Self-similar vortex-induced vibrations of a hanging string

Abstract

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. The evolution of the Strouhal number St with the Reynolds number Re first 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 on 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.

On the efficiency of energy harvesting using vortex-induced vibrations of cables

“…In order to understand the dependence of the efficiency on ξ, the motion of the hanging cable is plotted inFigure 10 for three different damping parameters and = opt . For both small and high dampings, Figure 10 (a) and (c), the motion is characterized by mainly-stationary waves, as in the case of a fixed upper extremity [15]. The corresponding mode shape is actually very close to a zero-order Bessel function of the first kind, with either a free-end condition, y ( ) = 0 for small ξ, Figure 10 (a), or a fixed-end condition, y ( ) = 0 for high ξ, Figure 10 (c).…”

“…The dimensionless cross-flow displacement y and time t are defined as in previous sections. Following Grouthier et al [15], the dimensionless spanwise coordinate is defined as z = Z/Z c where the characteristic length for the spanwise coordinate is Z c = m s g/m t ω 2 f . Given these characteristic dimensions, there are two dimensionless harvesting parameters.…”

“…The cable was placed in uniform flow of constant speed U in the water channel of the Fluid-Structure Interactions laboratory of University of Massachusetts, Amherst, whose test section dimensions are 38 cm × 50 cm × 150 cm. The experimental setup was similar to that used by Grouthier et al [15], except for the top dissipative boundary condition. The cable was hung by nylon strings and fixed to the dashpot, Figure 7.…”

“…The lift coefficient C L0 is adapted to the experimental range of Reynolds numbers, Re ≈ 100, C L0 = 0.3 [25,34]. The coupling parameter A is fitted to amplitude measurements of the hanging cable VIV in cases were the upper end is fixed, A = 2.5 [14], while the Strouhal number is taken from Grouthier et al [15]. The model is integrated in space and time using finite differences and the efficiency reads as…”

Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers

“…This analytical idea opened a new threshold for the interpretation of the frequency lock-in phenomenon. Besides, linear wake oscillator models have also been utilized to study VIV of slender flexible structures like cables and strings (Violette, De Langre & Szydlowski 2010;Grouthier et al 2013). The stability analysis results showed that linear models could capture a significant part of the underlying physics of the VIV phenomenon.…”