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Influence of Instabilities on the Trajectory of a Light Sphere

[+] Author Affiliations
Mathieu Jenny, Gilles Bouchet, Jan Dušek

Institut de Mécanique des Fluides et des Solides, Strasbourg, France

Paper No. FEDSM2002-31452, pp. 63-70; 8 pages
doi:10.1115/FEDSM2002-31452
From:
  • ASME 2002 Joint U.S.-European Fluids Engineering Division Conference
  • Volume 2: Symposia and General Papers, Parts A and B
  • Montreal, Quebec, Canada, July 14–18, 2002
  • Conference Sponsors: Fluids Engineering Division
  • ISBN: 0-7918-3616-9 | eISBN: 0-7918-3600-2
  • Copyright © 2002 by ASME

abstract

Recent numerical simulations of the wake of a fixed sphere have confirmed that hydrodynamic forces are likely to have a significant impact on the trajectory of a freely falling (or ascending) sphere. An ideally spherical body ceases to follow a straight vertical trajectory at the Reynolds number (based on its velocity U and diameter d) corresponding to the onset of the primary instability responsible for the breaking of axisymmetry in a fixed sphere wake, i.e. at Re = 212. This instability has been shown to generate a steady non axisymmetric flow with a symmetry plane containing the asymptotic flow velocity, the orientation of which is arbitrary, i.e. selected by any small perturbation at the instability onset. In this communication, we present further work focussed on the experimental investigation of the effect of instabilities on the trajectory of a free sphere. The axisymmetry breaking results in a lift and torque, the vector of lift lying in the symmetry plane and the torque being normal to this plane. This leads to the conclusion that a free-falling (ascending) sphere will be deviated from its vertical trajectory as soon as its Reynolds number reaches the threshold of 212. Moreover, the trajectory will be deflected in an arbitrarily selected vertical plane. An experimental setup has been implemented to investigate this effect. It consists of a 2.5 m high water tank with a .5 times .5 m cross section placed in an air-conditioned chamber allowing to control finely the asymptotic Reynolds number of small spheres (on the order of a mm in diameter) by varying the water temperature. Spheres of densities close to that of water, both lighter and heavier, are considered. The trajectories are investigated fully in three dimensions by processing of images of two cameras following the sphere movement. The preliminary results, presented here for polypropylene spheres lighter than water, confirm the numerically and theoretically predicted effect. After a short acceleration phase roughly in vertical direction the primary instability deflects the trajectories each time in a different vertical plane. The investigation of the fixed sphere wake showed the onset of a secondary Hopf-type instability at Re ≈ 275. The same type of instability develops clearly for free spheres. Unlike for the fixed sphere, the secondary instability is observed to dominate and to yield a wavy trajectory with a vertical mean direction.

Copyright © 2002 by ASME

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