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Viscous flow past a flexible fibre tethered at its centre point: vortex shedding

Published online by Cambridge University Press:  31 August 2007

LUODING ZHU
LUODING ZHU*
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis Indianapolis, Indiana, USAlzhu@math.iupui.edu
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Abstract

Motivated by a laboratory experiment reported in Alben, Shelley & Zhang (Nature, vol. 420, 2002, p. 479), we performed simulations of an elastic fibre anchored at its centre point and immersed in a flowing viscous incompressible fluid by the immersed boundary (IB) method. We focus on the influence of some dimensionless parameters on vortex shedding from the fibre for Re in the range [30, 800]. Three sets of simulationswere designed to investigate the influence of Reynolds number Re, dimensionless fibre flexure modulus b, and dimensionless fibre length on vortex shedding. According to the simulation results, Re, b, and each has a significant influence on the structure of shed vortices. However, Re has little influence on the vortex shedding frequency. With the increase of dimensionless bending modulus, the dimensionless vortex shedding frequency (fvs) and the critical Reynolds number (Rec) decrease approximately as power-law functions. Both fvs and Rec increase approximately linearly as dimensionless fibre length increases.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 587 , 25 September 2007 , pp. 217 - 234
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Abarbanel, S. S., Don, W. S., Gottlieb, D., Rudy, D. H. & Townsend, J. C. 1991 Secondary frequencies in the wake of a circular cylinder with vortex shedding. J. Fluid Mech. 225, 557.CrossRefGoogle Scholar
Alben, S. 2004 Drag reduction by self-similar bending and a transition to forward flight by a symmetry breaking instability. PhD thesis, Courant Institute of Mathematical Sciences, New York University.Google Scholar
Alben, S., Shelley, M. & Zhang, J. 2002 Drag reduction through self-similar bending of a flexible body. Natur. 420, 479.CrossRefGoogle ScholarPubMed
Alben, S., Shelley, M. & Zhang, J. 2004 How flexibility induces streamlining in two-dimensional flow. Phys. Fluid. 16, 1694.CrossRefGoogle Scholar
Bearman, P. W. 1989 Vortex shedding from oscillating bluff bodies. Annu. Rev. Fluid Mech. 16, 195.CrossRefGoogle Scholar
Griffin, O. M. & Ramberg, S. E. 1982 Some recent studies of vortex shedding with application to marine tubulars and risers. Trans. ASME: J. Energy Resour. Technol. 104, 2.Google Scholar
Jung, S. W., Mareck, K., Shelley, M. & Zhang, J. 2006 Dynamics of a deformable body in a fast flowing soap film. Phy. Rev. Lett. 97, 134502.CrossRefGoogle Scholar
Krasny, R. 1990 Vortex sheet roll-up due to the motion of a flat plate. In International Symposium on Nonsteady Fluid Dynamics (ed. Miller, J. A. & Telionis, D. P.). ASME FED Vol. 92.Google Scholar
Lee, S. 2000 A numerical study of the unsteady wake behind a sphere in a uniform flow at moderate Reynolds numbers. Computers & Fluid. 29, 639.CrossRefGoogle Scholar
Nitsche, M. & Krasny, R. 1994 A numerical study of vortex ring formation at the edge of a circular tube, J. Fluid Mech. 276, 139.CrossRefGoogle Scholar
Parkinson, G. V. 1989 Phenomena and modelling of flow-induced vibrations of bluff bodies. Prog. Aerosp. Sci. 26, 169.CrossRefGoogle Scholar
Peskin, C. S. 1977 Flow patterns around heart valves: a numerical method. J. Comput. Phys. 25, 220.CrossRefGoogle Scholar
Peskin, C. S. 2002 The immersed boundary method. Acta Numeric. 11, 479.CrossRefGoogle Scholar
Peskin, C. S. & McQueen, D. M. 1996 Fluid dynamics of the heart and its valves. In Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology (ed. Othmer, H. G., Adler, F. R., Lewis, M. A. & Dallon, J. C.), p. 309. Prentice-Hall.Google Scholar
Sarpkaya, T. 1975 An inviscid model of two-dimensional vortex shedding for transient and asymptotically steady separated flow over an inclined flat plate. J. Fluid Mech. 68, 109.CrossRefGoogle Scholar
Sarpkaya, T. 1979 Vortex-induced oscillations. Trans. ASME: J. Appl. Mech. 46, 241.CrossRefGoogle Scholar
Wang, Z. J. & Zhou, Y. 2005 Vortex interactions in a two side-by-side cylinder near-wake. Intl J. Heat Fluid Flo. 26, 362.CrossRefGoogle Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413.CrossRefGoogle Scholar
Zhu, L. 2001 Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. PhD thesis, Courant Institute of Mathematical Sciences, New York University.Google Scholar
Zhu, L. & Peskin, C. S. 2002 Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. J. Comput. Phys. 179, 452.CrossRefGoogle Scholar
Zhu, L. & Peskin, C. S. 2003 Interaction of two flapping filaments in a flowing soap film. Phys. Fluid. 15, 1954–1960.CrossRefGoogle Scholar
Zhu, L. & Peskin, C. S. 2007 Drag of a flexible fibre in a two-dimensional moving viscous fluid. Computers & Fluids, 36, 398.CrossRefGoogle Scholar