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Interaction of panel flutter with inviscid boundary layer instability in supersonic flow

  • Vasily Vedeneev (a1)

Abstract

We investigate the stability of an elastic plate in supersonic gas flow. This problem has been studied in many papers regarding panel flutter, where uniform flow is usually considered. In this paper, we take the boundary layer on the plate into account and investigate its influence on plate stability. Three problem formulations are studied. First, we investigate the stability of travelling waves in an infinite-length plate. Second, the nature of the instability (absolute or convective instability) is examined. Finally, by using solutions of the first two problems, instability of a long finite-length plate is studied by using Kulikovskii’s global instability criterion. The following results are obtained. All the eigenmodes of a finite-length plate are split into two types, which we call subsonic and supersonic. The influence of the boundary layer on these eigenmodes can be of two kinds. First, for a generalized convex boundary layer profile (typical for accelerating flow), supersonic eigenmodes are stabilized by the boundary layer, whereas subsonic disturbances are destabilized. Second, for a profile with a generalized inflection point (typical for constant and decelerating flows), supersonic eigenmodes are destabilized in a thin boundary layer and stabilized in a thick layer; subsonic eigenmodes are damped. The correspondence between the influence of the boundary layer on panel flutter and the stability of the boundary layer over a rigid wall is established. Examples of stable boundary layer profiles of both types are given.

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Corresponding author

Email address for correspondence: vasily@vedeneev.ru

References

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Bers, A. 1983 Space–time evolution of plasma instabilities: absolute and convective. In Handbook of Plasma Physics (ed. Galeev, A. A. & Sudan, R. N.), chap. 3.2, pp. 451517. North-Holland.
Boiko, A. V. & Kulik, V. M. 2012 Stability of flat plate boundary layer over monolithic viscoelastic coatings. Dokl. Phys. 57 (7), 285287.
Bolotin, V. V. 1963 Nonconservative Problems of the Theory of Elastic Stability. Pergamon Press.
Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas. MIT Press.
Carpenter, P. W. & Garrad, A. D. 1985 The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 1. Tollmien–Schlichting instabilities. J. Fluid Mech. 155, 465510.
Carpenter, P. W. & Garrad, A. D. 1986 The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities. J. Fluid Mech. 170, 199232.
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357392.
Doaré, O. & de Langre, E. 2006 The role of boundary conditions in the instability of one-dimensional systems. Eur. J. Mech. B 25 (6), 948959.
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), 834841.
Dowell, E. H. 1973 Aerodynamic boundary layer effect on flutter and damping of plates. J. Aircraft 10 (12), 734738.
Dowell, E. H. 1974 Aeroelasticity of Plates and Shells. Noordhoff International.
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge University Press.
Gaponov, S. A. & Maslov, A. A. 1980 Development of perturbations in compressible flows (in Russian). Nauka.
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 TN D-5798.
Hashimoto, A., Aoyama, T. & Nakamura, Y. 2009 Effect of turbulent boundary layer on panel flutter. AIAA J. 47 (12), 27852791.
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151168.
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473537.
Hunt, R. E. & Crighton, D. G. 1991 Instability of flow in spatially developing media. Proc. R. Soc. Lond. A 435, 109128.
Kornecki, A. 1979 Aeroelastic and hydroelastic instabilities of infinitely long plates. Part 2. Solid Mech. Archives 4 (4), 241346.
Kramer, M. O. 1960 Boundary layer stabilization by distributed damping. J. Am. Soc. Nav. Engrs 72, 25.
Kulikovskii, A. G. 1966a On the stability of homogeneous states. J. Appl. Math. Mech. 30 (1), 180187.
Kulikovskii, A. G. 1966b On the stability of Poiseuille flow and certain other plane-parallel flows in a flat pipe of large but finite length for large Reynolds numbers. J. Appl. Math. Mech. 30 (5), 975989.
Kulikovskii, A. G. 1968 Stability of flows of a weakly compressible fluid in a plane pipe of large, but finite length. J. Appl. Math. Mech. 32 (1), 100102.
Kulikovskii, A. G. 2006 The global instability of uniform flows in non-one-dimensional regions. J. Appl. Math. Mech. 70 (2), 229234.
Kulikovskii, A. G. & Shikina, I. S. 1988 On bending vibrations of a long tube with moving fluid (in Russian). Mechanics. Proc. Natl Acad. Sci. Armenia 41(1), 31–39.
Lees, L. & Lin, C. C. 1946 Investigation of the stability of the laminar boundary layer in a compressible fluid. NACA TN 1115.
Lees, L. & Reshotko, E. 1962 Stability of the compressible laminar boundary layer. J. Fluid Mech. 12, 555590.
Le Dizès, S., Huerre, P., Chomaz, J. M. & Monkewitz, P. A. 1996 Linear global modes in spatially developing media. Phil. Trans. R. Soc. Lond. A 354, 169212.
Lin, C. C. 1966 The Theory of Hydrodynamic Stability. Cambridge University Press.
Lingwood, R. J. & Peake, N. 1999 On the causal behaviour of flow over an elastic wall. J. Fluid Mech. 396, 319344.
Miles, J. W. 1959 On panel flutter in the presence of a boundary layer. J. Aerosp. Sci. 26 (2), 8193, 107.
Miles, J. 2001 Stability of inviscid shear flow over a flexible boundary. J. Fluid Mech. 434, 371378.
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 TN D-4486.
Peake, N. 2004 On the unsteady motion of a long fluid-loaded elastic plate with mean flow. J. Fluid Mech. 507, 335366.
Pier, B., Huerre, P. & Chomaz, J.-M. 2001 Bifurcation to fully nonlinear synchronized structures in slowly varying media. Physica D 148, 4996.
Reutov, V. P. & Rybushkina, G. V. 1998 Hydroelastic instability threshold in a turbulent boundary layer over a compliant coating. Phys. Fluids 10 (2), 417425.
Savenkov, I. V. 1995 The suppression of the growth of nonlinear wave packets by the elasticity of the surface around which flow occurs. Comput. Math. Math. Phys. 35 (1), 7379.
Schlichting, H. 1960 Boundary Layer Theory. McGraw-Hill.
Vedeneev, V. V. 2005 Flutter of a wide strip plate in a supersonic gas flow. Fluid Dyn. 5, 805817.
Vedeneev, V. V. 2006 High-frequency plate flutter. Fluid Dyn. 2, 313321.
Vedeneev, V. V. 2012 Panel flutter at low supersonic speeds. J. Fluids Struct. 29, 7996.
Vedeneev, V. V., Guvernyuk, S. V., Zubkov, A. F. & Kolotnikov, M. E. 2010 Experimental observation of single mode panel flutter in supersonic gas flow. J. Fluids Struct. 26, 764779.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
Wiplier, O. & Ehrenstein, U. 2001 On the absolute instability in a boundary-layer flow with compliant coatings. Eur. J. Mech. B 20 (1), 127144.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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