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Inertial exit dynamics of a horizontal cylinder out of a liquid bath

Published online by Cambridge University Press:  20 February 2026

Lionel Vincent Open the ORCID record for Lionel Vincent [Opens in a new window] ,
Javier Rivero-Rodriguez Open the ORCID record for Javier Rivero-Rodriguez [Opens in a new window] ,
Romain Falla ,
Intesaaf Ashraf ,
Vincent Emmanuel Terrapon Open the ORCID record for Vincent Emmanuel Terrapon [Opens in a new window] ,
Stephane Dorbolo Open the ORCID record for Stephane Dorbolo [Opens in a new window]  and
Benoit Scheid Open the ORCID record for Benoit Scheid [Opens in a new window]
Lionel Vincent*
Affiliation:
Transfers Interfaces and Processes (TIPs), Université Libre de Bruxelles (ULB) , 1050 Brussels, Belgium Campus Innovation Paris, Air Liquide R&D, 1 ch. de la Porte des Loges , 78350 Les Loges-en-Josas, France
Javier Rivero-Rodriguez
Affiliation:
Transfers Interfaces and Processes (TIPs), Université Libre de Bruxelles (ULB) , 1050 Brussels, Belgium Escuela de Ingenierias Industriales, Universidad de Màlaga, Campus de Teatinos, 29071 Màlaga, Spain
Romain Falla
Affiliation:
Aerospace and Mechanical Engineering Department, Université de Liège (ULiège), 4000 Liège, Belgium
Intesaaf Ashraf
Affiliation:
PtYX, Département de Physique, Université de Liège (ULiège), 4000 Liège, Belgium
Vincent Emmanuel Terrapon
Affiliation:
Aerospace and Mechanical Engineering Department, Université de Liège (ULiège), 4000 Liège, Belgium
Stephane Dorbolo
Affiliation:
PtYX, Département de Physique, Université de Liège (ULiège), 4000 Liège, Belgium
Benoit Scheid
Affiliation:
Transfers Interfaces and Processes (TIPs), Université Libre de Bruxelles (ULB) , 1050 Brussels, Belgium
*
Corresponding author: Lionel Vincent, lv.vincent@gmail.com
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Abstract

We present a combined theoretical and numerical investigation of the inertial exit dynamics of a long horizontal circular cylinder vertically lifted out of a finite-size liquid bath at constant velocity. The various steps of the exit dynamics are studied in detail: from the formation of a bulge on the surface ahead of the cylinder to the coating of the cylinder by a liquid film while crossing the interface. We focus on inertial dynamics, a regime characteristic of large exit velocities, i.e. large Reynolds numbers ($500 \lt \textit{Re} \lt 10\,000$) and negligible interfacial effects. The dynamics is investigated through two-dimensional computations of the Navier–Stokes equations using a finite element method with moving boundaries. We describe in detail the exit dynamics while emphasising the effect of various parameters on surface deformation and resistive force. We identify subtle effects and interplay, such as initial free-surface response after impulsive start-up, the important role of the lateral bounding of the reservoir, and the close relationship between wake size and surge amplitudes as revealed by comparing with free-slip cylinder simulations. All these aspects are shown to be crucial to accurately predict the coated film thickness and the exit force.

JFM classification

Waves/Free-surface Flows: Waves/Free-surface Flows Wakes/Jets: Wakes Interfacial Flows (free surface): Thin films

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1029 , 25 February 2026 , A39
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© The Author(s), 2026. Published by Cambridge University Press

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References

Ashraf, I., Vincent, L., Falla, R., Terrapon, V.E., Scheid, B. & Dorbolo, S. 2024 Experimental investigation of the exit dynamics of a horizontal circular cylinder out of water and silicone oil. Phys. Rev. Fluids 9 (12), 124005.10.1103/PhysRevFluids.9.124005CrossRefGoogle Scholar
Basic, J., Degiuli, N. & Werner, A. 2014 Simulation of water entry and exit of a circular cylinder using the ISPH method. In Trans. Famena Xxxviii-1, p. 45–62.Google Scholar
Batchelor, G.K. 2000 An Introduction to Fluid Dynamics, 1st edn. Cambridge University Press.10.1017/CBO9780511800955CrossRefGoogle Scholar
Bouard, R. & Coutanceau, M. 1980 The early stage of development of the wake behind an impulsively started cylinder for 40 $\lt$ Re $\lt$ 10 4 . J. Fluid Mech. 101 (3), 583–607.10.1017/S0022112080001814CrossRefGoogle Scholar
Bourrier, P., Guyon, E. & Jorre, J.P. 1984 The ‘pop off’ effect: different regimes of a light ball in water. Eur. J. Phys. 5 (4), 225.10.1088/0143-0807/5/4/007CrossRefGoogle Scholar
Buruchenko, S.K. & Canelas, R.B. 2017 Validation of open-source SPH code DualSPHysics for numerical simulations of water entry and exit of a rigid body. In Proceedings of the ASME. 2017 36th International Conference on Ocean, Offshore and Arctic Engineering OMAE2017.Google Scholar
Cerquaglia, M.L., Deliége, G., Boman, R., Terrapon, V. & Ponthot, J.-P. 2017 Free-slip boundary conditions for simulating free-surface incompressible flows through the particle finite element method. Num. Meth Engng 110 (10), 921–946.10.1002/nme.5439CrossRefGoogle Scholar
Champougny, L., Rio, E., Restagno, F. & Scheid, B. 2017 The break-up of free films pulled out of a pure liquid bath. J. Fluid Mech. 811, 499–524.10.1017/jfm.2016.758CrossRefGoogle Scholar
Chang, B., Myeong, J., Virot, E., Clanet, C., Kim, H.-Y. & Jung, S. 2019 Jumping dynamics of aquatic animals. J. R. Soc. Interface 16 (152), 20190014.10.1098/rsif.2019.0014CrossRefGoogle ScholarPubMed
Chateau, X. & Pitois, O. 2003 Quasistatic detachment of a sphere from a liquid interface. J. Colloid Interface Sci. 259, 346–353.10.1016/S0021-9797(02)00219-9CrossRefGoogle ScholarPubMed
Chatzimanolakis, M., Weber, P. & Koumoutsakos, P. 2022 Vortex separation cascades in simulations of the planar flow past an impulsively started cylinder up to. J. Fluid Mech. 953, R2.10.1017/jfm.2022.988CrossRefGoogle Scholar
Colicchio, G., Greco, M., Miozzi, M. & Lugni, C. 2009 Experimental and numerical investigation of the water-entry and water-exit of a circular cylinder. In Proceedings of the 24th International Workshop on Water Waves and Floating Bodies Zelenogorsk.Google Scholar
Cremonesi, M., Franci, A., Idelsohn, S. & Oñate, E. 2020 A state of the art review of the particle finite element method (PFEM). Arch. Comput. Meth. Engng 27 (5), 1709–1735.10.1007/s11831-020-09468-4CrossRefGoogle Scholar
Eghbali, S., Djambov, S. & Gallaire, F. 2024 Stability of a liquid layer draining around a horizontal cylinder: interplay of capillary and gravity forces. Phys. Rev. Fluids 9 (6), 063903.10.1103/PhysRevFluids.9.063903CrossRefGoogle Scholar
Falla, R., Bobach, B.-J., Boman, R., Ponthot, J.-P. & Terrapon, V. 2023 Mesh adaption for two-dimensional bounded and free-surface flows with the particle finite element method. Comput. Part. Mech. 10 (5), 1049–1076.10.1007/s40571-022-00541-2CrossRefGoogle Scholar
Faltinsen, O. 1993 Sea Loads on Ships and Offshore Structures, vol. 1. Cambridge University Press.Google Scholar
Gorlov, S.I. 2000 Nonlinear problem of a circular cylinder rising vertically to an interface between liquid media. J. Appl. Mech. Tech. Phys. 41 (2), 280–285.10.1007/BF02465269CrossRefGoogle Scholar
Greenhow, M. 1988 Water-entry and -exit of a horizontal circular cylinder. Appl. Ocean Res. 10 (4), 191–198.10.1016/S0141-1187(88)80003-8CrossRefGoogle Scholar
Greenhow, M. & Lin, W.-M. 1983 Nonlinear free surface effects: experiments and theory. Tech. Rep. No. 83-19. Massachusetts Institute of Technology – Department of Ocean Engineering.Google Scholar
Ibrahim, R.A. 2005 Liquid Sloshing Dynamics: Theory and Applications. Cambridge University Press.10.1017/CBO9780511536656CrossRefGoogle Scholar
Kalita, J.C. & Sen, S. 2017 $\alpha$ -, $\beta$ -phenomena in the post-symmetry break for the flow past a circular cylinder. Phys. Fluids 29 (3), 033603.10.1063/1.4979065CrossRefGoogle Scholar
Kostikov, V.K. & Makarenko, N.I. 2018 Unsteady free surface flow above a moving circular cylinder. J. Engng Maths 112, 1–16.10.1007/s10665-018-9962-xCrossRefGoogle Scholar
Koumoutsakos, P. & Leonard, A. 1995 High-resolution simulations of the flow around an impulsively started cylinder using vortex methods. J. Fluid Mech. 296, 1–38.10.1017/S0022112095002059CrossRefGoogle Scholar
Liju, P.Y., Machane, R. & Cartellier, A. 2001 Surge effect during the water exit of an axisymmetric body traveling normal to a plane interface: experiments and BEM simulation. Exp. Fluids 31 (3), 241–248.10.1007/s003480100277CrossRefGoogle Scholar
Lin, C., Hsieh, S.-C., Lin, W.-J. & Raikar, R.V. 2012 Characteristics of recirculation zone structure behind an impulsively started circular cylinder. J. Engng Mech. 138 (2), 184–198.Google Scholar
Lynch, K.P. & Wagner, J.L. 2018 Time-resolved pulse-burst tomographic PIV of impulsively-started cylinder wakes in a shock tube. In 2018 AIAA Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics.10.2514/6.2018-2038CrossRefGoogle Scholar
Makarenko, N.I. 2003 Nonlinear interaction of submerged cylinder with free surface. J. Offshore Mech. Arct. Engng 125, 72–75.10.1115/1.1537729CrossRefGoogle Scholar
Manga, M. & Stone, H.A. 1995 Low Reynolds number motion of bubbles, drops and rigid spheres through fluid–fluid interfaces. J. Fluid Mech. 287, 279–298.10.1017/S0022112095000954CrossRefGoogle Scholar
Miao, G. 1989 Hydrodynamic forces and dynamic response of circular cylinders in wave zones. PhD thesis. University of Trondheim.Google Scholar
Moshari, S., Nikseresht, A.H. & Mehryar, R. 2014 Numerical analysis of two and three dimensional buoyancy driven water-exit of a circular cylinder. Intl J. Nav. Arch. Ocean Engng 6, 219–235.10.2478/IJNAOE-2013-0174CrossRefGoogle Scholar
Moyo, S. & Greenhow, M. 2000 Free motion of a cylinder moving below and through a free surface. Appl. Ocean Res. 22 (1), 31–44.10.1016/S0141-1187(99)00024-3CrossRefGoogle Scholar
Oñate, E., Idelsohn, S.R., Del Pin, F. & Aubry, R. 2004 The particle finite element method – an overview. Intl J. Comput. Meth. 01 (02), 267–307.10.1142/S0219876204000204CrossRefGoogle Scholar
Panahi, R. 2012 Simulation of water-entry and water-exit problems using a moving mesh algorithm. J. Theor. Appl. Mech. Sofia 42 (2), 79–92.Google Scholar
Pierson, J.-L. & Magnaudet, J. 2018 Inertial settling of a sphere through an interface. Part 2. Sphere and tail dynamics. J. Fluid Mech. 835, 808–851.10.1017/jfm.2017.748CrossRefGoogle Scholar
Pitois, O., Moucheront, P. & Weill, C. 1999 Franchissement d’interface et enrobage d’une sphère. C. R. Acad. Sci. Paris 327 (IIb), 605–611.Google Scholar
Prandtl, W. 1925 The Magnus effect and wind powered ships. Wissenschaften 13, 93–108.10.1007/BF01585456CrossRefGoogle Scholar
Rajavaheinthan, R. & Greenhow, M. 2015 Constant acceleration exit of two-dimensional free-surface-piercing bodies. Appl. Ocean Res. 50, 30–46.10.1016/j.apor.2014.07.007CrossRefGoogle Scholar
Rivero-Rodríguez, J., Pérez-Saborid, M. & Scheid, B. 2021 An alternative choice of the boundary condition for the arbitrary Lagrangian-Eulerian method. J. Comput. Phys. 443, 110494.10.1016/j.jcp.2021.110494CrossRefGoogle Scholar
Telste, J.H. 1987 Inviscid flow about a cylinder rising to a free surface. J. Fluid Mech. 182, 149–168.10.1017/S0022112087002283CrossRefGoogle Scholar
Truscott, T.T., Epps, B.P. & Munns, R.H. 2016 Water exit dynamics of buoyant spheres. Phys. Rev. Fluids 1, 074501.10.1103/PhysRevFluids.1.074501CrossRefGoogle Scholar
Tumbleston, J.R. et al. 2015 Continuous liquid interface production of 3D objects. Science 347 (6228), 1349–1352.10.1126/science.aaa2397CrossRefGoogle ScholarPubMed
Tyvand, P.A. & Miloh, T. 1995 a Free-surface flow due to impulsive motion of a submerged circular cylinder. J. Fluid Mech. 286, 67–101.10.1017/S0022112095000656CrossRefGoogle Scholar
Tyvand, P.A. & Miloh, T. 1995 b Free-surface flow generated by a small submerged circular cylinder starting from rest. J. Fluid Mech. 286, 103–116.10.1017/S0022112095000668CrossRefGoogle Scholar
Van Dyke, M. (ed.), 2008 An Album of Fluid Motion, 12th edn Parabolic Press.Google Scholar
Vincent, L., Xiao, T., Yohann, D., Jung, S. & Kanso, E. 2018 Dynamics of water entry. J. Fluid Mech. 846, 508–535.10.1017/jfm.2018.273CrossRefGoogle Scholar
Wagner, J.L., DeMauro, E.P., Casper, K.M., Beresh, S.J., Lynch, K.P. & Pruett, B.O. 2018 Pulse-burst PIV of an impulsively started cylinder in a shock tube for Re $\gt$ 105. Exp Fluids 59 (6), 106.10.1007/s00348-018-2558-4CrossRefGoogle Scholar
Wei, X., Li, D., Lei, J., Li, J., Rivero-Rodríguez, J., Lin, F., Wang, D. & Scheid, B. 2024 Exit dynamics of a sphere launched underneath a liquid bath surface. Phys. Rev. Fluids 9, 054003.10.1103/PhysRevFluids.9.054003CrossRefGoogle Scholar
Weinstein, S.J. & Ruschak, K.J. 2004 Coating flows. Annu. Rev. Fluid Mech. 36 (1), 29–53.10.1146/annurev.fluid.36.050802.122049CrossRefGoogle Scholar
Weisler, W.A., Waghela, R., Granlund, K. & Bryant, M. 2021 Finite wing lift during water-to-air transition. Phys. Rev. Fluids 6 (5), 054002.10.1103/PhysRevFluids.6.054002CrossRefGoogle Scholar
Wilson, S.D.R. 1982 The drag-out problem in film coating theory. J. Engng Maths 16 (3), 209–221.10.1007/BF00042717CrossRefGoogle Scholar
Wu, C., Kinnas, S.A., Li, Z. & Wu, Y. 2019 a A conservative viscous vorticity method for unsteady unidirectional and oscillatory flow past a circular cylinder. Ocean Engng 191, 106504.10.1016/j.oceaneng.2019.106504CrossRefGoogle Scholar
Wu, J.-T., Carvalho, M.S. & Kumar, S. 2019 b Effects of shear and extensional rheology on liquid transfer between two flat surfaces. J. Non-Newtonian Fluid Mech. 274, 104173.10.1016/j.jnnfm.2019.104173CrossRefGoogle Scholar
Wu, Q.G., Ni, B.Y., Bai, X.L., Cui, B. & Sun, S.L. 2017 Experimental study on large deformation of free surface during water exit of a sphere. Ocean Engng 140, 369–376.10.1016/j.oceaneng.2017.06.009CrossRefGoogle Scholar
Zhang, X.-Y., Lyu, X.-J. & Fan, X.-D. 2022 Numerical study on the vertical water exit of a cylinder with cavity. China Ocean Engng 36 (5), 734–742.10.1007/s13344-022-0065-0CrossRefGoogle Scholar
Zhu, X., Faltinsen, O.M. & Hu, C. 2007 Water entry and exit of a horizontal circular cylinder. J. Offshore Mech. Arct. Engng 129, 253–264.10.1115/1.2199558CrossRefGoogle Scholar
Zufferey, R., Ancel, A.O., Farinha, A., Siddall, R., Armanini, S.F., Nasr, M., Brahmal, R.V., Kennedy, G. & Kovac, M. 2019 Consecutive aquatic jump-gliding with water-reactive fuel. Sci. Robot. 4 (34), eaax7330.10.1126/scirobotics.aax7330CrossRefGoogle ScholarPubMed