Application of the finite element method to aeroelasticity

Authors

  • Jean-Pierre Grisval Office National d'Etudes et de Recherches Aerospatiales B.P 72, F-92322 Chdtillon cedex
  • Cedric Liauzun Office National d'Etudes et de Recherches Aerospatiales B.P 72, F-92322 Chdtillon cedex

Keywords:

Finite Element Method, turbulence models, ALE formulation, aeroelasticity

Abstract

This paper presents a multiphysic method for unsteady turbulent flows and fluidstructure computations. This method is based on a Galerkin Least Square Finite Element formulation for both solid and fluid equations. The viscous effects are taken into account using Spalart-Allmaras and k-E turbulence models. The fluid boundaries motion is taken into account using an ALE formulation of the compressible equations. The fluid domain is then modeled as a hyperelastic material. For fluid-structure interactions problems, both solid and fluid equations are time discretized using an implicit time-stepping scheme based on the Newmark's one. Coupling between fluid and structure is achieved through non-matching interfaces. This numerical strategy is applied to a 2D airfoil buffeting simulation, to a 2D fluid-structure computation, and to a flutter analysis of a 3D wing.

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References

[BIS 62] BISPLINGHOFF R.L. et ASHLEY H., Principles of Aeroelasticity, John Wiley and

Sons, 1962.

[CHI 82] CHIEN K. Y., Predictions of channel and boundary layer flows with a low-Reynoldsnumber

turbulence model. In , AIAA journal, 20, 1982 p. 33-38.

[FAR 95] FARHAT C., LESO!NNE M. et MAMAN N., Mixed explicit/implicit time integration

of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed

solution In Eds., International Journal for Numerical Methods in Fluids, 21, p.

-835, Janvier 1995.

[HU 87] HUGHES T.J.R., The Finite Element Method: Linear Static and Dynamic Finite Element

Analysis, Prentice-Hall 1987.

[HFH 89] HUGHES T.J.R., FRANCA L.P. et HULBERT G.M., A new finite element formulation

for computational fluid dynamics: VIII. The Galerkin/1east-squares method for

advective-diffusive equations, In Eds., Computer Methods in Applied Mechanics and Engineering,

, p. 173-189, 1989.

[HFM 86] HUGHES T.J.R., FRANCA L.P. et MALLET M., A new finite element formulation

for computational fluid dynamics: I. Symmetric forms of the compressible Euler and

Navier-Stokes equations and the second Jaw of thermodynamics, In Eds., Computer Methods

in Applied Mechanics and Engineering, 54, p. 223-234, 1986.

[HFM 87] HUGHES T.J.R., FRANCA L.P. et MALLET M., A new finite element formulation

for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation

for linear time-dependent multidimensional advective-diffusive systems, In Eds.,

Computer Methods in Applied Mechanics and Engineering, 63, p. 97-12, 1987.

[HM 86] HUGHES T.J.R., et MALLET M., A new finite element formulation for computational

fluid dynamics: III. The generalized streamline operator for multidimensional

advection-diffusion systems, In Eds., Computer Methods in Applied Mechanics and Engineering,

, p. 305-328, 1986.

[MOR 91] MORTCHELEWICZ G.D., Resolution des equations d'Euler tridimensionelles instationnaires

en maillage non structure, In , La Rcherche Aerospatiale, 6, 1991 p. 17-25.

[SPA 92] SPALART P.R., et ALLMARAS S.R., A one-equation turbulence model for aerodynamic

flows, In , A!AA paper, 1992-0439.

[SPE 93] CENTRIC ENGINEERING SYSTEMS, Spectrum Solver Theory Manual, 1993.

[LAU 74] LAUNDER B.E., et SPALDING D.B., The numerical computation of turbulent flows,

In Eds., Computer Methods in Applied Mechanics and Engineering, 3, p. 269-289, 1974.

[WHI 91] WHITE F.M., Viscous Fluid Flow, McGraw-Hilll991.

[MOL 84] MOLINARO R., et SIMON E., Etude instationnaire du decollement sur un profil

d'aube dans Ia soufflerie S3MA, In, ONERA 0312894 RNG, 1984.

[NOT 85] NOTIN C., et SIMON E., Etude de l'ecoulement autour d'un profil d'aube de compresseur

en regime subsonique, In, ONERA 3411621 R 046R, 1985.

[JOH 91] JOHAN Z., HUGHES T.J.R., et SHAKIB F., A globally convergent matrix-free algorithm

for implicit time-marching schemes arising in finite element analysis in fluids, In

Eds., Computer Methods in Applied Mechanics and Engineering, 87, p. 281-304, 1991.

[BAT 89] BATINA J.T., Unsteady Euler airfoilsolutions using unstructured dynamic meshes,

In, AIAA paper, 89-0115, 1989.

[DAY 83] DAVIS S.S., NACA 64AOIO (NASA Ames model) oscillatory pitching, In, Compendium

of Unsteady Aerodynamic Measurements, AGARD Report No. 702,1983.

[PO 91] POIRION F., Analyse des signaux temporels dans !'etude du flottement des avions par

Ia methode du couplage direct, In, ONERA Technical Report RT5913064 RY 101 R, 1991

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Published

1999-05-12

How to Cite

Grisval, J.-P. ., & Liauzun, C. . (1999). Application of the finite element method to aeroelasticity. European Journal of Computational Mechanics, 8(5-6), 553–579. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/2987

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Original Article