Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-06-02T22:31:00.066Z Has data issue: false hasContentIssue false
  • English
  • Français

Critical effect of fore-aft tapering on galloping triggering for a trapezoidal body

Published online by Cambridge University Press:  17 July 2023

Zhi Cheng Open the ORCID record for Zhi Cheng [Opens in a new window] ,
Fue-Sang Lien ,
Earl H. Dowell ,
Eugene Yee ,
Ryne Wang  and
Ji Hao Zhang
Zhi Cheng*
Affiliation:
AeroElasticity Group, Pratt School of Engineering, Duke University, 2080 Duke University Road, Durham, NC 27708, USA Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
Fue-Sang Lien
Affiliation:
Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
Earl H. Dowell
Affiliation:
AeroElasticity Group, Pratt School of Engineering, Duke University, 2080 Duke University Road, Durham, NC 27708, USA
Eugene Yee
Affiliation:
Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
Ryne Wang
Affiliation:
AeroElasticity Group, Pratt School of Engineering, Duke University, 2080 Duke University Road, Durham, NC 27708, USA
Ji Hao Zhang
Affiliation:
Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
*
†Email address for correspondence: vamoschengzhi@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

The critical effect of the windward interior angles of elastically mounted trapezoidal bodies on a galloping instability is numerically investigated in this paper using two methodologies of high-fidelity computational fluid dynamics simulations and data-driven stability analysis using the eigensystem realization algorithm. A micro exploration of the dynamical response is processed to understand the mechanism underpinning the structural amplification at the initial stage of the galloping instability and the competition between wake and structural modes. It is observed that very small changes in the windward interior angle of an isosceles-trapezoidal body can provoke or suppress galloping – indeed, a small decrease or increase (low to $1^\circ$) of the windward interior angle from a right angle ($90^\circ$) can result in a significant enhancement and complete suppression, respectively, of the galloping oscillations. This supports our hypothesis that the contraction and/or expansion (viz., fore-aft tapering and/or widening) of the cross-section in the streamline direction has potential influences on galloping triggering from the geometrical perspective. The data-driven stability analysis is also applied to verify and analyse this phenomenon from the perspective of modal analysis. The experimental measurements are also conducted in the wind tunnel to support this hypothesis.

JFM classification

Aerodynamics: Flow-structure interactions Flow Control: Instability control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 967 , 25 July 2023 , A18
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Billah, K.Y. & Scanlan, R.H. 1991 Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks. Am. J. Phys. 59 (2), 118–124.CrossRefGoogle Scholar
Bukka, S.R., Magee, A.R. & Jaiman, R.K. 2020 Stability analysis of passive suppression for vortex-induced vibration. J. Fluid Mech. 886, A12.CrossRefGoogle Scholar
Chen, S. 2004 Dynamic performance of bridges and vehicles under strong wind. PhD thesis, Louisiana State University, Baton Rouge, LA.Google Scholar
Chen, W., Ji, C., Alam, M.M., Xu, D., An, H., Tong, F. & Zhao, Y. 2022 Flow-induced vibrations of a D-section prism at a low Reynolds number. J. Fluid Mech. 941, A52.10.1017/jfm.2022.314CrossRefGoogle Scholar
Cheng, Z., Lien, F.-S., Yee, E. & Zhang, J.-H. 2022 Mode transformation and interaction in vortex-induced vibration of laminar flow past a circular cylinder. Phys. Fluids 34, 033607.10.1063/5.0080722CrossRefGoogle Scholar
Den Hartog, J.P. 1956 Mechanical Vibrations. McGraw–Hill.Google Scholar
Ding, L., Zhang, L., Wu, C., Mao, X. & Jiang, D. 2015 Flow induced motion and energy harvesting of bluff bodies with different cross sections. Energy Convers. Manage. 91, 416–426.10.1016/j.enconman.2014.12.039CrossRefGoogle Scholar
Dullweber, A., Leimkuhler, B. & McLachlan, R. 1997 Symplectic splitting methods for rigid body molecular dynamics. J. Chem. Phys. 107 (15), 5840–5851.10.1063/1.474310CrossRefGoogle Scholar
Gao, C., Zhang, W., Li, X., Liu, Y., Quan, J., Ye, Z. & Jiang, Y. 2017 Mechanism of frequency lock-in in transonic buffeting flow. J. Fluid Mech. 818, 528–561.10.1017/jfm.2017.120CrossRefGoogle Scholar
Hollenbach, R., Kielb, R. & Hall, K. 2021 Extending a Van Der Pol-based reduced-order model for fluid-structure interaction applied to non-synchronous vibrations in turbomachinery. Trans. ASME J. Turbomach. 144 (3), 031006.Google Scholar
Huang, H. & Li, X. 2013 Experimental study on the influence factors of static aerodynamic characteristics of ice-coated commonly used conductors. Adv. Mat. Res. 774–776, 1227–1231.Google Scholar
Jaiman, R.K., Sen, S. & Gurugubelli, P.S. 2015 A fully implicit combined field scheme for freely vibrating square cylinders with sharp and rounded corners. Comput. Fluids 112, 1–18.10.1016/j.compfluid.2015.02.002CrossRefGoogle Scholar
Johns, K.W. & Dexter, R.J. 1998 The development of fatigue design load ranges for cantilevered sign and signal support structures. J. Wind Engng Ind. Aerodyn. 77–78, 315–326.10.1016/S0167-6105(98)00152-4CrossRefGoogle 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
Lian, J., Yan, X., Liu, F., Zhang, J., Ren, Q. & Yang, X. 2017 Experimental investigation on soft galloping and hard galloping of triangular prisms. Appl. Sci. 7 (2), 198.10.3390/app7020198CrossRefGoogle Scholar
Mao, X., Zhang, L., Hu, D. & Ding, L. 2019 Flow induced motion of an elastically mounted trapezoid cylinder with different rear edges at high Reynolds numbers. Fluid Dyn. Res. 51 (2), 025509.10.1088/1873-7005/aaf832CrossRefGoogle Scholar
Menon, K. & Mittal, R. 2019 Flow physics and dynamics of flow-induced pitch oscillations of an airfoil. J. Fluid Mech. 877, 582–613.CrossRefGoogle Scholar
Menon, K. & Mittal, R. 2021 On the initiation and sustenance of flow-induced vibration of cylinders: insights from force partitioning. J. Fluid Mech. 907, A37.10.1017/jfm.2020.854CrossRefGoogle Scholar
Mittal, S. 2008 Global linear stability analysis of time-averaged flows. Intl J. Numer. Meth. Fluids 58 (1), 111–118.10.1002/fld.1714CrossRefGoogle Scholar
Modi, V.J. & Munshi, S.R. 1998 An efficient liquid sloshing damper for vibration control. J. Fluids Struct. 12 (8), 1055–1071.10.1006/jfls.1998.0182CrossRefGoogle Scholar
Morse, T.L. & Williamson, C.H.K. 2009 Prediction of vortex-induced vibration response by employing controlled motion. J. Fluid Mech. 634, 5–39.10.1017/S0022112009990516CrossRefGoogle Scholar
Nakamura, Y. & Tomonari, Y. 1977 Galloping of rectangular prisms in a smooth and in a turbulent flow. J. Sound Vib. 52 (2), 233–241.10.1016/0022-460X(77)90642-3CrossRefGoogle Scholar
Navrose, & Mittal, S. 2016 Lock-in in vortex-induced vibration. J. Fluid Mech. 794, 565–594.10.1017/jfm.2016.157CrossRefGoogle Scholar
Novak, M. & Tanaka, H. 1974 Effect of turbulence on galloping instability. J. Engng Mech. ASCE 100 (1), 27–47.Google Scholar
OpenFOAM/v2006 2019 OpenCFD, User Guide v2006. Available at: https://www.openfoam.com/documentation/guides/latest/doc/.Google Scholar
Païdoussis, M.P., Price, S.J. & De Langre, E. 2010 Fluid-Structure Interactions: Cross-Flow-Induced Instabilities. Cambridge University Press.10.1017/CBO9780511760792CrossRefGoogle Scholar
Park, D. & Yang, K.S. 2016 Flow instabilities in the wake of a rounded square cylinder. J. Fluid Mech. 793, 915–932.10.1017/jfm.2016.156CrossRefGoogle Scholar
Park, H., Kumar, R.A. & Bernitsas, M.M. 2013 Enhancement of flow-induced motion of rigid circular cylinder on springs by localized surface roughness at $3\times 10^4\leqslant Re \leqslant 1.2\times 10^5$. Ocean Engng 72, 403–415.10.1016/j.oceaneng.2013.06.026CrossRefGoogle Scholar
Pippard, A. 1953 Behaviour of engineering structures. Nature 171, 766–769.10.1038/171766a0CrossRefGoogle Scholar
Sanders, A.J. 2004 Non-synchronous vibration (NSV) due to a flow-induced aerodynamic instability in a composite fan stator. Trans. ASME J. Turbomach. 6, 507–516.Google Scholar
Service, S. 1942 “Galloping Gertie” bridge. Science 95 (2462), 10–10.Google Scholar
Seyed-Aghazadeh, B., Carlson, D.W. & Modarres-Sadeghi, Y. 2017 Vortex-induced vibration and galloping of prisms with triangular cross-sections. J. Fluid Mech. 817, 590–618.10.1017/jfm.2017.119CrossRefGoogle Scholar
Shieh, L.S., Wang, H. & Yates, R.E. 1980 Discrete-continuous model conversion. Appl. Math. Model. 4 (6), 449–455.10.1016/0307-904X(80)90177-8CrossRefGoogle Scholar
Tang, Y., Chi, Y., Sun, J., Huang, T.-H., Maghsoudi, O.H., Spence, A., Zhao, J., Su, H. & Yin, J. 2020 Leveraging elastic instabilities for amplified performance: spine-inspired high-speed and high-force soft robots. Sci. Adv. 6 (19), eaaz6912.10.1126/sciadv.aaz6912CrossRefGoogle ScholarPubMed
Tulsi, R.S., Mohd, F., Yashl, J. & Sanjay, M. 2019 Flow-induced vibration of a circular cylinder with rigid splitter plate. J. Fluids Struct. 89, 244–256.Google Scholar
Waals, O.J., Phadke, A.C. & Bultema, S. 2007 Flow induced motions on multi column floaters. In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering, San Diego, California, USA, vol. 1: Offshore Technology; Special Symposium on Ocean Measurements and their Influence on Design, p. 669–678. ASME.10.1115/OMAE2007-29539CrossRefGoogle Scholar
Walker, A. & Sibly, P. 1977 The Tacoma bridge collapse. Nature 266, 675.10.1038/266675b0CrossRefGoogle Scholar
Wang, E., Xu, W., Gao, X., Liu, L., Xiao, Q. & Ramesh, K. 2019 The effect of cubic stiffness nonlinearity on the vortex-induced vibration of a circular cylinder at low Reynolds numbers. Ocean Engng 173, 12–27.10.1016/j.oceaneng.2018.12.039CrossRefGoogle Scholar
Wang, S., Cheng, W., Du, R., Wang, Y. & Chen, Q. 2021 a Effect of mass ratio on flow-induced vibration of a trapezoidal cylinder at low Reynolds numbers. AIP Adv. 11 (7), 075215.10.1063/5.0057243CrossRefGoogle Scholar
Wang, S., Cheng, W., Du, R., Wang, Y. & Chen, Q. 2021 b Flow-induced vibration of a trapezoidal cylinder at low Reynolds numbers. Phys. Fluids 33 (5), 053602.10.1063/5.0047081CrossRefGoogle Scholar
Weaver, D.S. & Veljkovic, I. 2005 Vortex shedding and galloping of open semi-circular and parabolic cylinders in cross-flow. J. Fluids Struct. 21 (1), 65–74.10.1016/j.jfluidstructs.2005.06.004CrossRefGoogle Scholar
Yao, W. & Jaiman, R.K. 2017 Model reduction and mechanism for the vortex-induced vibrations of bluff bodies. J. Fluid Mech. 827, 357–393.10.1017/jfm.2017.525CrossRefGoogle Scholar
Zhang, B., Yang, X., Yang, W., Liu, B., Ai, W. & Ma, J. 2016 a The study on the applicability of aluminum conductor carbon core in the high incidence area of galloping for transmission lines. In 2016 IEEE International Conference on High Voltage Engineering and Application (ICHVE), Chengdu, China, p. 1–4. IEEE.10.1109/ICHVE.2016.7800927CrossRefGoogle Scholar
Zhang, J., Xu, G., Liu, F., Lian, J. & Yan, X. 2016 b Experimental investigation on the flow induced vibration of an equilateral triangle prism in water. Appl. Ocean Res. 61, 92–100.10.1016/j.apor.2016.08.002CrossRefGoogle Scholar
Zhang, M, Øiseth, O., Petersen, Ø.W. & Wu, T. 2022 Experimental investigation on flow-induced vibrations of a circular cylinder with radial and longitudinal fins. J. Wind Engng Ind. Aerodyn. 223, 104948.10.1016/j.jweia.2022.104948CrossRefGoogle 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, 72–102.10.1017/jfm.2015.548CrossRefGoogle Scholar
Zhao, J., Hourigan, K. & Thompson, M. 2019 An experimental investigation of flow-induced vibration of high-side-ratio rectangular cylinders. J. Fluids Struct. 91, 102580.10.1016/j.jfluidstructs.2019.01.021CrossRefGoogle Scholar
Zhao, J., Hourigan, K. & Thompson, M.C. 2018 Flow-induced vibration of D-section cylinders: an afterbody is not essential for vortex-induced vibration. J. Fluid Mech. 851, 317–343.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, M. 2015 Flow-induced vibrations of square and rectangular cylinders at low Reynolds number. Fluid Dyn. Res. 47 (2), 025502.10.1088/0169-5983/47/2/025502CrossRefGoogle 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), 023603.10.1063/1.4792351CrossRefGoogle Scholar
Zhu, H., Tang, T., Gao, Y., Zhou, T. & Wang, J. 2021 Flow-induced vibration of a trapezoidal cylinder placed at typical flow orientations. J. Fluids Struct. 103, 103291.10.1016/j.jfluidstructs.2021.103291CrossRefGoogle Scholar
Zhu, Y., Su, Y. & Breuer, K. 2020 Nonlinear flow-induced instability of an elastically mounted pitching wing. J. Fluid Mech. 899, A35.10.1017/jfm.2020.481CrossRefGoogle Scholar