The stability of a flexible cantilever in viscous channel flow

Most studies of the flow-induced flutter instability of a flexible cantilever have assumed inviscid flow because of the high flow speeds and the large scale of the structures encountered in the wide range of applications of this fluid-structure interaction (FSI) system. However, for instance, in the fields of energy harvesting and biomechanics, low flow speeds and small- and micro-scale systems can give relatively low Reynolds numbers so that fluid viscosity needs to be explicitly accounted for to provide reliable predictions of channel-immersed-cantilever stability. In this study, we employ a numerical model coupling the Navier-Stokes equations and a one-dimensional elastic beam model. We conduct a parametric investigation to determine the conditions leading to flutter instability of a slender flexible cantilever immersed in two-dimensional viscous channel flow for Reynolds numbers lower than 1000. The large set of numerical simulations carried out allows predictions of the influence of decreasing Reynolds numbers and of the cantilever confinement on the single-mode neutral stability of the FSI system and on the pre- and post-critical cantilever motion. This model's predictions are also compared to those of a FSI model containing a two-dimensional solid model in order to assess, primarily, the effect of the cantilever slenderness in the simulations. Results show that an increasing contribution of viscosity to the hydrodynamic forces significantly alters the instability boundaries. In general, a decrease in Reynolds number is predicted to produce a stabilisation of the FSI system, which is more pronounced for high fluid-to-solid mass ratios. For particular fluid-to-solid mass ratios, viscous effects can lower the critical velocity and lead to a change in the first unstable structural mode. However, at constant Reynolds number, the effects of viscosity on the system stability are diminished by the confinement of the cantilever, which strengthens the importance of flow inertia.