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The motion of a 2D pendulum in a channel subjected to an incoming flow

Published online by Cambridge University Press:  22 December 2014

Andrea Fani  and
François Gallaire
Andrea Fani*
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
François Gallaire
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
*
†Email address for correspondence: andrea.fani@epfl.ch
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Abstract

The flow around a tethered cylinder subjected to an incoming flow transverse to its main axis and confined in a channel is investigated by means of global stability analysis of the full coupled body–fluid problem. When the cylinder is strongly confined (ratio of cylinder diameter to cell height, $D/H=0.66$) we retrieve the confinement-induced instability (CIV) discovered by Semin et al. (J. Fluid Mech., vol. 690, 2011, pp. 345–365), which sets in at a Reynolds number below the vortex-induced vibration threshold. For a moderately confined case ($D/H=0.3$), a new steady static instability is discovered, referred to as confinement-induced divergence (CID). This instability saturates into an asymmetric steady solution through a supercritical pitchfork bifurcation. In addition, the CIV and CID instabilities are studied via a reduced model obtained by considering a quasi-static response of the fluid, allowing for tracing back the physical mechanisms responsible for the instabilities.

JFM classification

Aerodynamics: Aerodynamics Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 764 , 10 February 2015 , pp. 5 - 25
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Copyright
© 2014 Cambridge University Press 

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References

Assemat, P., Fabre, D. & Magnaudet, J. 2011 The onset of unsteadiness of two-dimensional bodies falling or rising freely in a viscous fluid: a linear study. J. Fluid Mech. 690, 173–202.CrossRefGoogle Scholar
Bandi, M. M., Concha, A., Wood, R. & Mahadevan, L. 2013 A pendulum in a flowing soap film. Phys. Fluids 25 (4), 041702.CrossRefGoogle Scholar
Biancofiore, L., Gallaire, F. & Pasquetti, R. 2011 Influence of confinement on a two-dimensional wake. J. Fluid Mech. 688, 297–320.CrossRefGoogle Scholar
Bolster, D., Hershberger, R. E. & Donnelly, R. J. 2010 Oscillating pendulum decay by emission of vortex rings. Phys. Rev. E 81 (4), 046317.CrossRefGoogle ScholarPubMed
Camarri, S. & Giannetti, F. 2007 On the inversion of the von Kármán street in the wake of a confined square cylinder. J. Fluid Mech. 574, 169–178.CrossRefGoogle Scholar
Chen, J.-H., Pritchard, W. G. & Tavener, S. J. 1995 Bifurcation for flow past a cylinder between parallel planes. J. Fluid Mech. 284, 23–41.CrossRefGoogle Scholar
Cossu, C. & Morino, L. 2000 On the instabiliry of a spring-mounted circular cylinder in a viscous flow at low Reynolds numbers. J. Fluids Struct. 14, 183–196.CrossRefGoogle Scholar
Fabre, D., Assemat, P. & Magnaudet, J. 2011 A quasi-static approach to the stability of the path of heavy bodies falling within a viscous fluid. J. Fluids Struct. 27 (5–6), 758–767.CrossRefGoogle Scholar
Fabre, D., Auguste, F. & Magnaudet, J. 2008 Bifurcations and symmetry breaking in the wake of axisymmetric bodies. Phys. Fluids 20 (5), 051702.CrossRefGoogle Scholar
Fani, A., Camarri, S. & Salvetti, M. V. 2012 Stability analysis and control of the flow in a symmetric channel with a sudden expansion. Phys. Fluids 24 (8), 084102.CrossRefGoogle Scholar
Govardhan, R. N. & Williamson, C. H. K. 2005 Vortex-induced vibrations of a sphere. J. Fluid Mech. 531, 11–47.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media, Vol. 1. Springer.CrossRefGoogle Scholar
Hecht, F. 2012 New development in Freefem $++$ . J. Numer. Math. 20 (3–4), 251–265.CrossRefGoogle Scholar
Lehoucq, R. B., Sorensen, D. C. & Yang, C. 1998 ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, Vol. 6. SIAM.CrossRefGoogle Scholar
Meis, M., Varas, F., Velázquez, A. & Vega, J. M. 2010 Heat transfer enhancement in micro-channels caused by vortex promoters. Intl J. Heat Mass Transfer 53 (1–3), 29–40.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
Meliga, P., Sipp, D. & Chomaz, J. 2010 Open-loop control of compressible afterbody flows using adjoint methods. Phys. Fluids 22 (5), 1–18.CrossRefGoogle Scholar
Mittal, S. & Singh, S. 2005 Vortex-induced vibrations at subcritical $\mathit{Re}$ . J. Fluid Mech. 534, 185–194.CrossRefGoogle Scholar
Nakabayashi, K., Yoshida, N. & Aoi, T. 1993 Numerical analysis for viscous shear flows past a circular cylinder at intermediate reynolds numbers. JSME Intl J. Ser. B, Fluids Therm. Engng 36 (1), 34–41.CrossRefGoogle Scholar
Obligado, M., Puy, M. & Bourgoin, M. 2013 Bi-stability of a pendular disk in laminar and turbulent flows. J. Fluid Mech. 728, R2, doi:10.1017/jfm.2013.312.CrossRefGoogle Scholar
Ryan, K., Pregnalato, C. J., Thompson, M. C. & Hourigan, K. 2004 Flow-induced vibrations of a tethered circular cylinder. J. Fluids Struct. 19 (8), 1085–1102.CrossRefGoogle Scholar
Sahin, M. & Owens, R. G. 2004 A numerical investigation of wall effects up to high blockage ratios on two-dimensional flow past a confined circular cylinder. Phys. Fluids 16 (5), 1305–1320.CrossRefGoogle Scholar
Sanchez-Sanz, M., Fernandez, B. & Velazquez, A. 2009 Energy-harvesting microresonator based on the forces generated by the Kármán street around a rectangular prism. J. Microelectromech. Syst. 18 (2), 449–457.CrossRefGoogle Scholar
Semin, B., Decoene, A., Hulin, J.-P., François, M. L. M. & Auradou, H. 2011 New oscillatory instability of a confined cylinder in a flow below the vortex shedding threshold. J. Fluid Mech. 690, 345–365.CrossRefGoogle Scholar
Taylor, C. & Hood, P. 1973 A numerical solution of the Navier–Stokes equations using the finite element technique. Comput. Fluids 1 (1), 73–100.CrossRefGoogle Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36 (1), 413–455.CrossRefGoogle Scholar
Zovatto, L. & Pedrizzetti, G. 2001 Flow about a circular cylinder between parallel walls. J.  Fluid Mech. 440, 1–25.CrossRefGoogle Scholar