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On the freely falling circular cylinder with a splitter plate

Published online by Cambridge University Press:  17 September 2025

Yue-Hao Sun Open the ORCID record for Yue-Hao Sun [Opens in a new window] ,
Yi-Ming Huang  and
Zhen Chen Open the ORCID record for Zhen Chen [Opens in a new window]
Yue-Hao Sun
Affiliation:
Marine Numerical Experiment Center, State Key Laboratory of Ocean Engineering, Shanghai 200240, PR China School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Yi-Ming Huang
Affiliation:
Marine Numerical Experiment Center, State Key Laboratory of Ocean Engineering, Shanghai 200240, PR China School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Zhen Chen*
Affiliation:
Marine Numerical Experiment Center, State Key Laboratory of Ocean Engineering, Shanghai 200240, PR China School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
*
Corresponding author: Zhen Chen, zhen.chen@sjtu.edu.cn
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Abstract

In this paper, a freely falling circular cylinder attached by a splitter plate in an infinite fluid domain under gravity is investigated numerically. The kinematic modes and wake patterns are summarised, and their parametric sensitivity with the dimensionless plate length ($L^\ast$), the Galileo number ($Ga$) and the cylindric-fluid density ratio ($\rho ^\ast$) is studied. The kinematic modes of a freely falling circular cylinder with a splitter plate can be classified into six types: the steady falling, the steady oblique falling, the small vibration oblique falling, the zigzag oblique falling, the locked falling and the chaotic falling. In the meantime, the wake patterns can be summarised into five types: the steady wake, the 2S wake, the 2P + nS wake, the 2P + 2S wake, and the chaotic wake. The effect of the length of the splitter plate on the vortex shedding characteristics represented by the Strouhal number is also discussed. Further investigation reveals that the attachment of a splitter plate of different lengths to the rear not only influences the kinematic mode and the vortex shedding of the circular cylinder, but also allows the passive and precise control of its falling posture and trajectory. Finally, through theoretical analysis, scaling laws are proposed to estimate the turn angle $\alpha$ and the drift angle $\beta$. The present study can deepen the understanding of similar natural phenomena, such as gliding birds and falling maple seeds, and provide valuable reference for engineering design of drag-reduction devices or air-dropped objects.

JFM classification

Aerodynamics: Flow-structure interactions Vortex Flows: Vortex shedding

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JFM Papers
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Journal of Fluid Mechanics , Volume 1019 , 25 September 2025 , A26
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© The Author(s), 2025. Published by Cambridge University Press

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References

Andersen, A., Pesavento, U. & Wang, Z.J. 2005 Unsteady aerodynamics of fluttering and tumbling plates. J. Fluid Mech. 541, 65–90.10.1017/S002211200500594XCrossRefGoogle Scholar
Apelt, C.J., West, G.S. & Szewczyk, A.A. 1973 The effects of wake splitter plates on the flow past a circular cylinder in the range $10^{4} \lt R \lt 5 \times 10^{4}$ . J. Fluid Mech. 61 (1), 187–198.10.1017/S0022112073000649CrossRefGoogle Scholar
Assi, G.R.S., Bearman, P.W. & Kitney, N. 2009 Low drag solutions for suppressing vortex-induced vibration of circular cylinders. J. Fluids Struct. 25 (4), 666–675.10.1016/j.jfluidstructs.2008.11.002CrossRefGoogle Scholar
Bagheri, S., Mazzino, A. & Bottaro, A. 2012 Spontaneous symmetry breaking of a hinged flapping filament generates lift. Phys. Rev. Lett. 109 (15), 154502.10.1103/PhysRevLett.109.154502CrossRefGoogle ScholarPubMed
Basso, R.L.G., Hwang, Y., Assi, G.R.S. & Sherwin, S.J. 2021 Instabilities and sensitivities in a flow over a rotationally flexible cylinder with a rigid splitter plate. J. Fluid Mech. 928, A24.CrossRefGoogle Scholar
Choi, H., Jeon, W.-P. & Kim, J. 2008 Control of flow over a bluff body. Annu. Rev. Fluid Mech. 40, 113–139.10.1146/annurev.fluid.39.050905.110149CrossRefGoogle Scholar
Choi, S., Lee, M., Roh, C. & Kim, D. 2025 Freely falling sphere with a rigid rear-side filament. J. Fluid Mech. 1010, A43.10.1017/jfm.2025.271CrossRefGoogle Scholar
Cimbala, J.M. & Chen, K.T. 1994 Supercritical Reynolds number experiments on a freely rotatable cylinder/splitter plate body. Phys. Fluids 6 (7), 2440–2445.10.1063/1.868191CrossRefGoogle Scholar
Cimbala, J.M. & Garg, S. 1991 Flow in the wake of a freely rotatable cylinder with splitter plate. AIAA J. 29 (6), 1001–1003.10.2514/3.10692CrossRefGoogle Scholar
Cimbala, J.M. & Leon, J. 1996 Drag of freely rotatable cylinder/splitter-plate body at subcritical Reynolds number. AIAA J. 34 (11), 2446–2448.10.2514/3.13412CrossRefGoogle Scholar
Cummins, C., Seale, M., Macente, A., Certini, D., Mastropaolo, E., Viola, I.M. & Nakayama, N. 2018 A separated vortex ring underlies the flight of the dandelion. Nature 562 (7727), 414–418.10.1038/s41586-018-0604-2CrossRefGoogle ScholarPubMed
Favier, J., Dauptain, A., Basso, D. & Bottaro, A. 2009 Passive separation control using a self-adaptive hairy coating. J. Fluid Mech. 627, 451–483.CrossRefGoogle Scholar
Fish, F.E. & Lauder, G.V. 2006 Passive and active flow control by swimming fishes and mammals. Annu. Rev. Fluid Mech. 38, 193–224.CrossRefGoogle Scholar
Gu, F., Wang, J.S., Qiao, X.Q. & Huang, Z. 2012 Pressure distribution, fluctuating forces and vortex shedding behavior of circular cylinder with rotatable splitter plates. J. Fluids Struct. 28, 263–278.CrossRefGoogle Scholar
Horowitz, M. & Williamson, C.H.K. 2010 The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres. J. Fluid Mech. 651, 251–294.10.1017/S0022112009993934CrossRefGoogle Scholar
Huang, W.-X., Shin, S.J. & Sung, H.J. 2007 Simulation of flexible filaments in a uniform flow by the immersed boundary method. J. Comput. Phys. 226 (2), 2206–2228.10.1016/j.jcp.2007.07.002CrossRefGoogle Scholar
Jenny, M., Duek, J. & Bouchet, G. 2004 Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid. J. Fluid Mech. 508, 201–239.10.1017/S0022112004009164CrossRefGoogle Scholar
Jiang, H., Pfister, J.-L., Huang, D.Z. & Cao, S. 2025 Koopman reduced-order modeling and analysis of flag flapping in the wake of a cylinder. Phys. Rev. E 111, 045101.CrossRefGoogle ScholarPubMed
Kwon, K. & Choi, H. 1996 Control of laminar vortex shedding behind a circular cylinder using splitter plates. Phys. Fluids 8 (2), 479–486.CrossRefGoogle Scholar
Lācis, U., Brosse, N., Ingremeau, F., Mazzino, A., Lundell, F., Kellay, H. & Bagheri, S. 2014 Passive appendages generate drift through symmetry breaking. Nat. Commun. 5, 5310.10.1038/ncomms6310CrossRefGoogle ScholarPubMed
Lācis, U., Olivieri, S., Mazzino, A. & Bagheri, S. 2017 Passive control of a falling sphere by elliptic-shaped appendages. Phys. Rev. Fluids 2 (3), 033901.10.1103/PhysRevFluids.2.033901CrossRefGoogle Scholar
Lentink, D., Dickson, W.B., Van Leeuwen, J.L. & Dickinson, M.H. 2009 Leading-edge vortices elevate lift of autorotating plant seeds. Science 324 (5933), 1438–1440.10.1126/science.1174196CrossRefGoogle ScholarPubMed
Muñoz-Hervás, J.C., Lorite-Díez, M., Ruiz-Rus, J. & Jiménez-González, J.I. 2024 Experimental study on the flow-induced vibrations of a circular cylinder with a rear flexibly hinged splitter plate. Phys. Fluids 36 (2), 027106.10.1063/5.0184410CrossRefGoogle Scholar
Namkoong, K., Yoo, J.Y. & Choi, H.G. 2008 Numerical analysis of two-dimensional motion of a freely falling circular cylinder in an infinite fluid. J. Fluid Mech. 604, 33–53.10.1017/S0022112008001304CrossRefGoogle Scholar
Peng, Z.-R., Sun, Y., Yang, D., Xiong, Y., Wang, Lei & Wang, L. 2022 Scaling laws for drag-to-thrust transition and propulsive performance in pitching flexible plates. J. Fluid Mech. 941, R2.CrossRefGoogle Scholar
Qin, J., Yu, H. & Wu, J. 2024 On the investigation of shock wave/boundary layer interaction with a high-order scheme based on lattice Boltzmann flux solver. Adv. Aerodyn. 6 (1), 6.CrossRefGoogle Scholar
Roshko, A. 1954 On the drag and shedding frequency of two-dimensional bluff bodies. NACA TN 3169. Available at: https://ntrs.nasa.gov/citations/19930083869.Google Scholar
Seyed-Ahmadi, A. & Wachs, A. 2019 Dynamics and wakes of freely settling and rising cubes. Phys. Rev. Fluids 4 (7), 074304.10.1103/PhysRevFluids.4.074304CrossRefGoogle Scholar
Sun, X., Suh, C.S., Ye, Z.-H. & Yu, B. 2020 Dynamics of a circular cylinder with an attached splitter plate in laminar flow: a transition from vortex-induced vibration to galloping. Phys. Fluids 32 (2), 027104.10.1063/1.5125588CrossRefGoogle Scholar
Sun, Y., Peng, Z.-R., Yang, D., Xiong, Y., Wang, L. & Wang, Lin 2022 Dynamics of a rigid-flexible coupling system in a uniform flow. J. Fluid Mech. 943, A44.CrossRefGoogle Scholar
Tang, T., Zhu, H., Wang, J., Alam, M.M., Song, J. & Chen, Q. 2022 Flow-induced rotation modes and wake characteristics of a circular cylinder attached with a splitter plate at low Reynolds numbers. Ocean Engng 266, 112823.CrossRefGoogle Scholar
Wang, Y., Shu, C., Teo, C.J. & Wu, J. 2015 An immersed boundary–lattice Boltzmann flux solver and its applications to fluid–structure interaction problems. J. Fluids Struct. 54, 440–465.CrossRefGoogle Scholar
Wang, Y., Shu, C., Yang, L.M. & Sun, Y. 2017 On the immersed boundary–lattice Boltzmann simulations of incompressible flows with freely moving objects. Intl J. Numer. Meth. Fluids 83 (4), 331–350.10.1002/fld.4270CrossRefGoogle Scholar
Williamson, C.H.K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.CrossRefGoogle Scholar
Williamson, C.H.K. & Brown, G.L. 1998 A series in (1/ $\sqrt {{\textit{Re}}}$ ) to represent the Strouhal–Reynolds number relationship of the cylinder wake. J. Fluids Struct. 12 (8), 1073–1085.10.1006/jfls.1998.0184CrossRefGoogle Scholar
Wolf, A., Swift, J.B., Swinney, H.L. & Vastano, J.A. 1985 Determining Lyapunov exponents from a time series. Physica D 16 (3), 285–317.10.1016/0167-2789(85)90011-9CrossRefGoogle Scholar
Wu, J., Qiu, Y.L., Shu, C. & Zhao, N. 2014 Flow control of a circular cylinder by using an attached flexible filament. Phys. Fluids 26 (10), 103601.10.1063/1.4896942CrossRefGoogle Scholar
Wu, J. & Shu, C. 2009 Implicit velocity correction-based immersed boundary–lattice Boltzmann method and its applications. J. Comput. Phys. 228 (6), 1963–1979.10.1016/j.jcp.2008.11.019CrossRefGoogle Scholar
Xu, J.C., Sen, M. & Gad-el Hak, M. 1990 Low-Reynolds number flow over a rotatable cylinder–splitter plate body. Phys. Fluids A 2 (11), 1925–1927.CrossRefGoogle Scholar