Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-19T03:33:25.842Z Has data issue: false hasContentIssue false
  • English
  • Français

Wake structure of a transversely rotating sphere at moderate Reynolds numbers

Published online by Cambridge University Press:  12 February 2009

M. GIACOBELLO ,
A. OOI  and
S. BALACHANDAR
M. GIACOBELLO*
Affiliation:
Air Vehicles Division, Defence Science and Technology Organisation, Fishermans Bend, Australia, 3207
A. OOI
Affiliation:
Department of Mechanical and Manufacturing Engineering, The University of Melbourne, Parkville, Melbourne, Australia, 3052
S. BALACHANDAR
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
*
†Email address for correspondence: matteo.giacobello@dsto.defence.gov.au
Get access Rights & Permissions [Opens in a new window]

Abstract

The uniform flow past a sphere undergoing steady rotation about an axis transverse to the free stream flow was investigated numerically. The objective was to reveal the effect of sphere rotation on the characteristics of the vortical wake structure and on the forces exerted on the sphere. This was achieved by solving the time-dependent, incompressible Navier–Stokes equations, using an accurate Fourier–Chebyshev spectral collocation method. Reynolds numbers Re of 100, 250 and 300 were considered, which for a stationary sphere cover the axisymmetric steady, non-axisymmetric steady and vortex shedding regimes. The study identified wake transitions that occur over the range of non-dimensional rotational speeds Ω* = 0 to 1.00, where Ω* is the maximum velocity on the sphere surface normalized by the free stream velocity. At Re = 100, sphere rotation triggers a transition to a steady double-threaded structure. At Re = 250, the wake undergoes a transition to vortex shedding for Ω* ≥ 0.08. With an increasing rotation rate, the recirculating region is progressively reduced until a further transition to a steady double-threaded wake structure for Ω* ≥ 0.30. At Re = 300, wake shedding is suppressed for Ω* ≥ 0.50 via the same mechanism found at Re = 250. For Ω* ≥ 0.80, the wake undergoes a further transition to vortex shedding, through what appears to be a shear layer instability of the Kelvin–Helmholtz type.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 621 , 25 February 2009 , pp. 103 - 130
Copyright
Copyright © Cambridge University Press 2009

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

Bagchi, P. & Balachandar, S. 2002 Steady planar straining flow past a rigid sphere at moderate Reynolds number. J. Fluid Mech. 466, 365–407.CrossRefGoogle Scholar
Bagchi, P. & Balachandar, S. 2003 Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15 (11), 3496–3513.CrossRefGoogle Scholar
Best, J. L. 1998 The influence of particle rotation on wake stability at particle Reynolds numbers, Re P < 300; implications for turbulence modulation in two-phase flows. Intl. J. Multiphase Flow 24, 693–720.CrossRefGoogle Scholar
Constantinescu, G. S. & Squires, K. D. 2000 LES and DNS investigation of turbulent flow over a sphere. AIAA Paper 2000-0540.CrossRefGoogle Scholar
Giacobello, M. 2005 Wake structure of a transversely rotating sphere at moderate Reynolds numbers. PhD thesis, University of Melbourne, Melbourne, VIC, Australia.Google 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
Kim, D. & Choi, H. 2002 Laminar flow past a sphere rotating in the streamwise direction. J. Fluid Mech. 461, 365–386.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comp. Phys. 59, 308–323.CrossRefGoogle Scholar
Kurose, R. & Komori, S. 1999 Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 384, 183–206.CrossRefGoogle Scholar
Maccoll, J. H. 1928 Aerodynamics of a spinning sphere. J. Roy. Aero. Soc. 32, 777–798.CrossRefGoogle Scholar
Mittal, R. 1999 A {F}ourier–{C}hebyshev collocation method for simulating flow past spheres and spheroids. Int. J. Numer. Meth. Fluids 30, 921–937.3.0.CO;2-3>CrossRefGoogle Scholar
Mittal, S. & Kumar, B. 2003 Flow past a rotating cylinder. J. Fluid Mech. 476, 303–334.CrossRefGoogle Scholar
Nakamura, I. 1976 Steady wake behind a sphere. Phys. Fluids 19 (1), 5–8.CrossRefGoogle Scholar
Niazmand, H. & Renksizbulut, M. 2003 Surface effects on transient three-dimensional flows around rotating spheres at moderate Reynolds numbers. Comput. Fluids 32, 1405–1433.CrossRefGoogle Scholar
Oesterlé, B. & Dinh, B. 1998 Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers. Exps. Fluids 25, 16–22.Google Scholar
Pan, Y., Tanaka, T. & Tsuji, Y. 2001 Direct numerical simulation of particle-laden rotating turbulent channel flow. J. Fluid Mech. 13 (8), 222–230.Google Scholar
Perry, A. E. & Lim, T. T. 1978 Coherent structures in coflowing jets and wakes. J. Fluid Mech. 88 (3), 451–463.CrossRefGoogle Scholar
Perry, A. E., Lim, T. T. & Chong, M. S. 1980 The instantaneous velocity fields of coherent structures in coflowing jets and wakes. J. Fluid Mech. 101 (2), 243–256.CrossRefGoogle Scholar
Perry, A. E. & Tan, D. K. M. 1984 Simple three-dimensional vortex motions in coflowing jets and wakes. J. Fluid Mech. 141, 197–231.CrossRefGoogle Scholar
Rubinow, S. I. & Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447–459.CrossRefGoogle Scholar
Steiner, T. R. 1984 A study of turbulent wakes and the vortex formation process. PhD thesis, University of Melbourne, Melbourne, VIC, Australia.Google Scholar
Taneda, S. 1956 Experimental investigation of the wake behind a sphere at low Reynolds numbers. J. Phys. Soc. Jpn 11, 1104.CrossRefGoogle Scholar
Tomboulides, A. G. & Orszag, S. A. 2000 Numerical investigation of transition and weak turbulent flow past a sphere. J. Fluid Mech. 416, 45–73.CrossRefGoogle Scholar
Torobin, L. B. & Gauvin, W. H. 1960 Fundamental aspects of solids-gas flow, part iv: The effects of particle rotation, roughness and shape. Can. J. Chem. Engng. 38, 142–153.CrossRefGoogle Scholar
Tsuji, Y., Morikawa, Y. & Mizuno, O. 1985 Experimental measurements of the Magnus force on a rotating sphere at low Reynolds numbers. Trans. ASME 107, 484–488.Google Scholar
You, C. F., Qi, H. Y. & Xu, X. C. 2003 Lift force on rotating sphere at low Reynolds numbers and high rotational speeds. ACTA Mech. Sin. 19 (4), 300–307.Google Scholar