叶型的主要特征是吸力面型线前缘附近型线弯度降低，使得激波强度降低，激波损失与边界层损失降低，同时中后部位置处的负荷增大，扩张通道扩压能力增强；超声叶型优化由于边界层影响更显著，因此还需要更多考虑吸力面扩张通道区域型线；叶型喉部位置与喉部宽度会影响堵塞冲角的变化。
Abstract:To improve the optimization design quality of axial compressor airfoil, the parametric modeling method based on superimposing thickness on suction surface was proposed. The compressor airfoil optimization platform based on Kriging surrogate model and Differential Evolution algorithms was developed, and the control parameters of the suction surface were used as optimization variables to optimize the performance of transonic and supersonic airfoils. The results showed that the parametric modeling method based on superposing thickness distribution on suction surface can express the airfoil well and was successfully applied to the optimization design platform. The loss of optimized transonic and supersonic airfoils at design condition decreased by 10.66 % and 7.4%, respectively. The analysis showed that as for the main characteristics of optimized transonic airfoil, the curvature of the profile near the leading edge of suction surface decreased, and the shock wave intensity decreased. Therefore, the shock wave loss and boundary layer loss decreased, the load at the middle and rear positions increased and the expansion capacity of the expansion channel increased. The optimization of supersonic airfoil should consider the profile of suction surface within the aft expansion passage additionally, because of more significant boundary layer influence. The position and width of throat can affect the chocking incidence angle.
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图 2 吸力面控制点及辅助点
Figure 2. Control points and auxiliary geometry points of suction surface
图 4 CFD与实验结果叶片表面压力系数对比
Figure 4. Comparison of blade pressure coefficient between CFD and experiment result
图 5 叶型A和重构叶型几何对比
Figure 5. Comparison of geometry between baseline A and reconstructive airfoil
图 6 叶型A和重构叶型等熵马赫数分布对比
Figure 6. Comparison of isentropic Mach number between baseline A and reconstructive airfoil
图 9 数据库叶型设计点扩散因子-总压损失特性
Figure 9. Diffusion factor-total pressure loss characteristics of database airfoils at design condition
图 10 叶型 A 与优化叶型气动性能特性对比
Figure 10. Comparison of aerodynamic characteristics between baseline A and optimized airfoils
图 11 叶型 A 与优化叶型几何特性对比
Figure 11. Comparison of aerodynamic characteristics between baseline A and optimized airfoils
图 12 叶型 A 和优化叶型设计工况等熵马赫数对比
Figure 12. Comparison of geometry characteristics between baseline A and optimized airfoils
图 13 叶型 A 和 OPT1 叶栅通道设计工况熵变分布对比
Figure 13. Comparison of entropy change distribution in cascade channel at design condition between baseline A and OPT1
图 14 叶型 B 优化叶型气动性能特性对比
Figure 14. Comparison of aerodynamic characteristics between baseline B and optimized airfoils
图 15 优化叶型与叶型 B 几何特性对比
Figure 15. Comparison of geometry characteristics between baseline B and optimized airfoils
图 16 叶型B和优化叶型设计工况等熵马赫数对比
Figure 16. Comparison of isentropic Mach number at design condition between baseline B and optimized airfoils
图 17 叶型B和OPT2叶栅通道设计工况熵变分布对比
Figure 17. Comparison of entropy change distribution in cascade channel at design condition between baseline B and OPT2
表 1 DFVLR叶型设计参数
Table 1. Design parameters of the DFVLR cascade
设计参数 数值 安装角/（°） 48.51 弦长/mm 90 叶型弯角/（°） 14.9 稠度 1.610 设计进口马赫数 1.09 设计进气角/（°） 58.5 
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表 2 原始叶型设计参数
Table 2. Design parameters of the baseline
参数 叶型A 叶型B 设计进口马赫数 0.95 1.08 设计冲角/（°） −0.81 3.21 安装角/（°） 44.3 59.7 叶型弯角/（°） 21.3 6.7 弦长/mm 291 291 稠度 1.31 1.04 Re/106 5.3 6.02
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表 3 叶型A和重构叶型气动参数对比
Table 3. Comparisons of aerodynamic parameters between baseline A and reconstructive airfoil
参数 叶型A 重构叶型 相对误差/% 设计进口马赫数 0.95 0.95 0 设计冲角/（°） −0.81 −0.81 0 总压损失系数 0.0366 0.0373 1.9 气流折转角/（°） 12.97 13.00 0.2 静压比 1.442 1.442 0
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表 4 叶型优化参数值及其变化范围
Table 4. Optimized parameter values and variation ranges
参数 叶型A 叶型B 原型参数值 变化下限 变化上限 原型参数值 变化下限 变化上限 $ {c_{{\text{b1}}}} $ 0.361 0.3 0.5 0.166 0.08 0.33 ${c_{{\text{b2}}}} $/（°） 4.24 2.29 5.73 2.91 1.15 5.16 $ {c_{{\text{p}}3}} $ 0.456 0.35 0.55 0.529 0.4 0.65 $ {c_{{\text{p}}1}} $ 0.720 0.6 0.78 1.341 0.6 1.4 $ {c_{{\text{p}}2}} $ 0.617 0.5 0.65 0.443 0.35 0.65 $ {c_{{\text{q}}1}} $ 2.0 1 2.1 1 0.75 1.4
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表 5 总压损失系数逐步线性回归结果
Table 5. Stepwise linear regression results of total pressure loss coefficient
叶型 参数 系数 显著性 ${R^2}$ $R_{{\text{adj}}}^2$ 叶型A （常数） 0.033 0 0.873 0.859 $ {c_{{\text{b1}}}} $ 0.033 0 $ {c_{{\text{p}}3}} $ −0.015 0 $ {c_{{\text{b2}}}} $ −0.006 0.007 叶型B （常数） 0.063 0 0.711 0.698 $ {c_{{\text{q}}1}} $ −0.009 0 $ {c_{{\text{p}}3}} $ −0.005 0 $ {c_{{\text{p}}2}} $ −0.003 0.001
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表 6 扩散因子逐步线性回归结果
Table 6. Stepwise linear regression results of diffusion factor
叶型 参数 系数 显著性 ${R^2}$ $R_{{\text{adj}}}^2$ 叶型A （常数） 0.548 0 0.719 0.689 $ {c_{{\text{b1}}}} $ −0.057 0 $ {c_{{\text{p}}3}} $ 0.045 0 叶型B （常数） 0.407 0 0.708 0.685 $ {c_{{\text{b1}}}} $ 0.049 0 $ {c_{{\text{p}}3}} $ 0.019 0 $ {c_{{\text{p1}}}} $ 0.017 0 $ {c_{{\text{b2}}}} $ 0.058 0 $ {c_{{\text{q}}1}} $ 0.008 0.028
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表 7 叶型A与优化叶型的喉部特性与堵塞工况特性对比
Table 7. Comparison of throat and choking condition characteristics between baseline A and optimized airfoils
叶型 喉部位置 喉部宽度 通道扩张比 堵塞工况 堵塞流量/（kg/s） 堵塞冲角/（°） ORI A 0.489 0.610 1.217 43.11 −1.772 OPT1 0.492 0.602 1.241 43.13 −1.791 OPT2 0.487 0.600 1.253 42.90 −1.560 OPT3 0.495 0.611 1.213 43.60 −2.251 OPT4 0.495 0.611 1.214 43.64 −2.292
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表 8 叶型B与优化叶型的喉部特性与堵塞工况特性对比
Table 8. Comparison of throat and choking condition characteristics between baseline B and optimized airfoils
叶型 喉部位置 喉部宽度 通道扩张比 堵塞工况 堵塞流量/（kg/s） 堵塞冲角/（°） ORI B 0.751 0.470 1.051 46.67 2.61 OPT1 0.747 0.468 1.054 46.67 2.61 OPT2 0.751 0.469 1.044 46.87 2.49
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