The stability of a flexible cantilever in viscous channel flow

Abstract

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 fluidstructure 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.

Fluid–structure stability analyses and nonlinear dynamics of flexible splitter plates interacting with a circular cylinder flow

“…Fewer authors have investigated the linear stability of fully deformable structures in flows. The flutter instability of a thin flexible plate in channel flow was first investigated by Shoele & Mittal (2016) using an inviscid flow model, and then by Cisonni et al (2017) using a viscous flow model and time-marching simulations. The effect of structural inhomogeneity on the flutter instability of elastic cantilevers was further investigated by Cisonni, Lucey & Elliott (2019).…”

Modeling and simulation of a fluttering cantilever in channel flow

“…By refining ∆x * , we are also decreasing the beam's effective thickness, and slightly increasing the channel size. This effect would be more pronounced asĥ decreases, when the dynamics become a stronger function ofĥ (Guo & Paidoussis, 2000;Shoele & Mittal, 2014Cisonni et al, 2017).…”

“…With recent advancements, it has become possible to directly simulate the fluid-structure interaction (FSI) numerically by solving the Navier-Stokes equations coupled to a model of the structure. Two di-mensional FSI algorithms have been used to study the stability of an elastic member within channel flow (Tetlow & Lucey, 2009;Shoele & Mittal, 2016), and more recently to assess the effect of Reynolds number on the ensuring flutter boundary (Cisonni et al, 2017). Yet, one of the challenges with fluid-structure systems is the large number of parameters necessary to describe the subset of possible system regimes; fully coupled computational approaches require considerable computing time to capture the flutter instability, often only being able to span a fraction of this parameter space.…”

“…As recently evident from (Cisonni et al, 2017), the inviscid treatment of channel flow for small throatto-length ratios is unable to predict stability boundaries that more generally depend on the Reynolds number. Large deviations are observed between their results and the inviscid models, particularly when both Reynolds number and throat-to-length ratio are small.…”

“…Large deviations are observed between their results and the inviscid models, particularly when both Reynolds number and throat-to-length ratio are small. Moreover, Cisonni et al (Cisonni et al, 2017) are unable to address the bridge between the viscous and inviscid stability regimes due to the Reynolds number restriction in their numerical simulations.…”