An experimental investigation of the equilibrium and stability of long towed cable systems

Abstract

The dynamics of towed objects in a fluid environment is of interest for many practical situations. We investigate experimentally the equilibrium and stability of the trajectory of a sphere towed at constant velocity at the tip of a cable with an unprecedented large length-to-diameter aspect ratio, exceeding 10 4 . The towing configuration is artificially obtained by considering a steady cable (with one fixed end and a free end to which a sphere is eventually attached) in a low-turbulence wind tunnel. We consider three different configurations: (i) the cable towed by itself; (ii) a light millimetric towed sphere made of expanded polystyrene; and (iii) a denser millimetric towed sphere made of lead. The trajectory of the cable tip is monitored using high-speed Lagrangian tracking, which allows one to characterize the average position and the dynamical fluctuations of the towed object. We show that the mean equilibrium position is well predicted by a simple model including the aerodynamical forces acting along the cable and on the towed sphere (when present). Concerning stability issues, we find that the heavy lead particle is always towed in stable conditions (within the accessible range of velocities) with only very low energy oscillations related to a weak pendulum-like motion. In contrast, the free end and light sphere cases are shown to become unstable when the towing velocity exceeds a certain threshold. Spectral analysis shows a flutter-type instability for the sphere, with a dominant oscillatory motion, while the cable alone develops a divergence-type instability with random fluctuations.

Flow-induced motions of flexible filaments hanging in cross-flow

“…Fluid-structure interaction problems with flexible structures are becoming increasingly important in engineering applications. Examples include flexible marine propellers (Young, 2008), flexible turbomachinery for biomedical applications (Campbell and Paterson, 2011), flapping wing propulsion for micro aerial vehicles (Unger et al, 2012), flexible bladed wind turbines (MacPhee and Beyene, 2016), towing cables (Obligado and Bourgoin, 2013;Wang et al, 2008), cable-stayed bridges and antennae (Poulin and Larsen, 2007). Flexible fluidstructure interactions are also ubiquitous in nature: flexible vegetation reconfigures dynamically under the action of wind (de Langre, 2008) or water flow, birds use their feathers as passive flow control devices (Dauptain et al, 2008), and the biology of reproduction in mammals heavily depends on the interaction of flexible structures with a surrounding fluid environment, as the flagellar motion allows the sperm to make its way through the female reproductive tract (Simons et al, 2014;Sniderman, 2016;Wrobel et al, 2016).…”

Dynamics of towed particles in a turbulent flow

“…It is this transverse dynamics that we record and analyse using high-speed imaging. We have previously addressed the relevance of the elasticity of the wire in a similar system [19], and it was found to be only significant in the large frequency range in the trajectories' spectral dynamics.…”

Untitled

“…Motion is then confined to the lower end, corresponding to edge flutter. This has been studied both experimentally and numerically in three of the problems of flow-induced vibrations mentioned above: hanging fluid-conveying pipes [7,10], hanging ribbons under axial flow [12] and towed cylinders under axial flow [3,14]. In all these systems it was observed that there exists a limit state in which the length does not affect the stability.…”