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Parametric study of the transition in the wake of oblate spheroids and flat cylinders

Published online by Cambridge University Press:  06 December 2010

MARCIN CHRUST ,
GILLES BOUCHET  and
JAN DUŠEK
MARCIN CHRUST*
Affiliation:
Institut de Mécanique des Fluides et des Solides, Université de Strasbourg/CNRS, Strasbourg 67000, France
GILLES BOUCHET
Affiliation:
Institut de Mécanique des Fluides et des Solides, Université de Strasbourg/CNRS, Strasbourg 67000, France
JAN DUŠEK
Affiliation:
Institut de Mécanique des Fluides et des Solides, Université de Strasbourg/CNRS, Strasbourg 67000, France
*
†Email address for correspondence: Marcin.Chrust@etu.unistra.fr
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Abstract

An exhaustive parametric study of the transition scenario in the wake of oblate spheroids and flat cylinders placed with their rotation axis parallel to the flow is presented. The flatness of the investigated objects is classified by the aspect ratio χ defined as χ = d/a for spheroids (with d the diameter and a the length of the polar axis) and as χ = d/h) for cylinders (with h the cylinder height). We find a significant qualitative similarity between both configurations. At large aspect ratios (χ > 2.3 for spheroids and χ ≥ 4 for cylinders), the secondary bifurcation giving rise to a periodic state without planar symmetry is subcritical with a hysteresis interval of about two Reynolds number units. For spheroids, the sphere-like scenario is recovered only at aspect ratios very close to one (χ ≥ 1 are considered), while for cylindrical bodies the same holds for χ ≤ 1.7. For intermediate aspect ratios, a domain of states with non-zero net helicity separates states typical for the sphere wake from those of an infinitely flat disk.

JFM classification

Instability: Instability Instability: Transition to turbulence Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 665 , 25 December 2010 , pp. 199 - 208
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Auguste, F., Fabre, D. & Magnaudet, J. 2010 Bifurcations in the wake of a thick circular disk. Theor. Comput. Fluid Dyn. 24, 305–313.CrossRefGoogle Scholar
Bouchet, G., Mebarek, M. & Dušek, J. 2006 Hydrodynamic forces acting on a rigid fixed sphere in early transitional regimes. Eur. J. Mech. B Fluids 25, 321–336.CrossRefGoogle Scholar
Fabre, D., Auguste, F. & Magnaudet, J. 2008 Bifurcations and symmetry breaking in the wake of axisymmetric bodies. Phys. Fluids 20, 051702.CrossRefGoogle Scholar
Fernandes, P. C., Risso, F., Ern, P. & Magnaudet, J. 2007 Oscillatory motion and wake instability of freely rising axisymmetric bodies. J. Fluid Mech. 573, 479–502.CrossRefGoogle Scholar
Field, S. B., Klaus, M. & Moore, M. G. 1997 Chaotic dynamics of falling disks. Nature 388, 252–254.CrossRefGoogle Scholar
Ghidersa, B. & Dušek, J. 2000 Breaking of axisymetry and onset of unsteadiness in the wake of a sphere. J. Fluid Mech. 423, 33–69.CrossRefGoogle Scholar
Jenny, M. & Dušek, J. 2004 Efficient numerical method for the direct numerical simulation of the flow past a single light moving spherical body in transitional regimes. J. Comput. Phys. 194, 215–232.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
Kotouč, M., Bouchet, G. & Dušek, J. 2009 a Drag and flow reversal in mixed convection past a heated sphere. Phys. Fluids 21, 054104.CrossRefGoogle Scholar
Kotouč, M., Bouchet, G. & Dušek, J. 2009 b Transition to turbulence in the wake of a fixed sphere in mixed convection. J. Fluid Mech. 625, 205–248.CrossRefGoogle Scholar
Meliga, P., Chomaz, J. M. & Sipp, D. 2009 Global mode interaction and pattern selection in the wake of a disk: a weakly nonlinear expansion. J. Fluid Mech. 633, 159–189.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
Shenoy, A. R. & Kleinstreuer, C. 2008 Flow over a thin circular disk at low to moderate Reynolds number. J. Fluid Mech. 605, 253–262.CrossRefGoogle Scholar
Strogatz, S. H. 1994 Nonlinear Dynamics and Chaos. Addison-Wesley.Google Scholar