An energy method for flutter analysis of wing using one-way fluid structure coupling

Abstract

In this paper, an energy method for flutter analysis of wing using one-way fluid structure coupling was developed. To consider the effect of wing vibration, Reynolds-averaged Navier–Stokes equations based on the arbitrary Lagrangian Eulerian coordinates were employed to model the flow. The flow mesh was updated using a fast dynamic mesh technology proposed by our research group. The pressure was calculated by solving the Reynolds-averaged Navier–Stokes equations through the SIMPLE algorithm with the updated flow mesh. The aerodynamic force for the wing was computed using the pressure on the wing surface. Then the aerodynamic damping of the wing vibration was computed. Finally, the flutter stability for the wing was decided according to whether the aerodynamic damping was positive or not. Considering the first four modes, the aerodynamic damping for wing 445.6 was calculated using the present method. The results show that the aerodynamic damping of the first mode is lower than the aerodynamic damping of higher order modes. The aerodynamic damping increases with the increase of the mode order. The flutter boundary for wing 445.6 was computed using the aerodynamic damping of the first mode in this paper. The calculated flutter boundary is consistent well with the experimental data.

Keywords

Wing flutter one-way coupling energy method fast dynamic mesh technology aerodynamic damping

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References

Crickmore P. Nighthawk F-117 stealth fighter. Zenith Imprint, 2003.

Burnett E, Atkinson C, Beranek J, et al. NDOF Simulation model for flight control development with flight test correlation. In: AIAA modeling and simulation technologies conference, Toronto, Ontario Canada, 2010, pp.7780–7794.

Anderson WD. Mortara S. F-22 aeroelastic design and test validation. AIAA paper, 2007, pp.23–26.

Schuster

Liu

Huttsell

. Computational aeroelasticity: Success, progress, challenge. J Aircraft 2003; 40: 843–856.

Albano

Rodden

. A doublet-lattice method for calculating lift distributions on oscillating surfaces in subsonic flows. AIAA J 1969; 7: 279–285.

Chen

Liu

. A harmonic gradient method for unsteady supersonic flow calculations. J Aircraft 1985; 22: 371–379.

Yurkovich RN, Liu DD and Chen PC. The state-of-the-art of unsteady aerodynamics for high performance aircraft. AIAA paper, 2001.

Liu

Cai

Zhu

et al.

Calculation of wing flutter by a coupled fluid-structure method. J Aircraft 2001; 38: 334–342.

Keye

. Fluid-structure coupled analysis of a transport aircraft and flight-test validation. J Aircraft 2011; 48: 381–390.

10.

Chen

Zha

Yang

. Numerical simulation of 3-D wing flutter with fully coupled fluid–structural interaction. Comput Fluids 2007; 36: 856–867.

11.

Storti

Nigro

Paz

et al.

Strong coupling strategy for fluid–structure interaction problems in supersonic regime via fixed point iteration. J Sound Vib 2009; 320: 859–877.

12.

Bottasso

Detomi

Serra

. The ball-vertex method: A new simple spring analogy method for unstructured dynamic meshes. Comput Meth Appl Mech Eng 2005; 194: 4244–4264.

13.

Rendall

TCS

Allen

. Efficient mesh motion using radial basis functions with data reduction algorithms. J Comput Phys 2009; 228: 6231–6249.

14.

Markou

Mouroutis

Charmpis

et al.

The ortho-semi-torsional (OST) spring analogy method for 3D mesh moving boundary problems. Comput Meth Appl Mech Eng 2007; 196: 747–765.

15.

Huo

Wang

Yan

et al.

Layered elastic solid method for the generation of unstructured dynamic mesh. Finite Elem Anal Des 2010; 46: 949–955.

16.

Zhang

Chang

Duan

et al.

A block LU-SGS implicit unsteady incompressible flow solver on hybrid dynamic grids for 2D external bio-fluid simulations. Comput Fluids 2009; 38: 290–308.

17.

Sheng

Allen

. Efficient mesh deformation using radial basis functions on unstructured meshes. AIAA J 2012; 51: 707–720.

18.

Tezduyar

. Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 1991; 28: 1–44.

19.

Tezduyar

Behr

Mittal

et al.

A new strategy for finite element computations involving moving boundaries and interfaces-the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary tests. Comput Meth Appl Mech Eng 1992; 94: 339–351.

20.

Tezduyar

Behr

Mittal

et al.

A new strategy for finite element computations involving moving boundaries and interfaces-the deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Meth Appl Mech Eng 1992; 94: 353–371.

21.

Bar-Yoseph

Mereu

Chippada

et al.

Automatic monitoring of element shape quality in 2-D and 3-D computational mesh dynamics. Comput Mech 2001; 27: 378–395.

22.

Stein

Tezduyar

Benney

. Mesh moving techniques for fluid-structure interactions with large displacements. J Appl Mech 2003; 70: 58–63.

23.

Bendiksen OO. A new approach to computational aeroelasticity. AIAA paper, 1991, p. 939.

24.

Carta

. Coupled blade-disk-shroud flutter instabilities in turbojet engine rotors. J Eng Gas Turbines Power 1967; 89: 419–426.

25.

Zienkiewicz

Taylor

. The finite element method for solid and structural mechanics, Oxford: Butterworth-Heinemann, 2005, pp. 563–588.

26.

Mian

Wang

. Numerical investigation of structural geometric nonlinearity effect in high-aspect-ratio wing using CFD/CSD coupled approach. J Fluids Struct 2014; 49: 186–201.

27.

Spalart PR and Allmaras SR. A one-equation turbulence model for aerodynamic flows. AIAA Paper 92: 0439, 1992.

28.

Demirdžić

Lilek

Perić

. A collocated finite volume method for predicting flows at all speeds. Int J Numer Meth Fluids 1993; 16: 1029–1050.

29.

Yates EC Jr. AGARD standard aeroelastic configurations for dynamic response I-wing 445.6. Advisory Group for Aerospace Research and Development Neuilly-Sur-Seine, France, 1988.

30.

Im HS, Chen XY and Zha GC. Prediction of a supersonic wing flutter boundary using a high fidelity detached eddy simulation. AIAA Paper, 2012, pp. 9–12.