旋翼翼型高维多目标气动优化设计

宋超; 周铸; 李伟斌; 罗骁

doi:10.13700/j.bh.1001-5965.2020.0543

旋翼翼型高维多目标气动优化设计

doi: 10.13700/j.bh.1001-5965.2020.0543

中国空气动力研究与发展中心计算空气动力研究所, 绵阳 621000

详细信息

通讯作者:
李伟斌, E-mail: liweibin@nudt.edu.cn

中图分类号: V221.52
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- 被引次数: 0
出版历程
- 收稿日期: 2020-09-23
- 录用日期: 2021-02-05
- 网络出版日期: 2022-01-20

Many-objective aerodynamic optimization design for rotor airfoils

Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China

More Information

Corresponding author: LI Weibin, E-mail: liweibin@nudt.edu.cn

摘要

摘要:
先进旋翼翼型设计是典型的多设计点、多目标优化问题，常规优化方法已无法满足翼型高维多目标优化设计的要求。基于分解的多目标优化算法（MOEA/D），建立了考虑高低速升阻特性、力矩特性、阻力发散特性等的旋翼翼型高维多目标优化设计方法，并采用高精度kriging模型以提高优化设计效率。针对旋翼内段、中段翼型进行了5个设计目标的全局优化设计，采用自组织图映射（SOM）方法对最优Pareto解集进行了聚类分析。典型翼型CFD结果分析表明，中段翼型低速力矩系数幅值减小约50.7%，高速最大升力系数提高约6.5%，最大升阻比提高约7.7%，同时阻力发散特性得到改善，内段翼型同样取得了良好的多目标优化效果。研究表明，MOEA/D算法对高维多目标气动优化设计问题具有很好的适应性，能有效提升旋翼高低速气动性能设计的能力。
- 旋翼翼型 /
- 高维多目标 /
- 气动优化 /
- 基于分解的多目标优化算法(MOEA/D) /
- 自组织图映射(SOM)
Abstract:
The design of advanced rotor airfoils is a typical multi-design-condition and multi-objective optimization problem, and traditional optimization methods cannot meet the requirement of high-dimensional multi-objective optimization design for airfoils. In this paper, a many-objective optimization design method for rotor airfoils is proposed based on the multi-objective evolutionary algorithm based on decomposition (MOEA/D), which considers the lift and drag performance under both low-and high-speed conditions, moment performance and drag divergence performance. The high-precision kriging model is utilized to improve the optimization design efficiency. Five-objective global optimization design for the inner section and middle section of the rotor airfoil is conducted in this paper. The optimal Pareto solution set is clustering analyzed by the self-organizing mapping (SOM) and a representative rotor airfoil is selected and analyzed using the CFD solver. The results show that, for the airfoil in the middle section, the magnitude of the moment coefficient at low speed is reduced by about 50.7%. At high speed, the maximum lift coefficient is improved by about 6.5%, and the maximum lift-to-drag ratio is increased by about 7.7%, and meanwhile the drag divergence performance is enhanced. Evident performance improvement for the inner section airfoil is also achieved. The results show that the MODA/D is suitable for many-objective aerodynamic optimization design problems, and the proposed method can effectively improve the low-and high-speed aerodynamic performance design capability for the rotor airfoil.
- rotor airfoil /
- many-objective /
- aerodynamic optimization /
- multi-objective evolutionary algorithm based on decomposition (MOEA/D) /
- self-organizing mapping (SOM)

HTML全文

图 1 OA309翼型计算网格

Figure 1. Computational grids for OA309 airfoil

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图 2 OA309翼型表面压力系数分布计算值与实验值对比(Ma=0.6, Re=2.5×10⁶, C_l=0.6)

Figure 2. Comparison of pressure coefficient at surface between numerical results and experimental data for OA309 airfoil (Ma=0.6, Re=2.5×10⁶, C_l=0.6)

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图 3 OA309翼型极曲线计算值与实验值对比(Ma=0.6, Re=2.5×10⁶)

Figure 3. Comparison of polars between numerical results and experimental data for OA309 airfoil (Ma=0.6, Re=2.5×10⁶)

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图 4 旋翼翼型优化最优Pareto前沿

Figure 4. Optimal Pareto front for optimization of rotor airfoil

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图 5 最优Pareto前沿SOM可视化结果(9%厚度翼型)

Figure 5. Visualization results of optimal Pareto front using SOM (airfoil with 9% thickness)

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图 6 OA309翼型与优化翼型形状

Figure 6. Geometry shape of OA309 and optimized airfoils

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图 7 OA309翼型与优化翼型升阻特性对比(Ma=0.4, Re=3.2×10⁶)

Figure 7. Comparison of lift drag ratio curves between OA309 and optimized airfoils(Ma=0.4, Re=3.2×10⁶)

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图 8 OA309翼型与优化翼型力矩特性对比(Ma=0.4, Re=3.2×10⁶)

Figure 8. Comparison of moment coefficient curves between OA309 and optimized airfoils(Ma=0.4, Re=3.2×10⁶)

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图 9 OA309翼型与优化翼型升阻特性对比(Ma=0.6, Re=4.8×10⁶)

Figure 9. Comparison of lift drag ratio curves between OA309 and optimized airfoils(Ma=0.6, Re=4.8×10⁶)

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图 10 OA309翼型与优化翼型力矩特性对比(Ma=0.6, Re=4.8×10⁶)

Figure 10. Comparison of moment coefficient curves between OA309 and optimized airfoil(Ma=0.6, Re=4.8×10⁶)

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图 11 OA309翼型与优化翼型阻力系数随马赫数变化特性对比(C_l=0, Re=Ma×8×10⁶)

Figure 11. Comparison of drag coefficient varying with Mach number between OA309 and optimized airfoils(C_l=0, Re=Ma×8×10⁶)

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图 12 最优Pareto前沿SOM可视化结果(12%厚度翼型)

Figure 12. Visualization results of optimal Pareto front using SOM (airfoil with 12% thickness)

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图 13 OA312翼型与优化翼型形状

Figure 13. Geometry shape of OA312 and optimized airfoils

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图 14 OA312翼型与优化翼型升阻比对比(Ma=0.4, Re=3.2×10⁶)

Figure 14. Comparison of lift-to-drag ratio curves between OA312 and optimized airfoils (Ma=0.4, Re=3.2×10⁶)

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图 15 OA312翼型与优化翼型力矩特性对比(Ma=0.4, Re=3.2×10⁶)

Figure 15. Comparison of moment coefficient curves between OA312 and optimized airfoils (Ma=0.4, Re=3.2×10⁶)

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图 16 OA312翼型与优化翼型升阻特性对比(Ma=0.6, Re=4.8×10⁶)

Figure 16. Comparison of lift-to-drag ratio curves between OA312 and optimized airfoils (Ma=0.6, Re=4.8×10⁶)

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图 17 OA312翼型与优化翼型力矩特性对比(Ma=0.6, Re=4.8×10⁶)

Figure 17. Comparison of moment coefficient curves between OA312 and optimized airfoils (Ma=0.6, Re=4.8×10⁶)

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图 18 OA312翼型与优化翼型阻力系数随马赫数变化特性对比(C_l=0, Re=Ma×8×10⁶)

Figure 18. Comparison of drag coefficient varying with Mach number between OA312 and optimized airfoils (C_l=0, Re=Ma×8×10⁶)

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表 1 OA309翼型气动特性随网格量的变化

Table 1. Aerodynamic performance of OA309 airfoil with different amounts of computational grids

网格编号	网格量	C_l	C_d
1	16 714	0.50	0. 011 293
2	33 744	0.50	0. 010 831
3	50 370	0.50	0. 010 758

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表 2 9%厚度旋翼翼型设计目标与约束

Table 2. Design objectives and constraints for a rotor airfoil with 9% thickness

编号	设计状态	设计目标	约束
1	Ma=0.4, Re=3.2×10⁶, C_l=C_lmax	max: C_l
2	Ma=0.4, Re=3.2×10⁶, \|C_m\|=\|C_mmax\|	min: \|C_m\|
3	Ma=0.6, Re=4.8×10⁶, C_l=C_lmax	max: C_l
4	Ma=0.6, Re=4.8×10⁶, C_l=0.6	min: C_d
5	Ma=Mdd0, Re=Ma×8×10⁶，C_l=0	min: C_d	·C_m·(design) < \|C_m\|(OA309)

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表 3 设计状态1的kriging模型交叉验证结果

Table 3. Results of cross validation for kriging model under design condition 1

气动性能	最大预测误差/%	平均预测误差/%
C_l	0.043 7	0.016 1
C_d	0.191 1	0.088 0
C_m	2.596 0	0.697 4

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表 4 Pareto前沿中选取的8组最优目标

Table 4. Eight groups of optimal objectives selected from Pareto front

ID	f₁	f₂	f₃	f₄	f₅
1	-1.006 9	0.485 2	-0.973 2	1.027 5	0.338 7
2	-1.000 7	0.494 3	-1.002 6	0.991 5	0.169 0
3	-1.000 8	0.476 9	-1.004 9	0.992 6	0.128 4
4	-1.009 8	0.478 3	-0.984 1	1.024 3	0.131 0
5	-1.009 0	0.423 1	-0.983 8	1.020 1	0.111 5
6	-1.009 0	0.471 0	-0.984 2	1.021 4	0.108 8
7	-1.007 5	0.489 1	-0.984 7	1.015 4	0.090 7
8	-1.002 8	0.431 9	-0.976 9	1.014 5	0.179 6

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表 5 OA309翼型与优化翼型几何信息

Table 5. Geometry information of OA309 and optimized airfoils

翼型	最大相对厚度	面积
OA309翼型	0.087 9	0.063 76
优化翼型	0.088 4	0.063 12

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表 6 12%厚度旋翼翼型设计目标与约束

Table 6. Design objectives and constraints for a rotor airfoil with 12% thickness

编号	设计状态	设计目标	约束
1	Ma=0.4, Re=3.2×10⁶, C_l=C_lmax	max: C_l
2	Ma=0.4, Re=3.2×10⁶, \|C_m\|=\|C_mmax\|	min: \|C_m\|
3	Ma=0.6, Re=4.8×10⁶, C_l/C_d=(C_l/C_d)_max	max: C_l/C_d
4	Ma=0.72, Re=5.8×10⁶, C_l=0	min: C_d
5	Ma=Mdd0, Re=Ma×8×10⁶，C_l=0	min: C_d	\|C_m\|(design) < \|C_m\|(OA312)

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表 7 Pareto前沿中选取的5组最优目标

Table 7. Five groups of optimal objectives selected from Pareto front

ID	f₁	f₂	f₃	f₄	f₅
1	-1.000 0	0.992 8	-0.998 9	0.958 4	0.963 7
2	-0.992 6	0.992 5	-1.005 4	0.953 6	0.946 3
3	-1.000 1	0.994 3	-0.990 0	0.957 1	0.956 1
4	-0.992 9	0.992 4	-1.002 4	0.954 1	0.997 4
5	-0.992 6	0.994 8	-0.995 7	0.952 9	0.995 7

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表 8 OA312翼型与优化翼型几何信息

Table 8. Geometry information of OA312 and optimized airfoils

翼型	最大相对厚度	面积
OA309翼型	0.119 8	0.084 1
优化翼型	0.119 8	0.083 7

下载: 导出CSV

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