An analysis method of the vortex-induced vibrations of a tethered sphere
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An analysis method of the vortex-induced vibrations of a tethered sphere Marco Negri . Domenica Mirauda . Stefano Malavasi
Received: 8 September 2019 / Accepted: 20 August 2020 The Author(s) 2020
Abstract Vortex-induced vibrations (VIV) in systems with more than one degree of freedom often present complex synchronization among the motion components, also hidden by the randomness that characterizes the motion itself. A phase average method has been here developed and applied to the displacements of a tethered sphere, at low mass and damping, to analyze its xy trajectories over a wide range of reduced velocities, 5 B U* B 25 (Reynolds numbers, 5.1 9 103 B Re B 2.67 9 104). This method has allowed the identification of both the periodic and chaotic contribution of each motion component, accurately reconstructing the underlying trajectory periodic pattern. The two classical vibration modes, I and II, have been also observed. The method developed here was able to better rebuild the experimental data compared to other methods found in the relevant literature, providing useful insights into the study of the dynamic response of a freely-oscillating tethered sphere immersed in a steady flow.
M. Negri S. Malavasi Department of Civil and Environmental Engineering, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milan, Italy D. Mirauda (&) School of Engineering, Basilicata University, viale dell’Ateneo Lucano 10, 85100 Potenza, Italy e-mail: [email protected]
Keywords Vortex-induced vibrations Tethered sphere Phase average Trajectory Reduced velocity Laboratory experiments
1 Introduction The dynamic response analysis of bodies completely or partly immersed in steady flows is crucial in marine engineering, when analyzing the stability of various off-shore structures including production and drilling risers, pipelines, moorings, tethers of tension leg platforms, spar platforms and the members of jacket structures. Interest in this field of research has increased, given its relevance in green-energy exploitation techniques (e.g., [1]). Most of the existing works focus on bodies with multiple degrees of freedom, and mainly cylinders. Only a few of them investigate the flow interactions with a sphere, due to the difficulties encountered in measuring, modelling, and analyzing its complex three-dimensional wake [2–4]. Early studies evaluated the action of surface waves on tethered buoyant spheres, empirically obtaining drag and inertia coefficients through Morison’s equation [5, 6]. Later, the focus moved to analyzing the tethered sphere oscillations, taking into account the mass ratio, m* (ratio between the mass of the sphere, m, and the mass of displaced fluid, md), which defines a body as ‘light’ (m* \ 1) or ‘heavy’ (m* [ 1).
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Meccanica
In 1997, Williamson and Govardhan [7] and Govardhan and Williamson [8] mainly investigated the VIV of light tethered spheres, finding large crossflow oscillation amplitudes with typical figureof-eight or cre
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