Self-similar vortex-induced vibrations of a hanging string

Clément Grouthier (1) , Sébastien Michelin (1) , Y. Modarres-Sadeghi (2) , Emmanuel de Langre (1)

1 LadHyX - Laboratoire d'hydrodynamique
2 Department of Mechanical and Industrial Engineering

An experimental analysis of the vortex-induced vibrations of a hanging string with variable tension along its length is presented in this paper. It is shown that standing waves develop along the hanging string. First, the evolution of the Strouhal number S t with the Reynolds number R e follows a trend similar to what is observed for a circular cylinder in a flow for relatively low Reynolds numbers (32 < Re < 700). Second, the extracted mode shapes are self-similar: a rescaling of the spanwise coordinate by a self-similarity coefficient allows all of them to collapse onto a unique function. The self-similar behaviour of the spatial distribution of the vibrations along the hanging string is then explained theoretically by performing a linear stability analysis of an adapted wake-oscillator model. This linear stability analysis finally provides an accurate description of the mode shapes and of the evolution of the self-similarity coefficient with the flow speed.

Domains: Fluid mechanics [physics.class-ph]; Fluids mechanics [physics.class-ph]

Clément Grouthier, Sébastien Michelin, Y. Modarres-Sadeghi, Emmanuel de Langre. Self-similar vortex-induced vibrations of a hanging string. Journal of Fluid Mechanics, 2013, 724, pp.R2. ⟨10.1017/jfm.2013.204⟩. ⟨hal-00996483⟩