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

本期目录 | 过刊浏览 | 高级检索

前一篇 | 后一篇

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.

参考文献

[1] Elliott J, Peraire J. Practical three-dimensional aerodynamic design and optimization using unstructured grids[J]. AIAA Journal, 1997, 35(9): 1479-1485.

[2] Nielsen E J, Anderson W K. Implementation of a parallel framework for aerodynamic design optimization on unstructured meshes[C]//Proceedings of Parallel Computational Fluid Dynamics, 1999.

[3] Nielsen E J, Anderson W K. Recent improvements in aerodynamic design optimization on unstructured meshes[J]. AIAA Journal, 2002, 40(6): 1155-1163.

[4] Nielsen E J, Kleb B. Efficient construction of discrete adjoint operators on unstructured grids by using complex variables, AIAA-2005-0324[R]. Reston: AIAA, 2005.

[5] Mavriplis D J. Formulation and multigrid solution of the discrete adjoint for optimization problems on unstructured meshes, AIAA-2005-0319[R]. Reston: AIAA, 2005.

[6] Mavriplis D J. A discrete adjoint-based approach for optimization problems on three-dimensional unstructured meshes, AIAA-2006-0050[R]. Reston: AIAA, 2006.

[7] Brezillon J, Dwight R P. Aerodynamic shape optimization using the discrete adjoint of the Navier-Stokes equations: applications towards complex 3D configurations[C]//KATnet Ⅱ Conference on Key Aerodynamic Technologies, 2009.

[8] Dwight R P, Brezillon J. Effect of various approximations of the discrete adjoint on gradient-based optimization, AIAA-2006-0690[R]. Reston: AIAA, 2006.

[9] Kim H J, Nakahashi K. Discrete adjoint method for unstructured Navier-Stokes solver, AIAA-2005-0449[R]. Reston: AIAA, 2005.

[10] Carpentieri G, Koren B. Development of the discrete adjoint for a 3D unstructured Euler solver, AIAA-2007-3954[R]. Reston: AIAA, 2007.

[11] Giles M B, Duta M C. Algorithm developments for discrete adjoint methods[J]. AIAA Journal, 2003, 41(2): 198-205.

[12] Lee B J, Kim C. Strategies for robust convergence characteristics of discrete adjoint method[J]. Computational Fluid Dynamics, 2009, 33: 633-639.

[13] Huang Y, Chen Z B, Liu G. Aerodynamic design method based on N-S equations and discrete adjoint approach[J]. Acta Aerodynamica Sinica, 1999, 17(4): 413-433. (in Chinese) 黄勇, 陈作斌, 刘刚. 基于伴随方程的翼型数值优化设计方法研究[J]. 空气动力学学报, 1999, 17(4): 413-433.

[14] Zhou Z, Chen Z B. Aerodynamic design method based on N-S equations and discrete adjoint approach[J]. Acta Aerodynamica Sinica, 2002, 20(2): 141-149. (in Chinese) 周铸, 陈作斌. 基于N-S方程的翼型气动优化设计[J]. 空气动力学学报, 2002, 20(2): 141-149.

[15] Xiong J T, Qiao Z D, Yang X D, et al. Optimum aerodynamic design of transonic wing based on viscous adjoint method[J]. Acta Aeronautica et Astronautica Sinica, 2007, 28(2): 281-285. (in Chinese) 熊俊涛, 乔志德, 杨旭东, 等. 基于黏性伴随方法的跨声速机翼气动优化设计[J]. 航空学报, 2007, 28(2): 281-285.

[16] Du L, Ning F F. Aerodynamic inverse design method for low Mach number airfoils[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(7): 1180-1188.(in Chinese) 杜磊, 宁方飞. 低速叶型气动反问题设计方法[J]. 航空学报, 2011, 32(7): 1180-1188.

[17] Du L, Ning F F. An approximate method for viscous inverse design based on adjoint equations[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(4): 597-606.(in Chinese) 杜磊, 宁方飞. 一种基于共轭方程法求解黏性反问题的简化方法[J]. 航空学报, 2012, 33(4): 597-606.

[18] Zuo Y T, Gao Z Z, Xia L. Aerodynamic design based on Euler equations and discrete adjoint approach[J]. Chinese Journal of Applied Mechanics, 2009, 26(1): 22-26. (in Chinese) 左英桃, 高正红, 夏露. 基于Euler 方程和离散共轭方法的气动外形优化设计[J]. 应用力学学报, 2009, 26(1): 22-26.

[19] Zuo Y T, Gao Z H, Zhan H. Aerodynamic design method based on N-S equations and discrete adjoint approach[J]. Acta Aerodynamica Sinica, 2009, 27(1): 67-72. (in Chinese) 左英桃, 高正红, 詹浩. 基于N-S方程和离散共轭方法的气动设计方法研究[J]. 空气动力学学报, 2009, 27(1): 67-72.

[20] Zuo Y T, Gao Z H, He J. Aerodynamic design method based on N-S equations and discrete adjoint approach[J]. Acta Aerodynamica Sinica, 2010, 28(5): 509-512. (in Chinese) 左英桃, 高正红, 何俊. 基于N-S 方程和离散共轭方法的气动外形设计[J]. 空气动力学学报, 2010, 28(5): 509-512.

[21] Wu W H, Fan Z L, Qin N. Adjoint operator method based aerodynamics optimization of airliner[C]//Computational Technologies for Commercial Aircraft and High Resolution, 2010: 309-317. (in Chinese) 吴文华, 范召林, 覃宁.基于伴随算子的大飞机布局多参数高精度优化[C]//大型客机与高精度计算方法学术研讨会, 2010: 309-317.

[22] Ma X Y, Fan Z L, Wu W H, et al. Aerodynamic shape optimization for wing based on NURBS[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(9): 1616-1621. (in Chinese) 马晓永, 范召林, 吴文华, 等. 基于NURBS方法的机翼气动外形优化[J]. 航空学报, 2011, 32(9): 1616-1621.

[23] Liu X Q, Qin N. Design of transonic wing based on adjoint method[C]//Computational Technologies for Commercial Aircraft and High Resolution, 2010: 256-265. (in Chinese) 刘学强, 覃宁. 基于伴随算子的跨音速机翼优化设计[C]//大型客机与高精度计算方法学术研讨会, 2010: 256-265.

[24] Guan J. Aerodynamic shape optimization for 2D airfoil based on adjoint equations[D]. Nanjing: College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 2011. (in Chinese) 关键. 基于伴随方程的二维翼型气动外形优化设计[D]. 南京: 南京航空航天大学航空宇航学院, 2011.

[25] Sharov D, Nakahashi K. Reordering of 3D hybrid unstrucrured grids for vectorized LU-SGS Navier-Stokes computations, AIAA-1998-0614[R]. Reston: AIAA, 1998.

[26] Venkatakrishnan V. On the accuracy of limiters and convergence to steady state solutions, AIAA-1993-0880[R]. Reston: AIAA, 1993.

[27] Van Leer B. Flux vector splitting for the Euler equations[J]. Lecture Notes in Physics, 1982, 170: 507-512.

[28] Spalart P R, Allmaras S R. A one-equation turbulence model for aerodynamic flows, AIAA-1992-0439[R]. Reston: AIAA, 1992.

[29] Moigne A L, Qin N. Variable-fidelity aerodynamic optimization for turbulent flows using a discrete adjoint formulation, AIAA-2004-1234[R]. Reston: AIAA, 2004.

[30] Amoiralis E I, Nikolos I K. Freeform deformation versus B-spline representation in inverse airfoil design[J]. Journal of Computing and Information Science in Engineering, 2008, 8(2): 13.

[31] Lamousin H J, Waggenspack W N. NURBS-based free-form deformations [J]. Computer Graphics and Applications, 1994, 14(6): 59-65.

E-mail：hkxb@buaa.edu.cn

关于我们

期刊社服务

专业学科

封面文章

友情链接

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

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	杨体浩, 王一雯, 王雨桐, 史亚云, 周铸. 基于离散伴随的层流翼优化设计方法[J]. 航空学报, 2022, 43(12): 126132-126132.
[2]	杨鲤铭, 吴杰, 董昊, 杜银杰. 基于速度空间非结构网格和守恒修正的改进离散速度方法[J]. 航空学报, 2022, 43(12): 627033-627033.
[3]	王一雯, 兰夏毓, 史亚云, 华俊, 白俊强, 周铸. 考虑吸气影响的层流翼型梯度优化设计[J]. 航空学报, 2022, 43(11): 527323-527323.
[4]	陈坚强, 吴晓军, 张健, 李彬, 贾洪印, 周乃春. FlowStar:国家数值风洞(NNW)工程非结构通用CFD软件[J]. 航空学报, 2021, 42(9): 625739-625739.
[5]	任玉新, 王乾, 潘建华, 章雨思, 黄乾旻. 构建非结构网格高精度有限体积方法的新途径[J]. 航空学报, 2021, 42(9): 625783-625783.
[6]	刘君, 魏雁昕, 陈洁. 基于非结构网格有限差分法的扎染算法[J]. 航空学报, 2021, 42(7): 124557-124557.
[7]	闫重阳, 张宇飞, 陈海昕. 基于离散伴随的流场反演在湍流模拟中的应用[J]. 航空学报, 2021, 42(4): 524695-524695.
[8]	刘峰博, 蒋城, 马涂亮, 梁益华. 伴随压力分布反设计方法在大型客机气动优化中的初步探索[J]. 航空学报, 2020, 41(5): 623372-623372.
[9]	周琳, 黄江涛, 高正红. 基于离散伴随方程的三维雷达散射截面几何敏感度计算[J]. 航空学报, 2020, 41(5): 623361-623361.
[10]	刘君, 陈洁, 韩芳. 基于离散等价方程的非结构网格有限差分法[J]. 航空学报, 2020, 41(1): 123248-123248.
[11]	黄江涛, 张绎典, 高正红, 余婧, 周铸, 余雷. 基于流场/声爆耦合伴随方程的超声速公务机声爆优化[J]. 航空学报, 2019, 40(5): 122505-122505.
[12]	黄江涛, 高正红, 余婧, 郑传宇, 周铸. 大型民用飞机气动外形典型综合设计方法[J]. 航空学报, 2019, 40(2): 522369-522369.
[13]	谭伟伟, 颜洪, 聂智军, 马涂亮, 梁益华. 大型客机涡扇发动机动力特性模拟[J]. 航空学报, 2019, 40(1): 522428-522428.
[14]	郭中州, 何志强, 赵文文, 陈伟芳. 高效非结构网格变形与流场插值方法[J]. 航空学报, 2018, 39(12): 122411-122411.
[15]	李立, 白俊强, 郭同彪, 陈颂. 考虑放宽静稳定度的民用客机气动优化设计[J]. 航空学报, 2017, 38(9): 121112-121112.