Flow-induced vibrations of a cylinder along a circular arc

Abstract

An elastically mounted circular cylinder, immersed in a cross-current and free to move along a rectilinear path, is subjected to vortex-induced vibrations (VIV). These vibrations develop through a mechanism referred to as lock-in, where body motion and vortex shedding synchronize at a frequency that may deviate both from the oscillator natural frequency and from the vortex shedding frequency past a fixed cylinder. The present numerical study aims at extending the analysis to curved trajectories, by considering that the cylinder is free to translate along a circular path. The Reynolds number based on the body diameter ( $D$ ) and current velocity ( $U$ ) is set to $100$ . A wide range of path radii, from $0.05D$ to $10D$ , and values of the reduced velocity (inverse of the oscillator natural frequency non-dimensionalized by $D$ and $U$ ) up to $30$ are examined, for the concave and convex configurations, i.e. the circular path centre located upstream or downstream of the cylinder. Path curvature results in a major alteration of the flow–body system behaviour compared with rectilinear VIV, with substantially different evolutions in the concave and convex configurations. In addition to the typical lock-in mechanism, two subharmonic forms of synchronization, at half and one third of vortex formation frequency, are uncovered in the convex configuration. They coexist with a desynchronized regime where the body and the flow oscillate at incommensurable frequencies. The four interaction regimes exhibit contrasted trends in terms of structural response, spatiotemporal organization of the wake and associated forces. They particularly differ by their symmetry properties, which are closely linked to the possible reconfiguration of the oscillator due to mean fluid forcing.

Path curvature enhances the flow-induced vibrations of a cylinder without structural restoring force

“…Assuming a decoupling of the flow and moving cylinder time scales, a quasi-steady model of , identified by the superscript , and its first-order approximation about can be expressed as (Bourguet 2023 b ) where is the mean in-line force (or drag) coefficient in the fixed body case. The symbol denotes the time-averaged value.…”

“…The numerical method is the same as in previous works concerning comparable systems (Bourguet 2023 a , b ). It is briefly summarized here, and some additional convergence/validation results are presented.…”

“…However, the peak amplitude at a given is systematically larger for than the rectilinear response amplitude, including in the low- range. For an elastically mounted body, the increasing evolution of the displacement frequency with denotes a reduction of the effective added mass, which may become negative for peak amplitude responses (figure 7 in Bourguet 2023 b ). This suggests that the subset of responses reached once the elastic support is removed should include the peak amplitude vibrations (Govardhan & Williamson 2002).…”

“…Some insights may be gained from prior works analysing the related problem of a tethered cylinder, despite the difference in the nature of body motion, i.e. rotation versus translation (Carberry & Sheridan 2007;Ryan, Thompson & Hourigan 2007). For m < 1 and postcritical Re, these works emphasized the effect of m , with a sharp amplification of the vibrations in the lower-m range, as in the rectilinear path case.…”

“…The object of this work is to examine the impact of a curved trajectory on the flow–structure system behaviour. It was triggered by a recent study concerning an elastically mounted cylinder, free to translate along a circular arc within a cross-current at (Bourguet 2023 b ). This study pointed out a major alteration of the vibration properties compared to the rectilinear path configuration, and the emergence of novel interaction regimes.…”