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Numerical and experimental studies of the rolling sphere wake

Published online by Cambridge University Press:  15 January 2010

B. E. STEWART ,
M. C. THOMPSON ,
T. LEWEKE  and
K. HOURIGAN
B. E. STEWART*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia Institut de Recherche sur les Phénomènes Hors Equilibre, CNRS/Universités Aix-Marseille, 49 rue Frédéric Joliot-Curie, BP 146, F-13384 Marseille cedex 13, France
M. C. THOMPSON
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia
T. LEWEKE
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, CNRS/Universités Aix-Marseille, 49 rue Frédéric Joliot-Curie, BP 146, F-13384 Marseille cedex 13, France
K. HOURIGAN
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia Division of Biological Engineering, Monash University, Melbourne, Victoria 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

A numerical and experimental investigation is reported for the flow around a rolling sphere when moving adjacent to a plane wall. The dimensionless rotation rate of the sphere is varied from forward to reversed rolling and the resulting wake modes are found to be strongly dependent on the value of this parameter. Results are reported for the Reynolds number range 100 < Re < 350, which has been shown to capture the unsteady transitions in the wake. Over this range of Reynolds number, both steady and unsteady wake modes are observed. As the sphere undergoes forward rolling, the wake displays similarities to the flow behind an isolated sphere in a free stream. As the Reynolds number of the flow increases, hairpin vortices form and are shed over the surface of the sphere. However, for cases with reversed rotation, the wake takes the form of two distinct streamwise vortices that form around the sides of the body. These streamwise structures in the wake undergo a transition to a new unsteady mode as the Reynolds number increases. During the evolution of this unsteady mode, the streamwise vortices form an out-of-phase spiral pair. Four primary wake modes are identified and a very good qualitative agreement is observed between the numerical and experimental results. The numerical simulations also reveal the existence of an additional unsteady mode that is found to be unstable to small perturbations in the flow.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 137 - 162
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Ashmore, J., del Pino, C. & Mullin, T. 2005 Cavitation in a lubrication flow between a moving sphere and a boundary. Phys. Rev. Lett. 94, 124501 (1–4).CrossRefGoogle Scholar
Cherukat, P. & McLaughlin, J. B. 1990 Wall-induced lift on a sphere. Intl J. Multiphase Flow 16 (5), 899–907.CrossRefGoogle Scholar
Cherukat, P. & McLaughlin, J. B. 1994 The inertial lift on a rigid sphere in a linear shear flow field near a flat wall. J. Fluid Mech. 263, 1–18.CrossRefGoogle Scholar
Chorin, A. J. 1968 Numerical solution of the Navier–Stokes equations. Math. Comput. 22, 745–762.CrossRefGoogle Scholar
Cox, R. G. & Hsu, S. K. 1977 The lateral migration of solid particles in a laminar flow near a plane. Intl J. Multiphase Flow 3, 201–222.CrossRefGoogle Scholar
Crouch, J. D. 1997 Instability and transient growth for two trailing-vortex pairs. J. Fluid Mech 350, 311–330.CrossRefGoogle Scholar
Ersoy, S. & Walker, J. D. A. 1985 Viscous flow induced by counter-rotating vortices. Phys. Fluids 28 (9), 2687–2698.CrossRefGoogle Scholar
Fabre, D., Jacquin, L. & Loof, A. 2002 Optimal perturbations in a four-vortex aircraft wake in counter-rotating configuration. J. Fluid Mech. 451, 319–328.CrossRefGoogle Scholar
Ghidersa, B. & Dušek, J. 2000 Breaking of axisymmetry and onset of unsteadiness in the wake of a sphere. J. Fluid Mech. 423, 33–69.CrossRefGoogle Scholar
Humphrey, J. A. C. & Murata, H. 1992 On the motion of solid spheres falling through viscous fluids in vertical and inclined tubes. Transactions ASME: J. Fluids Engng 114, 2–11.Google Scholar
Jackson, S. P. 2007 The growing complexity of platelet aggregation. Blood 109 (12), 5087–5095.CrossRefGoogle ScholarPubMed
Jacquin, L., Fabre, D., Sipp, D., Theofilis, V. & Vollmers, H. 2003 Instability and unsteadiness of aircraft wake vortices. Aerosp. Sci. Technol. 7, 577–593.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.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
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414–443.CrossRefGoogle Scholar
Leontini, J. S., Thompson, M. C. & Hourigan, K. 2007 Three-dimensional transition in the wake of a transversely oscillating cylinder. J. Fluid Mech. 577, 79–104.CrossRefGoogle Scholar
Liu, Y. J., Nelson, J., Feng, J. & Joseph, D. D. 1993 Anomalous rolling of spheres down an inclined plane. J. Non-Newtonian Fluid Mech. 50, 305–329.CrossRefGoogle Scholar
Magarvey, R. H. & Bishop, R. L. 1961 Transition ranges for three-dimensional wakes. Can. J. Phys. 39, 1418–1422.CrossRefGoogle Scholar
Mittal, R. 1999 Planar symmetry in the unsteady wake of a sphere. AIAA J. 37 (3), 388–390.CrossRefGoogle Scholar
Natarajan, R. & Acrivos, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323–344.CrossRefGoogle Scholar
Ormières, D. & Provansal, M. 1999 Transition to turbulence in the wake of a sphere. Phys. Rev. Lett. 83 (1), 80–83.CrossRefGoogle Scholar
Prokunin, A. N. 2004 Microcavitation in the slow motion of a solid spherical particle along a wall in a fluid. Fluid Dyn. 39 (5), 771–778.CrossRefGoogle Scholar
Prokunin, A. N. 2007 The effects of atmospheric pressure, air concentration in the fluid, and the surface roughness on the solid-sphere motion along a wall. Phys. Fluids 19, 113601 (1–10).CrossRefGoogle Scholar
Ryan, K., Thompson, M. C. & Hourigan, K. 2005 Three-dimensional transition in the wake of bluff elongated cylinders. J. Fluid Mech. 538, 1–29.CrossRefGoogle Scholar
Ryan, K., Thompson, M. C. & Hourigan, K. 2007 The effect of mass ratio and tether length on the flow around a tethered cylinder. J. Fluid Mech. 591, 117–144.CrossRefGoogle Scholar
Sakamoto, H. & Haniu, H. 1995 The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow. J. Fluid Mech. 287, 151–171.CrossRefGoogle Scholar
Schouveiler, L. & Provansal, M. 2002 Self-sustained oscillations in the wake of a sphere. Phys. Fluids 14 (11), 3846–3854.CrossRefGoogle Scholar
Seddon, J. R. T. & Mullin, T. 2008 Cavitation in anisotropic fluids. Phys. Fluids 20 (2), 023102 (1–5).CrossRefGoogle Scholar
Sheard, G. J., Thompson, M. C. & Hourigan, K. 2004 From spheres to circular cylinders: non-axisymmetric transitions in the flow past rings. J. Fluid Mech. 506, 45–78.CrossRefGoogle Scholar
Stewart, B. E. 2008 The dynamics and stability of flows around rolling bluff bodies. PhD thesis, Monash University.Google Scholar
Stewart, B. E., Leweke, T., Hourigan, K. & Thompson, M. C. 2008 Wake formation behind a rolling sphere. Phys. Fluids 20, 071704 (1–4).CrossRefGoogle Scholar
Takemura, F. & Magnaudet, J. 2003 The transverse force on clean and contaminated bubbles rising near a vertical wall at moderate Reynolds number. J. Fluid Mech. 495, 235–253.CrossRefGoogle Scholar
Taneda, S. 1956 Experimental investigation of the wake behind a sphere at low Reynolds numbers. Phys. Soc. Japan 11 (10), 1104–1108.CrossRefGoogle Scholar
Thompson, M. C., Hourigan, K., Cheung, A. & Leweke, T. 2006 Hydrodynamics of a particle impact on a wall. Appl. Math. Model. 30, 1356–1369.CrossRefGoogle Scholar
Thompson, M. C., Leweke, T. & Provansal, M. 2001 Kinematics and dynamics of sphere wake transition. J. Fluids Struct. 15, 575–585.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
Woollard, K. J., Suhartoyo, A., Harris, E. E., Eisenhardt, S. U., Jackson, S. P., Peter, K., Dart, A. M., Hickey, M. J. & Chin-Dusting, J. P. F. 2008 Pathophysiological levels of soluble p-selectin mediate adhesion of leukocytes to the endothelium through mac-1 activation. Circulat. Res. 103 (10), 1128–1138.CrossRefGoogle Scholar
Zeng, L., Balachandar, S. & Fischer, P. 2005 Wall-induced forces on a rigid sphere at finite Reynolds number. J. Fluid Mech. 536, 1–25.CrossRefGoogle Scholar
Zeng, L., Najjar, F., Balachandar, S. & Fischer, P. 2009 Forces on a finite-sized particle located close to a wall in a linear shear flow. Phys. Fluids 21, 033302 (1–18).CrossRefGoogle Scholar