Skip to main content Accessibility help
×
Home

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

  • Eric K. W. Poon (a1), Andrew S. H. Ooi (a1), Matteo Giacobello (a2), Gianluca Iaccarino (a3) and Daniel Chung (a1)...

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.

Copyright

Corresponding author

Email address for correspondence: epoon@unimelb.edu.au

References

Hide All
Achenbach, E. 1974 Vortex shedding from spheres. J. Fluid Mech. 62, 209221.
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), 7077.
Almedeij, J. 2008 Drag coefficient of flow around a sphere: matching asymptotically the wide trend. Powder Technol. 186, 218223.
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), 27192737.
Bagchi, P. & Balachandar, S. 2003 Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15 (11), 34963513.
Bagchi, P. & Balachandar, S. 2004 Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518, 95123.
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, 347358.
Bonneton, P. & Chomax, J. M. 1992 Instability of the wake generated by a sphere. C. R. Acad. Sci. Paris 314, 10011006.
Brown, P. P. & Lawler, D. F. 2003 Sphere drag and settling velocity revisited. J. Environ. Engng 129, 222231.
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765777.
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Academic Press.
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, 257279.
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, 26462935.
Fornberg, B. 1988 Steady viscous flow past a sphere at high Reynolds numbers. J. Fluid Mech. 190, 471489.
Giacobello, M., Ooi, A. & Balachandar, S. 2009 Wake structure of a transversely rotating sphere at moderate Reynolds numbers. J. Fluid Mech. 621, 103130.
Goff, J. E. & Carre, M. J. 2010 Soccer ball lift coefficients via trajectory analysis. Eur. J. Phys. 31 (4), 775784.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 1970.
Kim, D. 2009 Laminar flow past a sphere rotating in the transverse direction. J. Mech. Sci. Technol. 23, 578589.
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, 411428.
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), 32603265.
Kurien, S. & Taylor, M. A. 2005 Direct numerical simulations of turbulence. Los Alamos Sci. 29, 142151.
Kurose, R. & Komori, S. 1999 Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 384, 183206.
Lee, S. 2000 A numerical study of the unsteady wake behind a sphere in a uniform flow at moderate Reynolds numbers. Comput. Fluids 29, 639667.
Liu, N. & Bogy, D. B. 2008 Forces on a rotating particle in a shear flow of a highly rarefied gas. Phys. Fluids 20, 107102.
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.
Liu, Q. & Prosperetti, A. 2010 Wall effects on a rotating sphere. J. Fluid Mech. 657, 121.
Lopez, O. D. & Moser, R. D. 2008 Delayed detached eddy simulation of flow over an airfoil with synthetic jet control. Mec. Comput. 17, 32253245.
Loth, E. 2008 Lift of a solid spherical particle subject to vorticity and/or spin. AIAA J. 4, 801809.
Magarvey, R. H. & Bishop, R. L. 1961 Wakes in liquid–liquid systems. Phys. Fluids 4 (7), 800805.
Mahesh, K., Constantinescu, G. & Moin, P. 2004 A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197, 215240.
Mittal, R. 1999 A Fourier–Chebyshev spectral collocation method for simulating flow past spheres and spheroids. Intl J. Numer. Meth. Fluids 30, 921937.
Mittal, S. & Kumar, B. 2003 Flow past a rotating cylinder. J. Fluid Mech. 476, 303334.
Mittal, R. & Najjar, F. M. 1999 Vortex dynamics in the sphere wake. In Proceedings of the 30th AIAA Fluid Dynamics Conference, AIAA.
Mittal, R., Wilson, J. J. & Najjar, F. M. 2002 Symmetry properties of translation sphere wake. AIAA J. 40, 579582.
Niazmand, H. & Renksizbukut, M. 2003 Surface effects on transient three-dimensional flows around rotating spheres at moderate Reynolds numbers. Comput. Fluids 32, 14051433.
Oesterlé, B. & Dinh, B. 1998 Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers. Exp. Fluids 25, 1622.
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, 195205.
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, 427463.
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, 961972.
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, 278288.
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, 781790.
Rubinow, S. I. & Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447459.
Sakamoto, H. & Haniu, H. 1990 A study on vortex shedding from spheres in a uniform flow. Trans. ASME 112, 386392.
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. 2945. Springer.
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.
Tomboulides, A. G. & Orszag, S. A. 2000 Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 4573.
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, 2731.
Tsuji, Y., Morikawa, Y. & Mizuno, O. 1985 Experimental measurement of the Magnus force on a rotating sphere at low Reynolds numbers. Trans. ASME 107, 484488.
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, 11171128.
Wu, J. S. & Faeth, G. M. 1993 Sphere wakes in still surroundings at intermediate Reynolds numbers. AIAA J. 31, 14481455.
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, 2130.
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.
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), 300307.
Yun, G., Kim, D. & Choi, H. 2006 Vortical structures behind a sphere at subcritical Reynolds numbers. Phys. Fluids 18, 015102.
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, 1833.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed