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Research Papers

Analysis of Supersonic and Transonic Panel Flutter Using a Fluid-Structure Coupling Algorithm

[+] Author and Article Information
Guanhua Mei, Guang Xi, Xu Sun, Jiahui Chen

School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an, Shaanxi 710049, China

Jiazhong Zhang

School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an, Shaanxi 710049, China
e-mail: jzzhang@mail.xjtu.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 29, 2013; final manuscript received January 15, 2014; published online April 3, 2014. Assoc. Editor: Massimo Ruzzene.

J. Vib. Acoust 136(3), 031013 (Apr 03, 2014) (11 pages) Paper No: VIB-13-1099; doi: 10.1115/1.4027135 History: Received March 29, 2013; Revised January 15, 2014

In order to analyze the supersonic and transonic panel flutter behaviors quantitatively and accurately, a fluid-structure coupling algorithm based on the finite element method (FEM) is proposed to study the two-dimensional panel flutter problem. First, the Von Kármán's large deformation is used to model the panel, and the high speed airflow is approached by the Euler equations. Then, the equation of panel is discretized spatially by the standard Galerkin FEM, and the equations of fluid are discretized by the characteristic-based split finite element method (CBS-FEM) with dual time stepping; thus, the numerical oscillation encountered frequently in the numerical simulation of flow field could be removed efficiently. Further, a staggered algorithm is used to transfer the information on the interface between the fluid and the structure. Finally, the aeroelastic behaviors of the panel in both the supersonic and transonic airflows are studied in details. And the results show that the system can present the flat and stable, simple harmonic oscillation, buckling, and inharmonic oscillation states at Mach 2, considering the effect of the pretightening force; at Mach 1.2, as the panel loses stability, the ensuing limit cycle oscillation is born; at Mach 0.8 and 0.9, positive and negative bucklings are the typical states of the panel as it loses its stability. Further, the transonic stability boundary is obtained and the transonic bucket is precisely captured. More, this algorithm can be applied to the numerical analysis of other complicated problems related to aeroelasticity.

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References

Dowell, E. H., 1975, Aeroelasticity of Plates and Shells, Noordhoff, Groningen, Netherlands.
Dowell, E. H., 2005, A Modern Course in Aeroelasticity, Kluwer, New York.
Kang, W., Zhang, J. Z., and Feng, P. H., 2012, “Aerodynamic Analysis of a Localized Flexible Airfoil at Low Reynolds Numbers,” Commun. Comput. Phys., 11(4), pp. 1300–1310 [CrossRef].
Dowell, E. H., 1966, “Nonlinear Oscillations of a Fluttering Plate,” AIAA J., 4(7), pp. 1267–1275. [CrossRef]
Dowell, E. H., 1967, “Nonlinear Oscillations of a Fluttering Plate II,” AIAA J., 5(10), pp. 1856–1862. [CrossRef]
Dowell, E. H., 1970, “A Review of the Aeroelastic Stability of Plates and Shells,” AIAA J., 8(1), pp. 385–399. [CrossRef]
Olson, M. D., 1967, “Finite Element Approach to Panel Flutter,” AIAA J., 5(12), pp. 226–227. [CrossRef]
Olson, M. D., 1970, “Some Flutter Solutions Using Finite Element,” AIAA J., 8(4), pp. 747–752. [CrossRef]
Mei, C. H., Abdel-Motagly, K., and Chen, R., 1999, “Review of Nonlinear Panel Flutter at Supersonic and Hypersonic Speeds,” ASME Appl. Mech. Rev., 52(10), pp. 321–332. [CrossRef]
Cheng, G. F., and Mei, C. H., 2004, “Finite Element Modal Formulation for Hypersonic Panel Flutter Analysis With Thermal Effects,” AIAA J., 42(4), pp. 687–695. [CrossRef]
Ashley, H., and Zartarian, G., 1956, “Piston Theory—A New Aerodynamic Tool for the Aeroelastician,” J. Aeronaut. Sci., 23(12), pp. 1109–1118. [CrossRef]
Zhang, W. W., Ye, Z. Y., Zhang, C. A., and Liu, F., 2009, “Supersonic Flutter Analysis Based on a Local Piston Theory,” AIAA J., 47(10), pp. 2321–2328. [CrossRef]
Davis, G. A., and Bendiksen, O. O., 1993, “Unsteady Transonic Two-Dimensional Euler Solutions Using Finite Elements,” AIAA J., 31(6), pp. 1051–1059. [CrossRef]
Davis, G. A., 1994, “Transonic Aeroelasticity Solutions Using Finite Elements in an Arbitrary Larangian-Eulerian Formulation,” Ph.D. thesis, University of California, Los Angeles, CA.
Gordiner, R. E., and Fithen, R., 2003, “Coupling of a Nonlinear Finite Element Structural Method With a Navier–Stokes Solver,” Comput. Struct., 81(2), pp. 75–89. [CrossRef]
Hashimoto, A., and Aoyama, T., 2009, “Effects of Turbulent Boundary Layer on Panel Flutter,” AIAA J., 47(12), pp. 2785–2791. [CrossRef]
Mublstein, L., Gaspers, P. A., and Riddle, D. W., 1968, “An Experimental Study of the Influence of the Turbulent Boundary Layer on Panel Flutter,” NASA Paper No. TN D–4486.
Zhang, J. Z., Ren, S., and Mei, G. H., 2011, “Model Reduction on Inertial Manifolds for N-S Equations Approached by Multilevel Finite Element Method,” Commun. Nonlinear Sci. Numer. Simulation, 16(1), pp. 195–205. [CrossRef]
Zienkiewicz, O. C., Taylor, R. L., and Nithiarasu, P., 2009, The Finite Element Method for Fluid Dynamics, 6th ed., Elsevier, Singapore.
Wang, Y. T., and Zhang, J. Z., 2011, “An Improved ALE and CBS-Based Finite Element Algorithm for Analyzing Flows Around Forced Oscillating Bodies,” Finite Elements Anal. Des., 47(9), pp. 1058–1065. [CrossRef]
Sun, X., Zhang, J. Z., and Ren, X. L., 2012, “Characteristic-Based Split (CBS) Finite Element Method for Incompressible Viscous Flow With Moving Boundaries,” Eng. Appl. Comput. Fluid Mech., 6(3), pp. 461–474.
Massarotti, N., Arpino, F., Lewis, R. W., and Nithiarasu, P., 2006, “Explicit and Semi-Implicit CBS Procedures for Incompressible Viscous Flows,” Int. J. Numer. Methods Eng., 66(10), pp. 1618–1640. [CrossRef]
Nithiarasu, P., Mathur, J. S., Weatherill, N. P., and Morgan, K., 2004, “Three-Dimensional Incompressible Flow Calculations Using the Characteristic Based Split (CBS) Scheme,” Int. J. Numer. Methods Fluids, 44(11), pp. 1207–1229. [CrossRef]
Nithiarasu, P., 2003, “An Efficient Artificial Compressibility (AC) Scheme Based on the Characteristic Based Split (CBS) Method for Incompressible Flows,” Int. J. Numer. Methods Eng., 56(13), pp. 1815–1845. [CrossRef]
Nithiarasu, P., Zienkiewicz, O. C., SatyaSai, B. V. K., Morgan, K., Codina, R., and Vazquez, M., 1998, “Shock Capturing Viscosities for the General Fluid Mechanics Algorithm,” Int. J. Numer. Methods Eng., 28(9), pp. 1325–1353. [CrossRef]
Thomas, J. L., and Salas, M. D., 1986, “Far-Field Boundary Conditions for Transonic Lifting Solutions to the Euler Equations,” AIAA J., 24(7), pp. 1074–1080. [CrossRef]
Kamakoti, R., and Shyy, W., 2004, “Fluid-Structure Interaction for Aeroelastic Applications,” Prog. Aerosp. Sci., 40(8), pp. 535–558. [CrossRef]

Figures

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Fig. 1

Schematic of two-dimensional panel flutter

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Fig. 2

Computational domain of flow field

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Fig. 3

Full view of mesh for flow field

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Fig. 4

Partial view of mesh for flow field

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Fig. 5

Verification of moving mesh method (mesh for flow over a curved panel of w=0.05asin(2πx/a))

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Fig. 6

Grid-independence analysis of flow field

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Fig. 7

Grid-independence analysis of panel structure

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Fig. 8

Analysis of time step independence in presented algorithm for fluid-structure interaction

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Fig. 9

Time history of displacement of a flat and stable state (Ma∞ = 2, ρ¯ = 0.02, R = 0, λ = 300)

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Fig. 10

Time history of displacement of a simple harmonic oscillation (Ma∞ = 2, ρ¯ = 0.02, R = 0, λ = 500)

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Fig. 11

Instantaneous panel deformation in one period (Ma∞ = 2, ρ¯ = 0.02, R = 0, λ = 500)

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Fig. 12

Instantaneous aerodynamic loads over panel in one period (Ma∞ = 2, ρ¯ = 0.02, R = 0, λ = 500)

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Fig. 13

Effect of λ on maximum and minimum displacements of limit cycle oscillations (Ma∞ = 2, ρ¯ = 0.02, R = 0)

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Fig. 14

Time history of displacement of a system in buckling (Ma∞ = 2, ρ¯ = 0.02, R = 2, λ = 50)

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Fig. 15

Deflection of a buckled panel (Ma∞ = 2, ρ¯ = 0.02, R = 2, λ = 50)

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Fig. 16

Pressure distribution over a buckled panel (Ma∞ = 2, ρ¯ = 0.02, R = 2, λ = 50)

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Fig. 17

Steady state response of an inharmonic oscillation (Ma∞ = 2, ρ¯ = 0.02, R = 5, λ = 140)

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Fig. 18

Phase portrait of an inharmonic oscillation system (Ma∞ = 2, ρ¯ = 0.02, R = 5, λ = 140)

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Fig. 19

Spectrum analysis of an inharmonic oscillation system (Ma∞ = 2, ρ¯ = 0.02, R = 5, λ = 140)

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Fig. 20

Stability regions (Ma∞ = 2, ρ¯ = 0.02)

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Fig. 21

Time history of displacement of a limit cycle oscillation (Ma∞ = 1.2, λ* = 100, ρ¯ = 0.1)

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Fig. 22

Amplitude of limit cycle as function of dynamic pressure (Ma∞ = 1.2, ρ¯ = 0.1)

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Fig. 23

Time history of deformation of buckling panel in positive direction (Ma∞ = 0.9, h/a = 0.004, aluminum panel at sea level)

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Fig. 24

Buckling shape of panel in positive direction (Ma∞ = 0.9, h/a = 0.004, aluminum panel at sea level)

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Fig. 25

Time history of deformation of buckling panel in negative direction (Ma∞ = 0.9, h/a = 0.004, aluminum panel at sea level)

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Fig. 26

Buckling shape of panel in negative direction (Ma∞ = 0.9, h/a = 0.004, aluminum panel at sea level)

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Fig. 27

Effect of h/a on peak buckling deformation at Ma∞ = 0.8

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Fig. 28

Effect of h/a on peak buckling deformation at Ma∞ = 0.9

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Fig. 29

Stability boundary (ρ¯ = 0.1)

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