Oscillations of a channel with a flexible wall conveying viscous flow



The interaction between a flexible structure and flowing fluid can cause flow-induced vibrations and the steady state may loose stability by divergence or flutter, thus leading to undesirable dynamic behaviour.

As a model for fluid-structure-interaction a planar channel guiding a flowing fluid is studied. It can be shown that for thin channels the coupling effects are strong [1] and therefore the focus of this contribution is to investigate the behaviour of a channel, where the structural displacements are non-negligible compared to the gap width. Due to this comparatively large amplitudes a linear description of the interface between fluid and structure will not be sufficient anymore and the relation between the Eulerian description of the fluid and the Lagrangian description of the structure must be taken into account: eventually, this yields nonlinear boundary conditions. Furthermore in narrow gaps the viscosity of the fluid cannot be ignored [2]. Hence the effect of viscosity will also be considered within this contribution. In order to allow for analytical results and keep the focus on the effects due to the moving interface, the fluid flow is modelled using lubrication theory. The linear stability of the steady state ist investigated as well as the influence of the inherent nonlinearities of the coupled problem. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)