提高基于Adjoint方法翼型优化设计鲁棒性的研究  

Improving Robustness of Adjoint-Based Airfoil Optimization Design

作　　者：樊艳红[1] 宋文萍[1] 韩忠华[1] 

机构地区：[1]西北工业大学翼型叶栅空气动力学国防科技重点实验室,陕西西安710072

出　　处：《西北工业大学学报》2013年第4期547-555,共9页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(11272265);国家高技术发展计划(2012AA051301)资助

摘　　要：通过引入线搜索方法,提高了基于Adjoint方法翼型优化设计的鲁棒性。针对给定的目标函数,推导了贴体坐标系下相应的Adjoint方程与边界条件的具体表达形式,以及梯度表达式。通过数值求解流动控制方程和Adjoint方程,得到目标函数对设计变量的梯度,并采用线搜索方法获得最优步长,由此提高了优化算法的鲁棒性。算例表明,线搜索方法可以自动寻找最优的步长,有效解决了传统的取常数步长优化步长选取受到限制,优化结果受步长影响的问题,使得优化方法对步长的依赖性变小,提高了基于Adjoint方法翼型优化设计的鲁棒性。By introducing the line search method, the robustness of the adjoint-based airfoil optimization design method is improved. For a given objective function, its corresponding adjoint equations, boundary conditions and the gradient expression in the body-fitted coordinate system are derived. In the optimization process, the gradient of the objective function is obtained by solving the flow equations and the adjoint equations, and for the traditional ad- joint-based optimization method, a constant step is used, while in this research, the line search method is intro- duced to obtain the optimal step. The results illustrate that it can automatically find the optimal step, and overcome the restriction imposed by the choice of user-defined constant step, which is used in the traditional adjoint-based optimization method, thus improving the robustness of the adjoint-based airfoil optimization design method.

关 键 词：Adjoint方法 气动优化设计 Navier—Stokes方程 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]