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

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.

Motions of a cantilevered flexible plate in viscous channel flow driven by a constant pressure drop

“…Compressional waves would not influence the present flow structure interactions because their characteristic speeds are far higher that those associated with the flutter predicted herein. Shear waves can be prone to flow-induced instabilities as demonstrated, for example, in water flow over a compliant coating [30,31]. However, the dynamic pressure required for this to occur would require air speeds that vastly exceed those in the present study and its application.…”

On the direct determination of the eigenmodes of finite flow–structure systems

“…Such a case could be considered as the fluid-side inhomogeneous problem having its structural parallel in the material inhomogeneity studied in this paper. Volumebased wall models (Carpenter 1990) are usually solved via a Helmholtz decomposition of the Navier equations (Duncan et al 1985) in a travelling-wave approach or the finite-element method in a discretized model. For the interaction of such a wall with an ideal flow, our approach is equally applicable, although computationally expensive, since the single governing equation would be framed in the displacement of all the wall's collocation points.…”

Verification of drag-reduction capabilities of stiff compliant coatings in air flow at moderate speeds

“…As V coat depends significantly on the frequency of the interaction (Gad-el-Hak et al 1984;Duncan et al 1985;Kulik et al 2008), it is reasonable to select the V coat at the resonance frequency f=f 0 for the maximum interaction between the coating and the flow. According to Kulik et al (2008), the wave propagation velocity at the resonance frequency is given as 2 0 2.826 4.5 3.9…”