大长细比导弹的气动弹性降阶模型
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摘要
对于大长细比导弹,需要在设计阶段准确计算气动弹性/气动伺服弹性,但其复杂的气动力给计算带来困难,因此气动力降阶模型是突破大长细比导弹跨音速气动弹性分析与控制瓶颈的关键技术.虽然气动力模型降阶方法已在预测二维机翼结构的气动弹性方面取得重要进展,但几乎未见关于全机模型的气动力降阶模型研究报道.本文基于递归Wiener模型的气动力降阶方法,利用CFD计算的气动力作为模型辨识数据,用鲁棒子空间和Levenberg-Marquardt算法辨识降阶模型参数,建立了大长细比导弹气动力降阶模型.在此基础上与大长细比导弹有限元模型相结合,构造出气动弹性降阶模型,并在数值仿真中测试气动弹性降阶模型在不同马赫数下的适用性.数值仿真结果表明,该气动弹性降阶模型能够精确预测导弹模型在不同飞行条件下的非定常气动力和导弹模型的气动弹性频率响应特性.
In the design phase of slender missiles, it is essential to predict their aeroelastic/aeroservoelastic behaviors accurately. The accurate prediction, however, is faced with the tough problem of CFD for the aerodynamic loads on slender missiles. How to establish the aerodynamic models of reduced-order is the key technology to break through the bottleneck in the transonic aeroelastic analysis and control of the slender missiles. Although the aerodynamic reducedorder methods have made important progress in predicting the aerodynamic loads and aeroelastic response of the twodimensional airfoil, still there are few research reports about the aerodynamic reduced-order models of the more complex airplane models. In this study, the recursive Wiener model of reduced-order is constructed for the aerodynamic loads on a slender missile according to the training data of CFD, while the parameters of the model can be estimated via the predictorbased subspace identification algorithm and Levenberg-Marquardt algorithm. The recursive Wiener model of reducedorder can be integrated with the finite element model of the missile structure so that the aeroelastic/aeroservoelastic model of reduced-order is established for the missile. The accuracy of the aeroelastic models of reduced-order is tested under different Mach number in the numerical simulations. The numerical simulations show that the aeroelastic modelsof reduced-order can accurately predict the unsteady aerodynamic loads and the aeroservoelastic frequency response of the slender missile model under different flight conditions.
In the design phase of slender missiles, it is essential to predict their aeroelastic/aeroservoelastic behaviors accurately. The accurate prediction, however, is faced with the tough problem of CFD for the aerodynamic loads on slender missiles. How to establish the aerodynamic models of reduced-order is the key technology to break through the bottleneck in the transonic aeroelastic analysis and control of the slender missiles. Although the aerodynamic reducedorder methods have made important progress in predicting the aerodynamic loads and aeroelastic response of the twodimensional airfoil, still there are few research reports about the aerodynamic reduced-order models of the more complex airplane models. In this study, the recursive Wiener model of reduced-order is constructed for the aerodynamic loads on a slender missile according to the training data of CFD, while the parameters of the model can be estimated via the predictorbased subspace identification algorithm and Levenberg-Marquardt algorithm. The recursive Wiener model of reducedorder can be integrated with the finite element model of the missile structure so that the aeroelastic/aeroservoelastic model of reduced-order is established for the missile. The accuracy of the aeroelastic models of reduced-order is tested under different Mach number in the numerical simulations. The numerical simulations show that the aeroelastic modelsof reduced-order can accurately predict the unsteady aerodynamic loads and the aeroservoelastic frequency response of the slender missile model under different flight conditions.
引文
1胡海岩,赵永辉,黄锐.飞机结构气动弹性分析与控制研究.力学学报,2016,48(1):1-27(Hu Haiyan,Zhao Yonghui,Huang Rui.Studies on aeroelastic analysis and control of aircraft structures.Chinese Journal of Theoretical and Applied Mechanics,2016,48(1):1-27(in Chinese))
2陈桂彬,邹丛青,杨超.气动弹性设计基础.北京:北京航空航天大学出版社,2004(Chen Guibin,Zou Congqing,Yang Chao.Fundamentals of Aeroelastic Design.Beijing:Press of Beijing University of Aeronautics and Astronautics,2004(in Chinese))
3 Bismarck-Nasr MN.Kernel function occurring in subsonic unsteady potential flow.AIAA Journal,1991,29(6):878-879
4 Rodden WP,Taylor PF,Mc Intosh SC.Further refinement of the subsonic doublet-lattice method.Journal of Aircraft,1998,35(5):720-727
5 Liu F,Cai J,Zhu Y,et al.Calculation of wing flutter by a coupled fluid-structure method.Journal of Aircraft,2001,38(2):334-342
6 Marques FD,Anderson J.Identification and prediction of unsteady transonic aerodynamic loads by multi-layer functionals.Journal of Fluids and Structures,2001,15(1):83-106
7 Hall KC,Thomas JP,Dowell EH.Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows.AIAA Journal,2000,38(10):1853-1862
8 Xie D,Xu M,Dowell EH.Proper orthogonal decomposition reduced-order model for nonlinear aeroelastic oscillations.AIAAJournal,2014,52(2):229-241
9 Liu Haojie,Hu Haiyan,Zhao Yonghui,et al.Efficient reduced-order modeling of unsteady aerodynamics robust to flight parameter variations.Journal of Fluids and Structures,2014,49(8):728-741
10 Mannarino A,Mantegazza P.Nonlinear aeroelastic reduced order modeling by recurrent neural networks.Journal of Fluids and Structures,2014,48:103-121
11 Zhang Weiwei,Wang Bobin,Ye Zhengyin,et al.Efficient method for limit cycle flutter analysis based on nonlinear aerodynamic reduced-order models.AIAA Journal,2012,50(5):1019-1028
12陈刚,徐敏,陈士橹.基于Volterra级数的非线性非定常气动力降阶模型.宇航学报,2009,25(5):492-495(Chen Gang,Xu Min,Chen Shilu.Reduced-order model based on volterra series in nonlinear unsteady aerodynamics.Journal of Astronautics,2009,25(5):492-495(in Chinese))
13陈刚,李跃明.非定常流场降阶模型及应用研究进展与展望.力学进展,2011,41(6):686-701(Chen Gang,Li Yueming.Advances and prospects of the reduced order model for unsteady flow and its application.Advances in Mechanics,2011,41(6):686-701(in Chinese))
14 Wu Zhigang,Chu Longfei,Yuan Ruizhi,et al.Studies on aeroservoelasticity semi-physical simulation test for missiles.Science China Technological Sciences,2012,55(9):2482-2488
15杨超,吴志刚.导弹气动伺服弹性稳定性分析.飞行力学,2000,18(4):1-5(Yang Chao,Wu Zhigang.Aeroservoelastic stability of missile.Flight Dynamics,2000,18(4):1-5(in Chinese))
16吴志刚,杨超.弹性导弹的连续与离散阵风响应.北京航空航天大学学报,2007,33(2):136-140(Wu Zhigang,Yang Chao.Continuous and discrete gust responses of elastic missiles.Journal of Beijing University of Aeronautics and Astronautics,2007,33(2):136-140(in Chinese))
17全景阁,叶正寅,张伟伟.轴向载荷对大长细比导弹稳定性的影响研究.兵工学报,2015,36(1):94-102(Quan Jingge,Ye Zhengyin,Zhang Weiwei.Analysis on stability of a slender missile under axial loads.Acta Armamentarii,2015,36(1):94-102(in Chinese))
18 Huang Rui,Li Hongkun,Hu Haiyan,et al.Open/closed-loop aeroservoelastic predictions via nonlinear,reduced-order aerodynamic models.AIAA Journal,2015,53(7):1812-1824
19 Chiuso A,Picci G.Consistency analysis of some closed-loop subspace identification methods.Automatica,2005,41(3):377-391
20 Chiuso A.The role of vector autoregressive modeling in predictorbased subspace identification.Automatica,2007,43(6):1034-1048
21 Houtzager I,Wingerden JW,Verhaegen M.Recursive predictorbased subspace identification with application to the real-time closed-loop tracking of flutter.IEEE Transactions on Control Systems Technology,2012,20(4):934-949
22 Mor′e JJ.The Levenberg-Marquardt algorithm:implementation and theory//Numerical analysis.Berlin Heidelberg:Springer,1978:105-116
23 Waszak MR.Modeling the benchmark active control technology wind-tunnel model for application to flutter suppression.AIAA Paper,1996,3437
24 Mc Namara JJ,Friedmann PP.Flutter boundary identification for time-domain computational aeroelasticity.AIAA Journal,2007,45(7):1546-1555
25 Borglund D,Ringertz U.Efficient computation of robust flutter boundaries using the mu-k method.Journal of Aircraft,2006,43(6):1763-1769
26 Guruswamy GP.Frequency domain flutter boundary computations using Navier-Stokes equations on superclusters.Journal of Aircraft,2014,51(5):1640-1642
27张伟伟,王博斌,叶正寅.跨音速极限环型颤振的高效数值分析方法.力学学报,2010,42(6):1023-1033(Zhang Weiwei,Wang Bobin,Ye Zhengyin.High efficient numerical method for LCO analysis in transonic flow.Chinese Journal of Theoretical and Applied Mechanics,2010,42(6):1023-1033(in Chinese))
28 Denegri CM.Limit cycle oscillation flight test results of a fighter with external stores.Journal of Aircraft,2000,37(5):761-769
29 Thomas JP,Dowell EH,Hall KC.Modeling viscous transonic limit cycle oscillation behavior using a harmonic balance approach.Journal of Aircraft,2004,41(6):1266-1274
30 Chen YM,Liu JK,Meng G.Equivalent damping of aeroelastic system of an airfoil with cubic stiffness.Journal of Fluids and Structures,2011,27(8):1447-1454
31 Cui Peng,Han Jinglong.Numerical investigation of the effects of structural geometric and material nonlinearities on limit-cycle oscillation of a cropped delta wing.Journal of Fluids and Structures,2011,27(4):611-622
32 Stanford B,Beran P.Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization.Journal of Fluids and Structures,2013,36(1):111-123
2陈桂彬,邹丛青,杨超.气动弹性设计基础.北京:北京航空航天大学出版社,2004(Chen Guibin,Zou Congqing,Yang Chao.Fundamentals of Aeroelastic Design.Beijing:Press of Beijing University of Aeronautics and Astronautics,2004(in Chinese))
3 Bismarck-Nasr MN.Kernel function occurring in subsonic unsteady potential flow.AIAA Journal,1991,29(6):878-879
4 Rodden WP,Taylor PF,Mc Intosh SC.Further refinement of the subsonic doublet-lattice method.Journal of Aircraft,1998,35(5):720-727
5 Liu F,Cai J,Zhu Y,et al.Calculation of wing flutter by a coupled fluid-structure method.Journal of Aircraft,2001,38(2):334-342
6 Marques FD,Anderson J.Identification and prediction of unsteady transonic aerodynamic loads by multi-layer functionals.Journal of Fluids and Structures,2001,15(1):83-106
7 Hall KC,Thomas JP,Dowell EH.Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows.AIAA Journal,2000,38(10):1853-1862
8 Xie D,Xu M,Dowell EH.Proper orthogonal decomposition reduced-order model for nonlinear aeroelastic oscillations.AIAAJournal,2014,52(2):229-241
9 Liu Haojie,Hu Haiyan,Zhao Yonghui,et al.Efficient reduced-order modeling of unsteady aerodynamics robust to flight parameter variations.Journal of Fluids and Structures,2014,49(8):728-741
10 Mannarino A,Mantegazza P.Nonlinear aeroelastic reduced order modeling by recurrent neural networks.Journal of Fluids and Structures,2014,48:103-121
11 Zhang Weiwei,Wang Bobin,Ye Zhengyin,et al.Efficient method for limit cycle flutter analysis based on nonlinear aerodynamic reduced-order models.AIAA Journal,2012,50(5):1019-1028
12陈刚,徐敏,陈士橹.基于Volterra级数的非线性非定常气动力降阶模型.宇航学报,2009,25(5):492-495(Chen Gang,Xu Min,Chen Shilu.Reduced-order model based on volterra series in nonlinear unsteady aerodynamics.Journal of Astronautics,2009,25(5):492-495(in Chinese))
13陈刚,李跃明.非定常流场降阶模型及应用研究进展与展望.力学进展,2011,41(6):686-701(Chen Gang,Li Yueming.Advances and prospects of the reduced order model for unsteady flow and its application.Advances in Mechanics,2011,41(6):686-701(in Chinese))
14 Wu Zhigang,Chu Longfei,Yuan Ruizhi,et al.Studies on aeroservoelasticity semi-physical simulation test for missiles.Science China Technological Sciences,2012,55(9):2482-2488
15杨超,吴志刚.导弹气动伺服弹性稳定性分析.飞行力学,2000,18(4):1-5(Yang Chao,Wu Zhigang.Aeroservoelastic stability of missile.Flight Dynamics,2000,18(4):1-5(in Chinese))
16吴志刚,杨超.弹性导弹的连续与离散阵风响应.北京航空航天大学学报,2007,33(2):136-140(Wu Zhigang,Yang Chao.Continuous and discrete gust responses of elastic missiles.Journal of Beijing University of Aeronautics and Astronautics,2007,33(2):136-140(in Chinese))
17全景阁,叶正寅,张伟伟.轴向载荷对大长细比导弹稳定性的影响研究.兵工学报,2015,36(1):94-102(Quan Jingge,Ye Zhengyin,Zhang Weiwei.Analysis on stability of a slender missile under axial loads.Acta Armamentarii,2015,36(1):94-102(in Chinese))
18 Huang Rui,Li Hongkun,Hu Haiyan,et al.Open/closed-loop aeroservoelastic predictions via nonlinear,reduced-order aerodynamic models.AIAA Journal,2015,53(7):1812-1824
19 Chiuso A,Picci G.Consistency analysis of some closed-loop subspace identification methods.Automatica,2005,41(3):377-391
20 Chiuso A.The role of vector autoregressive modeling in predictorbased subspace identification.Automatica,2007,43(6):1034-1048
21 Houtzager I,Wingerden JW,Verhaegen M.Recursive predictorbased subspace identification with application to the real-time closed-loop tracking of flutter.IEEE Transactions on Control Systems Technology,2012,20(4):934-949
22 Mor′e JJ.The Levenberg-Marquardt algorithm:implementation and theory//Numerical analysis.Berlin Heidelberg:Springer,1978:105-116
23 Waszak MR.Modeling the benchmark active control technology wind-tunnel model for application to flutter suppression.AIAA Paper,1996,3437
24 Mc Namara JJ,Friedmann PP.Flutter boundary identification for time-domain computational aeroelasticity.AIAA Journal,2007,45(7):1546-1555
25 Borglund D,Ringertz U.Efficient computation of robust flutter boundaries using the mu-k method.Journal of Aircraft,2006,43(6):1763-1769
26 Guruswamy GP.Frequency domain flutter boundary computations using Navier-Stokes equations on superclusters.Journal of Aircraft,2014,51(5):1640-1642
27张伟伟,王博斌,叶正寅.跨音速极限环型颤振的高效数值分析方法.力学学报,2010,42(6):1023-1033(Zhang Weiwei,Wang Bobin,Ye Zhengyin.High efficient numerical method for LCO analysis in transonic flow.Chinese Journal of Theoretical and Applied Mechanics,2010,42(6):1023-1033(in Chinese))
28 Denegri CM.Limit cycle oscillation flight test results of a fighter with external stores.Journal of Aircraft,2000,37(5):761-769
29 Thomas JP,Dowell EH,Hall KC.Modeling viscous transonic limit cycle oscillation behavior using a harmonic balance approach.Journal of Aircraft,2004,41(6):1266-1274
30 Chen YM,Liu JK,Meng G.Equivalent damping of aeroelastic system of an airfoil with cubic stiffness.Journal of Fluids and Structures,2011,27(8):1447-1454
31 Cui Peng,Han Jinglong.Numerical investigation of the effects of structural geometric and material nonlinearities on limit-cycle oscillation of a cropped delta wing.Journal of Fluids and Structures,2011,27(4):611-622
32 Stanford B,Beran P.Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization.Journal of Fluids and Structures,2013,36(1):111-123