Skip to main content Accessibility help

The effect of imposed rotary oscillation on the flow-induced vibration of a sphere

  • A. Sareen (a1), J. Zhao (a1), J. Sheridan (a1), K. Hourigan (a1) and M. C. Thompson (a1)...


This experimental study investigates the effect of imposed rotary oscillation on the flow-induced vibration of a sphere that is elastically mounted in the cross-flow direction, employing simultaneous displacement, force and vorticity measurements. The response is studied over a wide range of forcing parameters, including the frequency ratio $f_{R}$ and velocity ratio $\unicode[STIX]{x1D6FC}_{R}$ of the oscillatory forcing, which vary between $0\leqslant f_{R}\leqslant 5$ and $0\leqslant \unicode[STIX]{x1D6FC}_{R}\leqslant 2$ . The effect of another important flow parameter, the reduced velocity, $U^{\ast }$ , is also investigated by varying it in small increments between $0\leqslant U^{\ast }\leqslant 20$ , corresponding to the Reynolds number range of $5000\lesssim Re\lesssim 30\,000$ . It has been found that when the forcing frequency of the imposed rotary oscillations, $f_{r}$ , is close to the natural frequency of the system, $f_{nw}$ , (so that $f_{R}=f_{r}/f_{nw}\sim 1$ ), the sphere vibrations lock on to $f_{r}$ instead of $f_{nw}$ . This inhibits the normal resonance or lock-in leading to a highly reduced vibration response amplitude. This phenomenon has been termed ‘rotary lock-on’, and occurs for only a narrow range of $f_{R}$ in the vicinity of $f_{R}=1$ . When rotary lock-on occurs, the phase difference between the total transverse force coefficient and the sphere displacement, $\unicode[STIX]{x1D719}_{total}$ , jumps from $0^{\circ }$ (in phase) to $180^{\circ }$ (out of phase). A corresponding dip in the total transverse force coefficient $C_{y\,(rms)}$ is also observed. Outside the lock-on boundaries, a highly modulated amplitude response is observed. Higher velocity ratios ( $\unicode[STIX]{x1D6FC}_{R}\geqslant 0.5$ ) are more effective in reducing the vibration response of a sphere to much lower values. The mode I sphere vortex-induced vibration (VIV) response is found to resist suppression, requiring very high velocity ratios ( $\unicode[STIX]{x1D6FC}_{R}>1.5$ ) to significantly suppress vibrations for the entire range of $f_{R}$ tested. On the other hand, mode II and mode III are suppressed for $\unicode[STIX]{x1D6FC}_{R}\geqslant 1$ . The width of the lock-on region increases with an increase in $\unicode[STIX]{x1D6FC}_{R}$ . Interestingly, a reduction of VIV is also observed in non-lock-on regions for high $f_{R}$ and $\unicode[STIX]{x1D6FC}_{R}$ values. For a fixed $\unicode[STIX]{x1D6FC}_{R}$ , when $U^{\ast }$ is progressively increased, the response of the sphere is very rich, exhibiting characteristically different vibration responses for different $f_{R}$ values. The phase difference between the imposed rotary oscillation and the sphere displacement $\unicode[STIX]{x1D719}_{rot}$ is found to be crucial in determining the response. For selected $f_{R}$ values, the vibration amplitude increases monotonically with an increase in flow velocity, reaching magnitudes much higher than the peak VIV response for a non-rotating sphere. For these cases, the vibrations are always locked to the forcing frequency, and there is a linear decrease in $\unicode[STIX]{x1D719}_{rot}$ . Such vibrations have been termed ‘rotary-induced vibrations’. The wake measurements in the cross-plane $1.5D$ downstream of the sphere position reveal that the sphere wake consists of vortex loops, similar to the wake of a sphere without any imposed rotation; however, there is a change in the timing of vortex formation. On the other hand, for high $f_{R}$ values, there is a reduction in the streamwise vorticity, presumably leading to a decreased total transverse force acting on the sphere and resulting in a reduced response.


Corresponding author

Email address for correspondence:


Hide All
Assi, G. R. S., Bearman, P. W. & Meneghini, J. R. 2010 On the wake-induced vibration of tandem circular cylinders: the vortex interaction excitation mechanism. J. Fluid Mech. 661, 365401.
Baek, S. J. & Sung, H. J. 2000 Quasi-periodicity in the wake of a rotationally oscillating cylinder. J. Fluid Mech. 408, 275300.
Bearman, P. W. 1984 Vortex shedding from oscillating bluff bodies. Annu. Rev. Fluid Mech. 16 (1), 195222.
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, 426450.
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, 5468.
Blevins, R. D. 1990 Flow-Induced Vibration, 2nd edn. Krieger Publishing Company.
Bokaian, A. & Geoola, F. 1984 Wake-induced galloping of two interfering circular cylinders. J. Fluid Mech. 146, 383415.
Brika, D. & Laneville, A. 1999 The flow interaction between a stationary cylinder and a downstream flexible cylinder. J. Fluids Struct. 13 (5), 579606.
Cheng, M., Chew, Y. T. & Luo, S. C. 2001 Numerical investigation of a rotationally oscillating cylinder in mean flow. J. Fluids Struct. 15 (7), 9811007.
Choi, H., Jeon, W. & Kim, J. 2008 Control of flow over a bluff body. Annu. Rev. Fluid Mech. 40, 113139.
Choi, S., Choi, H. & Kang, S. 2002 Characteristics of flow over a rotationally oscillating cylinder at low Reynolds number. Phys. Fluids 14 (8), 27672777.
Chou, M. H. 1997 Synchronization of vortex shedding from a cylinder under rotary oscillation. Comput. Fluids 26 (8), 755774.
Dong, S., Triantafyllou, G. S. & Karniadakis, G. E. 2008 Elimination of vortex streets in bluff-body flows. Phys. Rev. Lett. 100 (20), 204501.
Du, L. & Sun, X. 2015 Suppression of vortex-induced vibration using the rotary oscillation of a cylinder. Phys. Fluids 27 (2), 023603.
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), 317329.
Govardhan, R. & Williamson, C. H. K. 1997 Vortex-induced motions of a tethered sphere. J. Wind Engng Ind. Aerodyn. 69, 375385.
Govardhan, R. N. & Williamson, C. H. K. 2005 Vortex-induced vibrations of a sphere. J. Fluid Mech. 531, 1147.
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.
Jauvtis, N., Govardhan, R. & Williamson, C. H. K. 2001 Multiple modes of vortex-induced vibration of a sphere. J. Fluids Struct. 15 (3–4), 555563.
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.
Kumar, S., Lopez, C., Probst, O., Francisco, G., Askari, D. & Yang, Y. 2013 Flow past a rotationally oscillating cylinder. J. Fluid Mech. 735, 307346.
Lee, H., Hourigan, K. & Thompson, M. C. 2013 Vortex-induced vibration of a neutrally buoyant tethered sphere. J. Fluid Mech. 719, 97128.
Lee, S. & Lee, J. 2006 Flow structure of wake behind a rotationally oscillating circular cylinder. J. Fluids Struct. 22 (8), 10971112.
Lu, X. Y. & Sato, J. 1996 A numerical study of flow past a rotationally oscillating circular cylinder. J. Fluids Struct. 10 (8), 829849.
Mahfouz, F. M. & Badr, H. M. 2000 Flow structure in the wake of a rotationally oscillating cylinder. Trans. ASME J. Fluids Engng 122 (2), 290301.
Mittal, S. 2001 Control of flow past bluff bodies using rotating control cylinders. J. Fluids Struct. 15 (2), 291326.
Naudascher, E. & Rockwell, D. 2012 Flow-Induced Vibrations: An Engineering Guide. Courier Corporation.
Païdoussis, M. P., Price, S. & De Langre, E. 2010 Fluid-Structure Interactions: Cross-Flow-Induced Instabilities. Cambridge University Press.
Pregnalato, C. J.2003 Flow-induced vibrations of a tethered sphere. PhD thesis, Monash University.
Sakamoto, H. & Haniu, H. 1990 A study on vortex shedding from spheres in a uniform flow. Trans. ASME J. Fluids Engng 112, 386392.
Sareen, A., Zhao, J., Lo Jacono, D., Sheridan, J., Hourigan, K. & Thompson, M. C. 2018a Vortex-induced vibration of a rotating sphere. J. Fluid Mech. 837, 258292.
Sareen, A., Zhao, J., Sheridan, J., Hourigan, K. & Thompson, M. C. 2018b Vortex-induced vibrations of a sphere close to a free surface. J. Fluid Mech. 846, 10231058.
Sarpkaya, T. 2004 A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19 (4), 389447.
Shiels, D. & Leonard, A. 2001 Investigation of a drag reduction on a circular cylinder in rotary oscillation. J. Fluid Mech. 431, 297322.
Taneda, S. 1978 Visual observations of the flow past a circular cylinder performing a rotatory oscillation. J. Phys. Soc. Japan 45 (3), 10381043.
Thiria, B., Goujon-Durand, S. & Wesfreid, J. E. 2006 The wake of a cylinder performing rotary oscillations. J. Fluid Mech. 560, 123147.
Tokumaru, P. T. & Dimotakis, P. E. 1991 Rotary oscillation control of a cylinder wake. J. Fluid Mech. 224, 7790.
Venning, J. A.2016 Vortex structures in the wakes of two- and three-dimensional bodies. PhD thesis, Monash University.
Williamson, C. H. K. & Govardhan, R. 1997 Dynamics and forcing of a tethered sphere in a fluid flow. J. Fluids Struct. 11 (3), 293305.
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36 (1), 413455.
Wong, K. W. L., Zhao, J., Lo Jacono, D., Thompson, M. & Sheridan, J. 2018 Experimental investigation of flow-induced vibrations of a sinusoidally rotating circular cylinder. J. Fluid Mech. 848, 430466.
Zhao, J., Leontini, J. S., Lo Jacono, D. & Sheridan, J. 2014a Chaotic vortex induced vibrations. Phys. Fluids 26 (12), 121702.
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, 688721.
Zhao, J., Lo Jacono, D., Sheridan, J., Hourigan, K. & Thompson, M. C. 2018 Experimental investigation of in-line flow-induced vibration of a rotating circular cylinder. J. Fluid Mech. 847, 664699.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed