三维机翼气动结构多学科优化方法
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摘要
采用Euler方程、连续伴随优化方法、自由形面变形技术(free-form deformation,FFD)以及一种四边形线性壳单元模型对三维机翼气动结构多学科优化方法开展了研究。目标函数为阻力系数和机翼翼盒结构质量的加权和,设计变量为FFD控制点以及10段蒙皮的厚度。气动方面升阻力系数对设计变量的梯度由伴随方法求得,结构方面翼盒质量对于蒙皮厚度的梯度可直接计算,应力的梯度采用有限差分方法获得。对跨声速大展弦比机翼进行气动结构多学科优化,并将该计算结果与机翼气动单学科优化设计后的静气弹计算结果进行对比,结果表明:该气动结构多学科优化方法能够在满足约束条件下,实现阻力系数和翼盒质量同时降低,保证优化结果的合理性。
An aero-structural multi-disciplinary optimization method for 3 D wing was developed using Euler equations,continuous adjoint method,FFD(free-form deformation)strategy and a linear quadrilateral shell model.The objective function is the weighted sum of drag coefficient and the structural weight of the wing box.The design variables include the control points of FFD volume and the thicknesses of ten skin segments.The gradients of lift coefficient and drag coefficient with respect to design variables were adopted by continuous adjoint method,the gradients of wing box weight were acquired directly,and the gradients of the stress were obtained with finite difference method.The aero-structural multi-disciplinary optimization method was applied to a high aspect ratio wing in transonic regime,and a comparison between the results from aero-structural analysis of single-disciplinary optimization and aero-structural optimization was presented.It showed that the drag coefficient and the weight can decrease simultaneously through aero-structural optimization while the constraints were satisfied to keep the results reasonable.
An aero-structural multi-disciplinary optimization method for 3 D wing was developed using Euler equations,continuous adjoint method,FFD(free-form deformation)strategy and a linear quadrilateral shell model.The objective function is the weighted sum of drag coefficient and the structural weight of the wing box.The design variables include the control points of FFD volume and the thicknesses of ten skin segments.The gradients of lift coefficient and drag coefficient with respect to design variables were adopted by continuous adjoint method,the gradients of wing box weight were acquired directly,and the gradients of the stress were obtained with finite difference method.The aero-structural multi-disciplinary optimization method was applied to a high aspect ratio wing in transonic regime,and a comparison between the results from aero-structural analysis of single-disciplinary optimization and aero-structural optimization was presented.It showed that the drag coefficient and the weight can decrease simultaneously through aero-structural optimization while the constraints were satisfied to keep the results reasonable.
引文
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[23]左英桃,傅林,高正红,等.机翼/机身/短舱/挂架外形气动优化设计方法[J].航空动力学报,2013,28(9):2009-2015.ZUO Yingtao,FU Lin,GAO Zhenghong,et al.Research on aerodynamic optimization design of wing-body-nacellepylon configuration[J].Journal of Aerospace Power,2013,28(9):2009-2015.(in Chinese)
[24]熊俊涛,乔志德,杨旭东,等.一种计及静气动弹性变形影响的跨声速机翼气动优化设计方法研究[J].空气动力学学报,2009,27(2):154-159.XIONG Juntao,QIAO Zhide,YANG Xudong,et al.An aerodynamic shape optimization of transonic wing design method for aeroelastic system[J].Acta Aerodynamic Sinica,2009,27(2):154-159.(in Chinese)
[25]VASSBERG J,TINOCO E,MANI M,et al.Summary of the third AIAA CFD drag prediction workshop[R].AIAA-2007-260,2007.
[26]OLAF S,KLAUS G,GEORGE K,et al.PARDISO 5.0.0solver project[EB/OL].[2017-01-10].Https://pardisoproject.org/.
[27]GRUTTMANN F,WAGNER W.A linear quadrilateral shell element with fast stiffness computation[J].Computer Methods in Applied Mechanics and Engineering,2005,194(39):4279-4300.
[28]DUCHON J.Splines minimizing rotation-invariant seminorms in Sobolev spaces[M].Berlin:Springer,1977.
[2]REUTHER J,JAMESON A,FARMER J,et al.Aerodynamic shape optimization of complex aircraft configurations via an adjoint formulation[R].AIAA 96-0094,1996.
[3]KIM S,ALONSO J J,JAMESON A.A gradient accuracy study for the adjoint-based Navier-Stokes design method[R].AIAA 99-0299,1999.
[4]BAYSAL O,ELESHAKY M E.Aerodynamic sensitivity analysis methods for the compressible Euler equations[J].Journal of Fluids Engineering,1991,113(4):681-688.
[5]BURGREEN G W,BAYSAL O.Three-dimensional aerodynamic shape optimization of wings using sensitivity analysis[R].AIAA 94-0094,1994.
[6]ANDERSON W K,VENKATAKRISHNAN V.Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation[J].Computers and Fluids,1999,28(4):443-480.
[7]MAVRIPLIS D J.Formulation and multigrid solution of the discrete adjoint problem on unstructured meshes[R].AIAA-2005-319,2005.
[8]MAVRIPLIS D J.A discrete adjoint-based approach for optimization problems on three-dimensional unstructured meshes[R].AIAA-2006-0050,2006.
[9]PALACIOS F,COLONNO M R,ARANAKE A C,et al.Stanford university unstructured(SU2):an open-source integrated computational environment for multi-physics simulation and design[R].AIAA-2013-0287,2013.
[10]唐智礼.约束最优控制理论及其在气动优化中的应用[J].力学学报,2007,39(2):273-277.TANG Zhili.Constrained optimum control theory:application to aerodynamic design[J].Chinese Journal of Theoretical and Applied Mechanics,2007,39(2):273-277.(in Chinese)
[11]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.ZUO Yingtao,GAO Zhenghong,HE Jun.Aerodynamic design method based on N-S equations and discrete adjoint approach[J].Acta Aerodynamica Sinica,2010,28(5):509-512.(in Chinese)
[12]李彬,邓有奇,唐静,等.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,et al.Discrete adjoint method for 3Dunstructured grid[J].Acta Aeronautica et Astronautica Sinica,2014,35(3):674-686.(in Chinese)
[13]KIM Y,LEE D H,KIM Y,et al.Multidisciplinary design optimization of supersonic fighter wing using response surface methodology[R].AIAA-2002-5408,2002.
[14]LIEM R P,MADER C A,LEE E,et al.Aerostructural design optimization of a 100-passenger regional jet with surrogate-based mission analysis[R].AIAA-2013-4372,2013.
[15]MARTINS J R R A,LAMBE A B.Multidisciplinary design optimization:a survey of architectures[J].AIAA Journal,2013,51(9):2049-2075.
[16]KENWAY G K W,MARTINS J R R A.Multipoint highfidelity aerostructural optimization of a transport aircraft configuration[J].Journal of Aircraft,2014,52(1):144-160.
[17]KENWAY G K W,KENNEDY G J,MARTINS J R R A.Scalable parallel approach for high-fidelity steady-state aeroelastic analysis and adjoint derivative computations[J].AIAA Journal,2014,52(5):935-951.
[18]朱华光,刘莉,龙腾,等.机翼气动结构多学科设计优化研究[J].北京理工大学学报,2011,31(10):1147-1152.ZHU Huaguang,LIU Li,LONG Teng,et al.Research of wings aero-structural multidisciplinary design optimization[J].Transactions of Beijing Institute of Technology,2011,31(10):1147-1152.(in Chinese)
[19]粟华,谷良贤,龚春林.基于高拟真度模型的高超声速飞行器静气动弹性优化[J].航空动力学报,2013,28(8):1836-1842.SU Hua,GU Liangxian,GONG Chunlin.Static aeroelastic optimization of hypersonic aircraft based on high-fidelity model[J].Journal of Aerospace Power,2013,28(8):1836-1842.(in Chinese)
[20]车竞,唐硕,王文正,等.一种新的蚁群算法及其在飞行器设计中的应用[J].航空动力学报,2009,24(2):262-268.CHE Jing,TANG Shuo,WANG Wenzheng,et al.New ant colony algorithm and its application on optimization design of flight vehicle[J].Journal of Aerospace Power,2009,24(2):262-268.(in Chinese)
[21]左英桃,王晓鹏,陈云,等.一种高效的CFD/CSD耦合飞行器多学科优化设计方法[J].航空动力学报,2014,29(12):2898-2904.ZUO Yingtao,WANG Xiaopeng,CHEN Yun,et al.An efficient method for multidisciplinary design optimization of aircraft based on CFD/CSD coupling[J].Journal of Aerospace Power,2014,29(12):2898-2904.(in Chinese)
[22]张校,陈平剑,左英桃.CFD/CSD耦合飞行器多学科优化设计新方法[J].气体物理,2016,1(2):47-54.ZHANG Xiao,CHEN Pingjian,ZUO Yingtao.A novel multidisciplinary design optimization of aircraft based on CFD/CSD coupling[J].Physics of Gases,2016,1(2):47-54.(in Chinese)
[23]左英桃,傅林,高正红,等.机翼/机身/短舱/挂架外形气动优化设计方法[J].航空动力学报,2013,28(9):2009-2015.ZUO Yingtao,FU Lin,GAO Zhenghong,et al.Research on aerodynamic optimization design of wing-body-nacellepylon configuration[J].Journal of Aerospace Power,2013,28(9):2009-2015.(in Chinese)
[24]熊俊涛,乔志德,杨旭东,等.一种计及静气动弹性变形影响的跨声速机翼气动优化设计方法研究[J].空气动力学学报,2009,27(2):154-159.XIONG Juntao,QIAO Zhide,YANG Xudong,et al.An aerodynamic shape optimization of transonic wing design method for aeroelastic system[J].Acta Aerodynamic Sinica,2009,27(2):154-159.(in Chinese)
[25]VASSBERG J,TINOCO E,MANI M,et al.Summary of the third AIAA CFD drag prediction workshop[R].AIAA-2007-260,2007.
[26]OLAF S,KLAUS G,GEORGE K,et al.PARDISO 5.0.0solver project[EB/OL].[2017-01-10].Https://pardisoproject.org/.
[27]GRUTTMANN F,WAGNER W.A linear quadrilateral shell element with fast stiffness computation[J].Computer Methods in Applied Mechanics and Engineering,2005,194(39):4279-4300.
[28]DUCHON J.Splines minimizing rotation-invariant seminorms in Sobolev spaces[M].Berlin:Springer,1977.