Abstract
This study experimentally investigates the vortex structure induced by sphere-wall collision and a falling sphere in a viscous liquid. The velocity fields of sphere-induced vortices were measured with refractive-index-matched materials and particle tracking velocimetry. The Reynolds number, based on the sphere diameter and the falling velocity, was in the range of 350–3200. The results revealed that the sphere-induced vortex ring was axisymmetric when the Reynolds number Re is \(\le\) 800. For the case of Re = 2000, the vortex structure developed into a non-symmetric flow after the sphere collided on the wall. Nonetheless, the influence of the Reynolds number on the vortex trajectory is insignificant. The moving speed of the primary vortex increases as the Reynolds number increases. In addition, the trajectories of free-falling spheres at a high Reynolds number of Re = 3200 deviate from a vertical straight line, owing to the non-axisymmetric flow field around the sphere. The experimental results presented in this work can be used to validate numerical schemes for solid/vortex interaction problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The data that support the findings of this study are available from the first author, Prof. Young, upon request.
References
Adrian RJ (1991) Particle-imaging techniques for experimental fluid mechanics. Ann Rev Fluid Mech 23:261–304
Ardekani AM, Rangel RH (2008) Numerical investigation of particle–particle and particle-wall collisions in a viscous fluid. J Fluid Mech 596:437–466
Capart H, Young DL, Zech Y (2002) Voronoï imaging methods for the measurement of granular flows. Exp Fluids 32:121–135. https://doi.org/10.1007/s003480200013
Cheng M, Lou J, Luo LS (2010) Numerical study of a vortex ring impacting a flat wall. J Fluid Mech 660:430–455. https://doi.org/10.1017/S0022112010002727
Chu C-R, Wu T-R, Tu Y-F, Hu S-K, Chiu C-L (2020) Interaction of two free-falling spheres in water. Phys Fluids 32(3):033304. https://doi.org/10.1063/1.5130467
David T, Eshbal L, Rinsky V, van Hout R (2020) Flow measurements in the near wake of a smooth sphere and one mimicking a pine cone. Phys Rev Fluids 5:074301. https://doi.org/10.1103/PhysRevFluids.5.074301
Eames I, Dalziel SB (2000) Dust resuspension by the flow around an impacting sphere. J Fluid Mech 403:305–328. https://doi.org/10.1017/S0022112099007120
Eshbal L, Rinsky V, David T, Greenblatt D, van Hout R (2019) Measurement of vortex shedding in the wake of a sphere at Re = 465. J Fluid Mech 870:290–315. https://doi.org/10.1017/jfm.2019.250
Gondret P, Lance PM, Petit L (2002) Bouncing motion of spherical particles in fluids. Phys Fluids 14(2):643. https://doi.org/10.1063/1.1427920
Haam SJ, Brodkey RS, Fort I, Klaboch L, Placnik M, Vanecek V (2002) Laser Doppler anemometry measurements in an index of refraction matched column in a presence of dispersed beads—Part I. Int J Multiphase Flow 26(9):1401–1418. https://doi.org/10.1016/S0301-9322(99)00094-4
Horowitz M, Williamson CHK (2010) The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres. J Fluid Mech 651:251–294. https://doi.org/10.1017/S0022112009993934
Hsu HC, Capart H (2007) Enhanced upswing in immersed collisions of tethered sphere. Phys Fluids 19:101701. https://doi.org/10.1063/1.2771657
Inoue O, Sakuragi A (2008) Vortex shedding from a circular cylinder of finite length at low Reynolds numbers. Phys Fluids 20:033601. https://doi.org/10.1063/1.2844875
Lee H-Y, Chen Y-H, You J, Lin Y-T (2000) Investigations of continuous bed load saltating process. J Hydraulic Eng 126(9):691–700
Lee H-Y, Lin Y-T, You J, Wang H (2006) On three-dimensional continuous saltating process of sediment particles near the channel bed. J Hydraulic Res 44(3):374–389
Leweke T, Thompson MC, Hourigan K (2004) Vortex dynamics associated with the collision of a sphere with a wall. Phys Fluids 16:L74-77. https://doi.org/10.1063/1.1773854
Leweke T, Thompson MC, Hourigan K (2006) Instability of the flow around an impacting sphere. J Fluids Struct 22:961–971. https://doi.org/10.1016/j.jfluidstructs.2006.05.002
Leweke T, Schouveiler L, Thompson MC, Hourigan K (2008) Unsteady flow around impacting bluff bodies. J Fluids Struct 24:1194–1203. https://doi.org/10.1016/j.jfluidstructs.2008.08.003
Mongruel A, Lamriben C, Yahiaoui S, Feuillebois F (2010) The approach of a sphere to a wall at finite Reynolds number. J Fluid Mech 661:229–238. https://doi.org/10.1017/S0022112010003459
Munro RJ, Bethke N, Dalziel SB (2009) Sediment resuspension and erosion by vortex ring. Phys Fluids 21:046601. https://doi.org/10.1063/1.3083318
Nguyen LV, Takamure K, Uchiyama T (2019) Deformation of a vortex ring caused by its impingement on a sphere. Phys Fluids 31(10):107108. https://doi.org/10.1063/1.5122260
Swearingen JD, Crouch JD, Handler RA (1995) Dynamics and stability of a vortex ring impacting a solid boundary. J Fluid Mech 297:1–28. https://doi.org/10.1017/S0022112095002977
ten Cate A, Derksen JJ, Kramer HJM, van Rosmalen GM, van den Akker HEA (2001) The microscopic modelling of hydrodynamics in industrial crystallisers. Chem Eng Sci 56:2495–2001
ten Cate A, Nieuwstad CH, Derksen JJ, van den Akker HEA (2002) Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere setting under gravity. Phys Fluids 14(11):4012–4025. https://doi.org/10.1063/1.1512918
Thompson MC, Leweke T, Hourigan K (2007) Sphere-wall collision: vortex dynamics and stability. J Fluid Mech 575:121–148. https://doi.org/10.1017/S002211200600406X
van Hout R, Rinsky V, Grobman Y (2018) Experimental study of a round jet impinging on a flat surface: flow field and vortex characteristics in the wall jet. Int J Heat Fluid Flow 70:41–58. https://doi.org/10.1016/j.ijheatfluidflow.2018.01.010
Walker JDA, Smith CR, Cerra AW, Doligalski TL (1987) The impact of a vortex ring on a wall. J Fluid Mech 181:99–140. https://doi.org/10.1017/S0022112087002027
Weijermars R (1988) Progressive fluid deformation in low Reynolds number flow past a falling cylinder. Am J Phys 56(6):534–540
Young DL, Wu CS, Wu C, Lin YC (2015) Simulations of asymmetric flow structures around a moving sphere at moderate Reynolds number. J Mech 31(6):757–769
Young DL, Lin YC, Capart H, Chu C-R (2022) Vortex structures around two colliding spheres at high Reynolds number. Int J Multiphase Flow 157:140246. https://doi.org/10.1016/j.ijmultiphaseflow.2022.104246
Acknowledgements
The first author is grateful to the financial support of the Ministry of Science and Technology, Republic of China, Taiwan, through Grant No. NSC96-2221-E002-127-MY3.
Funding
This research is funded by the Ministry of Science and Technology, Republic of China, Taiwan, through Grant No. NSC96-2221-E002-127-MY3.
Author information
Authors and Affiliations
Contributions
Profs. Chu, C.-R. and Young, D.L. wrote the manuscript text, Li, J.-S. conducted the experiments and prepared figures, and Prof. Capart H. provided the experimental instrument, analyzing software and advice on the experimental method.
Corresponding author
Ethics declarations
Conflict of interest
The authors have no competing interests that might be perceived to influence the results and discussion reported in this paper.
Ethics approval and consent to participate
The authors all consent to participate in the preparing this manuscript and approve the ethics standard of the publisher.
Consent for publication
The authors all consent to publish the content of the research results in Experiments in Fluids.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Young, D.L., Li, JS., Capart, H. et al. Velocity measurements of vortex structures induced by sphere/wall interaction. Exp Fluids 63, 170 (2022). https://doi.org/10.1007/s00348-022-03520-8
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-022-03520-8