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Modeling of Spinning Sphere Motion in Shear Flow of Viscous Fluid

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Distributed Computer and Communication Networks (DCCN 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 678))

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Abstract

Modeling the motion of a small rigid spinning spherical particle in viscous Navier—Stokes fluid, we generalize the Rubinow—Keller and Maxey—Riley method of estimating the force and the torque acting on the particle to the case of shear flow and arbitrary Reynolds number. We represent the velocity of the flow near the particle as solid body part and small perturbation. As for the velocity far from the particle, it includes a steady external shear flow part and again small perturbation. We use the simplest quadratic polynomial approximation for the small velocity parts and insert it in matching condition at some intermediate spherical surface. It appears that the force parallel to the angular velocity of the particle proves to contain the oscillatory part, with the frequency being proportional to the gradient of the external steady velocity.

Y.P. Rybakov—The author expresses his gratitude to Dr. Pavel Vlasak for fruitful discussion of the paper.

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References

  1. Rubinow, S.I., Keller, J.B.: The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447–459 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  2. Maxey, M.R., Riley, J.J.: Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 28, 883–889 (1983)

    Article  MATH  Google Scholar 

  3. Fenton, J.D., Abbott, J.E.: Initial movement of grains on a stream bed: the effect of relative protrusion. Proc. Roy. Soc. London A352, 523–537 (1977)

    Article  Google Scholar 

  4. Ikeda, S.: Incipient motion of sand particles on side slopes. J. Hydraul. Eng. Div. ASCE 108, 95–114 (1982)

    Google Scholar 

  5. Ling, C.-H.: Criteria for incipient motion of spherical sediment particles. J. Hydraul. Eng. Div. ASCE 121, 472–478 (1995)

    Article  Google Scholar 

  6. Nishimura, K., Hunt, J.C.R.: Saltation and incipient suspension above a flat particle bed below a turbulent boundary layer. J. Fluid Mech. 417, 72–102 (2000)

    Article  MATH  Google Scholar 

  7. Van Rijn, L.C.: Sediment transport, part I: bed load transport. J. Hydraul. Eng. Div. ASCE 110, 1431–1456 (1984)

    Article  Google Scholar 

  8. Yalin, M.S., Karahan, E.: Inception of sediment transport. J. Hydraul. Eng. Div. ASCE 105, 1433–1444 (1979)

    Google Scholar 

  9. Bagnold, R.A.: The nature of saltation and of “bed-load” transport in water. Proc. Roy. Soc. London A332, 473–504 (1973)

    Article  Google Scholar 

  10. Barkla, H.M., Auchterlonie, L.J.: The Magnus or Robins effect on rotating spheres. J. Fluid Mech. 47, 437–447 (1971)

    Article  Google Scholar 

  11. Francis, J.R.D.: Experiments on the motion of solitary grains along the bed of a water stream. Proc. Roy. Soc. London A332, 443–471 (1973)

    Article  Google Scholar 

  12. Lee, H.-Y., Hsu, I.-S.: Investigation of saltating patricle motions. J. Hydraul. Eng. Div. ASCE 120, 831–845 (1994)

    Article  Google Scholar 

  13. Lee, H.-Y., Chen, Y.-H., You, J.-Y., Lin, Y.-T.: Investigation of continuous bed load saltating process. J. Hydraul. Eng. Div. ASCE 126, 691–700 (2000)

    Article  Google Scholar 

  14. Lee, H.-Y., Lin, Y.-T., Chen, Y.-H., You, J.-Y., Wang, H.-W.: On three- dimensional continuous saltating process of sediment particles near the channel bed. J. Hydraul. Res. 44, 374–389 (2006)

    Article  Google Scholar 

  15. Mei, R., Adrian, R.J., Hanratty, T.J.: Particle dispersion in isotropic turbulence under Stokes drag and Basset force with gravitational settling. J. Fluid Mech. 225, 481–495 (1991)

    Article  MATH  Google Scholar 

  16. Michaelides, E.E.: Hydrodynamic force and heat/mass transfer from particles, bubbles, and drops - the Freeman scholar lecture. J. Fluids Eng. ASME 125, 209–238 (2003)

    Article  Google Scholar 

  17. Murphy, P.J., Hooshiari, H.: Saltation in water dynamics. J. Hydraul. Eng. Div. ASCE 108, 1251–1267 (1982)

    Google Scholar 

  18. Oesterle, B., Bui Dinh, T.: Experiments on the lift of a spinning sphear in the range of intermediate Reynolds numbers. Exp. Fluids 25, 16–22 (1998)

    Article  Google Scholar 

  19. Sawatzki, O.: Das Str\(\ddot{o}\)mungsfeld um eine Rotiendre Kugel. Acta Mechanica 9, 159–214 (1970)

    Article  MATH  Google Scholar 

  20. Tsuji, Y., Morikawa, Y., Mizuno, O.: Experimental measurements of the Magnus force on a rotating sphere at Low Reynolds numbers. ASME J. Fluid Eng. 107, 484–488 (1985)

    Article  Google Scholar 

  21. Ancey, C., Bigillon, F., Frey, P., Lanier, J., Ducret, R.: Saltating motion of a bead in a rapid water stream. Phys. Rev. E 66, 036306 (2002)

    Article  Google Scholar 

  22. Colombini, M.: Turbulence-driven secondary flows and formation of sand ridges. J. Fluid Mech. 254, 701–719 (1993)

    Article  MATH  Google Scholar 

  23. Lukerchenko, N., Platsevich, S., Chara, Z., Vlasak, P.: 3D numerical model of the spherical particle saltation in a channel with a rough fixed bed. J. Hydraul. Hydromech. 57, 100–112 (2009)

    Google Scholar 

  24. Lukerchenko, N., Kvurt, Y., Kharlamov, A., Chara, Z., Vlasak, P.: Experimental evaluation of the drag force and drag torque acting on a rotating spherical particle moving in fluid. J. Hydraul. Hydromech. 56, 88–94 (2008)

    Google Scholar 

  25. Nino, Y., Garcia, M.: Experiments on saltation of sand in water. J. Hydraul. Eng. ASCE 124, 1014–1025 (1998)

    Article  Google Scholar 

  26. Reizes, J.A.: Numerical study of continuous saltation. J. Hydraul. Hydromech. 104(HY9), 1303–1321 (1978)

    Google Scholar 

  27. Wiberg, D.L., Smith, J.D.: A theoretical model for saltating grains in water. J. Geophys. Res. 90(C4), 7341–7354 (1985)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical Physics and Mechanics, RUDN University, 6, Miklukho-Maklaya Street, Moscow, 117198, Russia

    Yuri P. Rybakov

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  1. Yuri P. Rybakov
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Correspondence to Yuri P. Rybakov .

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Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. RUDN University , Moscow, Russia

    Konstantin E. Samouylov

  3. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Rybakov, Y.P. (2016). Modeling of Spinning Sphere Motion in Shear Flow of Viscous Fluid. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2016. Communications in Computer and Information Science, vol 678. Springer, Cham. https://doi.org/10.1007/978-3-319-51917-3_54

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  • DOI: https://doi.org/10.1007/978-3-319-51917-3_54

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51916-6

  • Online ISBN: 978-3-319-51917-3

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