基于三维非结构混合网格的离散伴随优化方法

doi:10.7527/S1000-6893.2013.0383

流体力学与飞行力学

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基于三维非结构混合网格的离散伴随优化方法

李彬¹, 邓有奇¹, 唐静¹, 吕鸿鹰²

1. 中国空气动力研究与发展中心计算空气动力研究所, 四川绵阳 621000;
2. 西安现代控制技术研究所, 陕西西安 710065

收稿日期:2013-05-06 修回日期:2013-09-06 出版日期:2014-03-25 发布日期:2013-09-17
通讯作者: 李彬，Tel.：0816-2463091 E-mail：leebin2008@hotmail.com E-mail:leebin2008@hotmail.com
作者简介:李彬男，博士研究生，助理研究员。主要研究方向：飞行器气动外形优化设计，外挂物分离投放数值模拟。Tel：0816-2463091 E-mail：leebin2008@hotmail.com；邓有奇男，博士，研究员，博士生导师。主要研究方向：飞行器气动总体设计。Tel：0816-2463007 E-mail：cai@cardc.cn

Discrete Adjoint Optimization Method for 3D Unstructured Grid

LI Bin¹, DENG Youqi¹, TANG Jing¹, LV Hongying²

1. Computational Aerodynamic Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China;
2. Xi'an Advanced Control Technology Institute, Xi'an 710065, China

Received:2013-05-06 Revised:2013-09-06 Online:2014-03-25 Published:2013-09-17

摘要/Abstract

摘要：

伴随优化方法在优化过程中不受设计变量个数的限制，有巨大的工程应用前景。基于非结构混合网格技术，采用雷诺平均Navier-Stokes方程、离散伴随优化方法以及自由形面变形（FFD）技术，建立了飞行器气动外形优化设计系统。离散伴随方程采用公式推导的方法直接获取，并运用LU-SGS迭代求解。通过与差分结果进行比较的方式，对通量的雅可比矩阵和目标函数敏感导数开展了确认，并对文中黏性通量项、限制器以及湍流黏性系数的近似处理方法做了分析对比，验证了近似处理方法的合理性和可行性。采用建立的优化系统，完成了ONERA M6机翼在跨声速条件下的减阻优化，并比较了有无容积约束下优化结果的差别。模拟验证结果表明，建立的飞行器气动外形优化设计系统具有较高的可靠性和有效性，可以用于三维飞行器外形的减阻优化。

关键词: Navier-Stokes方程, 非结构网格, 气动外形优化, 离散伴随, LU-SGS方法

Abstract:

Because solving adjoint equation does not depend on the number of design variables, there is no relationship between the calculation amount of iterative optimization and the number of design variables. Based on the unstructured grid, a discrete adjoint solver is developed for a 3D Reynolds-averaged Navier-Stokes solver. Free-form deformation (FFD) technology is implemented to modify the mesh. Discrete adjoint equation can be acquired directly by formula derivation method and solved through LU-SGS iteration. The adjoint code is verified by comparing flux Jacobian and objective function gradient with finite differences. The design system is successfully applied to ONERA M6 wing transonic shape optimization design with the purpose of reducing drag, and the influence of volume constraint is also studied in this paper. It shows that the optimization method established is effective with a better application prospect.

Key words: Navier-Stokes equation, unstructured grid, aerodynamic shape optimization, discrete adjoint, LU-SGS method

中图分类号:

V211.3

李彬, 邓有奇, 唐静, 吕鸿鹰. 基于三维非结构混合网格的离散伴随优化方法[J]. 航空学报, 2014, 35(3): 674-686.

LI Bin, DENG Youqi, TANG Jing, LV Hongying. Discrete Adjoint Optimization Method for 3D Unstructured Grid[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(3): 674-686.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于三维非结构混合网格的离散伴随优化方法

Discrete Adjoint Optimization Method for 3D Unstructured Grid

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