Regarding the contradiction between computational efficiency, precision and robustness of design and analysis of unsteady fluid-structure coupling problems, a time spectral method which can couple with adjoint to solve the unsteady fluid-structure coupling optimization design problems of high-aspect-ratio wings is established in this paper. The time spectral method is built by directly coupling the Chebyshev spectral method with a fluid-structure interaction analysis method based on the unsteady panel method and the geometrically-nonlinear beam finite element model. The Chebyshev spectral method uses Chebyshev operators to replace the state parameters of the whole system, and then transforms the unsteady problems into steady problems. In this way, the built fluid-structure time spectral method has a high computational precision, high calculation efficiency and enough robustness. Validation cases and calculation of the flutter speed of Goland wings indicate that the calculation precision of the Chebyshev spectral method is improved continuously with the increase of the number of Chebyshev collocation points. With very few collocation points, the Chebyshev spectral method can obtain the calculation results of required accuracy. The time spectral method proposed is suitable for both periodic and non-periodic unsteady problems.
YANG Tihao
,
BAI Junqiang
,
SHI Yayun
,
YANG Yixiong
. Time spectral method for non-periodic fluid-structure coupling problems[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018
, 39(5)
: 121654
-121654
.
DOI: 10.7527/S1000-6893.2017.21654
[1] LIVNE E, WEISSHAARW T A. Aeroelasticity of nonconventional airplane configurations-past and future[J]. Journal of Aircraft, 2003, 40(6):1047-1065.
[2] XIANG J, YAN Y, LI D. Recent advance in nonlinear aeroelastic analysis and control of the aircraft[J]. Chinese Journal of Aeronautics, 2014, 27(1):12-22.
[3] SU W, CESNIK C E S. Strain-based geometrically nonlinear beam formulation for modeling very flexible aircraft[J]. International Journal of Solids and Structures, 2011, 48(16):2349-2360.
[4] LIEU T, FARHAT C. POD-based aeroelastic analysis of a complete F-16 configuration:ROM adaptation and demonstration:AIAA-2005-2295[R]. Reston, VA:AIAA, 2005.
[5] AMSALLEM D, FARHAT C. Interpolation method for adapting reduced-order models and application to aeroelasticity[J]. AIAA Journal, 2008, 46(7):1803-1813.
[6] LYU Z, KENWAY G K, PAIGE C, et al. Automatic differentiation adjoint of the reynolds-averaged navier-stokes equations with a turbulence model:AIAA-2013-2581[R]. Reston, VA:AIAA, 2013.
[7] HALL K C, THOMAS J P, CLARK W S. Computation of unsteady nonlinear flows in cascades using a harmonic balance technique[J]. AIAA Journal, 2002, 40(5):879-886.
[8] CHOI S, LEE K, POTSDAM M M, et al. Helicopter rotor design using a time-spectral and adjoint-based method[J]. Journal of Aircraft, 2014, 51(2):412-423.
[9] TIMME S. Transonic aeroelastic instability searches using a hierarchy of aerodynamic models[D]. Liverpool:University of Liverpool, 2010.
[10] PERERA M, GUO S. Structural and dynamic analysis of a seamless aeroelastic wing:AIAA-2010-2878[R]. Reston, VA:AIAA, 2010.
[11] HESSE H, PALACIOS R. Reduced-order aeroelastic models for dynamics of maneuvering flexible aircraft[J]. AIAA Journal, 2014, 52(8):1717-1732.
[12] HAGHIGHAT S, RA MATRINS J R, LIU H H. Aeroservoelastic design optimization of a flexible wing[J]. Journal of Aircraft, 2012, 49(2):432-443.
[13] STANFORD B, BERAN P. Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization[J]. Journal of Fluids and Structures, 2013, 36:111-123.
[14] MALLIK W, KAPANIA R K, SCHETZ J A. Effect of flutter on the multidisciplinary design optimization of truss-braced-wing aircraft[J]. Journal of Aircraft, 2015, 52(6):1858-1872.
[15] ZHANG Z, CHEN P C, WANG Q, et al. Adjoint based structure and shape optimization with flutter constraints:AIAA-2016-1176[R]. Reston, VA:AIAA, 2016.
[16] IM D K, CHOI S, MCCLURE J E, et al. Mapped Chebyshev pseudospectral method for unsteady flow analysis[J]. AIAA Journal, 2015, 53(12):3805-3820.
[17] CHOI J Y, CHOI S, PARK J, et al. Prediction of dynamic Stability using mapped Chebyshev pseudospectral method:AIAA-2016-1347[R]. Reston, VA:AIAA, 2016.
[18] MOIN P. Fundamentals of engineering numerical analysis[M]. Cambridge:Cambridge University Press, 2010.
[19] BAYLISS A, TURKEL E. Mappings and accuracy for Chebyshev pseudo-spectral approximations[J]. Journal of Computational Physics, 1992, 101(2):349-359.
[20] KOSLOFF D, TAL-EZER H. A modified Chebyshev pseudospectral method with an O (N-1) time step restriction[J]. Journal of Computational Physics, 1993, 104(2):457-469.
[21] KATZ J, PLOTKINP A. Low-speed aerodynamics[M]. Cambridge:Cambridge University Press, 2001.
[22] MURUA J. Flexible aircraft dynamics with a geometrically-nonlinear description of the unsteady aerodynamics[D]. London:Imperial College London, 2012.
[23] GERADIN M, CARDONA A. Flexible multibody dynamics:A finite element approach[M]. 2001.
[24] GOLAND M. The flutter of a uniform cantilever wing[J]. Journal of Applied Mechanics, 1945, 12(4):197-208.
[25] PATIL M J, HODEGES D H, CESNIK C E S. Nonlinear aeroelastic analysis of complete aircraft in subsonic flow[J]. Journal of Aircraft, 37(5):753-760.
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