基于结构动力学方法的气动弹性分析
摘要
由于现代飞行器朝高速度、轻结构、大柔性、超机动方向发展,导致其弹性结构和流体之间的强耦合,飞行器遭遇了更加严重的气动弹性问题。随着高性能计算机的发展,计算流体动力学/计算结构动力学(CFD/CSD)耦合数值模拟已能精确预测气动弹性响应,但计算规模庞大,耗时久。因此,在保证精度的同时如何提高计算效率是气动弹性力学领域的研究热点和难点。
本文研究了一种结合通用计算结构动力学程序的气动弹性方法：对于气动与弹性的耦合模型,给出气动力的频域公式,并表示成有理多项式,通过特定的等价变换,能够推导出与结构动力学方程完全相似的、关于求解变量的二阶常微分方程组。于是,可以在计算结构动力学框架下实现气动弹性问题的分析和计算。此方法将通用计算结构动力学程序的功能与试验或数值分析得到的气动力模型相结合,简化了气动弹性的耦合分析、提高计算效率。
本文的创新点在于：对非定常气动力进行等价变换,得到与结构动力学方程完全相似二阶常微分方程组,并结合通用计算结构动力学程序对二元机翼气动弹性耦合系统进行了颤振分析。
本文的主要工作内容为：
1)从有理多项式气动力表达式出发,以Theodorsen气动力模型为例,通过气动力有理多项式拟合及特定的等价变换,建立了气动力在时域内的二阶常微分方程组
2)使用通用计算结构动力学程序,实现气动弹性的耦合分析。
3)建立了闭环控制模型,应用次最优控制律,进行颤振的主动抑制研究
Modern aircrafts is required of high speed, light structure, great flexibility, and super maneuverability, which leads to strong interaction between the flexible structure and the surrounding flow. Consequently aircrafts suffers a more serious aeroelastic problem. With the development of high-performance computers, the computational fluid dynamic (CFD)/computational structure dynamic (CSD) numerical simulation can predict the aeroelastic response accurately, but the simulation remains too computationally expensive to be used in multi-disciplinary settings and the aeroelastic analysis of complicated systems. So the problem of how to improve the computational efficiency is a hot topic.
In this paper, the coupling for pneumatic and flexible model, given the frequency domain aerodynamic formula, and expressed as a rational polynomial of the equivalent transformation, to derive the full dynamic equations with a similar structure, on the two unknown variables order ordinary differential equations. Thus, in the calculation of structural dynamics can be achieved under the framework of Aeroelastic analysis of the problem and calculation. This method will be general computing structure, function and dynamics program testing or numerical analysis and the combination of aerodynamic models, simplifies analysis of aeroelastic coupling and increases efficiency.
The main innovations in this paper are as follows:
1. Using the Theodorsen aerodynamics as an example, adapting rational polynomial fitting and specific equivalent transformation to establish aerodynamics second order ordinary differential equations in the time domain.
2. Using the general computational structural dynamics program, to achieve a flexible coupling of aerodynamic.
3. Establish a closed-loop control model, application sub-optimal control law, for the active suppression of flutter.
本文研究了一种结合通用计算结构动力学程序的气动弹性方法：对于气动与弹性的耦合模型,给出气动力的频域公式,并表示成有理多项式,通过特定的等价变换,能够推导出与结构动力学方程完全相似的、关于求解变量的二阶常微分方程组。于是,可以在计算结构动力学框架下实现气动弹性问题的分析和计算。此方法将通用计算结构动力学程序的功能与试验或数值分析得到的气动力模型相结合,简化了气动弹性的耦合分析、提高计算效率。
本文的创新点在于：对非定常气动力进行等价变换,得到与结构动力学方程完全相似二阶常微分方程组,并结合通用计算结构动力学程序对二元机翼气动弹性耦合系统进行了颤振分析。
本文的主要工作内容为：
1)从有理多项式气动力表达式出发,以Theodorsen气动力模型为例,通过气动力有理多项式拟合及特定的等价变换,建立了气动力在时域内的二阶常微分方程组
2)使用通用计算结构动力学程序,实现气动弹性的耦合分析。
3)建立了闭环控制模型,应用次最优控制律,进行颤振的主动抑制研究
Modern aircrafts is required of high speed, light structure, great flexibility, and super maneuverability, which leads to strong interaction between the flexible structure and the surrounding flow. Consequently aircrafts suffers a more serious aeroelastic problem. With the development of high-performance computers, the computational fluid dynamic (CFD)/computational structure dynamic (CSD) numerical simulation can predict the aeroelastic response accurately, but the simulation remains too computationally expensive to be used in multi-disciplinary settings and the aeroelastic analysis of complicated systems. So the problem of how to improve the computational efficiency is a hot topic.
In this paper, the coupling for pneumatic and flexible model, given the frequency domain aerodynamic formula, and expressed as a rational polynomial of the equivalent transformation, to derive the full dynamic equations with a similar structure, on the two unknown variables order ordinary differential equations. Thus, in the calculation of structural dynamics can be achieved under the framework of Aeroelastic analysis of the problem and calculation. This method will be general computing structure, function and dynamics program testing or numerical analysis and the combination of aerodynamic models, simplifies analysis of aeroelastic coupling and increases efficiency.
The main innovations in this paper are as follows:
1. Using the Theodorsen aerodynamics as an example, adapting rational polynomial fitting and specific equivalent transformation to establish aerodynamics second order ordinary differential equations in the time domain.
2. Using the general computational structural dynamics program, to achieve a flexible coupling of aerodynamic.
3. Establish a closed-loop control model, application sub-optimal control law, for the active suppression of flutter.
引文
[1].伏欣H W.气动弹性力学原理[M].沈克杨译.上海：上海科学技术文献出版社,1982.
[2]. T. Theodorsen, General theory of aerodynamic instability and the mechanism of flutter. NACA TR-496 (1934).
[3]. H.G. Honlinger,J.Krammer, M.Stettner, MDO Technology Needs in Aeroelastic Structural Design [R], AIAA-98-4731,1998
[4]. William, Yeager Jr, Raymond et al., A Historical Overview of Aeroelasticity Branch and Transonic Dynamics Tunnel Contributions to Rotorcraft Technology and Development[R], NASA/TM-2001-211054,2001
[5].陈桂彬,邹丛青,杨超.气动弹性设计基础[M].北京：北京航空航天大学出版社.2004.10
[6].赵永辉,气动弹性力学与控制[M].北京：科学出版社,2007.
[7].牟让科,杨水年,叶正寅.超临界冀型的跨音速抖振特性[J].计算物理,2001,18(5)
[8].管德主编.非定常气动力计算[M].北京航空航天大学出版社,1992.
[9]. Albano E,Rodden W P. A doublet-lattice method for calculating lift distributions of oscillating surfaces in subsonic flow. AIAA Journal,1969,7(2):279-285
[10]. M. Landahl, Kernel Function for Nonplanar Oscillating Surface in a Subsonic Flow. AIAA Journal 1967, pp 1045-1046
[11].杨炳渊,樊则文.弹性飞行器气动伺服弹性耦合动力学仿真[J].宇航学报,2009(1),134-138
[12].樊则文,刘晓宁,杨炳渊.超声速飞行器气动伺服弹性稳定性分析[J].上海航天.2008(4),22-30
[13]. Pendleton E, Griffin K E. A flight research program for active aeroelastic wing technology. AIAA-96-1574-CP,1996
[14]. Ryan P D, Michael J A. Development and Testing of Control Laws for the Active Aeroelastic Wing Program. AIAA Paper,2005,2005-6314
[15]. Haftaka, R T, Optimization or Flexible Wing Structures Subject to Strength and Induced Drag Constraints[J]. AIAA Journal,1977,15(8):1101-1106
[16]. Noll T E, Aeroservoelasticity [R],AIAA-90-1073-CP,1990
[17]. Boyd, Stanley R C, Gerald D M, Summary of an Active Flexible Wing Programme[J], Journal of Aircraft,1995,32(2):10-15
[18]. Lee-Rausch E M, Batina J T. Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics AIAA 93-3476
[19]. Ramji Kamakoti, Wei Shyy, Siddharth Thakur, Bhavani Sankar. Time Dependent RANS Computation for an Aeroelastic Wing. AIAA-2004-0886
[20].李勇,基于Volterra级数的非定常气动力和气动弹性分析[D],西安：西北工业大学,2007
[21]. Silva W A. A methodology for using nonlinear aerodynamics in aeroservoelastic analysis and design [R]. AIAA paper-91-1110,1991
[22].姚伟刚,徐敏,基于Volterra级数降阶模型的气动弹性分析[J],宇航学报2008,29(6),1711-1716
[23]. Silva W A. Discrete-Time Linear and Nonlinear Aerodynamic Impulse Responses for Efficient CFD Analysis[D]. PH.D dissertation, College of William & Mary, December 1997
[24]. Rugh W J. Nonlinear system theory:the Volterra-Wiener approach [M]. The Johns Hopkins University Press,1981
[25].吴志刚,杨超,基于Volterra级数的跨音速非定常气动力建模[J],北京航空航天大学学报,2006年4月,第32卷,第4期373-376。
[26]. Piergionvanni Marzocca, Walter A Silva, Liviu Librescu. Open/Closed-Loop Nonlinear Aeoelasicity for Airfoils via Volterra Series Approach [R], AIAA-2002-1484.
[27].高淑华,含粘弹性阻尼结构的动力分析[D],上海：复旦大学,2004
[28].张伟伟,基于CFD技术的高效气动弹性分析方法研究[D],西安：西北工业大学
[29].杨智春,赵令诚,姜节胜.结构非线性颤振半主动抑制.应用力学学报,1994,11(1)
[30]. Livne. Eli, Li.wei-Lin. Aeroservoelastic Aspects of Wing/Control Surface Planform Shape Optimization. AIAA Journal,1995,33(2):302-311
[31]. P. C. Chen. Damping Perturbation Method for Flutter Solution: The g-Method. AIAA journal,2000,38(9)
[32]. Newsem RJ, Robertshaw HH, and Kapania RK. Control Law Design in A computational Aeroelasticity Environment. AIAA Paper,2003-1415.
[33].顾仲权,马口根,陈卫东.振动主动控制[M].北京：国防工业出版社,1997.
[34]. Dimitriads G, Cooper JE, Characterization of The Behaviour of a Simple Aeroservoelastic System with Control Nonlinearities, Journal of Fluids and Structures,2000,(14).
[35]. Borglund D, Kuttenkeuler J. Active wing flutter suppression using a trailing edge flap[J]. Journal of Fluids and Structures,2002,16(3):271-294.
[36].许进林,姜长生.二元机翼颤振抑制的次最优控制[J]，航空兵器,2009(6)：17-21
[37].于明礼,胡海岩.基于超声电机作动器的翼段颤振主动抑制[J],振动工程学报2005,Vol.18,No.4：418-425.
[2]. T. Theodorsen, General theory of aerodynamic instability and the mechanism of flutter. NACA TR-496 (1934).
[3]. H.G. Honlinger,J.Krammer, M.Stettner, MDO Technology Needs in Aeroelastic Structural Design [R], AIAA-98-4731,1998
[4]. William, Yeager Jr, Raymond et al., A Historical Overview of Aeroelasticity Branch and Transonic Dynamics Tunnel Contributions to Rotorcraft Technology and Development[R], NASA/TM-2001-211054,2001
[5].陈桂彬,邹丛青,杨超.气动弹性设计基础[M].北京：北京航空航天大学出版社.2004.10
[6].赵永辉,气动弹性力学与控制[M].北京：科学出版社,2007.
[7].牟让科,杨水年,叶正寅.超临界冀型的跨音速抖振特性[J].计算物理,2001,18(5)
[8].管德主编.非定常气动力计算[M].北京航空航天大学出版社,1992.
[9]. Albano E,Rodden W P. A doublet-lattice method for calculating lift distributions of oscillating surfaces in subsonic flow. AIAA Journal,1969,7(2):279-285
[10]. M. Landahl, Kernel Function for Nonplanar Oscillating Surface in a Subsonic Flow. AIAA Journal 1967, pp 1045-1046
[11].杨炳渊,樊则文.弹性飞行器气动伺服弹性耦合动力学仿真[J].宇航学报,2009(1),134-138
[12].樊则文,刘晓宁,杨炳渊.超声速飞行器气动伺服弹性稳定性分析[J].上海航天.2008(4),22-30
[13]. Pendleton E, Griffin K E. A flight research program for active aeroelastic wing technology. AIAA-96-1574-CP,1996
[14]. Ryan P D, Michael J A. Development and Testing of Control Laws for the Active Aeroelastic Wing Program. AIAA Paper,2005,2005-6314
[15]. Haftaka, R T, Optimization or Flexible Wing Structures Subject to Strength and Induced Drag Constraints[J]. AIAA Journal,1977,15(8):1101-1106
[16]. Noll T E, Aeroservoelasticity [R],AIAA-90-1073-CP,1990
[17]. Boyd, Stanley R C, Gerald D M, Summary of an Active Flexible Wing Programme[J], Journal of Aircraft,1995,32(2):10-15
[18]. Lee-Rausch E M, Batina J T. Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics AIAA 93-3476
[19]. Ramji Kamakoti, Wei Shyy, Siddharth Thakur, Bhavani Sankar. Time Dependent RANS Computation for an Aeroelastic Wing. AIAA-2004-0886
[20].李勇,基于Volterra级数的非定常气动力和气动弹性分析[D],西安：西北工业大学,2007
[21]. Silva W A. A methodology for using nonlinear aerodynamics in aeroservoelastic analysis and design [R]. AIAA paper-91-1110,1991
[22].姚伟刚,徐敏,基于Volterra级数降阶模型的气动弹性分析[J],宇航学报2008,29(6),1711-1716
[23]. Silva W A. Discrete-Time Linear and Nonlinear Aerodynamic Impulse Responses for Efficient CFD Analysis[D]. PH.D dissertation, College of William & Mary, December 1997
[24]. Rugh W J. Nonlinear system theory:the Volterra-Wiener approach [M]. The Johns Hopkins University Press,1981
[25].吴志刚,杨超,基于Volterra级数的跨音速非定常气动力建模[J],北京航空航天大学学报,2006年4月,第32卷,第4期373-376。
[26]. Piergionvanni Marzocca, Walter A Silva, Liviu Librescu. Open/Closed-Loop Nonlinear Aeoelasicity for Airfoils via Volterra Series Approach [R], AIAA-2002-1484.
[27].高淑华,含粘弹性阻尼结构的动力分析[D],上海：复旦大学,2004
[28].张伟伟,基于CFD技术的高效气动弹性分析方法研究[D],西安：西北工业大学
[29].杨智春,赵令诚,姜节胜.结构非线性颤振半主动抑制.应用力学学报,1994,11(1)
[30]. Livne. Eli, Li.wei-Lin. Aeroservoelastic Aspects of Wing/Control Surface Planform Shape Optimization. AIAA Journal,1995,33(2):302-311
[31]. P. C. Chen. Damping Perturbation Method for Flutter Solution: The g-Method. AIAA journal,2000,38(9)
[32]. Newsem RJ, Robertshaw HH, and Kapania RK. Control Law Design in A computational Aeroelasticity Environment. AIAA Paper,2003-1415.
[33].顾仲权,马口根,陈卫东.振动主动控制[M].北京：国防工业出版社,1997.
[34]. Dimitriads G, Cooper JE, Characterization of The Behaviour of a Simple Aeroservoelastic System with Control Nonlinearities, Journal of Fluids and Structures,2000,(14).
[35]. Borglund D, Kuttenkeuler J. Active wing flutter suppression using a trailing edge flap[J]. Journal of Fluids and Structures,2002,16(3):271-294.
[36].许进林,姜长生.二元机翼颤振抑制的次最优控制[J]，航空兵器,2009(6)：17-21
[37].于明礼,胡海岩.基于超声电机作动器的翼段颤振主动抑制[J],振动工程学报2005,Vol.18,No.4：418-425.