Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-22T08:04:12.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex-induced vibrations of a long flexible cylinder in shear flow

Published online by Cambridge University Press:  27 April 2011

REMI BOURGUET ,
GEORGE E. KARNIADAKIS  and
MICHAEL S. TRIANTAFYLLOU
REMI BOURGUET*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
GEORGE E. KARNIADAKIS
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
MICHAEL S. TRIANTAFYLLOU
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the in-line and cross-flow vortex-induced vibrations of a long cylindrical tensioned beam, with length to diameter ratio L/D = 200, placed within a linearly sheared oncoming flow, using three-dimensional direct numerical simulation. The study is conducted at three Reynolds numbers, from 110 to 1100 based on maximum velocity, so as to include the transition to turbulence in the wake. The selected tension and bending stiffness lead to high-wavenumber vibrations, similar to those encountered in long ocean structures. The resulting vortex-induced vibrations consist of a mixture of standing and travelling wave patterns in both the in-line and cross-flow directions; the travelling wave component is preferentially oriented from high to low velocity regions. The in-line and cross-flow vibrations have a frequency ratio approximately equal to 2. Lock-in, the phenomenon of self-excited vibrations accompanied by synchronization between the vortex shedding and cross-flow vibration frequencies, occurs in the high-velocity region, extending across 30% or more of the beam length. The occurrence of lock-in disrupts the spanwise regularity of the cellular patterns observed in the wake of stationary cylinders in shear flow. The wake exhibits an oblique vortex shedding pattern, inclined in the direction of the travelling wave component of the cylinder vibrations. Vortex splittings occur between spanwise cells of constant vortex shedding frequency. The flow excites the cylinder under the lock-in condition with a preferential in-line versus cross-flow motion phase difference corresponding to counter-clockwise, figure-eight orbits; but it damps cylinder vibrations in the non-lock-in region. Both mono-frequency and multi-frequency responses may be excited. In the case of multi-frequency response and within the lock-in region, the wake can lock in to different frequencies at various spanwise locations; however, lock-in is a locally mono-frequency event, and hence the flow supplies energy to the structure mainly at the local lock-in frequency.

JFM classification

Vortex Flows: Vortex shedding Wakes/Jets: Vortex streets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 342 - 382
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bearman, P. W. 1984 Vortex shedding from oscillating bluff bodies. Annu. Rev. Fluid Mech. 16, 195–222.CrossRefGoogle Scholar
Boashash, B. 2003 Time Frequency Signal Analysis and Processing: A Comprehensive Reference, 1st edn. Elsevier.Google Scholar
Braza, M., Faghani, D. & Persillon, H. 2001 Successive stages and the role of natural vortex dislocations in three-dimensional wake transition. J. Fluid Mech. 439, 1–41.CrossRefGoogle Scholar
Brika, D. & Laneville, A. 1993 Vortex-induced vibrations of a long flexible circular cylinder. J. Fluid Mech. 250, 481–508.CrossRefGoogle Scholar
Carberry, J., Sheridan, J. & Rockwell, D. 2005 Controlled oscillations of a cylinder: forces and wake modes. J. Fluid Mech. 538, 31–69.CrossRefGoogle 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, 3–24.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.CrossRefGoogle ScholarPubMed
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, 395–424.CrossRefGoogle 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, 91–124.CrossRefGoogle Scholar
Facchinetti, M. L., de Langre, E. & Biolley, F. 2004 Vortex-induced travelling waves along a cable. Eur. J. Mech. B/Fluids 23, 199–208.CrossRefGoogle Scholar
Flemming, F. & Williamson, C. H. K. 2005 Vortex-induced vibrations of a pivoted cylinder. J. Fluid Mech. 522, 215–252.CrossRefGoogle Scholar
Gaster, M. 1969 Vortex shedding from slender cones at low Reynolds numbers. J. Fluid Mech. 38, 565–576.CrossRefGoogle Scholar
Gaster, M. 1971 Vortex shedding from circular cylinders at low Reynolds numbers. J. Fluid Mech. 46, 749–756.CrossRefGoogle Scholar
Griffin, O. M. 1985 Vortex shedding from bluff bodies in a shear flow: a review. J. Fluids Engng 107, 298–306.CrossRefGoogle Scholar
Hover, F. S., Techet, A. H. & Triantafyllou, M. S. 1998 Forces on oscillating uniform and tapered cylinders in crossflow. J. Fluid Mech. 363, 97–114.CrossRefGoogle Scholar
Huera-Huarte, F. J. & Bearman, P. W. 2009 a Wake structures and vortex-induced vibrations of a long flexible cylinder. Part 1. Dynamic response. J. Fluids Struct. 25, 969–990.CrossRefGoogle Scholar
Huera-Huarte, F. J. & Bearman, P. W. 2009 b Wake structures and vortex-induced vibrations of a long flexible cylinder. Part 2: Drag coefficients and vortex modes. J. Fluids Struct. 25, 991–1006.CrossRefGoogle Scholar
Huera-Huarte, F. J., Bearman, P. W. & Chaplin, J. R. 2006 On the force distribution along the axis of a flexible circular cylinder undergoing multi-mode vortex-induced vibrations. J. Fluids Struct. 22, 897–903.CrossRefGoogle Scholar
Jaiswal, V. & Vandiver, J. K. 2007 VIV response prediction for long risers with variable damping. In Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering (OMAE2007-29353).CrossRefGoogle 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, 23–62.CrossRefGoogle Scholar
Jeon, D. & Gharib, M. 2001 On circular cylinders undergoing two-degree-of-freedom forced motions. J. Fluids Struct. 15, 533–541.CrossRefGoogle Scholar
Kappler, M., Rodi, W., Szepessy, S. & Badran, O. 2005 Experiments on the flow past long circular cylinders in a shear flow. Exp. Fluids 38, 269–284.CrossRefGoogle Scholar
Karniadakis, G. E. & Sherwin, S. 1999 Spectral/hp Element Methods for CFD, 1st edn. Oxford University Press.Google 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, 557–575.CrossRefGoogle Scholar
Lucor, D. 2004 Generalized polynomial chaos: applications to random oscillators and flowstructure interactions. PhD Thesis, Brown University.CrossRefGoogle 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, 641–650.CrossRefGoogle Scholar
Lucor, D., Mukundan, H. & Triantafyllou, M. S. 2006 Riser modal identification in CFD and full-scale experiments. J. Fluids Struct. 22, 905–917.CrossRefGoogle Scholar
Mathelin, L. & de Langre, E. 2005 Vortex-induced vibrations and waves under shear flow with a wake oscillator model. Eur. J. Mech. B/Fluids 24, 478–490.CrossRefGoogle Scholar
Modarres-Sadeghi, Y., Mukundan, H., Dahl, J. M., Hover, F. S. & Triantafyllou, M. S. 2010 The effect of higher harmonic forces on fatigue life of marine risers. J. Sound Vib. 329, 43–55.CrossRefGoogle Scholar
Mukhopadhyay, A., Venugopal, P. & Vanka, S. P. 1999 Numerical study of vortex shedding from a circular cylinder in linear shear flow. J. Fluids Engng 121, 460–468.CrossRefGoogle Scholar
Newman, D. J. & Karniadakis, G. E. 1997 A direct numerical simulation study of flow past a freely vibrating cable. J. Fluid Mech. 344, 95–136.CrossRefGoogle Scholar
Noack, B. R., Ohle, F. & Eckelmann, H. 1991 On cell formation in vortex streets. J. Fluid Mech. 227, 293–308.CrossRefGoogle Scholar
Peltzer, R. D. & Rooney, D. M. 1985 Vortex shedding in a linear shear flow from a vibrating marine cable with attached bluff bodies. J. Fluids Engng 107, 61–66.CrossRefGoogle Scholar
Persillon, H. & Braza, M. 1998 Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation. J. Fluid Mech. 365, 23–88.CrossRefGoogle Scholar
Piccirillo, P. S. & Van Atta, C. W. 1993 An experimental study of vortex shedding behind linearly tapered cylinders at low Reynolds number. J. Fluid Mech. 246, 163–195.CrossRefGoogle Scholar
Sarpkaya, T. 1995 Hydrodynamic damping, flow-induced oscillations, and biharmonic response. J. Offshore Mech. Arctic Engng 117, 232–238.CrossRefGoogle Scholar
Sarpkaya, T. 2004 A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19, 389–447.CrossRefGoogle Scholar
Stansby, P. K. 1976 The locking-on of vortex shedding due to the cross-stream vibration of circular cylinders in uniform and shear flows. J. Fluid Mech. 74, 641–665.CrossRefGoogle Scholar
Techet, A. H., Hover, F. S. & Triantafyllou, M. S. 1998 Vortical patterns behind a tapered cylinder oscillating transversely to a uniform flow. J. Fluid Mech. 363, 79–96.CrossRefGoogle Scholar
Trim, A. D., Braaten, H., Lie, H. & Tognarelli, M. A. 2005 Experimental investigation of vortex-induced vibration of long marine risers. J. Fluids Struct. 21, 335–361.CrossRefGoogle Scholar
Vandiver, J. K., Jaiswal, V. & Jhingran, V. 2009 Insights on vortex-induced, traveling waves on long risers. J. Fluids Struct. 25, 641–653.CrossRefGoogle Scholar
Violette, R., de Langre, E. & Szydlowski, J. 2007 Computation of vortex-induced vibrations of long structures using a wake oscillator model: comparison with DNS and experiments. Comput. Struct. 85, 1134–1141.CrossRefGoogle Scholar
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, 579–627.CrossRefGoogle Scholar
Williamson, C. H. K. 1992 The natural and forced formation of spot-like ‘vortex dislocations’ in the transition of a wake. J. Fluid Mech. 243, 393–441.CrossRefGoogle Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413–455.CrossRefGoogle Scholar
Williamson, C. H. K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2, 355–381.CrossRefGoogle Scholar
Zhang, H.-Q., Fey, U., Noack, B. R., Konig, M. & Eckelmann, H. 1995 On the transition of the cylinder wake. Phys. Fluids 7, 779–794.CrossRefGoogle Scholar