Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-17T11:25:45.399Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex-induced vibration of a rotating sphere

Published online by Cambridge University Press:  20 December 2017

A. Sareen Open the ORCID record for A. Sareen [Opens in a new window] ,
J. Zhao Open the ORCID record for J. Zhao [Opens in a new window] ,
D. Lo Jacono ,
J. Sheridan ,
K. Hourigan  and
M. C. Thompson
A. Sareen
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
J. Zhao*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
D. Lo Jacono
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France
J. Sheridan
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
K. Hourigan
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
M. C. Thompson
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Vortex-induced vibration (VIV) of a sphere represents one of the most generic fundamental fluid–structure interaction problems. Since vortex-induced vibration can lead to structural failure, numerous studies have focused on understanding the underlying principles of VIV and its suppression. This paper reports on an experimental investigation of the effect of imposed axial rotation on the dynamics of vortex-induced vibration of a sphere that is free to oscillate in the cross-flow direction, by employing simultaneous displacement and force measurements. The VIV response was investigated over a wide range of reduced velocities (i.e. velocity normalised by the natural frequency of the system): $3\leqslant U^{\ast }\leqslant 18$, corresponding to a Reynolds number range of $5000<Re<30\,000$, while the rotation ratio, defined as the ratio between the sphere surface and inflow speeds, $\unicode[STIX]{x1D6FC}=|\unicode[STIX]{x1D714}|D/(2U)$, was varied in increments over the range of $0\leqslant \unicode[STIX]{x1D6FC}\leqslant 7.5$. It is found that the vibration amplitude exhibits a typical inverted bell-shaped variation with reduced velocity, similar to the classic VIV response for a non-rotating sphere but without the higher reduced velocity response tail. The vibration amplitude decreases monotonically and gradually as the imposed transverse rotation rate is increased up to $\unicode[STIX]{x1D6FC}=6$, beyond which the body vibration is significantly reduced. The synchronisation regime, defined as the reduced velocity range where large vibrations close to the natural frequency are observed, also becomes narrower as $\unicode[STIX]{x1D6FC}$ is increased, with the peak saturation amplitude observed at progressively lower reduced velocities. In addition, for small rotation rates, the peak amplitude decreases almost linearly with $\unicode[STIX]{x1D6FC}$. The imposed rotation not only reduces vibration amplitudes, but also makes the body vibrations less periodic. The frequency spectra revealed the occurrence of a broadband spectrum with an increase in the imposed rotation rate. Recurrence analysis of the structural vibration response demonstrated a transition from periodic to chaotic in a modified recurrence map complementing the appearance of broadband spectra at the onset of bifurcation. Despite considerable changes in flow structure, the vortex phase ($\unicode[STIX]{x1D719}_{vortex}$), defined as the phase between the vortex force and the body displacement, follows the same pattern as for the non-rotating case, with the $\unicode[STIX]{x1D719}_{vortex}$ increasing gradually from low values in Mode I of the sphere vibration to almost $180^{\circ }$ as the system undergoes a continuous transition to Mode II of the sphere vibration at higher reduced velocity. The total phase ($\unicode[STIX]{x1D719}_{total}$), defined as the phase between the transverse lift force and the body displacement, only increases from low values after the peak amplitude response in Mode II has been reached. It reaches its maximum value (${\sim}165^{\circ }$) close to the transition from the Mode II upper plateau to the lower plateau, reminiscent of the behaviour seen for the upper to lower branch transition for cylinder VIV. Hydrogen-bubble visualisations and particle image velocimetry (PIV) performed in the equatorial plane provided further insights into the flow dynamics near the sphere surface. The mean wake is found to be deflected towards the advancing side of the sphere, associated with an increase in the Magnus force. For higher rotation ratios, the near-wake rear recirculation zone is absent and the flow is highly vectored from the retreating side to the advancing side, giving rise to large-scale shedding. For a very high rotation ratio of $\unicode[STIX]{x1D6FC}=6$, for which vibrations are found to be suppressed, a one-sided large-scale shedding pattern is observed, similar to the shear-layer instability one-sided shedding observed previously for a rigidly mounted rotating sphere.

JFM classification

Wakes/Jets: Vortex streets Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 258 - 292
Copyright
© 2017 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

Barlow, J. B. & Domanski, M. J. 2008 Lift on stationary and rotating spheres under varying flow and surface conditions. AIAA J. 46 (8), 1932–1936.Google Scholar
Bearman, P. W. 1984 Vortex shedding from oscillating bluff bodies. Annu. Rev. Fluid Mech. 16 (1), 195–222.10.1146/annurev.fl.16.010184.001211Google Scholar
Behara, S., Borazjani, I. & Sotiropoulos, F. 2011 Vortex-induced vibrations of an elastically mounted sphere with three degrees of freedom at Re = 300: hysteresis and vortex shedding modes. J. Fluid Mech. 686, 426–450.Google Scholar
Behara, S. & Sotiropoulos, F. 2016 Vortex-induced vibrations of an elastically mounted sphere: the effects of Reynolds number and reduced velocity. J. Fluids Struct. 66, 54–68.10.1016/j.jfluidstructs.2016.07.005Google Scholar
Blevins, R. D. 1990 Flow-Induced Vibration, 2nd edn. Krieger Publishing Company.Google Scholar
Bourguet, R. & Lo Jacono, D. 2014 Flow-induced vibrations of a rotating cylinder. J. Fluid Mech. 740, 342–380.10.1017/jfm.2013.665Google Scholar
Brücker, C. 1999 Structure and dynamics of the wake of bubbles and its relevance for bubble interaction. Phys. Fluids 11 (7), 1781–1796.10.1063/1.870043Google Scholar
Eckmann, J., Kamphorst, S. O. & Ruelle, D. 1987 Recurrence plots of dynamical systems. Europhys. Lett. 4 (9), 973–977.10.1209/0295-5075/4/9/004Google Scholar
Fouras, A., Lo Jacono, D. & Hourigan, K. 2008 Target-free stereo PIV: a novel technique with inherent error estimation and improved accuracy. Exp. Fluids 44 (2), 317–329.10.1007/s00348-007-0404-1Google Scholar
Giacobello, M., Ooi, A. & Balachandar, S. 2009 Wake structure of a transversely rotating sphere at moderate Reynolds numbers. J. Fluid Mech. 621, 103–130.Google Scholar
Govardhan, R. & Williamson, C. H. K. 1997 Vortex-induced motions of a tethered sphere. J. Wind Engng Indust. Aerodyn. 375, 69–71.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, 85–130.10.1017/S0022112000001233Google Scholar
Govardhan, R. & Williamson, C. H. K. 2002 Resonance forever: existence of a critical mass and an infinite regime of resonance in vortex-induced vibration. J. Fluid Mech. 473, 147–166.10.1017/S0022112002002318Google Scholar
Govardhan, R. N. & Williamson, C. H. K. 2005 Vortex-induced vibrations of a sphere. J. Fluid Mech. 531, 11–47.10.1017/S0022112005003757Google Scholar
van Hout, R., Katz, A. & Greenblatt, D. 2013a Acoustic control of vortex-induced vibrations of a tethered sphere. Phys. Fluids 25, 077102.Google Scholar
van Hout, R., Katz, A. & Greenblatt, D. 2013b Time-resolved particle image velocimetry measurements of vortex and shear layer dynamics in the near wake of a tethered sphere. Phys. Fluids 25 (7), 077102.Google Scholar
van Hout, R., Krakovich, A. & Gottlieb, O. 2010 Time resolved measurements of vortex-induced vibrations of a tethered sphere in uniform flow. Phys. Fluids 22 (8), 087101.10.1063/1.3466660Google Scholar
Hover, F. S., Miller, S. N. & Triantafyllou, M. S. 1997 Vortex-induced vibration of marine cables: experiments using force feedback. J. Fluids Struct. 11 (3), 307–326.10.1006/jfls.1996.0079Google Scholar
Jauvtis, N., Govardhan, R. & Williamson, C. H. K. 2001 Multiple modes of vortex-induced vibration of a sphere. J. Fluids Struct. 15 (3–4), 555–563.10.1006/jfls.2000.0348Google 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.Google Scholar
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70.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 (7–8), 813–851.10.1006/jfls.1999.0236Google Scholar
Kim, D. 2009 Laminar flow past a sphere rotating in the transverse direction. J. Mech. Sci. Technol. 23 (2), 578–589.10.1007/s12206-008-1001-9Google Scholar
Kim, J., Choi, H., Park, H. & Yoo, J. Y. 2014 Inverse Magnus effect on a rotating sphere: when and why. J. Fluid Mech. 754, R2.Google Scholar
Krakovich, A., Eshbal, L. & van Hout, R. 2013 Vortex dynamics and associated fluid forcing in the near wake of a light and heavy tethered sphere in uniform flow. Exp. Fluids 54 (11), 1615.10.1007/s00348-013-1615-2Google Scholar
Kray, T., Franke, J. & Frank, W. 2012 Magnus effect on a rotating sphere at high Reynolds numbers. J. Wind Engng Indust. Aerodyn. 110, 1–9.Google Scholar
Kray, T., Franke, J. & Frank, W. 2014 Magnus effect on a rotating soccer ball at high Reynolds numbers. J. Wind Engng Indust. Aerodyn. 124, 46–53.Google Scholar
Lee, H., Hourigan, K. & Thompson, M. C. 2013 Vortex-induced vibration of a neutrally buoyant tethered sphere. J. Fluid Mech. 719, 97–128.Google Scholar
Leweke, T., Provansal, M., Ormieres, D. & Lebescond, R. 1999 Vortex dynamics in the wake of a sphere. Phys. Fluids 11 (9), S12.10.1063/1.4739162Google Scholar
Lighthill, J. 1986 Fundamentals concerning wave loading on offshore structures. J. Fluid Mech. 173, 667–681.Google Scholar
Macoll, J. W. 1928 Aerodynamics of a spinning sphere. J. R. Aero. Soc. 28, 777–798.10.1017/S0368393100136260Google Scholar
Magarvey, R. H. & Bishop, R. L. 1961 Transition ranges for three-dimensional wakes. Can. J. Phys. 39 (10), 1418–1422.10.1139/p61-169Google Scholar
Magnus, G. 1853 Ueber die Abweichung der Geschosse, und: Ueber eine auffallende Erscheinung bei rotirenden Körpern. Annalen der Physik 164 (1), 1–29.10.1002/andp.18531640102Google Scholar
Marwan, N.2003 Encounters with neighbours: current developments of concepts based on recurrence plots and their applications. PhD thesis, Universität Potsdam.Google Scholar
Marwan, N. 2008 A historical review of recurrence plots. Eur. Phys. J. 164 (1), 3–12.Google Scholar
Marwan, N., Romano, M., Thiel, M. & Kurths, J. 2007 Recurrence plots for the analysis of complex systems. Phys. Rep. 438 (5), 237–329.Google Scholar
Mirauda, D., Volpe Plantamura, A. & Malavasi, S. 2014 Dynamic response of a sphere immersed in a shallow water flow. J. Offshore Mech. Arctic Engng 136 (2), 021101.Google Scholar
Mittal, R. 1999 A Fourier–Chebyshev spectral collocation method for simulating flow past spheres and spheroids. Intl J. Numer. Meth. Fluids 30 (7), 921–937.10.1002/(SICI)1097-0363(19990815)30:7<921::AID-FLD875>3.0.CO;2-33.0.CO;2-3>Google Scholar
Morse, T., Govardhan, R. & Williamson, C. H. K. 2008 The effect of end conditions on the vortex-induced vibration of cylinders. J. Fluids Struct. 24 (8), 1227–1239.10.1016/j.jfluidstructs.2008.06.004Google Scholar
Naudascher, E. & Rockwell, D. 2012 Flow-Induced Vibrations: An Engineering Guide. Courier Corporation.Google Scholar
Ormières, D. & Provansal, M. 1999 Transition to turbulence in the wake of a sphere. Phys. Rev. Lett. 83 (1), 80.10.1103/PhysRevLett.83.80Google Scholar
Païdoussis, M. P., Price, S. & De Langre, E. 2010 Fluid–Structure Interactions: Cross-Flow-Induced Instabilities. Cambridge University Press.10.1017/CBO9780511760792Google Scholar
Poon, E. K. W., Ooi, A. S., Giacobello, M., Iaccarino, G. & Chung, D. 2014 Flow past a transversely rotating sphere at Reynolds numbers above the laminar regime. J. Fluid Mech. 759, 751–781.10.1017/jfm.2014.570Google Scholar
Pregnalato, C. J.2003 Flow-induced vibrations of a tethered sphere. PhD thesis, Monash University.Google Scholar
Rao, A., Passaggia, P.-Y., Bolnot, H., Thompson, M., Leweke, T. & Hourigan, K. 2012 Transition to chaos in the wake of a rolling sphere. J. Fluid Mech. 695, 135–148.Google Scholar
Sakamoto, H. & Haniu, H. 1990 A study on vortex shedding from spheres in a uniform flow. J. Fluids Engng 112 (4), 386–392.Google Scholar
Sareen, A., Zhao, J., Lo Jacono, D., Sheridan, J., Hourigan, K. & Thompson, M. C. 2016 Flow past a transversely rotating sphere. In Proceedings of the 11th International Conference on Flow-Induced Vibration and Noise, The Hague, The Netherlands, 4–6 July 2016. The Netherlands Organisation for Applied Scientific Research.Google Scholar
Sarpkaya, T. 2004 A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19 (4), 389–447.10.1016/j.jfluidstructs.2004.02.005Google Scholar
Seyed-Aghazadeh, B. & Modarres-Sadeghi, Y. 2015 An experimental investigation of vortex-induced vibration of a rotating circular cylinder in the crossflow direction. Phys. Fluids 27 (6), 067101.Google Scholar
Thompson, M. C., Leweke, T. & Provansal, M. 2001 Kinematics and dynamics of sphere wake transition. J. Fluids Struct. 15 (3), 575–585.10.1006/jfls.2000.0362Google Scholar
Tomboulides, A., Orszag, S. & Karniadakis, G. 1993 Direct and large-eddy simulations of axisymmetric wakes. In 31st Aerospace Sciences Meeting, p. 546. AIAA.Google Scholar
Williamson, C. H. K. & Govardhan, R. 1997 Dynamics and forcing of a tethered sphere in a fluid flow. J. Fluids Struct. 11, 293–305.Google Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36 (1), 413–455.Google Scholar
Wong, K. W. L., Zhao, J., Lo Jacono, D., Thompson, M. C. & Sheridan, J. 2017 Experimental investigation of flow-induced vibration of a rotating circular cylinder. J. Fluid Mech. 829, 486–511.10.1017/jfm.2017.540Google Scholar
Zhao, J., Leontini, J. S., Lo Jacono, D. & Sheridan, J. 2014a Chaotic vortex induced vibrations. Phys. Fluids 26 (12), 121702.10.1063/1.4904975Google Scholar
Zhao, J., Leontini, J. S., Lo Jacono, D. & Sheridan, J. 2014b Fluid–structure interaction of a square cylinder at different angles of attack. J. Fluid Mech. 747, 688–721.10.1017/jfm.2014.167Google Scholar