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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.
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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

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