Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T13:38:38.007Z Has data issue: false hasContentIssue false
  • English
  • Français

Chaotic rotation of a towed elliptical cylinder

Published online by Cambridge University Press:  06 March 2014

G. D. Weymouth
G. D. Weymouth*
Affiliation:
Southampton Marine and Maritime Institute, University of Southampton, Southampton SO17 1BJ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper I consider the self-excited rotation of an elliptical cylinder towed in a viscous fluid as a canonical model of nonlinear fluid–structure interactions with possible applications in the design of sensors and energy extraction devices. First, the self-excited ellipse system is shown to be analogous to the forced bistable oscillators studied in classic chaos theory. A single variable, the distance between the pivot and the centroid, governs the system bifurcation into bistability. Next, fully coupled computational fluid dynamics simulations of the motion of the cylinder demonstrate limit cycle, period doubling, intermittently chaotic and fully chaotic dynamics as the distance is further adjusted. The viscous wake behind the cylinder is presented for the limit-cycle cases and new types of stable wakes are characterized for each. In contrast, a chaotic case demonstrates an independence of the wake and structural states. The rotational kinetic energy is quantified and correlated to the vortex shedding and the trajectory periodicity. Chaotic and high-period system responses are found to persist when structural damping is applied and for Reynolds numbers as low as 200.

JFM classification

Aerodynamics: Flow-structure interactions Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 743 , 25 March 2014 , pp. 385 - 398
Copyright
© 2014 Cambridge University Press 

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

Abdelkefi, A., Hajj, M. R. & Nayfeh, A. H. 2013 Piezoelectric energy harvesting from transverse galloping of bluff bodies. Smart Mater. Struct. 22 (1), 015014.Google Scholar
Alonso, G., Meseguer, J., Sanz-Andres, A. & Valero, E. 2010 On the galloping instability of two-dimensional bodies having elliptical cross-sections. J. Wind Engng Ind. Aerodyn. 98 (8–9), 438–448.CrossRefGoogle Scholar
Arrieta, A. F., Hagedorn, P., Erturk, A. & Inman, D. J. 2010 A piezoelectric bistable plate for nonlinear broadband energy harvesting. Appl. Phys. Lett. 97 (10), 104102.CrossRefGoogle Scholar
Barrero-Gil, A., Alonso, G. & Sanz-Andres, A. 2010 Energy harvesting from transverse galloping. J. Sound Vib. 329 (14), 2873–2883.CrossRefGoogle Scholar
Bearman, P. W. 1984 Vortex shedding from oscillating bluff bodies. Annu. Rev. Fluid Mech. 16 (1), 195–222.CrossRefGoogle Scholar
Beem, H., Hildner, M. & Triantafyllou, M. 2013 Calibration and validation of a harbor seal whisker-inspired flow sensor. Smart Mater. Struct. 22 (1), 014012.CrossRefGoogle Scholar
Bernitsas, M. M., Rasghavan, K., Ben-Simon, Y. & Garcia, E. M. H. 2008 VIVACE (vortex induced vibration aquatic clean energy): a new concept in generation of clean and renewable energy from fluid flow. J. Offshore Mech. Arctic Engng 130 (4), 041101.CrossRefGoogle Scholar
Connell, B. S. H. & Yue, D. K. P. 2007 Flapping dynamics of a flag in a uniform stream. J. Fluid Mech. 581 (1), 33–67.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 (14), 144503.CrossRefGoogle ScholarPubMed
Holmes, P. 1979 A nonlinear oscillator with a strange attractor. Phil. Trans. R. Soc. Lond. A Math. Phys. Sci. 292 (1394), 419–448.Google Scholar
Huang, L. 1995 Flutter of cantilevered plates in axial flow. J. Fluids Struct. 9 (2), 127–147.CrossRefGoogle Scholar
Lorenz, E. N. 1963 Deterministic nonperiodic flow. J. Atmos. Sci. 20 (2), 130–141.2.0.CO;2>CrossRefGoogle Scholar
Lugt, H. J. 1980 Autorotation of an elliptic cylinder about an axis perpendicular to the flow. J. Fluid Mech. 99 (04), 817–840.CrossRefGoogle Scholar
Lugt, H. J. 1983 Autorotation. Annu. Rev. Fluid Mech. 15 (1), 123–147.CrossRefGoogle Scholar
Modarres-Sadeghi, Y., Chasparis, F., Triantafyllou, M. S., Tognarelli, M. & Beynet, P. 2011 Chaotic response is a generic feature of vortex-induced vibrations of flexible risers. J. Sound Vib. 330 (11), 2565–2579.CrossRefGoogle Scholar
Nakamura, Y. 1990 Recent research into bluff-body flutter. J. Wind Engng Ind. Aerodyn. 33 (1), 1–10.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.CrossRefGoogle Scholar
Robertson, I., Li, L., Sherwin, S. J. & Bearman, P. W. 2003 A numerical study of rotational and transverse galloping rectangular bodies. J. Fluids Struct. 17 (5), 681–699.CrossRefGoogle Scholar
Sipcic, S. R. 1990 The chaotic response of a fluttering panel: The influence of maneuvering. Nonlinear Dyn. 1 (3), 243–264.CrossRefGoogle Scholar
Spyrou, K. J. & Thompson, J. M. T. 2000 The nonlinear dynamics of ship motions: a field overview and some recent developments. Phil. Trans. R. Soc. Lond. A 358 (1771), 1735–1760.CrossRefGoogle Scholar
Townsend, N. C. & Shenoi, R. A. 2013 Modelling and analysis of a single gimbal gyroscopic energy harvester. Nonlinear Dyn. 1–16.Google Scholar
Van Oudheusden, B. W. 1995 On the quasi-steady analysis of one-degree-of-freedom galloping with combined translational and rotational effects. Nonlinear Dyn. 8 (4), 435–451.CrossRefGoogle Scholar
Van Oudheusden, B. W. 1996 Rotational one-degree-of-freedom galloping in the presence of viscous and frictional damping. J. Fluids Struct. 10 (7), 673–689.CrossRefGoogle Scholar
Weymouth, G. D., Dommermuth, D. G., Hendrickson, K. & Yue, D. K.-P. 2006 Advancements in Cartesian-grid methods for computational ship hydrodynamics. In 26th Symposium on Naval Hydrodynamics. Rome, Italy .Google Scholar
Weymouth, G. D. & Triantafyllou, M. S. 2013 Ultra-fast escape of a deformable jet-propelled body. J. Fluid Mech. 721, 367–385.CrossRefGoogle Scholar
Weymouth, G. D. & Yue, D. K.-P. 2011 Boundary data immersion method for cartesian-grid simulations of fluid-body interaction problems. J. Comput. Phys. 230 (16), 6233–6247.CrossRefGoogle Scholar
Wibawa, M. S., Steele, S. C., Dahl, J. M., Rival, D. E., Weymouth, G. D. & Triantafyllou, M. S. 2012 Global vorticity shedding for a vanishing wing. J. Fluid Mech. 695, 112–134.CrossRefGoogle Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413–455.CrossRefGoogle Scholar

Weymouth supplementary movie

Limit cycle rotation of a towed elliptical cylinder

Download Weymouth supplementary movie(Video)
Video 10.5 MB

Weymouth supplementary movie

Chaotic rotation of a towed elliptical cylinder

Download Weymouth supplementary movie(Video)
Video 3.8 MB