基于共轭方程法的跨音速机翼气动力优化设计

Optimum Aerodynamic Design of Transonic Wing Based on Adjoint Equations Method

设计状态的机翼气动力特性是设计人员最为关心的指标 ,应用控制理论设计方法进行了有升力约束情形下跨音速机翼阻力优化设计研究 ,根据给定的目标函数推导了相应的共轭方程和边界条件 ,研究了共轭方程的数值求解方法 ,以及计算目标函数对设计变量的敏感性导数时所涉及的度量矩阵变分求解问题 ,研究了流场计算、共轭方程数值求解、敏感性导数求解和拟牛顿优化算法这几个主要方面的有效结合问题 ,发展出了一种跨音速机翼气动力优化设计方法 ,进行了跨音速机翼气动力优化设计研究验证 ,优化后机翼气动力特性有一定程度的改善 ,阻力系数能减少 2 0 %左右 ,而升力系数有所增大 ,说明所发展的设计方法是成功的 。

Aerodynamic characteristics of a wing under given flight conditions are much concerned to designers. This paper describes an aerodynamic characteristics optimization method of the transonic wing based on the control theory for using Euler equations. According to a given cost function, the corresponding adjoint equations and boundary conditions described in physical space are derived. A numerical method has been developed for solving it, and the sensitivity derivative of the cost function with respect to design variables can be obtained by using a grid perturbation method to calculate the variation of the metric matrix, the quasi-Newton algorithm is used and the procedure of optimization has been built by an effective combination of the above several aspects. Some numerical tests have been made for the wing drag minimization design and the lift coefficient improved as possible. The test results show the drag coefficient can reduce about twenty percent if the wing shape is optimized. So the present method is effective arid feasible, and this method may apply to aerodynamic optimization design of much more complex configurations, and the computational cost is inexpensive.