Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T16:13:22.538Z Has data issue: false hasContentIssue false
  • English
  • Français

Sphere–wall collisions: vortex dynamics and stability

Published online by Cambridge University Press:  07 March 2007

MARK C. THOMPSON ,
THOMAS LEWEKE  and
KERRY HOURIGAN
MARK C. THOMPSON
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical Engineering, PO Box 31, Monash University, Melbourne, Victoria 3800, Australia
THOMAS LEWEKE
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre (IRPHE), UMR 6594 CNRS/Universités Aix-Marseille I & II, 49, rue Frédéric Joliot-Curie, B.P. 146, F-13384 Marseille Cedex 13, France
KERRY HOURIGAN
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical Engineering, PO Box 31, Monash University, Melbourne, Victoria 3800, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

For moderate Reynolds numbers, a sphere colliding with a wall in the normal direction will lead to a trailing recirculating wake, threading over the sphere after impact and developing into a complex vortex-ring system as it interacts with vorticity generated at the wall. The primary vortex ring, consisting of the vorticity from the wake of the sphere prior to impact, persists and convects, relatively slowly, outwards away from the sphere owing to the motion induced from its image. The outward motion is arrested only a short distance from the axis because of the strong interaction with the secondary vorticity. In this paper, the structure and evolution of this combined vortex system, consisting of a strong compact primary vortex ring surrounded by and interacting with the secondary vorticity, is quantified through a combined experimental and numerical study. The Reynolds-number range investigated is (100 < Re < 2000). At Reynolds numbers higher than about 1000, a non-axisymmetric instability develops, leading to rapid distortion of the ring system. The growth of the instability does not continue indefinitely, because of the dissipative nature of the flow system; it appears to reach a peak when the wake vorticity first forms a clean primary vortex ring. A comparison of the wavelength, growth rate and perturbation fields predicted from both linear stability theory and direct simulations, together with theoretical predictions, indicates that the dominant physical mechanism for the observed non-axisymmetric instability is centrifugal in nature. The maximum growth occurs at the edge of the primary vortex core, where the vorticity changes sign. Notably, this is a physical mechanism different from that proposed previously to explain the development of the three-dimensional flow of an isolated vortex ring striking a wall.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 575 , March 2007 , pp. 121 - 148
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bayly, B. J. 1988 Three-dimensional centrifugal-type instabilities in inviscid two-dimensional flows. Phys. Fluids 31, 56–64.CrossRefGoogle Scholar
Eames, I. & Dalziel, S. B. 2000 Dust resuspension by the flow around an impacting sphere. J. Fluid Mech. 403, 305–328.CrossRefGoogle Scholar
Gondret, P., Lance, M. & Petit, L. 2002 Bouncing motion of spherical particles in fluids. Phys. Fluids 14, 643–652.CrossRefGoogle Scholar
Hirt, C., Amsden, A. & Cook, J. 1974 An Arbitrary Lagrangian Eulerian finite element method for all flow speeds. J. Comp. Phys. 14, 227–253.CrossRefGoogle Scholar
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70.CrossRefGoogle Scholar
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle-wall collisions in a viscous fluid. J. Fluid Mech. 433, 329–346.CrossRefGoogle Scholar
Kerswell, R. R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83–113.CrossRefGoogle Scholar
LeDizès, S. Dizès, S. 2000 Non-axisymmetric vortices in two-dimensional flows. J. Fluid Mech. 406, 175–198.Google Scholar
Leweke, T., Thompson, M. C. & Hourigan, K. 2004 a Touchdown of a sphere. Phys. Fluids 16, S5.CrossRefGoogle Scholar
Leweke, T., Thompson, M. C. & Hourigan, K. 2004 Vortex dynamics associated with the collision of a sphere with a wall. Phys. Fluids 16, L74–L77.CrossRefGoogle Scholar
Lim, T. T., Nichols, T. B. & Chong, M. S. 1992 A note on the cause of the rebound in the head-on collision of a vortex ring with a wall. Exps. Fluids 12, 41–48.Google Scholar
Naitoh, T., Banno, O. & Yamada, H. 2001 Longitudinal vortex structure in the flow field produced by a vortex ring impinging on a flat plate. Fluid. Dyn. Res. 28, 61–74.CrossRefGoogle Scholar
Orlandi, P. & Verzicco, R. 1993 Vortex rings impinging on walls: axisymmetric and three-dimensional simulations. J. Fluid Mech. 256, 615–646.CrossRefGoogle Scholar
Ormières, D. & Provansal, M. 1999 Transition to turbulence in the wake of a sphere. Phys. Rev. Lett. 83, 80–83.CrossRefGoogle Scholar
Ryan, K., Thompson, M. C. & Hourigan, K. 2005 Three-dimensional transition in the wake of elongated bluff bodies. J. Fluid Mech. 538, 1–29.CrossRefGoogle Scholar
Rice, M. A., Willetts, B. B. & McEwan, I. K. 1996 Wind erosion of crusted solid sediments. Earth Surface Processes Landforms 21, 279–293.3.0.CO;2-A>CrossRefGoogle Scholar
Shao, Y., Raupach, M. R. & Findlater, P. A. 1993 Effect of saltation bombardment on the entrainment of dust by the wind. J. Geophys. Res. 98, 12719–12726.CrossRefGoogle Scholar
Sheard, G. J., Thompson, M. C. & Hourigan, K. 2003 From spheres to circular cylinders: classification of bluff ring transitions and structure of bluff ring wakes. J. Fluid Mech. 492, 147–180.CrossRefGoogle Scholar
Swearingen, J. D., Crouch, J. D. & Handler, R. A. 1995 Dynamics and stability of a vortex ring impacting a solid boundary. J. Fluid Mech. 297, 1–28.CrossRefGoogle Scholar
Thompson, M. C., Hourigan, K. & Sheridan, J. 1996 Three-dimensional instabilities in the wake of a circular cylinder. Expl. Therm. Fluid Sci. 12, 190–196.CrossRefGoogle Scholar
Thompson, M. C., Leweke, T. & Provansal, M. 2001 Kinematics and dynamics of sphere wake transition. J. Fluids Struct. 15, 575–585.Google Scholar
Thompson, M. C., Leweke, T. & Williamson, C. H. K. 2001 The physical mechanism of transition in bluff body wakes. J. Fluids Struct. 15, 607–616.CrossRefGoogle Scholar
Tomboulides, A. G. & Orszag, S. A. 2000 Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 45–73.CrossRefGoogle Scholar
Walker, J. D. A., Smith, C. R., Cerra, A. W. & Doligalski, T. L. 1987 The impact of a vortex ring on a wall. J. Fluid Mech. 181, 99–140.CrossRefGoogle Scholar