Inverse design method of blade profile based on particle swarm optimization and Gappy POD method
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摘要:
为了解决基于Gappy POD（本征正交分解）的反设计方法鲁棒性差及约束条件添加难等问题，发展了一种结合粒子群优化算法与Gappy POD的反设计方法，并针对由过约束状态主导的精度降低，提出了基于CFD计算的压力面修正迭代方法以使反设计脱离过约束状态。对亚/跨声速压气机叶型的验证表明：该方法能够在最大厚度约束下实现高精度反设计，且较正向优化设计方法计算耗时显著降低。结合关键流动区域控制的改型设计结果表明：两种叶型整体攻角性能较原始叶型均显著提升，设计攻角下叶型静压升基本不变，总压损失分别降低9.53%和12.7%，同时亚声速叶型的可用攻角范围不变而跨声速叶型的可用攻角范围拓宽了14.3%。
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关键词:
- 压气机叶型 /
- 反设计方法 /
- 粒子群优化 /
- Gappy POD（本征正交分解） /
- 改型设计
Abstract:To solve the problems of poor robustness and difficulty in adding constraints of the inverse design method based on Gappy POD （proper orthogonal decomposition）, an inverse design method combining particle swarm optimization algorithm and Gappy POD was developed. For reducing the accuracy dominated by the overconstrained state, a pressure surface correction iteration method based on CFD calculation was proposed to make the inverse design out of the overconstrained state. The verification of subsonic and transonic compressor blade profiles showed that this method can achieve high-precision inverse design under the maximum thickness constraint, and the calculation time was shorter than the forward optimization design method. The modified design results combined with the control of key flow areas showed that the overall incidence angle performance of the two blade profiles were significantly improved compared with the original blade profiles. The static pressure rise of the blade profiles was basically unchanged at the design incidence angle, and the total pressure loss was reduced by 9.53% and 12.7%, respectively. At the same time, the available incidence angle range of subsonic blade profile remained unchanged, while that of transonic blade profile was expanded by 14.3%.
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图 3 不同网格节点数下叶型性能参数对比
Figure 3. Comparison of blade performance parameters under different numbers of mesh nodes
图 4 sub_blade表面等熵马赫数实验值与数值计算对比
Figure 4. Comparison between experimental and numerical values of surface isentropic Mach number for sub_blade
图 5 tran_blade表面压力系数的实验值与数值计算对比
Figure 5. Comparison between experimental and numerical values of surface isentropic Mach number for tran_blade
图 7 不同约束条件下几何偏差平均值变化
Figure 7. Changes in average geometric deviation under different constraint conditions
图 8 不同约束条件下几何偏差分布图
Figure 8. Geometric deviation distribution map under different constraint conditions
图 10 不同攻角下的等熵马赫数梯度曲线
Figure 10. Isentropic Mach number gradient curves at different incidence angles
图 11 原始、目标、反设计等熵马赫数曲线对比（sub_blade）
Figure 11. Comparison of the original, target, and inverse design isentropic Mach number curves （sub_blade）
图 12 原始叶型与反设计叶型对比（sub_blade）
Figure 12. Comparison between the original and inverse design blade profiles （sub_blade）
图 13 原始叶型与反设计叶型性能对比（sub_blade）
Figure 13. Performance comparison between the original and inverse design blade profiles （sub_blade）
图 14 原始、目标、反设计等熵马赫数曲线对比（tran_blade）
Figure 14. Comparison of the original, target, and inverse design isentropic Mach number curves （tran_blade）
图 15 原始叶型与反设计叶型对比（tran_blade）
Figure 15. Comparison between the original and inverse design blade profiles （tran_blade）
图 16 原始叶型与反设计叶型性能对比（tran_blade）
Figure 16. Performance comparison between the original and inverse design blade profiles （tran_blade）
图 17 亚/跨声速叶型反设计迭代过程的气动参数偏差变化
Figure 17. Variation of aerodynamic parameter deviation in the iterative process of subsonic/transonic blade profiles inverse design
表 1 sub_blade与tran_blade的主要设计参数
Table 1. Main design parameters of sub_blade and tran_blade
设计参数 sub_blade tran_blade 叶栅稠度 1.82 1.61 进口气流角/（°） 132 148.5 进口马赫数 0.67 0.92 叶型安装角/（°） 112.5 138.51 最大相对厚度 0.055 0.05 叶型弯角/（°） 48 14.9 
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表 2 不同设计方法计算时间对比
Table 2. Comparison of calculation time for different design methods
设计方法 计算时间/min 约束 无约束GPOD_PSO ～1.5 × 约束GPOD_PSO ～60 √ 正向优化设计方法 ～120 √
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