Published: 05 January 2022 Volume 35 , pages 891–904 ( 2021 ) Cite this article Flow-induced vibration (FIV) of four separately mounted cantilever cylinders are experimentally investigated in a water flume. The four cylinders with top ends screwed vertically into a turntable platform are subjected to uniform flows with Reynolds number ranging from 3840 to 16520. A non-intrusive measurement with high-speed cameras is employed to simultaneously capture the time-varying in-line and cross-flow vibrations in the reduced velocity range of 3.0–12.9. Experimental results highlight the continuous adjustment of flow regime caused by the spatial-temporal alteration of cylinders. Consequently, the space-time varying flow interference contributes to the occurrence of multiple response frequencies. The transition from a dominant frequency to a broad-band response illustrates the enhancement of wake interference. The combination of wake flow interactions results in the irregular oscillation trajectories and the appearance of a response trough with the associated switching in vortex shedding mode. The dual-resonance phenomenon is observed in the four cylinders due to the complicated wake-structure interaction. The greatest mechanical energy possessed by the four cylinders in an in-line square arrangement is mainly resulted from the downstream cylinders, signifying the positive role of wake excitation in extracting hydrokinetic energy from ambient flow. This is a preview of subscription content, log in via an institution to check access. Access this article Subscribe and save Starting from 10 chapters or articles per month Access and download chapters and articles from more than 300k books and 2,500 journals Price includes VAT (Hong Kong/P.R.China) Instant access to the full article PDF. 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Article Google Scholar Assi, G.R.S., Bearman, P.W., Carmo, B.S., Meneghini, J.R., Sherwin, S.J. and Willden, R.H.J., 2013. The role of wake stiffness on the wake-induced vibration of the downstream cylinder of a tandem pair, Journal of Fluid Mechanics , 718, 210–245. Article Google Scholar Bernitsas, M.M., Raghavan, K., Ben-Simon, Y. and Garcia, E.M.H., 2008. VIVACE (Vortex Induced Vibration Aquatic Clean Energy): A new concept in generation of clean and renewable energy from fluid flow, Journal of Offshore Mechanics and Arctic Engineering , 130(4), 041101. Article Google Scholar Bernitsas, M.M., Raghavan, K., Ben-Simon, Y. and Garcia, E.M.H., 2008. VIVACE (Vortex Induced Vibration Aquatic Clean Energy): A new concept in generation of clean and renewable energy from fluid flow, Journal of Offshore Mechanics and Arctic Engineering , 130(4), 041101. Article Google Scholar Gao, Y.Y., Yang, K., Zhang, B.F., Cheng, K.Y. and Chen, X.P., 2019. Numerical investigation on vortex-induced vibrations of four circular cylinders in a square configuration, Ocean Engineering , 175, 223–240. Article Google Scholar Gao, Y.Y., Yang, K., Zhang, B.F., Cheng, K.Y. and Chen, X.P., 2019. Numerical investigation on vortex-induced vibrations of four circular cylinders in a square configuration, Ocean Engineering , 175, 223–240. Article Google Scholar Govardhan, R. and Williamson, C.H.K., 2000. Modes of vortex formation and frequency response of a freely vibrating cylinder, Journal of Fluid Mechanics , 420, 85–130. Article MathSciNet Google Scholar Govardhan, R. and Williamson, C.H.K., 2000. Modes of vortex formation and frequency response of a freely vibrating cylinder, Journal of Fluid Mechanics , 420, 85–130. Article MathSciNet Google Scholar Han, Z.L., Zhou, D., Gui, X. L. and Tu, J. H., 2013. Numerical study of flow past four square-arranged cylinders using spectral element method, Computers and Fluids , 84, 100–112. Article MathSciNet Google Scholar Han, Z.L., Zhou, D., Gui, X. L. and Tu, J. H., 2013. Numerical study of flow past four square-arranged cylinders using spectral element method, Computers and Fluids , 84, 100–112. Article MathSciNet Google Scholar Han, Z.L., Zhou, D., He, T., Tu, J.H., Li, C.X., Kwok, C.S.K. and Fang, C.Q., 2015. Flow-induced vibrations of four circular cylinders with square arrangement at low Reynolds numbers, Ocean Engineering , 96, 21–33. Article Google Scholar Han, Z.L., Zhou, D., He, T., Tu, J.H., Li, C.X., Kwok, C.S.K. and Fang, C.Q., 2015. Flow-induced vibrations of four circular cylinders with square arrangement at low Reynolds numbers, Ocean Engineering , 96, 21–33. Article Google Scholar Huang, S. and Herfjord, K., 2013. Experimental investigation of the forces and motion responses of two interfering VIV circular cylinders at various tandem and staggered positions, Applied Ocean Research , 43, 264–273. Article Google Scholar Huang, S. and Herfjord, K., 2013. Experimental investigation of the forces and motion responses of two interfering VIV circular cylinders at various tandem and staggered positions, Applied Ocean Research , 43, 264–273. Article Google Scholar Kahil, Y., Benhamadouche, S., Berrouk, A.S. and Afgan, I., 2019. Simulation of subcritical-Reynolds-number flow around four cylinders in square arrangement configuration using LES, European Journal of Mechanics - B/Fluids , 74, 111–122. Article MathSciNet Google Scholar Kahil, Y., Benhamadouche, S., Berrouk, A.S. and Afgan, I., 2019. Simulation of subcritical-Reynolds-number flow around four cylinders in square arrangement configuration using LES, European Journal of Mechanics - B/Fluids , 74, 111–122. Article MathSciNet Google Scholar Khalak, A. and Williamson, C.H.K., 1996. Dynamics of a hydroelastic cylinder with very low mass and damping, Journal of Fluids and Structures , 10(5), 455–472. Article Google Scholar Khalak, A. and Williamson, C.H.K., 1996. Dynamics of a hydroelastic cylinder with very low mass and damping, Journal of Fluids and Structures , 10(5), 455–472. Article Google Scholar Khalak, A. and Williamson, C.H.K., 1997. Investigation of the relative effects of mass and damping in vortex-induced vibration of a circular cylinder, Journal of Wind Engineering and Industrial Aerodynamics , 69–71, 341–350. Article Google Scholar Khalak, A. and Williamson, C.H.K., 1997. Investigation of the relative effects of mass and damping in vortex-induced vibration of a circular cylinder, Journal of Wind Engineering and Industrial Aerodynamics , 69–71, 341–350. Article Google Scholar Lam, K. and Fang, X., 1995. The effect of interference of four equispaced cylinders in cross flow on pressure and force coefficients, Journal of Fluids and Structures , 9(2), 195–214. Article Google Scholar Lam, K. and Fang, X., 1995. The effect of interference of four equispaced cylinders in cross flow on pressure and force coefficients, Journal of Fluids and Structures , 9(2), 195–214. Article Google Scholar Lam, K. and Lo, S.C., 1992. A visualization study of cross-flow around four cylinders in a square configuration, Journal of Fluids and Structures , 6(1), 109–131. Article Google Scholar Lam, K. and Lo, S.C., 1992. A visualization study of cross-flow around four cylinders in a square configuration, Journal of Fluids and Structures , 6(1), 109–131. Article Google Scholar Lam, K. and Zou, L., 2009. Experimental study and large eddy simulation for the turbulent flow around four cylinders in an in-line square configuration, International Journal of Heat and Fluid Flow , 30, 276–285. Article Google Scholar Lam, K. and Zou, L., 2009. Experimental study and large eddy simulation for the turbulent flow around four cylinders in an in-line square configuration, International Journal of Heat and Fluid Flow , 30, 276–285. Article Google Scholar Lam, K. and Zou, L., 2010. Three-dimensional numerical simulations of cross-flow around four cylinders in an in-line square configuration, Journal of Fluids and Structures , 26(3), 482–502. Article Google Scholar Lam, K. and Zou, L., 2010. Three-dimensional numerical simulations of cross-flow around four cylinders in an in-line square configuration, Journal of Fluids and Structures , 26(3), 482–502. Article Google Scholar Lam, K., Gong, W. Q. and So, R.M.C., 2008. Numerical simulation of cross-flow around four cylinders in an in-line square configuration, Journal of Fluids and Structures , 24(1), 34–57. Article Google Scholar Lam, K., Gong, W. Q. and So, R.M.C., 2008. Numerical simulation of cross-flow around four cylinders in an in-line square configuration, Journal of Fluids and Structures , 24(1), 34–57. Article Google Scholar Lam, K., Li, J.Y. and So, R.M.C., 2003a. Force coefficients and strouhal numbers of four cylinders in cross flow, Journal of Fluids and Structures , 18(3–4), 305–324. Article Google Scholar Lam, K., Li, J.Y. and So, R.M.C., 2003a. Force coefficients and strouhal numbers of four cylinders in cross flow, Journal of Fluids and Structures , 18(3–4), 305–324. Article Google Scholar Lam, K., Li, J.Y., Chan, K.T., So, R.M.C., 2003b. Flow pattern and velocity field distribution of cross-flow around four cylinders in a square configuration at a low Reynolds number, Journal of Fluids and Structures , 17(5), 665–679. Article Google Scholar Lam, K., Li, J.Y., Chan, K.T., So, R.M.C., 2003b. Flow pattern and velocity field distribution of cross-flow around four cylinders in a square configuration at a low Reynolds number, Journal of Fluids and Structures , 17(5), 665–679. Article Google Scholar Sayers, A.T., 1990. Vortex shedding from groups of three and four equispaced cylinders situated in a cross flow, Journal of Wind Engineering and Industrial Aerodynamics , 34(2), 213–221. Article Google Scholar Sayers, A.T., 1990. Vortex shedding from groups of three and four equispaced cylinders situated in a cross flow, Journal of Wind Engineering and Industrial Aerodynamics , 34(2), 213–221. Article Google Scholar Sumner, D., 2010. Two circular cylinders in cross-flow: A review, Journal of Fluids and Structures , 26(6), 849–899. Article Google Scholar Sumner, D., 2010. Two circular cylinders in cross-flow: A review, Journal of Fluids and Structures , 26(6), 849–899. Article Google Scholar Wang, X.K., Gong, K., Liu, H., Zhang, J.X. and Tan, S.K., 2013. Flow around four cylinders arranged in a square configuration, Journal of Fluids and Structures , 43, 179–199. Article Google Scholar Wang, X.K., Gong, K., Liu, H., Zhang, J.X. and Tan, S.K., 2013. Flow around four cylinders arranged in a square configuration, Journal of Fluids and Structures , 43, 179–199. Article Google Scholar Wang, J.L., Geng, L.F., Ding, L., Zhu, H.J. and Yurchenko, D., 2020. The state-of-the-art review on energy harvesting from flow-induced vibrations, Applied Energy , 267, 114902. Article Google Scholar Wang, J.L., Geng, L.F., Ding, L., Zhu, H.J. and Yurchenko, D., 2020. The state-of-the-art review on energy harvesting from flow-induced vibrations, Applied Energy , 267, 114902. Article Google Scholar

Wang, E.H., Xu, W.H., Yu, Y., Zhou, L.D. and Incecik, A., 2019. Flow-induced vibrations of three and four long flexible cylinders in tandem arrangement: An experimental study, Ocean Engineering , 178, 170–184. Article Google Scholar Wang, E.H., Xu, W.H., Yu, Y., Zhou, L.D. and Incecik, A., 2019. Flow-induced vibrations of three and four long flexible cylinders in tandem arrangement: An experimental study, Ocean Engineering , 178, 170–184. Article Google Scholar Williamson, C.H.K. and Govardhan, R., 2004. Vortex-induced vibrations, Annual Review of FluidMechanics , 36, 413–455. Article MathSciNet Google Scholar Williamson, C.H.K. and Govardhan, R., 2004. Vortex-induced vibrations, Annual Review of FluidMechanics , 36, 413–455. Article MathSciNet Google Scholar Xu, F., Ou, J.P. and Xiao, Y.Q., 2009. Numerical study on vortex induced vibrations of four cylinders in an in-line square configuration, in: Yuan, Y., Cui, J.Z. and Mang, H.A. (eds.), Computational Structural Engineering , Springer, Dordrecht, pp. 553–567. Chapter Google Scholar Xu, F., Ou, J.P. and Xiao, Y.Q., 2009. Numerical study on vortex induced vibrations of four cylinders in an in-line square configuration, in: Yuan, Y., Cui, J.Z. and Mang, H.A. (eds.), Computational Structural Engineering , Springer, Dordrecht, pp. 553–567. Chapter Google Scholar Zdravkovich, M.M., 1977. REVIEW—review of flow interference between two circular cylinders in various arrangements, Journal of Fluids Engineering , 99(4), 618–633. Article Google Scholar Zdravkovich, M.M., 1977. REVIEW—review of flow interference between two circular cylinders in various arrangements, Journal of Fluids Engineering , 99(4), 618–633. Article Google Scholar Zdravkovich, M.M., 1987. The effects of interference between circular cylinders in cross flow, Journal of Fluids and Structures , 1(2), 239–261. Article Google Scholar Zdravkovich, M.M., 1987. The effects of interference between circular cylinders in cross flow, Journal of Fluids and Structures , 1(2), 239–261. Article Google Scholar Zhang, B.S., Mao, Z.Y., Song, B.W., Tian, W.L. and Ding, W.J., 2018. Numerical investigation on VIV energy harvesting of four cylinders in close staggered formation, Ocean Engineering , 165, 55–68. Article Google Scholar Zhang, B.S., Mao, Z.Y., Song, B.W., Tian, W.L. and Ding, W.J., 2018. Numerical investigation on VIV energy harvesting of four cylinders in close staggered formation, Ocean Engineering , 165, 55–68. Article Google Scholar Zhao, M. and Cheng, L., 2012. Numerical simulation of vortex-induced vibration of four circular cylinders in a square configuration, Journal of Fluids and Structures , 31, 125–140. Article Google Scholar Zhao, M. and Cheng, L., 2012. Numerical simulation of vortex-induced vibration of four circular cylinders in a square configuration, Journal of Fluids and Structures , 31, 125–140. Article Google Scholar Zhao, M., Kaja, K., Xiang, Y. and Cheng, L., 2016. Vortex-induced vibration of four cylinders in an in-line square configuration, Physics of Fluids , 28, 023602. Article Google Scholar Zhao, M., Kaja, K., Xiang, Y. and Cheng, L., 2016. Vortex-induced vibration of four cylinders in an in-line square configuration, Physics of Fluids , 28, 023602. Article Google Scholar Zhou, Y. and Alam, M., 2016. Wake of two interacting cylinders: A review, International Journal of Heat and Fluid Flow , 62, 510–537. Article Google Scholar Zhou, Y. and Alam, M., 2016. Wake of two interacting cylinders: A review, International Journal of Heat and Fluid Flow , 62, 510–537. Article Google Scholar Zhu, H.J., Gao, Y. and Zhao, H.L., 2018. Experimental investigation on the flow-induced vibration of a free-hanging flexible riser by internal unstable hydrodynamic slug flow, Ocean Engineering , 164, 488–507. Article Google Scholar Zhu, H.J., Gao, Y. and Zhao, H.L., 2018. Experimental investigation on the flow-induced vibration of a free-hanging flexible riser by internal unstable hydrodynamic slug flow, Ocean Engineering , 164, 488–507. Article Google Scholar Zhu, H.J., Yao, J., Ma, Y., Zhao, H.N. and Tang, Y.B., 2015. Simultaneous CFD evaluation of VIV suppression using smaller control cylinders, Journal of Fluids and Structures , 57, 66–80. Article Google Scholar Zhu, H.J., Yao, J., Ma, Y., Zhao, H.N. and Tang, Y.B., 2015. Simultaneous CFD evaluation of VIV suppression using smaller control cylinders, Journal of Fluids and Structures , 57, 66–80. Article Google Scholar Zou, L., Lin, Y.F. and Lu, H., 2011. Flow patterns and force characteristics of laminar flow past four cylinders in diamond arrangement, Journal of Hydrodynamics , 23(1), 55–64. Article Google Scholar Zou, L., Lin, Y.F. and Lu, H., 2011. Flow patterns and force characteristics of laminar flow past four cylinders in diamond arrangement, Journal of Hydrodynamics , 23(1), 55–64. Article Google Scholar Download references Acknowledgements Experiments were conducted in a water flume of Offshore Oil and Gas Laboratory at Southwest Petroleum University. The authors appreciate the support from the laboratory. Author information Authors and Affiliations State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610500, China Hong-jun Zhu & Wen-li Liu State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610500, China Hong-jun Zhu & Wen-li Liu School of Mechanical and Power Engineering, Zhengzhou University, Zhengzhou, 450000, China Jun-lei Wang School of Mechanical and Power Engineering, Zhengzhou University, Zhengzhou, 450000, China Hong-jun Zhu View author publications Search author on: PubMed Google Scholar Search author on: PubMed Google Scholar Wen-li Liu View author publications Search author on: PubMed Google Scholar Search author on: PubMed Google Scholar Jun-lei Wang View author publications Search author on: PubMed Google Scholar Search author on: PubMed Google Scholar Corresponding authors Correspondence to Hong-jun Zhu or Jun-lei Wang . Additional information Foundation item The research work was financially supported by the National Natural Science Foundation of China (Grant No. 51979238) and the Open Research Fund of State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University (Grant No. HSSE-2005). Rights and permissions Reprints and permissions About this article Cite this article Zhu, Hj., Liu, Wl. & Wang, Jl. Flow-Induced Vibration of Four Cantilever Cylinders Arranged in A Square Configuration. China Ocean Eng 35 , 891–904 (2021). https://doi.org/10.1007/s13344-021-0078-0 Download citation Received : 15 March 2021 Received : 15 March 2021 Revised : 11 August 2021 Revised : 11 August 2021 Accepted : 14 September 2021 Accepted : 14 September 2021 Published : 05 January 2022 Published : 05 January 2022 Version of record : 05 January 2022 Version of record : 05 January 2022 Issue date : December 2021 Issue date : December 2021 DOI : https://doi.org/10.1007/s13344-021-0078-0 DOI : https://doi.org/10.1007/s13344-021-0078-0 Share this article Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative flow-induced vibration mechanical energy cantilever cylinder time-varying spacing Jun-lei Wang View author profile