Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-20T19:41:09.507Z Has data issue: false hasContentIssue false
  • English
  • Français

The dynamics of waves at the interface between a viscoelastic coating and a fluid flow

Published online by Cambridge University Press:  20 April 2006

J. H. Duncan ,
A. M. Waxman  and
M. P. Tulin
J. H. Duncan
Affiliation:
Tracor Hydronautics, Inc., Pindell School Road, Laurel. Maryland 20747 Present address: Flow Research Company, 1320 Fenwick Lane, Silver Spring, Maryland 20910.
A. M. Waxman
Affiliation:
Tracor Hydronautics, Inc., Pindell School Road, Laurel. Maryland 20747 Present address: Computer Vision Laboratory, Center for Automation Research, University of Maryland, College Park, Maryland 20742.
M. P. Tulin
Affiliation:
Tracor Hydronautics, Inc., Pindell School Road, Laurel. Maryland 20747 Present address: Department of Mechanical and Environmental Engineering, University of California at Santa Barbara, California 93106.
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of two-dimensional uniform wavetrains on the interface between a viscoelastic compliant coating and a boundary-layer flow are explored theoretically. The coating is treated as a single-layer isotropic Voigt material of finite thickness that is bonded to a rigid half-space. The flow is modelled first by potential theory and then modified to incorporate pressure phase shifts and magnitudes found in boundary-layer flow over wavy walls. The consideration of viscoelastic effects has led to an important dimensionless damping parameter γt = Ct τt/d (where τt is the strain relaxation time, Ct is the elastic shear-wave speed and d is the layer depth) that seems to have been overlooked by experimentalists. The flow and the damping are found to have dramatic effects on wave propagation. Using flow pressure and material-damping parameters typical of experiments, the results show that both upstream- and downstream-propagating waves exist at low flow speeds. At higher flow speeds, shorter waves can no longer propagate upstream. At still higher velocities, two instabilities, ‘static divergence’ and ‘flutter’, are found. Static divergence occurs for flow speeds above 2.86Ct and consists of slow waves moving with speeds of about 0.02Ct. These results compare fairly well with published experimental data. Static divergence is found to be a damping instability for these coating systems. When the flow speed is increased further, the flutter instability appears consisting of waves with phase speeds about equal to Ct.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 158 , September 1985 , pp. 177 - 197
Copyright
© 1985 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Balasubramanian, R. & Orszag S. A. 1983 Numerical studies of laminar and turbulent drag reduction. NASA Contract Rep. 3669.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. Proc. 11th Intl Congr. Appl. Mech., Germany, pp. 109–128.
Bushnell D. M., Hefner, J. N. & Ash R. L. 1977 The effect of compliant wall motion on turbulent boundary layers. Phys. Fluids 20, 531–548.Google Scholar
Chyu, W. J. & Au-Yang M. K. 1973 Response of panels to turbulence-induced surface-pressure fluctuations and resulting acoustic radiation to the flow field. AIAA Paper 73-993, AIAA Acoustics Specialists Conf., Seattle.
Delves, L. M. & Lyness J. N. 1967 A numerical method for locating the zeros of an analytic function. Maths Comp. 21, 543–560.Google Scholar
Dowell E. H. 1975 Aeroelasticity of Plates and Shells. Noordhoff.
Dungundji J., Dowell, E. & Perkin B. 1963 Subsonic flutter of panels on continuous elastic foundations. AIAA J. 1, 1146.Google Scholar
Fung Y. C. 1965 Foundations of Solid Mechanics. Prentice-Hall.
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
Gislason T. 1971 Experimental investigation of panel divergence at subsonic speeds. AIAA J. 9, 2252–2258.Google Scholar
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. 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., Reischman, M. M. & Hoyt J. W. 1979 Hydrodynamic drag and surface deformations generated by liquid flows over flexible surfaces. In Viscous Flow Drag Reduction; Prog. Astro. Aero. 72, 439–451.Google Scholar
Hunston D. L., Yu, C. & Bullman G. W. 1984 Mechanical properties of compliant coating materials. In Laminar and Turbulent Boundary Layers, vol. 11 (ed. E. M. Uran & H. E. Weber). New York: ASME.
Kendall J. M. 1970 The turbulent boundary layer over a wall with progressive waves. J. Fluid Mech. 14, 259–281.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. & Kaplan R. E. 1965 Effect of compliant walls on boundary layer stability and transition. AGARDograph 97-1-353.Google Scholar
Miles J. W. 1956 On the aerodynamic instability of thin panels. J. Aero. Sci. 23, 771–791.Google Scholar
Rayleigh Lord 1885 On waves propagated along the plane surface of an elastic solid. Proc. Lond. Math. Soc. 17, 4–11.Google Scholar