Hostname: page-component-7479d7b7d-t6hkb Total loading time: 0 Render date: 2024-07-15T23:51:34.076Z Has data issue: false hasContentIssue false
  • English
  • Français

Prediction of vortex-induced vibration response by employing controlled motion

Published online by Cambridge University Press:  26 August 2009

T. L. MORSE  and
C. H. K. WILLIAMSON
T. L. MORSE
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
C. H. K. WILLIAMSON*
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In order to predict response and wake modes for elastically mounted circular cylinders in a fluid flow, we employ controlled-vibration experiments, comprised of prescribed transverse vibration of a cylinder in the flow, over a wide regime of amplitude and frequency. A key to this study is the compilation of high-resolution contour plots of fluid force, in the plane of normalized amplitude and wavelength. With such resolution, we are able to discover discontinuities in the force and phase contours, which enable us to clearly identify boundaries separating different fluid-forcing regimes. These appear remarkably similar to boundaries separating different vortex-formation modes in the map of regimes by Williamson & Roshko (J. Fluids Struct., vol. 2, 1988, pp. 355–381). Vorticity measurements exhibit the 2S, 2P and P + S vortex modes, as well as a regime in which the vortex formation is not synchronized with the body vibration. By employing such fine-resolution data, we discover a high-amplitude regime in which two vortex-formation modes overlap. Associated with this overlap regime, we identify a new distinct mode of vortex formation comprised of two pairs of vortices formed per cycle, where the secondary vortex in each pair is much weaker than the primary vortex. This vortex mode, which we define as the 2POVERLAP mode (2PO), is significant because it is responsible for generating the peak resonant response of the body. We find that the wake can switch intermittently between the 2P and 2PO modes, even as the cylinder is vibrating with constant amplitude and frequency. By examining the energy transfer from fluid to body motion, we predict a free-vibration response which agrees closely with measurements for an elastically mounted cylinder. In this work, we introduce the concept of an ‘energy portrait’, which is a plot of the energy transfer into the body motion and the energy dissipated by damping, as a function of normalized amplitude. Such a plot allows us to identify stable and unstable amplitude-response solutions, dependent on the rate of change of net energy transfer with amplitude (the sign of dE*/dA*). Our energy portraits show how the vibration system may exhibit a hysteretic mode transition or intermittent mode switching, both of which correspond with such phenomena measured from free vibration. Finally, we define the complete regime in the amplitude–wavelength plane in which free vibration may exist, which requires not only a periodic component of positive excitation but also stability of the equilibrium solutions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 634 , 10 September 2009 , pp. 5 - 39
Copyright
Copyright © Cambridge University Press 2009

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
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 227, 51–75.Google 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., Govardhan, R., Sheridan, J., Rockwell, D. & Williamson, C. H. K. 2004 Wake states and response branches of forced and freely oscillating cylinders. Eur. J. Mech. B 23, 89–97.CrossRefGoogle Scholar
Carberry, J., Sheridan, J. & Rockwell, D. 2001 Forces and wake modes of an oscillating cylinder. J. Fluids Struct. 15, 523–532.CrossRefGoogle Scholar
Carberry, J., Sheridan, J. & Rockwell, D. 2003 Controlled oscillations of a cylinder: a new wake state. J. Fluids Struct. 17, 337–343.CrossRefGoogle Scholar
Carberry, J., Sheridan, J. & Rockwell, D. 2005 Controlled oscillations of a cylinder: forces and wake modes. J. Fluid Mech. 538, 31–89.CrossRefGoogle Scholar
Feng, C. C. 1968 The measurement of vortex-induced effects in flow past stationary and oscillating circular and D-section cylinders. Master's thesis, University of British Columbia, Vancouver, BC, Canada.Google Scholar
Gopalkrishnan, R. 1993 Vortex-induced forces on oscillating bluff cylinders. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.Google 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
Govardhan, R. & Williamson, C. H. K. 2006 Defining the ‘modified Griffin plot’ in vortex-induced vibration: revealing the effect of Reynolds number using controlled damping. J. Fluid Mech. 561, 147–180.CrossRefGoogle Scholar
Griffin, O. M. 1980 Vortex-excited crossflow vibrations of a single cylindrical tube. Trans. ASME, J. Press. Vessel Technol. 102, 158–166.CrossRefGoogle Scholar
Griffin, O. M. & Ramberg, S. E. 1982 Some recent studies of vortex shedding with application to marine tubulars and risers. J. Energy Resource Technol. 104, 2–13.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
Khalak, A. & Williamson, C. H. K. 1996 Dynamics of a hydroelastic cylinder with very low mass and damping. J. Fluids Struct. 10, 455–472.CrossRefGoogle 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.CrossRefGoogle Scholar
Leontini, J. S., Stewart, B. E., Thompson, M. C. & Hourigan, K. 2006 a Predicting vortex-induced vibration from driven oscillation results. Appl. Math. Model. 30, 1096–1102.CrossRefGoogle Scholar
Leontini, J. S., Stewart, B. E., Thompson, M. C. & Hourigan, K. 2006 b Wake state and energy transitions of an oscillating cylinder at low Reynolds number. Phys. Fluids 18, 067101.CrossRefGoogle Scholar
Lighthill, J. 1986 Wave loading on offshore structures. J. Fluid Mech. 173, 667–681.CrossRefGoogle Scholar
Mercier, J. A. 1973 Large amplitude oscillations of a circular cylinder in a low speed stream. PhD thesis, Stevens Institute of Technology, Hoboken, NJ.Google Scholar
Morse, T. L. & Williamson, C. H. K. 2006 Employing controlled vibrations to predict fluid forces on a cylinder undergoing vortex-induced vibration. J. Fluids Struct. 22, 877–884.CrossRefGoogle Scholar
Morse, T. L. & Williamson, C. H. K. 2009 a Fluid forcing, wake modes, and transitions for a cylinder undergoing controlled oscillation. J. Fluids Struct. 25, 697–712.CrossRefGoogle Scholar
Morse, T. L. & Williamson, C. H. K. 2009 b Steady, unsteady, and transient vortex-induced vibration predicted using controlled motion data. J. Fluid Mech. (submitted).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
Parkinson, G. 1989 Phenomena and modelling of flow-induced vibrations of bluff bodies. Progr. Aerosp. Sci. 26, 169–224.CrossRefGoogle Scholar
Sarpkaya, T. 1977 Transverse oscillations of a circular cylinder in uniform flow. Part I. Tech Rep. NPS-69SL77071. Naval Postgraduate School, Monterey, CA.CrossRefGoogle Scholar
Sarpkaya, T. 1979 Vortex-induced oscillations. J. Appl. Mech. 46, 241–258.CrossRefGoogle Scholar
Staubli, T. 1983 Calculation of the vibration of an elastically mounted cylinder using experimental data from forced vibration. ASME J. Fluids Engng 105, 225–229.CrossRefGoogle Scholar
Willden, R. H. J., McSherry, R. J. & Graham, J. M. R. 2007 Prescribed cross-stream oscillations of a circular cylinder at laminar and early turbulent Reynolds numbers. In Fifth Conference on Bluff Body Wakes and Vortex-Induced Vibration (BBVIV-5), Costa do Sauipe, Brazil.Google 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