Abstract：In this paper,a reduced method for flow mesh deformation around a wing was developed based on the elastic solid method. The flow mesh domain was assumed to be a pseudo elastic solid. The total vibration equation for the wing with the pseudo elastic solid together was derived using the static equilibrium equation of the pseudo elastic solid and the vibration equation of the wing. The nodal displacements for the wing and flow mesh were computed through modal superposition and the deformed flow mesh was obtained. Considering that wing flutter often appeared as the 1st bending and torsion flutter,the nodal displacements for the flow mesh could be calculated by modal superposition of the 1st bending and torsion mode. To ensure the computational accuracy,the 2nd bending and torsion mode were also considered. The flutter boundary of the AGARD Wing 445.6 was predicted using the present dynamic mesh method coupled with the RANS equations and the Spalart-Allamras turbulent model. The relative error of the calculated results to the experimental data was less than 2%. The computing time was reduced by 54.8% compared with the pre-existing elastic solid method.
[1] Crickmore P. Nighthawk F-117 Stealth Fighter[M]. Zenith Imprint, 2003
[2] Burnett E, Atkinson C, Beranek J, et al. NDOF Simulation model for flight control development with flight test correlation[C]//AIAA Modeling and Simulation Technologies Conference. 2010, 3: 7780-7794
[3] Schuster D M, Liu D D, Huttsell L J. Computational aeroelasticity: success, progress, challenge[J]. Journal of Aircraft, 2003, 40(5): 843-856
[4] Albano E, Rodden W P. A doublet-lattice method for calculating lift distributions on oscillating surfaces in subsonic flows[J]. AIAA journal, 1969, 7(2): 279-285
[5] Ashley H. Piston theory-a new aerodynamic tool for the aeroelastician[J]. Journal of the Aeronautical Sciences (Institute of the Aeronautical Sciences), 1956, 23(12): 1109-1118
[6] Yurkovich R N, Liu D D, Chen P C. The state-of-the-art of unsteady aerodynamics for high performance aircraft[J]. AIAA paper, 2001, 428: 2001
[7] 谢亮, 徐敏, 李杰, 等. 基于 CFD/CSD 耦合的颤振与动载荷分析方法[J]. 振动与冲击, 2012, 31(3): 106-110
XieLiang,Xu Min, Li Jie,CaiTianxing. Flutter and dynamic analysis based on CFD/CSD coupling method [J]. Journal of Vibration and Shock, 2012, 31(3): 106-110
[8] Keye S. Fluid-structure coupled analysis of a transport aircraft and flight-test validation[J]. Journal of Aircraft, 2011, 48(2): 381-390
[9] Chen X, Zha G C, Yang M T. Numerical simulation of 3-D wing flutter with fully coupled fluid–structural interaction[J]. Computers & fluids, 2007, 36(5): 856-867
[10] 史爱明, 杨青, 杨永年. 非结构运动网格下的三维机翼颤振数值分析[J]. 振动与冲击, 2006, 24(6): 27-28
Shi Aiming, Yang Qing, Yang Yongnian. Numerical flutter analysis of a 3-D wing using unstructured dynamic mesh Euler method [J]. Journal of Vibration and Shock, 2006, 24(6): 27-28
[11] Tezduyar T E. Stabilized finite element formulations for incompressible flow computations[J]. Advances in applied mechanics, 1991, 28: 1-44
[12] 陈炎, 曹树良, 梁开洪, 等. 基于温度体模型的动网格生成方法及在流固耦合振动中的应用[J]. 振动与冲击, 2010, 29(4): 1-5
Chen Yan, Cao Shuliang, Liang Kaihong, Zhu Baoshan. A new dynamic grids based on temperature analogy and its application in vibration engineering with fluid-solid interaction [J]. Journal of Vibration and Shock, 2010, 29(4): 1-5
[13] 谢亮, 徐敏, 张斌, 等. 基于径向基函数的高效网格变形算法研究[J]. 振动与冲击, 2013, 32(10): 141-145
XieLiang, Xu Min, Zhang Bin, An Xiaoming. Space points reduction in grid deforming method based on radial basis functions[J]. Journal of Vibration and Shock, 2013, 32(10): 141-145
[14] Bottasso C L, Detomi D, Serra R. The ball-vertex method: a new simple spring analogy method for unstructured dynamic meshes [J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(39): 4244-4264
[15] Bar-Yoseph P Z, Mereu S, Chippada S, et al. Automatic monitoring of element shape quality in 2-D and 3-D computational mesh dynamics[J]. Computational Mechanics, 2001, 27(5): 378-395
[16] Stein K, Tezduyar T, Benney R. Mesh moving techniques for fluid-structure interactions with large displacements[J]. Journal of Applied Mechanics, 2003, 70(1): 58-63
[17] Huo S H, Wang F S, Yan W Z, et al. Layered elastic solid method for the generation of unstructured dynamic mesh[J]. Finite Elements in Analysis and Design, 2010, 46(10): 949-955
[18] Spalart P R, Allmaras S R. A one-equation turbulence model for aerodynamic flows[C]. AIAA Paper 92: 0439
[19] Zienkiewicz O C, Taylor R L. The finite element method for solid and structural mechanics[M]. Butterworth-heinemann, 2005：563-588
[20] Livne E, Weisshaar T A. Aeroelasticity of nonconventional airplane configurations-Past and future[J]. Journal of Aircraft, 2003, 40(6): 1047-1065
[21] Demirdžić I, Lilek Ž, Perić M. A collocated finite volume method for predicting flows at all speeds[J]. International Journal for Numerical Methods in Fluids, 1993, 16(12): 1029-1050
[22] Yates Jr E C. AGARD standard aeroelastic configurations for dynamic response I-wing 445.6[R]. ADVISORY GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT NEUILLY-SUR-SEINE (FRANCE), 1988
[23] Beaubien R J, Nitzsche F, Feszty D. Time and frequency domain flutter solutions for the AGARD 445.6 wing[C]. Paper No. IF-102, IFASD, 2005
[24] Rumsey C L, Sanetrik M D, Biedron R T, et al. Efficiency and accuracy of time-accurate turbulent Navier-Stokes computations[J]. Computers & Fluids, 1996, 25(2): 217-236
[25] Im H S, Chen X Y, Zha G C. Prediction of a Supersonic Wing Flutter Boundary Using a High Fidelity Detached Eddy Simulation[C]. AIAA Paper, 2012, 39: 9-12
