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The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities

Published online by Cambridge University Press:  21 April 2006

P. W. Carpenter  and
A. D. Garrad
P. W. Carpenter
Affiliation:
Department of Engineering Science, University of Exeter, Exeter
A. D. Garrad
Affiliation:
Garrad Hassan and Partners, 10 Northampton Square, London EC1M 5PQ
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Abstract

The flow-induced surface instabilities of Kramer-type compliant surfaces are investigated by a variety of theoretical approaches. This class of instability includes all those modes of instability for which the mechanism of generation involves essentially inviscid processes. The results should be applicable to all compliant surfaces that could be modelled theoretically by a thin elastic plate, with or without applied longitudinal tension, supported on a springy elastic foundation. with or without a viscous fluid substrate; material damping is also taken into account through the viscoelastic properties of the solid constituents of the coatings.

The simple case of a potential main flow is studied first. The eigenmodes for this case are subjected to an energy analysis following the methods of Landahl (1962). Instabilities that grow both in space and time are then considered, and absolute and convective instabilities identified and analysed.

The effects of irreversible processes on the flow-induced surface instabilities are investigated. The shear flow in the boundary layer gives rise to a fluctuating pressure component which is out of phase with the surface motion. This leads to an irreversible transfer of energy from the main stream to the compliant surface. This mechanism is studied in detail and is shown to be responsible for travelling-wave flutter. Simple results are obtained for the critical velocity, wavenumber and stability boundaries. These last are shown to be in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation. An analysis of the effects of a viscous fluid substrate and of material damping is then carried out. The simpler inviscid theory is shown to predict values of the maximum growth rate which are, again, in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation provided that the instability is fairly weak.

Compliant surfaces of finite length are analysed in the limit as wave-length tends to zero. In this way the static-divergence instability is predicted. Simple formulae for critical velocity and wavenumber are derived. These are in exact agreement with the results of the simpler infinite-length theory. But, whereas a substantial level of damping is required for the instability on a surface of infinite length, static divergence grows fastest in the absence of damping on a surface of finite length.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 170 , September 1986 , pp. 199 - 232
Copyright
© 1986 Cambridge University Press

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References

Aleev Yu. G.1973 Dolphins and women. Khimia i zhizn 9, 8–10 (in Russian).Google Scholar
Aleev Yu. G.1977 Nekton. The Hague: Junk.
Atkins D. J.1982 The effect of uniform flow on the dynamics and acoustics of force-excited infinite plates. Admiralty Marine Technology Establishment, Teddington. England, Tech. Memo, AMTE (N) TM 82087.Google Scholar
Benjamin T. B.1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161–205.Google Scholar
Benjamin T. B.1960 Effects of a flexible boundary on hydrodynamic stability. J. Fluid Mech. 9, 513–532.Google Scholar
Benjamin T. B.1963 The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows. J. Fluid Mech. 16, 436–450.Google Scholar
Benjamin T. B.1964 Fluid flow with flexible boundaries. In Proc. 11th Intl Congr. Appl. Maths., Munich, Germany (ed. H. Görtler), p. 109. Springer.
Brazier-Smith, P. R. & Scott J. F.1984 Stability of fluid flow in the presence of a compliant surface. Wave Motion 6, 547–560.Google Scholar
Briggs R. J.1964 Electron-Stream Interaction with Plasmas. M.I.T. Press.
Cairns R. A.1979 The role of negative energy waves in some instabilities of parallel flows. J. Fluid Mech. 92, 1–14.Google Scholar
Carpenter P. W. 1984a The effects of damping on the hydrodynamic stability of flows over Kramer-type compliant surfaces. in Laminar/Turbulent Boundary Layers (ed. E. M. Uram & H. E. Weber), pp. 53–59. ASME.
Carpenter P. W.1984b The effect of a boundary layer on the hydroelastic instability of infinitely long plates. J. Sound Vib. 93, 461–464.Google Scholar
Carpenter P. W.1984c A note on the hydroelastic instability of orthotropic panels. J. Sound Vib. 94, 553–554.Google Scholar
Carpenter, P. W. & Garrad A. D.1982 Effect of a viscous fluid substrate on the flow-induced vibrations of a compliant coating. In Proc. Intl Conf. on Flow Induced Vibrations in Fluid Engineering (ed. H. S. Stephens & G. B. Warren), pp. 369–382. BHRA Fluid Engineering, Cranfield, England.
Carpenter, P. W. & Garrad A. D.1985 The hydrodynamic stability of flows over Kramer-type compliant surfaces. Part 1. Tollmien—Schlichting instabilities. J. Fluid Mech. 155, 465–510.Google Scholar
Carpenter P. W., Gaster, M. & Willis G. J. K.1983 A numerical investigation into boundary layer stability on compliant surfaces. In Numerical Methods in Laminar and Turbulent Flow, pp. 166–172. Pineridge.
Dowell E. H.1971 Generalised aerodynamic forces on a flexible plate undergoing transient motion in a shear flow with an application to panel flutter. AIAA J. 9, 834–841.Google Scholar
Dowell E. H.1975 Aero-elasticity of Plates and Shells. Noordhoff.
Dowell E. H.1985 The effects of compliant walls on transition and turbulence. In Proc. Symp. on Shear Flow—Structure Interaction Phenomena, November 1985, pp. 37–52. ASME.
Dugundji J., Dowell, E. & Perkin B.1963 Subsonic flutter of panels on a continuous elastic foundation. AIAA J. 1, 1146–1154.Google Scholar
Duncan J. H., Waxman, A. M. & Tulin M. P.1985 The dynamics of waves at the interface between a visco-elastic coating and a fluid flow. J. Fluid Mech. 158, 177–197.Google Scholar
Essapian F. S.1955 Speed-induced skin folds in the bottle-nosed porpoise, Tursiops Truncatus. Breviora Mus. Comp. Zool. 43, 1–4.Google Scholar
Fraser, L. A. & Carpenter P. W.1985 A numerical investigation of hydroelastic and hydro-dynamic instabilities in laminar flows over compliant surfaces comprising one or two layers of visco-elastic material. In Numerical Methods in Laminar and Turbulent Flow, pp. 1171–1181. Pineridge.
Gad-El-Hak M.1985 Stability of compliant surfaces. Presentation at Drag Reduction & Boundary Layer Control Symp., Oct. 1985. Nat. Acad. Sci., Washington, D.C.
Gad-El-Hak M.1986a The response of elastic and visco-elastic surfaces to a turbulent boundary layer. Trans. ASME E: J. Appl. Mech. 53, 206–212.Google Scholar
Gad-El-Hak M.1986b Boundary layer interactions with compliant coatings: An overview. Appl. Mech. Rev. 39, 511–523.Google Scholar
Gad-El-Hak M., Blackwelder, R. F. & Riley J. J.1984 On the interaction of compliant coatings with boundary-layer flows. J. Fluid Mech. 140, 257–280.Google Scholar
Garrad, A. D. & Carpenter P. W.1982a On the aerodynamic forces involved in aeroelastic instability of two-dimensional panels in uniform incompressible flow. J. Sound Vib. 80, 437–439.Google Scholar
Garrad, A. D. & Carpenter P. W.1982b A theoretical investigation of flow-induced instabilities in compliant coatings. J. Sound Vib. 85, 483–500.Google Scholar
Gaster M.1962 A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222–224.Google Scholar
Gaster M.1965a On the generation of spatially growing waves in a boundary layer. J. Fluid Mech. 22, 433–441.Google Scholar
Gaster M.1965b The role of spatially growing waves in the theory of hydrodynamic stability. Prog. Aero. Sci. 6, 251–270.Google Scholar
Gaster M.1968 Growth of disturbances in both space and time. Phys. Fluids 11, 723–727.Google Scholar
Gaster, M. & Willis G. J. K.1984 A rapid eigenvalue finder for flows over a compliant surface. In Laminar/Turbulent Boundary Layers (ed. E. M. Uram & H. E. Weber), pp. 79–84. ASME.
Hansen, R. J. & Hunston D. L.1974 An experimental study of turbulent flows over compliant surfaces. J. Sound Vib. 34, 297–308.Google Scholar
Hansen, R. J. & Hunston D. L.1976 Further observations on flow-generated surface waves in compliant surfaces. J. Sound Vib. 46, 593–595.Google Scholar
Hansen, R. J. & Hunston D. L.1983 Fluid-property effects on flow-generated waves on a compliant surface. J. Fluid Mech. 133, 161–177.Google Scholar
Hansen R. J., Hunston D. L., Ni, C. C. & Reischmann M. M.1980a An experimental study of flow-generated waves on a flexible surface. J. Sound Vib. 68, 317–334.Google Scholar
Hansen R. J., Hunston D. L., Ni C. C., Reischmann, M. M. & Hoyt J. W.1980b Hydro-dynamic drag and surface deformations generated by liquid flows over flexible surfaces. In Viscous Flow Drag Reduction (ed. G. R. Hough), pp. 439–452. AIAA. Prog. Astro. Aero., vol. 72.
Hertel H.1963 Structure—Form—Movement. Reinhold.
Kornecki A.1978 Aeroelastic and hydroelastic instabilities of infinitely long plates. I. Solid Mech. Arch. 3, 381–440.Google Scholar
Kornecki A., Dowell, E. H. & O'Brien J.1976 On the aeroelastic instability of two-dimensional panels in uniform incompressible flow. J. Sound Vib. 47, 163–178.Google Scholar
Kramer M. O.1960 Boundary layer stabilization by distributed damping. J. Am. Soc. Nav. Engrs. 72, 25–33.Google Scholar
Landahl M. T.1962 On the stability of a laminar incompressible boundary layer over a flexible surface. J. Fluid Mech. 13, 609–632.Google Scholar
Landahl M. T.1964 Graphical technique for analysing marginally stable dynamic systems. J. Aircraft 1, 293–299.Google Scholar
Landahl, M. T. & Kaplan R. E.1965 Effect of compliant walls on boundary layer stability and transition. AGARDograph 97–1–353.Google Scholar
Macmichael J. M., Klebanoff, P. S. & Mease N. E.1980 Experimental investigation of drag on a compliant surface. In Viscous Flow Drag Reduction (ed. G. R. Hough), pp. 410–438. AIAA. Prog. Astro. Aero., vol. 72.
Melcher J. R.1981 Continuum Electromechanics. M.I.T. Press.
Miles J. W.1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185–199.Google Scholar
Miles J. W.1959a On the generation of surface waves by shear flows. Part 2. J. Fluid Mech. 6, 568–582.Google Scholar
Miles J. W.1959b On the generation of surface waves by shear flows. Part 3. Kelvin—Helmholtz instability. J. Fluid Mech. 6, 583–598.Google Scholar
Miles J. W.1962 On the generation of surface waves by shear flows. Part 4. J. Fluid Mech. 13, 433–448.Google Scholar
Nisewanger C. R.1964 Flow noise and drag measurements of vehicle with compliant coating. U.S. Naval Ordnance Test Station, China Lake, California. NAVWEPS Rep. 8518.Google Scholar
Puryear F. W.1962 Boundary layer control drag reduction by compliant surfaces. U.S. Dept. of Navy, David Taylor Model Basin. Rep. 1668.Google Scholar
Ritter, H. & Messum L. T.1964 Water tunnel measurements of turbulent skin friction on six different compliat surfacess of one foot length. Admiralty Research Lab. Rep. ARL/G/N9.Google Scholar
Ritter, H. & Porteous J. S.1965 Water tunnel measurements of skin friction on a compliant coating. Admiralty Research Lab. Rep. ARL/N3/G/HY/9/7.Google Scholar
Schubauer, G. B. & Skramstad H. K.1948 Laminar boundary layer oscillations and transition on a flat plate. NACA Rep. 909.Google Scholar
Weaver, D. S. & Unny T. E.1970 The hydroelastic stability of a flat plate. Trans. ASME E: J. Appl. Mech. 37, 823–827.Google Scholar