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摘要:
为解决当前翼型优化中广泛使用的冻结湍流黏性假设存在的固有缺陷和基于Spalart-Allmaras（S-A）全湍流伴随中湍流模型对气动力计算精度较差的问题，提出一套新的翼型优化方法，其耦合了全湍流连续伴随求解、剪切应力传递（SST）湍流模型封闭的雷诺平均Navier-Stokes (RANS) 方程、自由变形参数化方法和动网格变形技术。基于所提方法，在气动力系数相较于S-A模型有更高捕捉精度的基础上，对NPL9615翼型以最大升阻比为优化目标，并与冻结湍流黏性假设方法对比。结果表明：所提方法将原有翼型的升阻比提高了16.39%，而冻结湍流黏性假设方法获得最终翼型的升阻比仅提高了原有翼型的9.84%，说明所提方法在最优外形的获取上要领先于冻结湍流黏性假设，并且当翼型周围的湍流动能显著提高时，其优势愈发扩大。
Abstract:A new airfoil optimization method is proposed to address the inherent defects of the frozen eddy viscosity assumption widely used in airfoil optimization and the poor accuracy of aerodynamic calculation based on Spalart-Allmaras (S-A) adjoint turbulence model. This method couples the continuous adjoint turbulence solution, Reynolds-averaged Navier-Stokes（RANS） equations closed by shear stress transfer (SST) turbulence model, and free form deformation method with dynamic grid deformation technology. Based on the proposed method, the maximum lift to drag ratio is taken as the optimization objective for the NPL9615 airfoil, and compared with that of the method of the frozen eddy viscosity assumption. The results show that the optimized airfoil based on continuous SST adjoint turbulence method increases the lift to drag ratio of the original airfoil by 16.39%, while the frozen eddy viscosity assumption method increases the lift to drag ratio of the final airfoil only by 9.84%. This indicates that the proposed method is superior to the frozen eddy viscosity assumption in terms of optimization convergence. When the turbulent kinetic energy increases significantly, the advantage of the proposed model becomes more prominent.
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图 6 NACA0012优化与基础翼型形状对比
Figure 6. Comparison between optimized and baseline airfoil shapes of NACA0012
图 7 NACA0012优化与基础翼型的压力系数曲线对比
Figure 7. Comparison of pressure coefficient curve between optimized and baseline airfoils of NACA0012
图 9 两种优化方法的翼型升阻比变化过程
Figure 9. Variation process of lift to drag ratio of airfoil with two optimization methods
图 10 NPL9615最佳与基础翼型形状对比
Figure 10. Comparison between best and baseline airfoil shapes of NPL9615
图 11 NPL9615基础和最佳翼型的湍流动能
Figure 11. Turbulent kinetic energy contour of baseline and best airfoils of NPL9615
图 12 NPL9615最终与基础翼型形状对比
Figure 12. Comparison between final and baseline airfoil shapes of NPL9615
图 13 NPL9615基础和最终翼型的湍流动能
Figure 13. Turbulent kinetic energy contour of baseline and final airfoils of NPL9615
表 1 收敛性测试的网格参数
Table 1. Mesh parameters of sensitivity test
网格编号 周向网格数目 法向网格数目 增长率 网格总数 G01 140 90 1.20 12188 G02 220 150 1.15 32404 G03 300 210 1.10 61270 
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表 2 G01、G02计算结果与G03的差异
Table 2. Difference of calculation results between G01, G02 and G03
网格编号 $\Delta C_l$/% $\Delta C_d$/% $ \alpha = 4{\text{°}} $ $\alpha = 12{\text{°}} $ $\alpha = 4{\text{°}}$/% $\alpha = 12{\text{°}}$/% G01与G03 −1.6 −2.3 2.7 5.1 G02与G03 −0.2 0.8 0.3 1.1
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