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Short-wave instability of an elastic plate in supersonic flow in the presence of the boundary layer

Published online by Cambridge University Press:  05 August 2016

Vsevolod Bondarev  and
Vasily Vedeneev
Vsevolod Bondarev
Affiliation:
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991, Russia
Vasily Vedeneev*
Affiliation:
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991, Russia
*
†Email address for correspondence: [email protected]
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Abstract

Panel flutter is a dangerous aeroelastic instability of the skin panels of supersonic flight vehicles. Though the linear stability of panels in uniform flow has been studied in detail, the influence of the boundary layer is still an open question. Most studies of panel flutter in the presence of the boundary layer are devoted to the ($1/7$)th-power velocity law and yield a stabilising effect of the boundary layer. Recently, Vedeneev (J. Fluid Mech., vol. 736, 2013, pp. 216–249) considered arbitrary velocity and temperature profiles and showed that, for a generalised convex boundary layer profile, a decrease of the growth rates of ‘supersonic’ perturbations (responsible for single-mode panel flutter) is accompanied by destabilisation of ‘subsonic’ perturbations that are neutral in uniform flow. However, this result is not self-consistent, as the long-wave expansion for solutions of the Rayleigh equation was used, whereas subsonic perturbations, generally speaking, cannot be considered as long waves. More surprising results are obtained for the boundary layer profile with a generalised inflection point, where the effect of the layer is destabilising even for ‘supersonic’ perturbations, and such waves can also have short lengths. In order to overcome this inconsistency, in this paper, we solve the Rayleigh equation numerically and investigate the stability of short-wave perturbation of the elastic plate in the presence of the boundary layer. As before, two problem formulations are investigated. First, we study running waves in an infinite plate. Second, we analyse eigenmodes of the plate of large finite length and use Kulikovskii’s global instability criterion. Based on the results of calculations, we confirm that the effect of the boundary layer with a generalised inflection point can be essentially destabilising. On the other hand, for generalised convex boundary layers, calculations show that, unlike the prediction of the long-wave approximation, the finite plate is fully stabilised for sufficiently thick boundary layers.

JFM classification

Boundary Layers: Boundary layer stability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 802 , 10 September 2016 , pp. 528 - 552
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Copyright
© 2016 Cambridge University Press 

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References

Alder, M. 2015 Development and validation of a fluid-structure solver for transonic panel flutter. AIAA J. 53 (12), 3509–3521.Google Scholar
Alder, M. 2016 Nonlinear dynamics of pre-stressed panels in low supersonic turbulent flow. AIAA J.; (in press), doi:10.2514/1.J054783.Google Scholar
Bendiksen, O. O. & Davis, G. A.1995 Nonlinear traveling wave flutter of panels in transonic flow. AIAA Paper 95-1486.Google Scholar
Bolotin, V. V. 1963 Nonconservative Problems of the Theory of Elastic Stability. Pergamon.Google Scholar
Dowell, E. H. 1974 Aeroelasticity of Plates and Shells. Noordhoff International.Google Scholar
Dowell, E. H. 1971 Generalized aerodynamic forces on a flexible plate undergoing transient motion in a shear flow with an application to panel flutter. AIAA J. 9 (5), 834–841.Google Scholar
Dowell, E. H. 1973 Aerodynamic boundary layer effect on flutter and damping of plates. J. Aircraft 10 (12), 734–738.Google Scholar
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Duan, B., Abdel-Motagaly, K., Guo, X. & Mei, C.2003 Suppression of supersonic panel flutter and thermal deflection using shape memory alloy. AIAA Paper 2003-1513.Google Scholar
Gaponov, S. A. & Maslov, A. A. 1980 Development of Perturbations in Compressible Flows. Nauka; (in Russian).Google Scholar
Gaspers, P. A. Jr, Muhlstein, L. Jr & Petroff, D. N. 1970 Further results on the influence of the turbulent boundary layer on panel flutter. NASA Tech. Note TN D-5798.Google Scholar
Gordnier, R. E. & Visbal, M. R. 2002 Development of a three-dimensional viscous aeroelastic solver for nonlinear panel flutter. J. Fluids Struct. 16 (4), 497–527.Google Scholar
Hashimoto, A., Aoyama, T. & Nakamura, Y. 2009 Effect of turbulent boundary layer on panel flutter. AIAA J. 47 (12), 2785–2791.Google Scholar
Mei, C., Abdel-Motagaly, K. & Chen, R. R. 1999 Review of nonlinear panel flutter at supersonic and hypersonic speeds. Appl. Mech. Rev. 10, 321–332.Google Scholar
Miles, J. W. 1959 On panel flutter in the presence of a boundary layer. J. Aero/Space Sci. 26 (2), 81–93; 107.Google Scholar
Miles, J. 2001 Stability of inviscid shear flow over a flexible boundary. J. Fluid Mech. 434, 371–378.Google Scholar
Muhlstein, L. Jr, Gaspers, P. A. Jr & Riddle, D. W. 1968 An experimental study of the influence of the turbulent boundary layer on panel flutter. NASA Tech. Note TN D-4486.Google Scholar
Kornecki, A. 1979 Aeroelastic and hydroelastic instabilities of infinitely long plates. II. Solid Mech. Arch. 4 (4), 241–346.Google Scholar
Kulikovskii, A. G. 1966 On the stability of homogeneous states. J. Appl. Math. Mech. 30 (1), 180–187.Google Scholar
Lees, L. & Lin, C. C.1946 Investigation of the stability of the laminar boundary layer in a compressible fluid. NACA Tech. Note TN 1115.Google Scholar
Novichkov, Yu. N. 1978 Flutter of plates and shells. In Mechanics of Deformable Solids, Advances in Science and Technology, vol. 11, pp. 67–122. VINITI; (in Russian).Google Scholar
Schlichting, H. 1960 Boundary Layer Theory. McGraw-Hill.Google Scholar
Shishaeva, A., Vedeneev, V. & Aksenov, A. 2015 Nonlinear single-mode and multi-mode panel flutter oscillations at low supersonic speeds. J. Fluids Struct. 56, 205–223.Google Scholar
Vedeneev, V. V. 2005 Flutter of a wide strip plate in a supersonic gas flow. Fluid Dyn. 5, 805–817.Google Scholar
Vedeneev, V. V. 2007 Nonlinear high-frequency flutter of a plate. Fluid Dyn. 5, 858–868.Google Scholar
Vedeneev, V. V. 2012 Panel flutter at low supersonic speeds. J. Fluids Struct. 29, 79–96.Google Scholar
Vedeneev, V. V. 2013a Effect of damping on flutter of simply supported and clamped panels at low supersonic speeds. J. Fluids Struct. 40, 366–372.Google Scholar
Vedeneev, V. V. 2013b Interaction of panel flutter with inviscid boundary layer instability in supersonic flow. J. Fluid Mech. 736, 216–249.Google Scholar
Vedeneev, V. V. 2013c Limit oscillatory cycles in the single mode flutter of a plate. J. Appl. Math. Mech. 77 (3), 257–267.Google Scholar
Visbal, M. 2014 Viscous and inviscid interactions of an oblique shock with a flexible panel. J. Fluids Struct. 48, 27–45.Google Scholar
Zhou, R. C., Lai, Z., Xue, D. Y., Huang, J.-K. & Mei, C. 1995 Suppression of nonlinear panel flutter with piezoelectric actuators using finite element method. AIAA J. 33 (6), 1098–1105.Google Scholar