ANZIAM J. 46(E) pp.C1296--C1310, 2005.

Computing the flow past a cylinder with hemispherical ends

G. J. Sheard

M. C. Thompson

K. Hourigan
(Received 18 October 2004, revised 18 November 2005)

Abstract

A novel application of a spectral element method with a Fourier expansion in the third dimension is used to compute the flow past a cylinder with hemispherical ends. This cylinder is useful as it is a sphere at the small length ratio limit, while approaching a straight circular cylinder as the length ratio is increased. Measurements of the Strouhal frequency and mean drag are presented, and results of a grid independence study show that 128 Fourier planes were required to resolve the flow to an accuracy better than 1%. With 64 planes, forces were predicted accurate to 2%, but Strouhal frequencies were over predicted by approximately 8%. The measured Strouhal frequencies provide useful benchmark data for future low Reynolds number studies of the flow past short cylinders.

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Authors

G. J. Sheard
M. C. Thompson
K. Hourigan
Fluids Laboratory for Aeronautical and Industrial Research, Dept. of Mechanical Engineering, Monash University, Melbourne, Australia. mailto:Greg.Sheard@eng.monash.edu.au

Published December 1, 2005. ISSN 1446-8735

References

  1. A. Brydon and M. C. Thompson. Flow interaction between two spheres at moderate {R}eynolds number. In B. B. Dally, editor, Proceedings of the Fourteenth Australasian Fluid Mechanics Conference, pages 693--696, Department of Mechanical Engineering, Adelaide University, S.A. 5005, Australia, 2001. Published by Adelaide University.
  2. R. D. Henderson. Non-linear dynamics and pattern formation in turbulent wake transition. J. Fluid Mech., 352:65--112, 1997. URL
  3. R. D. Henderson and D. Barkley. Secondary instability in the wake of a circular cylinder. Phys. Fluids, 8:1683--1685, 1996. http://dx.doi.org/10.1063/1.868939
  4. T. A. Johnson and V. C. Patel. Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech., 378:19--70, 1999. URL
  5. G. E. Karniadakis and S. J. Sherwin. Spectral/hp Element Methods for CFD. Oxford University Press, 1999.
  6. G. E. Karniadakis and G. S. Triantafyllou. Three-dimensional dynamics and transition to turbulence in the wake of bluff objects. J. Fluid Mech., 238:1--30, 1992. URL
  7. N. W. M. Ko, C. W. Law, and K. W. Lo. Mutual interference on transition of wake of circular cylinder. Phys. Fluids, 12:1--34, 1962. http://dx.doi.org/10.1063/1.1767109
  8. C. Norberg. An experimental investigation of the flow around a circular cylinder: Influence of aspect ratio. J. Fluid Mech., 258:287--316, 1994. URL
  9. A. T. Patera. A spectral element method for fluid dynamics: Laminar flow in a channel expansion. J. Comp. Phys., 54:468--488, 1984. http://dx.doi.org/10.1016/0021-9991(84)90128-1
  10. M. Provansal, C. Mathis, and L. Boyer. Benard-von Karman instability: Transient and forced regimes. J. Fluid Mech., 182:1--22, 1987.
  11. M. Provansal, L. Schouveiler, and T. Leweke. From the double vortex street behind a cylinder to the wake of a sphere. Euro. J. Mech. B (Fluids), 23:65--80, 2004. http://dx.doi.org/10.1016/j.euromechflu.2003.09.007
  12. L. Schouveiler, A. Brydon, T. Leweke, and M. C. Thompson. Interactions of the wakes of two spheres placed side by side. 23:137--145, 2004. http://dx.doi.org/10.1016/j.euromechflu.2003.05.004
  13. L. Schouveiler and M. Provansal. Periodic wakes of low aspect ratio cylinders with free hemispherical ends. J. Fluids Struct., 14:565--573, 2001. http://dx.doi.org/10.1006/jfls.2000.0351
  14. G. J. Sheard. The Stability and Characteristics of the Flow Past Rings. PhD thesis, Monash University, Melbourne, Australia, 2004.
  15. G. J. Sheard, M. C. Thompson, and K. Hourigan. From spheres to circular cylinders: The stability and flow structures of bluff ring wakes. J. Fluid Mech., 492:147--180, 2003. URL
  16. G. J. Sheard, M. C. Thompson, and K. Hourigan. Asymmetric structure and non-linear transition behaviour of the wakes of toroidal bodies. Euro. J. Mech. B (Fluids), 23(1):167--179, 2004. http://dx.doi.org/10.1016/j.euromechflu.2003.04.005
  17. G. J. Sheard, M. C. Thompson, and K. Hourigan. From spheres to circular cylinders: Non-axisymmetric transitions in the flow past rings. J. Fluid Mech., 506:45--78, 2004. URL
  18. G. J. Sheard, M. C. Thompson, and K. Hourigan. Wake mode development for flow past low aspect ratio cylinders. In K.J. Bathe, editor, Computational Fluid and Solid Mechanics 2005, pages 850--853, Massachusetts Institute of Technology, Cambridge MA, USA, 2005. Published by Elsevier.
  19. M. C. Thompson, K. Hourigan, and J. Sheridan. Three-dimensional instabilities in the wake of a circular cylinder. Exp. Therm. Fluid Sci., 12:190--196, 1996. http://dx.doi.org/10.1016/0894-1777(95)00098-4
  20. M. C. Thompson, T. Leweke, and M. Provansal. Kinematics and dynamics of sphere wake transition. J. Fluids Struct., 15:575--585, 2001. http://dx.doi.org/10.1006/jfls.2000.0362
  21. A. G. Tomboulides and S. A. Orszag. Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech., 416:45--73, 2000. URL
  22. A. G. Tomboulides, S. A. Orszag, and G. E. Karniadakis. Direct and large-eddy simulation of the flow past a sphere. In Proceedings of the Second International Conference on Turbulence Modeling and Experiments (2nd ICTME), Florence, Italy, 1993.
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