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Abstract
We investigate the deformation of a linear viscoelastic compliant coating in a turbulent flow for a wide range of coating parameters. A one-way coupling model is proposed in which the turbulent surface stresses are expressed as a sum of streamwise-travelling waves with amplitudes determined from the stress spectra of the corresponding flow over a rigid wall. The analytically calculated coating deformation is analysed in terms of the root-mean-square (r.m.s.) surface displacement and the corresponding point frequency spectra. The present study systematically investigates the influence of five coating properties namely density, stiffness, thickness, viscoelasticity and compressibility. The surface displacements increase linearly with the fluid/solid density ratio. They are linearly proportional to the coating thickness for thin coatings, while they become independent of the thickness for thick coatings. Very soft coatings show resonant behaviour, but the displacement for stiffer coatings is proportional to the inverse of the shear modulus. The viscoelastic loss angle has only a significant influence when resonances occur in the coating response, while Poisson’s ratio has a minor effect for most cases. The modelled surface displacement is qualitatively compared with recent measurements on the deformation of three different coatings in a turbulent boundary-layer flow. The model predicts the order of magnitude of the surface displacement, and it captures the increase of the coating displacement with the Reynolds number and the coating softness. Finally, we propose a scaling that collapses all the experimental data for the r.m.s. of the vertical surface displacement onto a single curve.
Highlights
The interaction of compliant coatings with laminar, transitional and turbulent flows has been the subject of much research for several decades
We investigate the deformation of a linear viscoelastic compliant coating in a turbulent flow for a wide range of coating parameters
We computed the deformation of a compliant coating in a turbulent flow for a wide range of parameters, using the one-way coupling approach
Summary
The interaction of compliant coatings with laminar, transitional and turbulent flows has been the subject of much research for several decades. Studies were triggered by the work of Kramer (1962), who reported substantial drag reduction with. G. Benschop and others a compliant wall that modelled the dolphin skin. Follow-up research was motivated by the possible use of such compliant coatings to delay transition in laminar flows, to reduce drag in turbulent flows and to suppress vibrations or noise (Gad-el Hak 2002). We review some of the recent experimental, numerical and analytical work regarding the deformation of a compliant wall in a turbulent flow
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