气动/几何约束条件下翼型优化设计的最优控制理论方法

An Optimal Control Method for Aerodynamic Design of Airfoil with Multi-Constraint Conditions

基于最优控制理论原理和Navier-Stokes方程,研究了气动/几何约束条件下多设计变量的翼型气动优化设计问题.根据给定的目标函数表达形式,在计算坐标下详细推导了相应的共轭方程及边界条件,以及梯度方程的具体数学形式.通过合理数学变换,得到了物理空间上适应于CFD数值求解的共轭方程直观表达形式,并发展了有效数值求解方法.通过将流动方程、共轭方程、目标函数敏感性导数和优化算法相结合,发展了一种新的气动优化设计方法.相关设计算例表明该方法在设计理论、适用性以及时间费用等方面具有显著特色和优点,且设计结果更为可靠.

Based on the optimal control theory and Navier-Stokes equations, aerodynamic design of airfoil with multi-constraint conditions, such as aerodynamic and geometric constraint conditions, is studied. According to a given problem, the corresponding adjoint equations, boundary conditions and final cost function formulation are derived in the computational space. In order to achieve the requirements of the numerical solution, final formulations in the physical space is also achieved. Numerical methods are developed effectively. By integrating the aspects, such as the flow analysis, the solution of adjoint equations, gradient solution, optimal arithmetic and grid generation etc., an aerodynamic design method involving drag reduction is successfully developed. Testing results show that the method has outstanding merits in the above aspects. It is effective and feasible for aerodynamic design with a large number of design variables. Computational time consumption is less than the conventional aerodynamic design method.