首先分析了几何外形和相对厚度对超声速翼型气动特性的影响。基于遗传算法(GA)和气动力快速工程算法,对于相对厚度为3.5%的多边形翼型进行优化设计,多边形翼型的优化外形趋于四边形,最大厚度点后移到翼型弦线的60%左右,随着迎角或者马赫数增大下翼面会变薄,上翼面变厚,最大厚度点相应稍有后移。对于相对厚度为4%的双圆弧翼型,采用两步优化设计方法,第1步优化结合基于B样条的类别形状函数变换(CST)参数化方法与小波分解方法,实现几何外形的局部控制与光顺处理,并且采用本征正交分解(POD)代理模型降低优化过程中流场计算的工作量;第2步优化采用基于Navier-Stokes方程的最速下降法(SDA),修正第1步优化中代理模型和小波光顺引入的误差;优化设计得到的翼型近似为四边形,其相对厚度最大点后移到翼型弦线的60%~65%处,升阻比可以提高7%。 Firstly, the influence of geometric shape and relative thickness on aerodynamic characteristics of supersonic airfoil is analyzed. Based on genetic algorithm (GA) and aerodynamic fast engineering algorithm, the optimized shape of the polygonal airfoil with a relative thickness of 3.5% is optimized to a quadrilateral shape, and the maximum thickness point is moved to about 60% of the airfoil chord As the angle of attack or Mach increases, the airfoil becomes thinner and the upper airfoil becomes thicker. The maximum thickness point is slightly shifted backward. For the double arc airfoil with a relative thickness of 4%, a two-step optimization design method is adopted. In the first step, a CST parameterization method and a wavelet decomposition method are combined with the B-spline method to realize a part of the geometric shape Control and smoothing, and reduce the workload of flow field calculation during the optimization by using the method of intrinsic orthogonal decomposition (POD). Step 2 Optimize the steepest descent method (SDA) based on the Navier-Stokes equation, Step optimization model and the error introduced by the wavelet smoothing; the optimal design of the resulting airfoil is approximately a quadrilateral, the maximum relative thickness of the airfoil chord moved to 60% to 65%, the lift-drag ratio can be increased by 7% .