Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-19T20:46:13.878Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow past a transversely rotating sphere at Reynolds numbers above the laminar regime

Published online by Cambridge University Press:  30 October 2014

Eric K. W. Poon ,
Andrew S. H. Ooi ,
Matteo Giacobello ,
Gianluca Iaccarino  and
Daniel Chung
Eric K. W. Poon*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia
Andrew S. H. Ooi
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia
Matteo Giacobello
Affiliation:
Air Vehicles Division, Defence Science and Technology Organisation, 506 Lorimer Street, Fishermans Bend, Victoria 3207, Australia
Gianluca Iaccarino
Affiliation:
Department of Mechanical Engineering, Stanford University, 488 Escondido Mall, Bldg 02-500, Rm 500A, Stanford, CA 94305-3035, USA
Daniel Chung
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia
*
†Email address for correspondence: epoon@unimelb.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow past a transversely rotating sphere at Reynolds numbers of $\mathit{Re}=500{-}1000$ is directly simulated using an unstructured finite volume collocated code. The effect of rotation rate on the flow is studied by increasing the dimensionless rotation rate, ${\it\Omega}^{\ast }$, from 0 to 1.20, where ${\it\Omega}^{\ast }$ is the maximum sphere surface velocity normalised by the free stream velocity. This study investigates the marked unsteadiness of the flow structures at $\mathit{Re}=500{-}1000$. Comparison with previous numerical data (Giacobello et al., J. Fluid Mech., vol. 621, 2009, pp. 103–130; Kim, J. Mech. Sci. Technol., vol. 23, 2009, pp. 578–589) reveals a new flow regime, namely a ‘shear layer–stable foci’ regime, besides the widely reported ‘vortex shedding’ and ‘shear layer instability’ regimes. The ‘shear layer–stable foci’ regime is observed at $\mathit{Re}=500$ and ${\it\Omega}^{\ast }=1.00$; $\mathit{Re}=640{-}1000$ and ${\it\Omega}^{\ast }\geqslant 0.80$. In this flow regime, the shear layer on the advancing side of the sphere (where the sphere surface velocity vector opposes the free stream velocity) shortens significantly while fluid from the retreating side (opposite to the advancing side) is drawn towards the mid-plane normal to the peripheral velocity. This results in the formation of a stable focus near the onset of the shear layer instability. This stable focus becomes more pronounced with increasing $\mathit{Re}$ and ${\it\Omega}^{\ast }$. It increases the oscillation magnitude and decreases the oscillation frequency of the hydrodynamic forces.

JFM classification

Vortex Flows: Vortex Flows Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 759 , 25 November 2014 , pp. 751 - 781
Check for updates
Copyright
© 2014 Cambridge University Press 

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

Achenbach, E. 1974 Vortex shedding from spheres. J. Fluid Mech. 62, 209–221.Google Scholar
Alcock, A., Gilleard, W., Brown, N. A. T., Baker, J. & Hunter, A. 2012 Initial ball flight characteristics of curve and instep kicks in elite women’s football. J. Appl. Biomech. 28 (1), 70–77.Google Scholar
Almedeij, J. 2008 Drag coefficient of flow around a sphere: matching asymptotically the wide trend. Powder Technol. 186, 218–223.CrossRefGoogle Scholar
Bagchi, P. & Balachandar, S. 2002 Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate $\mathit{Re}$ . Phys. Fluids 14 (8), 2719–2737.Google Scholar
Bagchi, P. & Balachandar, S. 2003 Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15 (11), 3496–3513.Google Scholar
Bagchi, P. & Balachandar, S. 2004 Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518, 95–123.Google Scholar
Bagchi, P., Ha, M. Y. & Balachandar, S. 2001 Direct numerical simulation of flow and heat transfer from a sphere in a uniform cross-flow. Trans. ASME J. Fluids Engng 123, 347–358.Google Scholar
Bonneton, P. & Chomax, J. M. 1992 Instability of the wake generated by a sphere. C. R. Acad. Sci. Paris 314, 1001–1006.Google Scholar
Brown, P. P. & Lawler, D. F. 2003 Sphere drag and settling velocity revisited. J. Environ. Engng 129, 222–231.Google Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765–777.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Academic Press.Google Scholar
Dennis, S. C. R., Singh, S. N. & Ingham, D. B. 1980 The steady flow due to a rotating sphere at low and moderate Reynolds numbers. J. Fluid Mech. 101, 257–279.CrossRefGoogle Scholar
Dgheim, J., Abdallah, M., Habchi, R. & Zakhia, N. 2012 Heat and mass transfer investigation of rotating hydrocarbons droplet which behaves as a hard sphere. Appl. Math. Model. 36, 2646–2935.Google Scholar
Fornberg, B. 1988 Steady viscous flow past a sphere at high Reynolds numbers. J. Fluid Mech. 190, 471–489.Google Scholar
Giacobello, M., Ooi, A. & Balachandar, S. 2009 Wake structure of a transversely rotating sphere at moderate Reynolds numbers. J. Fluid Mech. 621, 103–130.Google Scholar
Goff, J. E. & Carre, M. J. 2010 Soccer ball lift coefficients via trajectory analysis. Eur. J. Phys. 31 (4), 775–784.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.Google 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.Google Scholar
Kim, D. 2009 Laminar flow past a sphere rotating in the transverse direction. J. Mech. Sci. Technol. 23, 578–589.Google Scholar
Kim, D. & Choi, H. 2000 A second-order time-accurate finite volume method for unsteady incompressible flow on hybrid unstructured grids. J. Comput. Phys. 162, 411–428.CrossRefGoogle Scholar
Kim, H. J. & Durbin, P. A. 1988 Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation. Phys. Fluids 31 (11), 3260–3265.CrossRefGoogle Scholar
Kurien, S. & Taylor, M. A. 2005 Direct numerical simulations of turbulence. Los Alamos Sci. 29, 142–151.Google 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.Google Scholar
Lee, S. 2000 A numerical study of the unsteady wake behind a sphere in a uniform flow at moderate Reynolds numbers. Comput. Fluids 29, 639–667.CrossRefGoogle Scholar
Liu, N. & Bogy, D. B. 2008 Forces on a rotating particle in a shear flow of a highly rarefied gas. Phys. Fluids 20, 107102.Google Scholar
Liu, N. & Bogy, D. B. 2009 Forces on a spherical particle with an arbitrary axis of rotation in a weak shear flow of a highly rarefied gas. Phys. Fluids 21, 047102.Google Scholar
Liu, Q. & Prosperetti, A. 2010 Wall effects on a rotating sphere. J. Fluid Mech. 657, 1–21.Google Scholar
Lopez, O. D. & Moser, R. D. 2008 Delayed detached eddy simulation of flow over an airfoil with synthetic jet control. Mec. Comput. 17, 3225–3245.Google Scholar
Loth, E. 2008 Lift of a solid spherical particle subject to vorticity and/or spin. AIAA J. 4, 801–809.Google Scholar
Magarvey, R. H. & Bishop, R. L. 1961 Wakes in liquid–liquid systems. Phys. Fluids 4 (7), 800–805.CrossRefGoogle Scholar
Mahesh, K., Constantinescu, G. & Moin, P. 2004 A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197, 215–240.Google Scholar
Mittal, R. 1999 A Fourier–Chebyshev spectral collocation method for simulating flow past spheres and spheroids. Intl 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.Google Scholar
Mittal, R. & Najjar, F. M. 1999 Vortex dynamics in the sphere wake. In Proceedings of the 30th AIAA Fluid Dynamics Conference, AIAA.Google Scholar
Mittal, R., Wilson, J. J. & Najjar, F. M. 2002 Symmetry properties of translation sphere wake. AIAA J. 40, 579–582.Google Scholar
Niazmand, H. & Renksizbukut, 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. Exp. Fluids 25, 16–22.Google Scholar
Passmore, M. A., Tuplin, S., Spencer, A. & Jones, R. 2008 Experimental studies of the aerodynamics of spinning and stationary footballs. Proc. Inst. Mech. Engrs 222, 195–205.Google Scholar
Ploumhans, P., Winckelmans, G. S., Salmon, J. K., Leonard, A. & Warren, M. S. 2002 Vortex methods for direct numerical simulation of three-dimensional bluff body flows: application to the sphere at $\mathit{Re}=300,500$ , and 1000. J. Comput. Phys. 178, 427–463.Google Scholar
Poon, E. K. W., Ooi, A. S. H., Giacobello, M. & Cohen, R. C. Z. 2010 Laminar flow structures from a rotating sphere: effect of rotating axis angle. Intl J. Heat Fluid Flow 31, 961–972.Google Scholar
Poon, E. K. W., Ooi, A. S. H., Giacobello, M. & Cohen, R. C. Z. 2013 Hydrodynamic forces on a rotating sphere. Intl J. Heat Fluid Flow 42, 278–288.CrossRefGoogle Scholar
Pruppacher, H. R., Clair, B. P. L. & Hamielec, A. E. 1970 Some relations between drag and flow patterns of viscous flow past a sphere and a cylinder at low and intermediate Reynolds numbers. J. Fluid Mech. 44, 781–790.Google 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.Google Scholar
Sakamoto, H. & Haniu, H. 1990 A study on vortex shedding from spheres in a uniform flow. Trans. ASME 112, 386–392.Google Scholar
Spalart, P. R. & Squires, K. D. 2004 The status of detached-eddy simulation for bluff bodies. In The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains (ed. McCallen, R., Browand, F. & Ross, J.), Lecture Notes in Applied and Computational Mechanics, vol. 19, pp. 29–45. Springer.Google Scholar
Tanaka, T., Yamagata, K. & Tsuji, Y.1990 Experiment on fluid forces on a rotating sphere and spheroid. In Proceedings of the 2nd KSME–JSME Fluids Engineering Conference.Google 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.Google Scholar
Tri, B. D., Oesterle, B. & Deneu, F. 1990 Premiers resultats sur la portance d’une sphere en rotation aux nombres de Reynolds intermediaies. C. R. Acad. Sci. Paris II 311, 27–31.Google Scholar
Tsuji, Y., Morikawa, Y. & Mizuno, O. 1985 Experimental measurement of the Magnus force on a rotating sphere at low Reynolds numbers. Trans. ASME 107, 484–488.Google Scholar
Wu, X., Cen, K., Luo, Z., Wang, Q. & Fang, M. 2008a Measurement on particle rotation speed in gas–solid flow based on identification of particle rotation axis. Exp. Fluids 45, 1117–1128.Google Scholar
Wu, J. S. & Faeth, G. M. 1993 Sphere wakes in still surroundings at intermediate Reynolds numbers. AIAA J. 31, 1448–1455.Google Scholar
Wu, X., Wang, Q., Luo, Z., Fang, M. & Cen, K. 2008b Experimental study of particle rotation characteristics with high-speed digital imaging system. Powder Technol. 181, 21–30.CrossRefGoogle Scholar
You, D., Ham, F. & Moin, P. 2008 Discrete conservation principles in large-eddy simulation with application to separation control over an airfoil. Phys. Fluids 20, 101515.Google Scholar
You, C. F., Qi, H. Y. & Xu, X. C. 2006 Lift force on rotating sphere at low Reynolds numbers and high rotational speed. Acta Mechanica Sin. (Engl. Ser.) (China) 19 (4), 300–307.Google Scholar
Yun, G., Kim, D. & Choi, H. 2006 Vortical structures behind a sphere at subcritical Reynolds numbers. Phys. Fluids 18, 015102.Google Scholar
Zang, Y., Street, R. L. & Koseff, J. R. 1994 A non-staggered grid, fractional-step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates. J. Comput. Phys. 114, 18–33.Google Scholar