Path instability on a sphere towed at constant speed

Abstract

The dynamics of towed objects in a fluid environment is of interest for many practical situations. In this paper we report results for wake instabilities of spheres towed in a water tank. Six particles of different diameter and/or density ratio have been investigated, towed at 5 different constant velocities. The explored density ratios lay within Γ∈[1.06;2.56], with particle Reynolds numbers Rep∈[100;1200], corresponding to Galileo numbers in the range Ga∈[1300;8000]. We introduce a surrogate Galileo number Ga⁎ that, by taking into account the towing force applied to the particle, allows a comparison with the case of free falling/ascending spheres. Using innovative 3D tracking techniques, the three-dimensional trajectory of each particle is reconstructed. The wake instability for the studied particles is found to be associated to a 3D helicoidal motion with an elliptical cross section in the plane perpendicular to the towing direction. The 3D oscillatory motion was found independent of the particle density ratio, with a threshold of the order of Repc~355 (or Ga⁎c~245). This threshold is slightly larger than the one found for the free falling particles’ transition to 3D chaotic motions (Repc~310 or Gac~225).