Advertisement

China Ocean Engineering

, Volume 32, Issue 5, pp 605–613 | Cite as

Effects of Degrees of Motion Freedom on Free-Fall of A Sphere in Fluid

  • Lei Liu
  • Jian-min Yang
  • Hai-ning Lyu
  • Xin-liang Tian
  • Tao Peng
Article
  • 25 Downloads

Abstract

Free-fall of a sphere in fluid is investigated at a Galileo number of 204 by direct numerical simulations (DNS). We mainly focus on the effects of different degrees-of-freedom (DOFs) of the sphere motion during free-fall. The characteristics of free-fall are compared with those of flow past a fixed sphere. Additional numerical tests are conducted with constraints placed on the translational or rotational DOFs of the sphere motion to analyze different DOFs of sphere motion. The transverse motion contributes significantly to the characteristics of free-fall; it results in the retardation of the vortex shedding, leading to the decrease of the Strouhal number. In addition, the transversal sphere motion exhibits the tendency to promote the sphere rotation. On the contrary, the effects of the sphere rotation and vertical oscillations during free-fall are negligible.

Key words

free-fall direct numerical simulation degree of motion freedom 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The authors would like to thank Mr. WU Cheng-hao and Mr. HU Zhi-huan for their assistance in the CFD simulation. The numerical simulations were supported by the Center for HPC, Shanghai Jiao Tong University.

References

  1. Allen, H.S., 1900. XXXI. The motion of a sphere in a viscous fluid, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 50(304), 323–338.CrossRefzbMATHGoogle Scholar
  2. Asao, S., Matsuno, K. and Yamakawa, M., 2013. Parallel computations of incompressible flow around falling spheres in a long pipe using moving computational domain method, Computers & Fluids, 88), 850–856.CrossRefGoogle Scholar
  3. CD-adapco, 2016. User Guide, Star-CCM+ Version 11.04, CD-adapcoGoogle Scholar
  4. Clift, R. and Gauvin, W.H., 1970. The motion of particles in turbulent gas streams, Proceedings of Chemeca, 70(1), 14–28.Google Scholar
  5. Feng, J., Hu, H.H. and Joseph, D.D., 1994. Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation, Journal of Fluid Mechanics, 261), 95–134.CrossRefzbMATHGoogle Scholar
  6. Hadžic, H., 2006. Development and Application of A Finite Volume Method for the Computation of Flows Around Moving Bodies on Unstructured, Overlapping Grids, Technische Universität Hamburg-Haburg, Hamburg.Google Scholar
  7. Haider, A. and Levenspiel, O., 1989. Drag coefficient and terminal velocity of spherical and nonspherical particles, Powder Technology, 58(1), 63–70.CrossRefGoogle Scholar
  8. Horowitz, M. and Williamson, C.H.K., 2010. The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres, Journal of Fluid Mechanics, 651), 251–294.CrossRefzbMATHGoogle Scholar
  9. Hunt, J.C.R., Wray, A.A. and Moin, P., 1988. Eddies, Streams, and Convergence Zones in Turbulent Flows, Center for Turbulence Research Report CTR-S88, pp.193–208.Google Scholar
  10. Jenny, M., Dušek, J. and Bouchet, G., 2004. Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid, Journal of Fluid Mechanics, 508), 201–239.MathSciNetCrossRefzbMATHGoogle Scholar
  11. Koblitz, A.R., Lovett, S., Nikiforakis, N. and Henshaw, W.D., 2017. Direct numerical simulation of particulate flows with an overset grid method, Journal of Computational Physics, 343), 414–431.MathSciNetCrossRefzbMATHGoogle Scholar
  12. Mordant, N. and Pinton, J.F., 2000. Velocity measurement of a settling sphere, The European Physical Journal B-Condensed Matter and Complex Systems, 18(2), 343–352.CrossRefGoogle Scholar
  13. Namkoong, K., Yoo, J.Y. and Choi, H.G., 2008. Numerical analysis of two-dimensional motion of a freely falling circular cylinder in an infinite fluid, Journal of Fluid Mechanics, 604), 33–53.CrossRefzbMATHGoogle Scholar
  14. Rahmani, M. and Wachs, A., 2014. Free falling and rising of spherical and angular particles, Physics of Fluids, 26(8), 083301.CrossRefGoogle Scholar
  15. Romero-Gomez, P. and Richmond, M.C., 2016. Numerical simulation of circular cylinders in free-fall, Journal of Fluids and Structures, 61), 154–167.CrossRefGoogle Scholar
  16. Terfous, A., Hazzab, A. and Ghenaim, A., 2013. Predicting the drag coefficient and settling velocity of spherical particles, Powder Technology, 239), 12–20.CrossRefGoogle Scholar
  17. Tian, X.L., Hu, Z.H., Lu, H.N. and Yang, J.M., 2017a. Direct numerical simulations on the flow past an inclined circular disk, Journal of Fluids and Structures, 72), 152–168.CrossRefGoogle Scholar
  18. Tian, X.L., Xiao, L.F., Zhang, X.D., Yang, J.M., Tao, L.B. and Yang, D., 2017b. Flow around an oscillating circular disk at low to moderate Reynolds numbers, Journal of Fluid Mechanics, 812), 1119–1145.MathSciNetCrossRefzbMATHGoogle Scholar
  19. Uhlmann, M. and Dušek, J., 2014. The motion of a single heavy sphere in ambient fluid: A benchmark for interface-resolved particulate flow simulations with significant relative velocities, International Journal of Multiphase Flow, 59), 221–243.CrossRefGoogle Scholar
  20. Veldhuis, C., Biesheuvel, A., van Wijngaarden, L. and Lohse, D., 2005. Motion and wake structure of spherical particles, Nonlinearity, 18(1), C1–C8.CrossRefzbMATHGoogle Scholar
  21. Veldhuis, C.H.J. and Biesheuvel, A., 2007. An experimental study of the regimes of motion of spheres falling or ascending freely in a Newtonian fluid, International Journal of Multiphase Flow, 33(10), 1074–1087.CrossRefGoogle Scholar
  22. Wang, L., Guo, Z.L. and Mi, J.C., 2014. Drafting kissing and tumbling process of two particles with different sizes,, Computers & Fluids, 96), 20–34.MathSciNetCrossRefzbMATHGoogle Scholar
  23. Yu, Z.S., Phan-Thien, N. and Tanner, R.I., 2004. Dynamic simulation of sphere motion in a vertical tube, Journal of Fluid Mechanics, 518), 61–93.CrossRefzbMATHGoogle Scholar
  24. Zhou, W. and Dušek, J., 2015. Chaotic states and order in the chaos of the paths of freely falling and ascending spheres, International Journal of Multiphase Flow, 75), 205–223.CrossRefGoogle Scholar

Copyright information

© Chinese Ocean Engineering Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Lei Liu
    • 1
    • 2
  • Jian-min Yang
    • 1
    • 2
  • Hai-ning Lyu
    • 1
    • 2
  • Xin-liang Tian
    • 1
    • 2
  • Tao Peng
    • 1
    • 2
  1. 1.State Key Laboratory of Ocean EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE)ShanghaiChina

Personalised recommendations