基于控制理论和NS方程的气动设计方法研究

Aerodynamic design method based on control theory and Navier-Stokes equations

研究了基于控制理论和NS方程的气动设计方法 ,针对给定的目标函数表达形式 ,应用该设计理论在计算坐标下详细推导了相应的共轭方程及边界条件具体表达形式 ,以及梯度方程求解表达式 ,通过合理的数学变换 ,导出了共轭方程在笛卡尔坐标系下的直观表达形式 ,发展了有效的共轭方程数值求解方法 ,通过流动控制方程数值求解、共轭方程数值求解、目标函数对设计变量的梯度求解和优化算法等方面的有效结合 ,研究与发展了一种新的气动设计方法 ,以二维机翼气动设计为例 ,成功进行了亚、跨音速情形下的相关设计算例研究 ,研究结果表明应用控制理论和NS方程的气动设计方法在设计理论、适用性以及时间花费等方面都有着很好的特色和优点 。

Based on control theory and Navier-Stokes equations, a new aerodynamic design method is studied. According to the given cost function, the adjoint equations and boundary conditions are derived by using the control theory in computational space. Meanwhile, a corresponding final formulation of variation of cost function for the requirement of numerical solution in physical space is also achieved by doing a reasonable mathematical transformation. The numerical method of solving adjoint equations and final gradient expression have been developed effectively. The optimization design programs for different cases involving in aerodynamic inverse design and drag reduction problem are developed by integrating the following several aspects, such as the flow analysis, solution of adjoint equations, gradient solution, optimal arithmetic and grid generation. Some test results show the present design method is much effective and feasible for aerodynamic design problems with a large number of design variables, and the cost of computational time is less than the former aerodynamic design method.