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There is no critical mass ratio for galloping of a square cylinder under flow

Published online by Cambridge University Press:  26 November 2021

Peng Han Open the ORCID record for Peng Han [Opens in a new window]  and
Emmanuel de Langre Open the ORCID record for Emmanuel de Langre [Opens in a new window]
Peng Han*
Affiliation:
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, PR China LadHyX, CNRS, Ecole polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
Emmanuel de Langre
Affiliation:
LadHyX, CNRS, Ecole polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
*
†Email address for correspondence: peng@ladhyx.polytechnique.fr
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Abstract

The flow-induced vibration of square cylinders under flow is known to be caused by two distinct mechanisms of interaction: vortex-induced vibrations and galloping. In the present paper we address the issue of the apparent suppression of galloping when the mass ratio between the solid and the fluid is low enough. By using a reduced-order model that we validate on pre-existing results, we show that galloping is actually not suppressed, but delayed to higher values of the flow velocity. This is explained using a linear stability analysis where the competition between unstable modes is related to the transition between vortex-induced vibration and galloping. Direct numerical simulations coupled with a moving square cylinder confirm that galloping can be found even at very low mass ratios.

JFM classification

Aerodynamics: Flow-structure interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 931 , 25 January 2022 , A27
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Barrero-Gil, A., Sanz-Andrés, A. & Roura, M. 2009 Transverse galloping at low Reynolds numbers. J. Fluids Struct. 25 (7), 1236–1242.CrossRefGoogle Scholar
Bhatt, R. & Alam, M.M. 2018 Vibrations of a square cylinder submerged in a wake. J. Fluid Mech. 853, 301–332.CrossRefGoogle Scholar
Blevins, R.D. 2001 Flow-Induced Vibration. Krieger Publishing Company.Google Scholar
Carassale, L., Freda, A. & Banfi, L. 2015 Motion excited forces acting on a square prism: a qualitative analysis. In The 14th International Conference on Wind Engineering. Porto Alegre, Brazil.Google Scholar
Facchinetti, M.L., de Langre, E. & Biolley, F. 2004 Coupling of structure and wake oscillators in vortex-induced vibrations. J. Fluids Struct. 19 (2), 123–140.CrossRefGoogle Scholar
Freda, A., Carassale, L. & Piccardo, G. 2015 Aeroelastic crosswind response of sharp-edge square sections: experiments versus theory. In The 14th International Conference on Wind Engineering. Porto Alegre, Brazil.Google 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.CrossRefGoogle Scholar
Grouthier, C., Michelin, S., Modarres-Sadeghi, Y. & de Langre, E. 2013 Self-similar vortex-induced vibrations of a hanging string. J. Fluid Mech. 724, R2.CrossRefGoogle Scholar
Han, P., Hémon, P., Pan, G. & de Langre, E. 2021 a Nonlinear modeling of combined galloping and vortex-induced vibration of square sections under flow. Nonlinear Dyn. 103 (4), 3113–3125.CrossRefGoogle Scholar
Han, P., Huang, Q., Pan, G., Wang, W., Zhang, T. & Qin, D. 2021 b Energy harvesting from flow-induced vibration of a low-mass square cylinder with different incidence angles. AIP Adv. 11 (2), 025126.CrossRefGoogle Scholar
Han, P., Pan, G. & Tian, W. 2018 Numerical simulation of flow-induced motion of three rigidly coupled cylinders in equilateral-triangle arrangement. Phys. Fluids 30 (12), 125107.Google Scholar
Han, P., Pan, G., Zhang, B., Wang, W. & Tian, W. 2020 Three-cylinder oscillator under flow: flow induced vibration and energy harvesting. Ocean Engng 211, 107619.CrossRefGoogle Scholar
Jayatunga, H.G.K.G., Tan, B.T. & Leontini, J.S. 2015 A study on the energy transfer of a square prism under fluid-elastic galloping. J. Fluids Struct. 55, 384–397.CrossRefGoogle Scholar
Joly, A., Etienne, S. & Pelletier, D. 2012 Galloping of square cylinders in cross-flow at low Reynolds numbers. J. Fluids Struct. 28, 232–243.CrossRefGoogle Scholar
de Langre, E. 2006 Frequency lock-in is caused by coupled-mode flutter. J. Fluids Struct. 22 (6–7), 783–791.CrossRefGoogle Scholar
Li, X., Lyu, Z., Kou, J. & Zhang, W. 2019 Mode competition in galloping of a square cylinder at low Reynolds number. J. Fluid Mech. 867, 516–555.CrossRefGoogle Scholar
Mannini, C., Massai, T. & Marra, A.M. 2018 Modeling the interference of vortex-induced vibration and galloping for a slender rectangular prism. J. Sound Vib. 419, 493–509.CrossRefGoogle Scholar
Mannini, C., Massai, T., Marra, A.M. & Bartoli, G. 2015 Modelling the interaction of VIV and galloping for rectangular cylinders. In The 14th International Conference on Wind Engineering, pp. 1–20. Porto Alegre, Brazil.Google Scholar
Meliga, P. & Chomaz, J.-M. 2011 An asymptotic expansion for the vortex-induced vibrations of a circular cylinder. J. Fluid Mech. 671, 137–167.CrossRefGoogle Scholar
Navrose, & Mittal, S. 2016 Lock-in in vortex-induced vibration. J. Fluid Mech. 794, 565–594.CrossRefGoogle Scholar
Navrose, & Mittal, S. 2017 The critical mass phenomenon in vortex-induced vibration at low Re. J. Fluid Mech. 820, 159–186.CrossRefGoogle Scholar
Nayfeh, A.H. 2011 Introduction to Perturbation Techniques. John Wiley & Sons.Google Scholar
Negi, P.S., Hanifi, A. & Henningson, D.S. 2020 On the linear global stability analysis of rigid-body motion fluid–structure-interaction problems. J. Fluid Mech. 903, A35.CrossRefGoogle Scholar
Nemes, A., Zhao, J., Lo Jacono, D. & Sheridan, J. 2012 The interaction between flow-induced vibration mechanisms of a square cylinder with varying angles of attack. J. Fluid Mech. 710, 102–130.CrossRefGoogle Scholar
Païdoussis, M.P., Price, S.J. & de Langre, E. 2010 Fluid–Structure Interactions: Cross-Flow-Induced Instabilities. Cambridge University Press.CrossRefGoogle Scholar
Parkinson, G.V. & Smith, J.D. 1964 The square prism as an aeroelastic non-linear oscillator. Q. J. Mech. Appl. Maths 17 (2), 225–239.CrossRefGoogle Scholar
Parkinson, G.V. & Wawzonek, M.A. 1981 Some considerations of combined effects of galloping and vortex resonance. J. Wind Engng Ind. Aerodyn. 8 (1), 135–143.CrossRefGoogle Scholar
Pettigrew, M.J., Taylor, C.E. & Kim, B.S. 1989 Vibration of tube bundles in two-phase cross-flow: part 1—hydrodynamic mass and damping. Trans. ASME: J. Pressure Vessel Technol. 111 (4), 466–477.Google Scholar
Sen, S. & Mittal, S. 2015 Effect of mass ratio on free vibrations of a square cylinder at low Reynolds numbers. J. Fluids Struct. 54, 661–678.CrossRefGoogle Scholar
Singh, A.P., De, A.K., Carpenter, V.K., Eswaran, V. & Muralidhar, K. 2009 Flow past a transversely oscillating square cylinder in free stream at low Reynolds numbers. Intl J. Numer. Meth. Fluids 61 (6), 658–682.CrossRefGoogle Scholar
Sourav, K. & Sen, S. 2019 Transition of VIV-only motion of a square cylinder to combined VIV and galloping at low Reynolds numbers. Ocean Engng 187, 106208.CrossRefGoogle Scholar
Sourav, K. & Sen, S. 2020 Determination of the transition mass ratio for onset of galloping of a square cylinder at the least permissible Reynolds number of 150. Phys. Fluids 32 (6), 063601.CrossRefGoogle Scholar
Violette, R., de Langre, E. & Szydlowski, J. 2007 Computation of vortex-induced vibrations of long structures using a wake oscillator model: comparison with DNS and experiments. Comput. Struct. 85 (11–14), 1134–1141.CrossRefGoogle Scholar
Violette, R., de Langre, E. & Szydlowski, J. 2010 A linear stability approach to vortex-induced vibrations and waves. J. Fluids Struct. 26 (3), 442–466.CrossRefGoogle Scholar
Williamson, C.H.K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36 (1), 413–455.CrossRefGoogle Scholar
Yao, W. & Jaiman, R.K. 2017 Model reduction and mechanism for the vortex-induced vibrations of bluff bodies. J. Fluid Mech. 827, 357–393.CrossRefGoogle Scholar
Zanganeh, H. & Srinil, N. 2016 Three-dimensional VIV prediction model for a long flexible cylinder with axial dynamics and mean drag magnifications. J. Fluids Struct. 66, 127–146.CrossRefGoogle Scholar
Zhang, W., Li, X., Ye, Z. & Jiang, Y. 2015 Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers. J. Fluid Mech. 783, 72–102.CrossRefGoogle Scholar
Zhao, M., Cheng, L. & Zhou, T. 2013 Numerical simulation of vortex-induced vibration of a square cylinder at a low Reynolds number. Phys. Fluids 25 (2), 023603.CrossRefGoogle Scholar
Zhao, J., Leontini, J.S., Lo Jacono, D. & Sheridan, J. 2014 Fluid–structure interaction of a square cylinder at different angles of attack. J. Fluid Mech. 747, 688–721.CrossRefGoogle Scholar
Zhao, J., Leontini, J.S., Lo Jacono, D. & Sheridan, J. 2019 The effect of mass ratio on the structural response of a freely vibrating square cylinder oriented at different angles of attack. J. Fluids Struct. 86, 200–212.CrossRefGoogle Scholar