Skip to main content
SpringerLink
Log in

A Novel Wake Oscillator Model for Vortex-Induced Vibrations Prediction of A Cylinder Considering the Influence of Reynolds Number

  • Published:
China Ocean Engineering Aims and scope Submit manuscript

Abstract

It is well known that the Reynolds number has a significant effect on the vortex-induced vibrations (VIV) of cylinders. In this paper, a novel in-line (IL) and cross-flow (CF) coupling VIV prediction model for circular cylinders has been proposed, in which the influence of the Reynolds number was comprehensively considered. The Strouhal number linked with the vortex shedding frequency was calculated through a function of the Reynolds number. The coefficient of the mean drag force was fitted as a new piecewise function of the Reynolds number, and its amplification resulted from the CF VIV was also taken into account. The oscillating drag and lift forces were modelled with classical van der Pol wake oscillators and their empirical parameters were determined based on the lock-in boundaries and the peak-amplitude formulas. A new peak-amplitude formula for the IL VIV was developed under the resonance condition with respect to the mass-damping ratio and the Reynolds number. When compared with the results from the experiments and some other prediction models, the present model could give good estimations on the vibration amplitudes and frequencies of the VIV both for elastically-mounted rigid and long flexible cylinders. The present model considering the influence of the Reynolds number could generally provide better results than that neglecting the effect of the Reynolds number.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Achenbach, E. and Heinecke, E., 1981. On vortex shedding from smooth and rough cylinders in the range of Reynolds numbers 6×103 to 5×106, Journal of Fluid Mechanics, 109, 239–251.

    Article  Google Scholar 

  • Allen, D.W. and Henning, D.L., 2001. Surface roughness effects on Vortex-Induced Vibration of cylindrical structures at critical and supercritical Reynolds Numbers, Proceedings of the 2001 Offshore Technology Conference, Houston, Texas, USA, Paper No. OTC-13302-MS.

    Google Scholar 

  • Anagnostopoulos, P., 2000. Numerical study of the flow past a cylin-der excited transversely to the incident stream. Part 1: lock-in zone. hydrodynamic forces and wake geometry, Journal of Fluids and Structures, 14(6), 819–851.

    Article  Google Scholar 

  • Barbi, C., Favier, D.P., Maresca, C.A. and Telionis D.P., 1986. Vortex shedding and lock-on of a circular cylinder in oscillatory flow, Journal of Fluid Mechanics, 170, 527–544.

    Article  Google Scholar 

  • Bearman, P.W., 1997. Near wake flows behind two-and three-dimensional bluff bodies, Journal of Wind Engineering and Industrial Aerodynamics, 69-71, 33–54.

    Article  Google Scholar 

  • Besem, F.M., Thomas, J.P., Kielb, R.E. and Dowell, E.H., 2016. An aeroelastic model for vortex-induced vibrating cylinders subject to frequency lock-in, Journal of Fluids and Structures, 61, 42–59.

    Article  Google Scholar 

  • Birkhoff, G. and Zarantonello, E.H., 1957. Jets, Wakes, and Cavities, Academic Press, New York.

    MATH  Google Scholar 

  • Blevins, R.D., 1990. Flow-Induced Vibration, second ed., Van Nostrand Reinhold, New York.

    MATH  Google Scholar 

  • Blevins, R.D., 2009. Models for vortex-induced vibration of cylinders based on measured forces, Journal of Fluids Engineering, 131(10), 101203.

    Article  Google Scholar 

  • Blevins, R.D. and Coughran, C.S., 2009. Experimental investigation of vortex-induced vibration in one and two dimensions with variable mass, damping, and Reynolds number, Journal of Fluids Engineering, 131(10), 101202.

    Article  Google Scholar 

  • Cagney, N. and Balabani, S., 2016. Fluid forces acting on a cylinder undergoing streamwise vortex-induced vibrations, Journal of Fluids and Structures, 62, 147–155.

    Article  Google Scholar 

  • Chaplin, J.R., Bearman, P.W., Cheng, Y., Fontaine, E., Graham, J.M.R., Herfjord, K., Huera Huarte, F.J., Isherwood, M., Lambrakos, K., Larsen, C.M., Meneghini, J.R., Moe, G., Pattenden, R.J., Triantafyllou, M.S. and Willden, R.H.J., 2005. Blind predictions of laboratory measurements of vortex-induced vibrations of a tension riser, Journal of Fluids and Structures, 21(1), 25–40.

    Article  Google Scholar 

  • Chen, W.L., Wang, X.J., Xu, F., Li, H. and Hu, H., 2017. Passive jet flow control method for suppressing unsteady vortex shedding from a circular cylinder, Journal of Aerospace Engineering, 30(1), 04016063.

    Article  Google Scholar 

  • Facchinetti, M.L., De Langre, E. and Biolley, F., 2004. Coupling of structure and wake oscillators in vortex-induced vibrations, Journal of Fluids and structures, 19(2), 123–140.

    Article  Google Scholar 

  • Farshidianfar, A. and Dolatabadi, N., 2013. Modified higher-order wake oscillator model for vortex-induced vibration of circular cylinders, Acta Mechanica, 224(7), 1441–1456.

    Article  MATH  Google Scholar 

  • Govardhan, R.N. and Williamson, C.H.K., 2006. Defining the ‘modified Griffin plot’ in vortex-induced vibration: Revealing the effect of Reynolds number using controlled damping, Journal of Fluid Mechanics, 561, 147–180.

    Article  MATH  Google Scholar 

  • Griffin, O.M. and Ramberg, S.E., 1976. Vortex shedding from a cylinder vibrating in line with an incident uniform flow, Journal of Fluid Mechanics, 75(2), 257–271.

    Article  Google Scholar 

  • Gu, C., Chikatamarla, S.S. and Karlin, I.V., 2014. Simulation of flow past a circular cylinder using entropic lattice boltzmann method, International Journal of Modern Physics C, 25(1), 1340024.

    Article  MathSciNet  Google Scholar 

  • Jarża, A. and Podolski, M., 2004. Turbulence structure in the vortex formation region behind a circular cylinder in lock-on conditions, European Journal of Mechanics-B/Fluids, 23(3), 535–550.

    Article  MATH  Google Scholar 

  • Jauvtis, N. and Williamson, C.H.K., 2004. The effect of two degrees of freedom on vortex-induced vibration at low mass and damping, Journal of Fluid Mechanics, 509, 23–62.

    Article  MATH  Google Scholar 

  • Kang, Z. and Jia, L.S., 2013. An experiment study of a cylinder’s two degree of freedom VIV trajectories, Ocean Engineering, 70, 129–140.

    Article  Google Scholar 

  • Koide, M., Tomida, S., Takahashi, T., Baranyi, L. and Shirakashi, M., 2002. Influence of cross-sectional configuration on the synchronization of Kármán vortex shedding with the cylinder oscillation, JSME International Journal Series B Fluids and Thermal Engineering, 45(2), 249–258.

    Article  Google Scholar 

  • Kondo, N., 2012. Three-dimensional computation for flow-induced vibrations in in-line and cross-flow directions of a circular cylinder, International Journal for Numerical Methods in Fluids, 70(2), 158–185.

    MathSciNet  Google Scholar 

  • Konstantinidis, E., Balabani, S. and Yianneskis, M., 2003. The effect of flow perturbations on the near wake characteristics of a circular cylinder, Journal of Fluids and Structures, 18(3–4), 367–386.

    Article  MATH  Google Scholar 

  • Konstantinidis, E. and Liang, C.L., 2011. Dynamic response of a turbulent cylinder wake to sinusoidal inflow perturbations across the vortex lock-on range, Physics of Fluids, 23(7), 075102.

    Article  Google Scholar 

  • Koopmann, G.H., 1967. The vortex wakes of vibrating cylinders at low Reynolds numbers, Journal of Fluid Mechanics, 28(3), 501–512.

    Article  Google Scholar 

  • Moon, J.S. and Kim, J.S., 2012. Numerical analysis of unsteady flow around a transversely oscillating circular cylinder, International Journal of Aeronautical and Space Sciences, 13(1), 27–33.

    Article  Google Scholar 

  • Nishihara, T., Kaneko, S. and Watanabe, T., 2005. Characteristics of fluid dynamic forces acting on a circular cylinder oscillated in the streamwise direction and its wake patterns, Journal of Fluids and Structures, 20(4), 505–518.

    Article  Google Scholar 

  • Nobari, M.R.H. and Naderan, H., 2006. A numerical study of flow past a cylinder with cross flow and inline oscillation, Computers & Fluids, 35(4), 393–415.

    Article  MATH  Google Scholar 

  • Ogink, R.H.M. and Metrikine, A.V., 2010. A wake oscillator with frequency dependent coupling for the modeling of vortex-induced vibration, Journal of Sound and Vibration, 329(26), 5452–5473.

    Article  Google Scholar 

  • Okajima, A., Kosugi, T. and Nakamura, A., 2001. Experiments on flow-induced in-line oscillation of a circular cylinder in a water tunnel (1st-report. the difference of the response characteristics when a cylinder is elastically supported at both ends and cantilevered), JSME International Journal Series B Fluids and Thermal Engineering, 44(4), 695–704.

    Article  Google Scholar 

  • Okajima, A., Ohtsuyama, S., Nagamori, T., Nakano, T. and Kiwata, T., 1999. In-line oscillation of structure with a circular or rectangular section, Transactions of the Japan Society of Mechanical Engineers Series B, 65(635), 2196–2203.

    Article  Google Scholar 

  • Pesce, C.P. and Fujarra, A.L.C., 2002. Vortex induced vibrations experiments with an elastically mounted cylinder in water, Proceedings of the 12th International Offshore and Polar Engineering Conference, ISOPE, Kitakyushu, Japan, pp. 502–509.

    Google Scholar 

  • Prasanth, T.K. and Mittal, S., 2008. Vortex-induced vibrations of a circular cylinder at low Reynolds numbers, Journal of Fluid Mechanics, 594, 463–491.

    Article  MATH  Google Scholar 

  • Raghavan, K. and Bernitsas, M.M., 2011. Experimental investigation of Reynolds number effect on vortex induced vibration of rigid circular cylinder on elastic supports, Ocean Engineering, 38(5–6), 719–731.

    Article  Google Scholar 

  • Roshko, A., 1961. Experiments on the flow past a circular cylinder at very high Reynolds number, Journal of Fluid Mechanics, 10(3), 345–356.

    Article  MATH  Google Scholar 

  • Sarpkaya, T., 2004. A critical review of the intrinsic nature of vortexinduced vibrations, Journal of Fluids and Structures, 19(4), 389–447.

    Article  Google Scholar 

  • Schewe G., 1983. On the force fluctuations acting on a circular cylin-der in crossflow from subcritical up to transcritical Reynolds numbers, Journal of Fluid Mechanics, 133, 265–285.

    Article  Google Scholar 

  • Shih, W.C.L., Wang, C., Coles, D. and Roshko, A., 1993. Experiments on flow past rough circular cylinders at large Reynolds numbers, Journal of Wind Engineering and Industrial Aerodynamics, 49(1–3), 351–368.

    Article  Google Scholar 

  • Singh, S.P. and Mittal, S., 2005. Vortex-induced oscillations at low Reynolds numbers: Hysteresis and vortex-shedding modes, Journal of Fluids and Structures, 20(8), 1085–1104.

    Article  Google Scholar 

  • Srinil, N., 2010. Multi-mode interactions in vortex-induced vibrations of flexible curved/straight structures with geometric nonlinearities, Journal of Fluids and Structures, 26(7–8), 1098–1122.

    Article  Google Scholar 

  • Srinil, N., Zanganeh, H. and Day, A., 2013. Two-degree-of-freedom VIV of circular cylinder with variable natural frequency ratio: Experimental and numerical investigations, Ocean Engineering, 73, 179–194.

    Article  Google Scholar 

  • Stansby, P.K., 1976. The locking-on of vortex shedding due to the cross-stream vibration of circular cylinders in uniform and shear flows, Journal of Fluid Mechanics, 74(4), 641–665.

    Article  MathSciNet  Google Scholar 

  • Tatsuno, M., 1972. Vortex streets behind a circular cylinder oscillating in the direction of flow, Bulletin of the Research Institute for Applied Mechanics of Kyushu University, 36, 25–37.

    Google Scholar 

  • Tritton, D.J., 1959. Experiments on the flow past a circular cylinder at low Reynolds numbers, Journal of Fluid Mechanics, 6(4), 547–567.

    Article  MATH  Google Scholar 

  • Watanabe, T. and Kondo, M., 2006. Numerical simulation of in-line and cross-flow oscillations of a cylinder, JSME International Journal B Fluids and Thermal Engineering, 49(2), 296–301.

    Article  Google Scholar 

  • Wen, P. and Qin, W., 2013. Numerical studies of VIV of a smooth cylinder, Proceedings of the 27th ITTC Workshop on Wave Run-up and Vortex Shedding, ITTC, Nantes, France.

    Google Scholar 

  • Wieselsberger, C., 1921. Neuere feststellungen uber die gesetze des flussigkeits-und luftwiderstands, Physikalische Zeitschrift, 22, 321–328.

    Google Scholar 

  • Xu, W.H., Gao, X.F. and Du, J., 2012. The prediction on in-line vortex-induced vibration of slender marine structures, Acta Mechanica Sinica, 28(5), 1303–1308.

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, W.H., Wu, Y.X., Zeng, X.H., Zhong, X.F. and Yu, J.X., 2010. A new wake oscillator model for predicting vortex induced vibration of a circular cylinder, Journal of Hydrodynamics, Series B, 22(3), 381–386.

    Article  Google Scholar 

  • Yeon, S.M., Yang, J.M. and Stern, F., 2016. Large-eddy simulation of the flow past a circular cylinder at sub-to super-critical Reynolds numbers, Applied Ocean Research, 59, 663–675.

    Article  Google Scholar 

  • Zanganeh, H. and Srinil, N., 2016. Three-dimensional VIV prediction model for a long flexible cylinder with axial dynamics and mean drag magnifications, Journal of Fluids and Structures, 66, 127–146.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin, 300072, China

    Xi-feng Gao, Wu-de Xie, Wan-hai Xu, Yu-chuan Bai & Hai-tao Zhu

  2. Collaborative Innovation Centre for Advanced Ship and Deep-Sea Exploration, Shanghai, 200240, China

    Xi-feng Gao & Wan-hai Xu

Authors
  1. Xi-feng Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wu-de Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wan-hai Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yu-chuan Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hai-tao Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wan-hai Xu.

Additional information

Foundation item: This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51379144, 51479135 and 51679167) and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51621092).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gao, Xf., Xie, Wd., Xu, Wh. et al. A Novel Wake Oscillator Model for Vortex-Induced Vibrations Prediction of A Cylinder Considering the Influence of Reynolds Number. China Ocean Eng 32, 132–143 (2018). https://doi.org/10.1007/s13344-018-0015-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13344-018-0015-z

Keywords

Search

Navigation