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Distributed lock-in drives broadband vortex-induced vibrations of a long flexible cylinder in shear flow

Published online by Cambridge University Press:  01 February 2013

Rémi Bourguet*
Affiliation:
Institut de Mécanique des Fluides de Toulouse, Université de Toulouse and CNRS, Toulouse, 31400, France
George Em Karniadakis
Affiliation:
Brown University, Providence, RI 02912, USA
Michael S. Triantafyllou
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
Email address for correspondence: bourguet@imft.fr

Abstract

A slender flexible body immersed in sheared cross-flow may exhibit vortex-induced vibrations (VIVs) involving a wide range of excited frequencies and structural wavenumbers. The mechanisms of broadband VIVs of a cylindrical tensioned beam of length-to-diameter aspect ratio 200 placed in shear flow, with an exponentially varying profile along the span, are investigated by means of direct numerical simulation. The Reynolds number is equal to 330 based on the maximum velocity, for comparison with previous work on narrowband vibrations in linear shear flow. The flow is found to excite the structure at a number of different locations under a condition of wake–body synchronization, or lock-in. Broadband responses are associated with a distributed occurrence of the lock-in condition along the span, as opposed to the localized lock-in regions limited to the high inflow velocity zone, reported for narrowband vibrations in sheared current. Despite the instantaneously multi-frequency nature of broadband responses, the lock-in phenomenon remains a locally mono-frequency event, since the vortex formation is generally synchronized with a single vibration frequency at a given location. The spanwise distribution of the excitation zones induces travelling structural waves moving in both directions; this contrasts with the narrowband case where the direction of propagation toward decreasing inflow velocity is preferred. A generalization of the mechanism of phase-locking between the in-line and cross-flow responses is proposed for broadband VIVs under the lock-in condition. A spanwise drift of the in-line/cross-flow phase difference is identified for the high-wavenumber vibration components; this drift is related to the strong travelling wave character of the corresponding structural waves.

Type
Papers
Copyright
©2013 Cambridge University Press

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References

Bearman, P. W. 1984 Vortex shedding from oscillating bluff bodies. Annu. Rev. Fluid Mech. 16, 195222.CrossRefGoogle Scholar
Bearman, P. W. 2011 Circular cylinder wakes and vortex-induced vibrations. J. Fluids Struct. 27, 648658.Google Scholar
Bourguet, R., Karniadakis, G. E. & Triantafyllou, M. S. 2011a Vortex-induced vibrations of a long flexible cylinder in shear flow. J. Fluid Mech. 677, 342382.CrossRefGoogle Scholar
Bourguet, R., Lucor, D. & Triantafyllou, M. S. 2012 Mono- and multi-frequency vortex-induced vibrations of a long tensioned beam in shear flow. J. Fluids Struct. 32, 5264.CrossRefGoogle Scholar
Bourguet, R., Modarres-Sadeghi, Y., Karniadakis, G. E. & Triantafyllou, M. S. 2011b Wake–body resonance of long flexible structures is dominated by counter-clockwise orbits. Phys. Rev. Lett. 107, 134502.CrossRefGoogle Scholar
Carberry, J., Sheridan, J. & Rockwell, D. 2001 Forces and wake modes of an oscillating cylinder. J. Fluids Struct. 15, 523532.Google Scholar
Chaplin, J. R., Bearman, P. W., Huera-Huarte, F. J. & Pattenden, R. J. 2005 Laboratory measurements of vortex-induced vibrations of a vertical tension riser in a stepped current. J. Fluids Struct. 21, 324.CrossRefGoogle Scholar
Dahl, J. M., Hover, F. S., Triantafyllou, M. S., Dong, S. & Karniadakis, G. E. 2007 Resonant vibrations of bluff bodies cause multivortex shedding and high frequency forces. Phys. Rev. Lett. 99, 144503.Google Scholar
Dahl, J. M., Hover, F. S., Triantafyllou, M. S. & Oakley, O. H. 2010 Dual resonance in vortex-induced vibrations at subcritical and supercritical Reynolds numbers. J. Fluid Mech. 643, 395424.Google Scholar
Evangelinos, C. & Karniadakis, G. E. 1999 Dynamics and flow structures in the turbulent wake of rigid and flexible cylinders subject to vortex-induced vibrations. J. Fluid Mech. 400, 91124.Google Scholar
Gaster, M. 1971 Vortex shedding from circular cylinders at low Reynolds numbers. J. Fluid Mech. 46, 749756.CrossRefGoogle Scholar
Griffin, O. M. 1985 Vortex shedding from bluff bodies in a shear flow: a review. Trans. ASME J. Fluids Engng 107, 298306.Google Scholar
Jauvtis, N. & Williamson, C. H. K. 2004 The effect of two degrees of freedom on vortex-induced vibration at low mass and damping. J. Fluid Mech. 509, 2362.CrossRefGoogle Scholar
Jeon, D. & Gharib, M. 2001 On circular cylinders undergoing two-degree-of-freedom forced motions. J. Fluids Struct. 15, 533541.Google Scholar
Karniadakis, G. E. & Sherwin, S. 1999 Spectral/HP Element Methods for CFD, 1st edn. Oxford University Press.Google Scholar
Klamo, J. T., Leonard, A. & Roshko, A. 2006 The effects of damping on the amplitude and frequency response of a freely vibrating cylinder in cross-flow. J. Fluids Struct. 22, 845856.Google Scholar
Leontini, J. S., Thompson, M. C. & Hourigan, K. 2006 The beginning of branching behaviour of vortex-induced vibration during two-dimensional flow. J. Fluids Struct. 22, 857864.CrossRefGoogle Scholar
Lie, H. & Kaasen, K. E. 2006 Modal analysis of measurements from a large-scale VIV model test of a riser in linearly sheared flow. J. Fluids Struct. 22, 557575.Google Scholar
Lucor, D., Imas, L. & Karniadakis, G. E. 2001 Vortex dislocations and force distribution of long flexible cylinders subjected to sheared flows. J. Fluids Struct. 15, 641650.Google Scholar
Lucor, D., Mukundan, H. & Triantafyllou, M. S. 2006 Riser modal identification in CFD and full-scale experiments. J. Fluids Struct. 22, 905917.Google Scholar
Mittal, S. & Tezduyar, T. E. 1992 A finite element study of incompressible flows past oscillating cylinders and aerofoils. Intl J. Numer. Meth. Fluids 15, 10731118.Google Scholar
Newman, D. J. & Karniadakis, G. E. 1997 A direct numerical simulation study of flow past a freely vibrating cable. J. Fluid Mech. 344, 95136.CrossRefGoogle Scholar
Sarpkaya, T. 1995 Hydrodynamic damping, flow-induced oscillations, and biharmonic response. J. Offshore Mech. Arctic Engng 117, 232238.CrossRefGoogle Scholar
Vandiver, J. K., Allen, D. & Li, L. 1996 The occurrence of lock-in under highly sheared conditions. J. Fluids Struct. 10, 555561.CrossRefGoogle Scholar
Vandiver, J. K., Jaiswal, V. & Jhingran, V. 2009 Insights on vortex-induced, travelling waves on long risers. J. Fluids Struct. 25, 641653.Google Scholar
Violette, R., de Langre, E. & Szydlowski, J. 2010 A linear stability approach to vortex-induced vibrations and waves. J. Fluids Struct. 26, 442466.Google Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413455.Google Scholar