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Vortex shedding from slender cones at low Reynolds numbers

Published online by Cambridge University Press:  26 April 2006

A. Papangelou
A. Papangelou
Affiliation:
Department of Engineering, University of Cambridge. Trumpineton Street. Cambridge CB2 1PZ, UK
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Abstract

Wind-tunnel experiments on the flows created by a number of slightly tapered models of circular cross-section have shown the presence of spanwise cells (regions of constant shedding frequency) at Reynolds numbers of the order of 100. The experiments have also shown a number of other interesting features of these flows: the cellular flow configuration is dependent on the base Reynolds number and independent of the tip Reynolds number, the frequency jump between adjacent cells is a function of flow speed, taper angle and kinematic viscosity, but is constant along a cone's span, and the unsteady hot-wire anemometer signal is both amplitude and phase modulated. A mathematical model is proposed based on the complex Landau—Stuart equation with a spanwise diffusive coupling term. Numerical solutions of this equation have shown many of the qualitative features observed in the experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 242 , September 1992 , pp. 299 - 321
Copyright
© 1992 Cambridge University Press

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References

Albarède, P., Provansal, M. & Boyer, L. 1990 Modélisation par l’équation de Ginzburg—Landau du sillage tridimensionnel d'un obstacle allongé. C. R. Acad. Sci. Paris, Ser. 2, 310, 459.Google Scholar
Eisenlohr, H. & Eckelmann, H. 1989a Visualization of three-dimensional vortex splitting in the wake of a thin flat plate. Proc. 5th Intl Symp. on Flow Visualization 21–25 August 1989 (ed. R. Reznicêk). Hemisphere, Washington, DC, USA.
Eisenlohr, H. & Eckelmann, H. 1989b Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds number. Phys. Fluids A1, 189.Google Scholar
Gaster, M. 1969 Vortex shedding from slender cones at low Reynolds numbers. J. Fluid Mech. 38, 565.Google Scholar
Gaster, M. 1971 Vortex shedding from circular cylinders at low Reynolds numbers. J. Fluid Mech. 46, 749.Google Scholar
Gaster, M. & Ponsford, P. J. 1984 The flows over tapered flat plates normal to the stream. Aeronaut. J. 88, 206.Google Scholar
Gerich, D. & Eckelmann, H. 1982 Influence of end plates and free ends on the shedding frequency of circular cylinders. J. Fluid Mech. 122, 109.Google Scholar
Kim, Y. C., Khadra, L. & Powers, E. J. 1980 Wave modulation in a non-linear dispersive medium. Phys. Fluids 23, 2250.Google Scholar
König, M., Eisenlohr, H. & Eckelmann, H. 1990 The fine structure in the Strouhal—Reynolds number relationship of the laminar wake of a circular cylinder. Phys. Fluids A2, 1607.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Miksad, R. W., Jones, F. L., Powers, E. J., Kim, Y. C. & Khadra, L. 1982 Experiments on the role of amplitude and phase modulations during transition to turbulence. J. Fluid Mech. 123, 1.Google Scholar
Noack, B. R. 1989 Untersuchung chaotischer Phänomene in der Nachlaufströmung eines Kreiszylinders. Diplomarbeit, Institut für Angewandte Mechanik und Strömungsphysik der Georg-August-Universität, Göttingen.
Noack, B. R., Ohle, F. & Eckelmann, H. 1991 On cell formation of vortex streets. J. Fluid Mech. 227, 293.Google Scholar
Papangelou, A. 1991 Vortex shedding from slender cones at low Reynolds numbers. PhD thesis, University of Cambridge.
Papangelou, A. 1992 A ‘robust’ vortex-shedding anemometer. Exps Fluids (to appear).Google Scholar
Piccirillo, P. S. 1990 An experimental study of vortex shedding behind a linearly tapered cylinder at low Reynolds number. MS thesis, University of California. San Diego.
Provansal, M., Mathis, C. & Boyer, L. 1987 Bénard—von Kármán instability: transient and forced regimes. J. Fluid Mech. 182, 1.Google Scholar
Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Rep. 1191.Google Scholar
Sreenivasan, K. R., Strykowski, P. J. & Olinger, D. J. 1987 On the Hopf bifurcation and Landau—Stuart constants associated with vortex ‘shedding’ behind circular cylinders. In American Society for Mechanical Engineers Forum on Unsteady Flow Separation (ed. K.N. Ghia), Fluids Engineering Division, vol. 52, p. 1. ASME.
Williamson, C. H. K. 1989 Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206, 579.Google Scholar