基于响应面法的跨声速机翼气动优化设计

Optimum Aerodynamic Design of Transonic Wing Based on Response Surface Methodology

响应面法由于其高效、实用的特点,近年来在优化设计领域受到越来越多的重视。本文将响应面法引入到气动数值优化设计中,完成了跨声速机翼单、多目标多约束气动优化设计。该方法采用D优化准则在设计空间内选择一系列样本点,通过求解三维Euler方程进行气动数值试验,来建立二次多项式响应面模型,并在此基础上得到优化的气动外形。以M6机翼为原始机翼的单、多目标多约束优化设计算例表明:采用的响应面法能够较好的捕捉在跨声速流动中目标函数的非线性特征和消除流动中的高频噪声;响应面模型精度满足设计要求,计算误差均小于3%,因而保证了设计方法的实用有效。对于单目标机翼阻力优化设计,阻力系数减少了19%左右。

In recent years the response surface methodology（RSM） has been applied in many design field, because of its high efficiency and practicality. In this paper, the optimization design of the transonic wing at single and multiple design points is performed by RSM. The flow solver is based on 3D Euler equations. The quadratic polynomials are employed to construct RS model and the set of candidate design points in design space is selected to satisfy D-optimality. The optimum shape is obtained based on the RS model. A M6 wing is chosen as the base wing. The design results indicate that the RSM can capture the nonlinear behavior of the objective function and smooth out high-frequency noises in transonic regime. The model fitting quality is satisfied to the design. The fitting errors are less than three percent. These features enable the method to be utilizable and valid. The drag coefficient can be reduced about 19 percent in the single design point for wing drag design.