Skip to main content
SpringerLink
Log in

Resonance in flow past oscillating cylinder under subcritical conditions

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Flow around an oscillating cylinder in a subcritical region are numerically studied with a lattice Boltzmann method (LBM). The effects of the Reynolds number, oscillation amplitude and frequency on the vortex wake modes and hydrodynamics forces on the cylinder surface are systematically investigated. Special attention is paid to the phenomenon of resonance induced by the cylinder oscillation. The results demonstrate that vortex shedding can be excited extensively under subcritical conditions, and the response region of vibration frequency broadens with increasing Reynolds number and oscillation amplitude. Two distinct types of vortex shedding regimes are observed. The first type of vortex shedding regime (VSR I) is excited at low frequencies close to the intrinsic frequency of flow, and the second type of vortex shedding regime (VSR II) occurs at high frequencies with the Reynolds number close to the critical value. In the VSR I, a pair of alternately rotating vortices are shed in the wake per oscillation cycle, and lock-in/synchronization occurs, while in the VSR II, two alternately rotating vortices are shed for several oscillation cycles, and the vortex shedding frequency is close to that of a stationary cylinder under the critical condition. The excitation mechanisms of the two types of vortex shedding modes are analyzed separately.

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

  1. Williamson, C. H. K. Vortex dynamics in the cylinder wake. Annual Review of Fluid Mechanics, 28, 477–539 (1996)

    Article  MathSciNet  Google Scholar 

  2. Roushan, P. and Wu, X. L. Structure-based interpretation of the Strouhal-Reynolds number relationship. Physical Review Letters, 94, 054504 (2005)

    Article  Google Scholar 

  3. Williamson, C. H. K. and Govardhan, R. Vortex-induced vibrations. Annual Review of Fluid Mechanics, 36, 413–455 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bishop, R. E. D. and Hassan, A. Y. The lift and drag forces on a circular cylinder oscillating in a flowing fluid. Proceedings of the Royal Society of London Series A, 277, 51–75 (1964)

    Article  Google Scholar 

  5. Olinger, D. J. and Sreenivasan, K. R. Nonlinear dynamics of the wake of an oscillating cylinder. Physical Review Letters, 60, 797–800 (1988)

    Article  Google Scholar 

  6. Williamson, C. H. K. and Roshko, A. Vortex formation in the wake of an oscillating cylinder. Journal of Fluids and Structures, 2, 355–381 (1988)

    Article  Google Scholar 

  7. Meneghini, J. R. and Bearman, P. W. Numerical simulation of high amplitude oscillatory flow about a circular cylinder. Journal of Fluids and Structures, 9, 435–455 (1995)

    Article  Google Scholar 

  8. Lu, X. Y. and Dalton, C. Calculation of the timing of vortex formation from an oscillating cylinder. Journal of Fluids and Structures, 10, 527–541 (1996)

    Article  Google Scholar 

  9. Blackburn, H. M. and Henderson, R. D. A study of two-dimensional flow past an oscillating cylinder. Journal of Fluid Mechanics, 385, 255–286 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Guilmineau, E. and Queutey, P. A numerical simulation of vortex shedding from an oscillating circular cylinder. Journal of Fluids and Structures, 16, 773–794 (2002)

    Article  Google Scholar 

  11. Buffoni, E. Vortex shedding in subcritical conditions. Physics of Fluids, 15, 814–816 (2003)

    Article  MATH  Google Scholar 

  12. Chen, S. S., Yen, R. H., and Wang, A. B. Investigation of the resonant phenomenon of flow around a vibrating cylinder in a subcritical regime. Physics of Fluids, 23, 014105 (2011)

    Article  Google Scholar 

  13. Dütsch, H., Durst, F., Becker, S., and Lienhart, H. Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan-Carpenter numbers. Journal of Fluid Mechanics, 360, 249–271 (1998)

    Article  MATH  Google Scholar 

  14. Leontini, J. S., Lo Jacono, D., and Thompson, M. C. A numerical study of an inline oscillating cylinder in a free stream. Journal of Fluid Mechanics, 688, 551–568 (2011)

    Article  MATH  Google Scholar 

  15. Mittal, S. and Singh, S. Vortex-induced vibrations at subcritical Re. Journal of Fluid Mechanics, 534, 185–194 (2005)

    Article  MATH  Google Scholar 

  16. Succi, S. The Lattice Boltzmann Method for Fluid Dynamics and Beyond, Oxford University Press, Oxford (2001)

    MATH  Google Scholar 

  17. Bhatnagar, P. L., Gross, E. P., and Krook, M. A model for collision processes in gases I: small amplitude processes in charged and neutral one-component systems. Physical Review, 94, 511–525 (1954)

    Article  MATH  Google Scholar 

  18. Chen, H., Chen S., and Matthaeus, W. H. Recovery of the Navier-Stokes equation using a latticegas Boltzmann method. Physical Review A, 45, 5339–5342 (1992)

    Article  Google Scholar 

  19. Qian, Y. H., d’Humières, D., and Lallemand, P. Lattice BGK models for Navier-Stokes equation. Europhysics Letters, 17, 479–484 (1992)

    Article  MATH  Google Scholar 

  20. He, X. Y. and Luo, L. S. Lattice Boltzmann model for the incompressible Navier-Stokes equation. Journal of Statistical Physics, 88, 927–944 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  21. Guo, Z., Zheng, C., and Shi, B. An extrapolation method for boundary conditions in lattice Boltzmann method. Physics of Fluids, 14, 2007–2010 (2002)

    Article  MATH  Google Scholar 

  22. Lin, J., Jiang, R., Chen, Z., and Ku, X. Poiseuille flow-induced vibrations of two cylinders in tandem. Journal of Fluids and Structures, 40, 70–85 (2013)

    Article  Google Scholar 

  23. Jiang, R., Lin, J., and Ku, X. Flow-induced vibrations of two tandem circular cylinders in a parallel-wall channel. Physics of Fluids, 26, 104102 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Maritime and Transportation, Ningbo University, Ningbo, Zhejiang Province, 315211, China

    Renjie Jiang & Pengjun Zheng

  2. National Traffic Management Engineering and Technology Research Centre, Ningbo University Sub-centre, Ningbo, Zhejiang Province, 315211, China

    Pengjun Zheng

  3. Jiangsu Province Collaborative Innovation Center for Modern Urban Traffic Technologies, Nanjing, 210096, China

    Pengjun Zheng

Authors
  1. Renjie Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pengjun Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Renjie Jiang.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11402129) and the Zhejiang Provincial Natural Science Foundation of China (No. LY17A020002)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, R., Zheng, P. Resonance in flow past oscillating cylinder under subcritical conditions. Appl. Math. Mech.-Engl. Ed. 38, 363–378 (2017). https://doi.org/10.1007/s10483-017-2175-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-017-2175-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation