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In-line flow-induced vibrations of a rotating cylinder

Published online by Cambridge University Press:  16 September 2015

Rémi Bourguet  and
David Lo Jacono
Rémi Bourguet*
Affiliation:
Institut de Mécanique des Fluides de Toulouse, CNRS, UPS and Université de Toulouse, Toulouse, 31400, France
David Lo Jacono
Affiliation:
Institut de Mécanique des Fluides de Toulouse, CNRS, UPS and Université de Toulouse, Toulouse, 31400, France
*
†Email address for correspondence: [email protected]
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Abstract

The flow-induced vibrations of an elastically mounted circular cylinder, free to oscillate in the direction parallel to the current and subjected to a forced rotation about its axis, are investigated by means of two- and three-dimensional numerical simulations, at a Reynolds number equal to 100 based on the cylinder diameter and inflow velocity. The cylinder is found to oscillate up to a rotation rate (ratio between the cylinder surface and inflow velocities) close to 2 (first vibration region), then the body and the flow are steady until a rotation rate close to 2.7 where a second vibration region begins. Each vibration region is characterized by a specific regime of response. In the first region, the vibration amplitude follows a bell-shaped evolution as a function of the reduced velocity (inverse of the oscillator natural frequency). The maximum vibration amplitudes, even though considerably augmented by the rotation relative to the non-rotating body case, remain lower than 0.1 cylinder diameters. Due to their trends as functions of the reduced velocity and to the fact that they develop under a condition of wake-body synchronization or lock-in, the responses of the rotating cylinder in this region are comparable to the vortex-induced vibrations previously described in the absence of rotation. The symmetry breaking due to the rotation is shown to directly impact the structure displacement and fluid force frequency contents. In the second region, the vibration amplitude tends to increase unboundedly with the reduced velocity. It may become very large, higher than 2.5 diameters in the parameter space under study. Such structural oscillations resemble the galloping responses reported for non-axisymmetric bodies. They are accompanied by a dramatic amplification of the fluid forces compared to the non-vibrating cylinder case. It is shown that body oscillation and flow unsteadiness remain synchronized and that a variety of wake topologies may be encountered in this vibration region. The low-frequency, large-amplitude responses are associated with novel asymmetric multi-vortex patterns, combining a pair and a triplet or a quartet of vortices per cycle. The flow is found to undergo three-dimensional transition in the second vibration region, with a limited influence on the system behaviour. It appears that the transition occurs for a substantially lower rotation rate than for a rigidly mounted cylinder.

JFM classification

Wakes/Jets: Vortex streets Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 781 , 25 October 2015 , pp. 127 - 165
Copyright
© 2015 Cambridge University Press 

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References

Abdel-Rohman, M. 1992 Galloping of tall prismatic structures: a two-dimensional analysis. J. Sound Vib. 153, 97–111.CrossRefGoogle Scholar
Badr, H. M., Coutanceau, M., Dennis, S. C. R. & Ménard, C. 1990 Unsteady flow past a rotating circular cylinder at Reynolds numbers $10^{3}$ and $10^{4}$ . J. Fluid Mech. 220, 459–484.Google Scholar
Bearman, P. W. 1984 Vortex shedding from oscillating bluff bodies. Annu. Rev. Fluid Mech. 16, 195–222.Google Scholar
Bearman, P. W. 2011 Circular cylinder wakes and vortex-induced vibrations. J. Fluids Struct. 27, 648–658.Google Scholar
Bearman, P. W., Gartshore, I. S., Maull, D. J. & Parkinson, G. V. 1987 Experiments on flow-induced vibration of a square-section cylinder. J. Fluids Struct. 1, 19–34.Google Scholar
Bishop, R. E. D. & Hassan, A. Y. 1964 The lift and drag forces on a circular cylinder oscillating in a flowing fluid. Proc. R. Soc. Lond. A 277, 51–75.Google Scholar
Blevins, R. D. 1990 Flow-induced Vibration. Van Nostrand Reinhold.Google Scholar
Bourguet, R., Karniadakis, G. E. & Triantafyllou, M. S. 2011 Vortex-induced vibrations of a long flexible cylinder in shear flow. J. Fluid Mech. 677, 342–382.CrossRefGoogle Scholar
Bourguet, R. & Lo Jacono, D. 2014 Flow-induced vibrations of a rotating cylinder. J. Fluid Mech. 740, 342–380.Google Scholar
Brika, D. & Laneville, A. 1993 Vortex-induced vibrations of a long flexible circular cylinder. J. Fluid Mech. 250, 481–508.Google Scholar
Cagney, N. & Balabani, S. 2013 Wake modes of a cylinder undergoing free streamwise vortex-induced vibrations. J. Fluids Struct. 38, 127–145.Google Scholar
Carberry, J., Sheridan, J. & Rockwell, D. 2001 Forces and wake modes of an oscillating cylinder. J. Fluids Struct. 15, 523–532.Google 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
Cetiner, O. & Rockwell, D. 2001 Streamwise oscillations of a cylinder in a steady current. Part 1. Locked-on states of vortex formation and loading. J. Fluid Mech. 427, 1–28.Google Scholar
Chew, Y. T., Cheng, M. & Luo, S. C. 1995 A numerical study of flow past a rotating circular cylinder using a hybrid vortex scheme. J. Fluid Mech. 299, 35–71.Google Scholar
Corless, R. M. & Parkinson, G. V. 1988 A model of the combined effects of vortex-induced oscillation and galloping. J. Fluids Struct. 2, 203–220.Google Scholar
Coutanceau, M. & Ménard, C. 1985 Influence of rotation on the near-wake development behind an impulsively started circular cylinder. J. Fluid Mech. 158, 399–446.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, 395–424.CrossRefGoogle Scholar
Den Hartog, J. P. 1932 Transmission line vibration due to sleet. Trans. Am. Inst. Electr. Engrs 51, 1074–1076.Google Scholar
El Akoury, R., Braza, M., Perrin, R., Harran, G. & Hoarau, Y. 2008 The three-dimensional transition in the flow around a rotating cylinder. J. Fluid Mech. 607, 1–11.CrossRefGoogle Scholar
Govardhan, R. & Williamson, C. H. K. 2000 Modes of vortex formation and frequency response of a freely vibrating cylinder. J. Fluid Mech. 420, 85–130.CrossRefGoogle Scholar
Griffin, O. M. & Ramberg, S. E. 1976 Vortex shedding from a cylinder vibrating in line with an incident uniform flow. J. Fluid Mech. 75, 257–271.Google 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.Google Scholar
Jeon, D. & Gharib, M. 2001 On circular cylinders undergoing two-degree-of-freedom forced motions. J. Fluids Struct. 15, 533–541.Google Scholar
Kang, S., Choi, H. & Lee, S. 1999 Laminar flow past a rotating circular cylinder. Phys. Fluids 11, 3312.Google Scholar
Karniadakis, G. E. & Sherwin, S. 1999 Spectral/hp Element Methods for CFD, 1st edn. Oxford University Press.Google Scholar
Khalak, A. & Williamson, C. H. K. 1999 Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping. J. Fluids Struct. 13, 813–851.Google Scholar
King, R., Prosser, M. J. & Johns, D. J. 1973 On vortex excitation of model piles in water. J. Sound Vib. 29, 169–188.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, 845–856.Google Scholar
Konstantinidis, E. 2014 On the response and wake modes of a cylinder undergoing streamwise vortex-induced vibration. J. Fluids Struct. 45, 256–262.Google Scholar
Leontini, J. S., Lo Jacono, D. & Thompson, M. C. 2011 A numerical study of an inline oscillating cylinder in a free stream. J. Fluid Mech. 688, 551–568.Google Scholar
Leontini, J. S., Lo Jacono, D. & Thompson, M. C. 2013 Wake states and frequency selection of a streamwise oscillating cylinder. J. Fluid Mech. 730, 162–192.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, 857–864.Google Scholar
Lucor, D. & Triantafyllou, M. S. 2008 Parametric study of a two degree-of-freedom cylinder subject to vortex-induced vibrations. J. Fluids Struct. 24, 1284–1293.Google Scholar
Mannini, C., Marra, A. M. & Bartoli, G. 2014 VIV-galloping instability of rectangular cylinders: review and new experiments. J. Wind Engng Ind. Aerodyn. 132, 109–124.Google Scholar
Meena, J., Sidarth, G. S., Khan, M. H. & Mittal, S. 2011 Three-dimensional instabilities in flow past a spinning and translating cylinder. In IUTAM Symposium on Bluff Body Flows, IIT-Kanpur, India (ed. Mittal, S. & Biswas, G.), pp. 75–78.Google Scholar
Mittal, S. 2004 A finite element study of incompressible flows past oscillating cylinders and aerofoils. J. Appl. Mech. 71, 89–95.Google Scholar
Mittal, S. & Kumar, B. 2003 Flow past a rotating cylinder. J. Fluid Mech. 476, 303–334.CrossRefGoogle 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, 1073–1118.Google Scholar
Mukhopadhyay, V. & Dugundji, J. 1976 Wind excited vibration of a square section cantilever beam in smooth flow. J. Sound Vib. 45, 329–339.CrossRefGoogle Scholar
Nakamura, Y. & Tomonari, Y. 1977 Galloping of rectangular prisms in a smooth and a turbulent flow. J. Sound Vib. 52, 233–241.Google Scholar
Naudascher, E. 1987 Flow-induced streamwise vibrations of structures. J. Fluids Struct. 1, 265–298.Google Scholar
Naudascher, E. & Rockwell, D. 1994 Flow-induced Vibrations: An Engineering Guide. Dover.Google Scholar
Navrose & Mittal, S. 2013 Free vibrations of a cylinder: 3-D computations at $Re=1000$ . J. Fluids Struct. 41, 109–118.Google Scholar
Nemes, A., Zhao, J., Lo Jacono, D. & Sheridan, J. 2012 The interaction between flow-induced vibration mechanisms of a square cylinder with varying angles of attack. J. Fluid Mech. 710, 102–130.Google Scholar
Obasaju, E. D., Ermshaus, R. & Naudascher, E. 1990 Vortex-induced streamwise oscillations of a square-section cylinder in a uniform stream. J. Fluid Mech. 213, 171–189.Google Scholar
Okajima, A., Kosugi, T. & Nakamura, A. 2002 Flow-induced in-line oscillation of a circular cylinder in a water tunnel. Trans. ASME: J. Press. Vessel Technol. 124, 89–96.Google Scholar
Okajima, A., Ohtsuyama, S., Nagamori, T., Nakano, T. & Kiwata, T. 1999 In-line oscillation of structure with a circular or rectangular section. Trans. Japan. Soc. Mech. Engng 65, 2196–2203.CrossRefGoogle Scholar
Ongoren, A. & Rockwell, D. 1988 Flow structure from an oscillating cylinder. Part 2. Mode competition in the near wake. J. Fluid Mech. 191, 225–245.CrossRefGoogle Scholar
Païdoussis, M. P., Price, S. J. & de Langre, E. 2010 Fluid–Structure Interactions: Cross-Flow-Induced Instabilities. Cambridge University Press.Google Scholar
Parkinson, G. V. & Smith, J. D. 1964 The square prism as an aeroelastic nonlinear oscillator. Q. J. Mech. Appl. Maths 17, 225–239.CrossRefGoogle Scholar
Perdikaris, P. G., Kaiktsis, L. & Triantafyllou, G. S. 2009 Chaos in a cylinder wake due to forcing at the Strouhal frequency. Phys. Fluids 21, 101705.CrossRefGoogle Scholar
Pralits, J. O., Brandt, L. & Giannetti, F. 2010 Instability and sensitivity of the flow around a rotating circular cylinder. J. Fluid Mech. 650, 513–536.Google Scholar
Pralits, J. O., Giannetti, F. & Brandt, L. 2013 Three-dimensional instability of the flow around a rotating circular cylinder. J. Fluid Mech. 730, 5–18.Google Scholar
Prandtl, L. 1925 Application of the ‘Magnus effect’ to the wind propulsion of ships. Naturwissenschaft 13, 93–108 (NACA Technical Memorandum, 367).Google Scholar
Prasanth, T. K. & Mittal, S. 2008 Vortex-induced vibrations of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 594, 463–491.Google Scholar
Radi, A., Thompson, M. C., Rao, A., Hourigan, K. & Sheridan, J. 2013 Experimental evidence of new three-dimensional modes in the wake of a rotating cylinder. J. Fluid Mech. 734, 567–594.Google Scholar
Rao, A., Leontini, J. S., Thompson, M. C. & Hourigan, K. 2013a Three-dimensionality in the wake of a rapidly rotating cylinder in uniform flow. J. Fluid Mech. 730, 379–391.Google Scholar
Rao, A., Leontini, J. S., Thompson, M. C. & Hourigan, K. 2013b Three-dimensionality in the wake of a rotating cylinder in a uniform flow. J. Fluid Mech. 717, 1–29.Google Scholar
Rao, A., Radi, A., Leontini, J. S., Thompson, M. C., Sheridan, J. & Hourigan, K. 2015 A review of rotating cylinder wake transitions. J. Fluids Struct. 53, 2–14.Google Scholar
Sarpkaya, T. 2004 A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19, 389–447.Google Scholar
Stansby, P. K. & Rainey, R. C. T. 2001 On the orbital response of a rotating cylinder in a current. J. Fluid Mech. 439, 87–108.Google Scholar
Stojković, D., Breuer, M. & Durst, F. 2002 Effect of high rotation rates on the laminar flow around a circular cylinder. Phys. Fluids 14, 3160.Google Scholar
Stojković, D., Schön, P., Breuer, M. & Durst, F. 2003 On the new vortex shedding mode past a rotating circular cylinder. Phys. Fluids 15, 1257.Google Scholar
Tudball-Smith, D., Leontini, J. S., Sheridan, J. & Lo Jacono, D. 2012 Streamwise forced oscillations of circular and square cylinders. Phys. Fluids 24, 111703.Google Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413–455.Google 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
Yogeswaran, V. & Mittal, S. 2011 Vortex-induced and galloping response of a rotating circular cylinder. In IUTAM Symposium on Bluff Body Flows, IIT-Kanpur, India (ed. Mittal, S. & Biswas, G.), pp. 153–156.Google Scholar
Zhao, J., Leontini, J. S., Lo Jacono, D. & Sheridan, J. 2014a Fluid–structure interaction of a square cylinder at different angles of attack. J. Fluid Mech. 747, 688–721.Google Scholar
Zhao, M., Cheng, L. & Lu, L. 2014b Vortex induced vibrations of a rotating circular cylinder at low Reynolds number. Phys. Fluids 26, 073602.Google Scholar
Zhao, M., Cheng, L. & Zhou, T. 2013 Numerical simulation of vortex-induced vibration of a square cylinder at a low Reynolds number. Phys. Fluids 25, 023603.Google Scholar