Multi-Objective Aerodynamic Shape Optimization of Wide-Mach-Number-Range Airfoil
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摘要: 高超声速飞行器正向着速域更宽、空域更广、航程更远的方向发展.因而对于现代高超声速飞行器的设计而言，除了保证高超声速的性能外，还必须兼顾满足工程需求的亚声速、跨声速、超声速特性.文章对薄翼型在不同速域下的流动机理进行分析，总结了不同速域下翼型增升减阻的设计准则，然后采用RANS方程流动求解器，结合基于Kriging模型的代理优化算法，开展了高超声速飞行器宽速域翼型的优化设计研究.首先，以NACA64A-204翼型为基准翼型，采用线性加权法进行了考虑亚、跨和高超声速气动特性的多轮次宽速域翼型优化设计研究，得到了一种宽速域性能得到改善的新翼型.然后，以优化得到的新翼型为原始翼型，开展多目标优化设计，获得了宽速域翼型两目标和三目标的Pareto最优化解集.Abstract: Hypersonic vehicle is developing towards wider speed range, wider airspace range and longer flight range. Therefore, besides the performance at hypersonic cruise, it must also take into account the sub-transonic and supersonic characteristics in the design of wide-Mach-number-range hypersonic aircraft. In this paper, the flow mechanism of thin airfoil in different speed ranges was analyzed, and the design criteria for increasing lift and reducing drag of airfoil in different speed ranges was summarized. Then, the design optimization of wide-Mach-number-range airfoil was carried out by using RANS equation flow solver and surrogate optimization algorithm based on Kriging model. Firstly, using NACA64A-204 airfoil as the baseline, a new airfoil with improved wide-speed performance was obtained by the linear weighting method. Considering the aerodynamic characteristics of sub-transonic and hypersonic flows, the airfoil was designed after multi-round optimization. Then, taking the optimized new airfoil as the original airfoil, multi-objective optimization design was carried out, and the Pareto optimal solution set of two and three objectives for wide-Mach-number range airfoil was obtained.
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图 2 多目标优化算法NSGA-Ⅱ流程图
Figure 2. Flow chart of multi-objective optimization algorithm NSGA-Ⅱ
图 3 基于Kriging代理模型的NSGA-Ⅱ多目标优化流程图
Figure 3. Multi-objective optimization flow chart of NSGA-Ⅱ based on Kriging surrogate model
图 4 RAE2822亚临界翼型计算网格示意图(417×129)
Figure 4. Computational grids of RAE2822 airfoil(417×129)
图 5 RAE2822翼型计算压力分布与实验值对比
Figure 5. Comparison of pressure coefficient distribution of RAE2822 airfoil
图 6 NPU-Hyper-04翼型不同迎角下的压力云图(Ma=0.3, Re=5.59×107)
Figure 6. Pressure contours of NPU-Hyper-04 airfoil at different angles of attack
图 7 NPU-Hyper-04翼型不同迎角下的压力分布对比
Figure 7. Comparisons of pressure coefficient distributions of NPU-Hyper-04 airfoil at different angles of attack
图 8 四边形翼型与NPU-Hyper-04翼型压力分布对比
Figure 8. Comparsions of pressure coefficient distributions of NPU-Hyper-04 airfoil at different angles
图 9 不同最大厚度位置的四边形翼型示意图
Figure 9. Quadrilateral airfoils with different maximum thickness locations
图 10 不同最大厚度位置的四边形翼型的阻力系数对比(Ma=1.2, Re=8.16×107, α=0°)
Figure 10. Comparisons of drag coefficients of quadrilateral airfoils with different maximum thickness positions (Ma=1.2, Re=8.16×107, α=0°)
图 11 不同最大厚度位置的四边形翼型超声速压力云图对比(Ma=1.2, Re=8.16×107, α=0°)
Figure 11. Comparison of pressure contours at supersonic state (Ma=1.2, Re=8.16×107, α=0°)
图 12 不同翼型高超声速状态下压力云图与压力系数分布对比
Figure 12. Comparisons of pressure contours and pressure coefficients for different airfoils at supersonic state
图 15 高超声速状态计算网格示意图(361×161)
Figure 15. Computational grids at hypersonic state(361×161)
图 17 优化翼型与基准翼型及四边形翼型亚声速压力分布对比
Figure 17. Comparison of pressure coefficient distributions at subsonic state
图 18 优化翼型与基准翼型及四边形翼型高超声速压力分布对比
Figure 18. Comparison of pressure coefficient distributions at hypersonic state
图 19 两目标优化的加点历程
Figure 19. Process of adding new sample points by two-objective optimization
图 21 翼型1与翼型4的亚声速压力分布与跨声速压力云图对比
Figure 21. Comparisons of pressure coefficient distributions and pressure contours of airfoil 1 and 4
图 22 三目标优化的加点历程
Figure 22. Process of adding new sample points by three-objective optimization
图 23 三目标优化得到的Pareto前沿
Figure 23. Pareto front obtained by three-objective optimization
图 25 三目标Pareto解集上3个典型翼型亚声速与高超声速下的压力分布对比
Figure 25. Comparisons of pressure coefficient distributions
图 26 Pareto前沿面上翼型的超声速压力云图对比(Ma=1.2, Re=8.16×107, α=0°)
Figure 26. Comparison of pressure contours at supersonic state
图 27 Pareto前沿面上翼型的高超声速压力云图对比(Ma=6, Re=2.47×107, α=4°)
Figure 27. Comparison of pressure contours at hypersonic state
表 1 RAE2822翼型力系数计算结果与实验值对比
Table 1. Comparisons of force coefficients of RAE2822 airfoil
Cl Cd Cm exp 0.803 0.016 8 -0.099 0 PMNS2D 0.802 0.017 8 -0.090 2 
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表 2 优化翼型与基准翼型气动特性对比
Table 2. Comparison of aerodynamic performance between baseline and optimized airfoil
parameters NACA64A-204 optimized comparison Cl，Ma=0.3 0.850 91 0.826 16 -2.91% Cd，Ma=1.2 0.024 60 0.015 73 -36.06% (Cl/Cd)Ma=6 2.77 5.10 +84.12%
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表 3 优化翼型与四边形翼型气动特性对比
Table 3. Comparison of aerodynamic performance between quadrilateral airfoil and optimized airfoil
parameters quadrilateral optimized comparison Cl，Ma=0.3 0.790 87 0.826 16 +4.46% Cd，Ma=1.2 0.015 09 0.015 73 +4.24% (Cl/Cd)Ma=6 5.25 5.10 -2.86%
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表 4 两目标Pareto解集上的典型翼型及其气动性能对比
Table 4. Typical airfoils on Pareto front and their aerodynamic performance
typical airfoils on pareto front aerodynamic performance 1 
Cl, Ma=0.3=0.829 9 Cd, Ma=1.2=0.016 0 (Cl/Cd)Ma=6.0=5.06 2 
Cl, Ma=0.3=0.859 3 Cd, Ma=1.2=0.018 4 (Cl/Cd)Ma=6.0=4.90 3 
Cl, Ma=0.3=0.870 8 Cd, Ma=1.2=0.021 7 (Cl/Cd)Ma=6.0=4.89 4 
Cl, Ma=0.3=0.875 6 Cd, Ma=1.2=0.024 1 (Cl/Cd)Ma=6.0=4.79
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