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Direct numerical simulations of inertial settling of non-Brownian particles

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Abstract

The dynamics of particles settling at moderate Reynolds number is studied with periodic boundary conditions. The particle Reynolds number ranges from 0.1 to 50, and the solid volume fraction ranges from single sphere to 0.4. Particle-fluid interactions are solved by immersed boundary method and particle-particle interactions are solved by discrete element method. The principal results are the average settling velocity and the structure formation of particles. The average sedimentation velocities of particles for moderate Reynolds number showed deviation from the well-known power law, and the difference keeps on increasing with decrease in solid volume fractions. This deviation is removed by proposing the division of the power law into three regions of Reynolds number for dilute and non-dilute regimes. By analyzing the particle structures, this difference is due to the particle arrangements by the wake interactions at moderate Reynolds number.

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References

  1. H. Nicolai and E. Guazzelli, Phys. Fluids, 7, 3 (1995).

    Article  CAS  Google Scholar 

  2. H. Nicolai, B. Herzhaft, E. J. Hinch, L. Oger and E. Guazzelli, Phys. Fluids, 7, 12 (1995).

    Article  CAS  Google Scholar 

  3. H. Nicolai, Y. Peysson and E. Guazzelli, Phys. Fluids, 8, 855 (1996).

    Article  CAS  Google Scholar 

  4. R. E. Caflisch and J.H. C. Luke, Phys. Fluids, 28, 759 (1985).

    Article  Google Scholar 

  5. M. P. Brenner, Phys. Fluids, 11, 754 (1999).

    Article  CAS  Google Scholar 

  6. N.Q. Nguyen and A. J. C. Ladd, J. Fluid Mech., 525, 73 (2005).

    Article  Google Scholar 

  7. A. J. C. Ladd and R. Verberg, J. Stat. Phys., 104, 1191 (2001).

    Article  CAS  Google Scholar 

  8. J.T. Padding and A. A. Louis, Phys. Rev. Lett., 93, 220601 (2004).

    Google Scholar 

  9. J. T. Padding and A. A. Louis, Phys. Rev. E, 74, 031402 (2006).

  10. J.W. Swan and J. F. Brady, Phys. Fluids, 19, 113306 (2007).

  11. S. Koo, Korean J. Chem. Eng., 28, 364 (2011).

    Article  CAS  Google Scholar 

  12. D. Nishiura, A. Shimosaka, Y. Shirakawa and J. Hidaka, Proc. Chem. Eng., 32, 331 (2006).

    CAS  Google Scholar 

  13. P. J. Hoogerbrugge and J. M.V. A. Koelman, Europhys. Lett., 19, 5 (1992).

    Article  Google Scholar 

  14. F.R. Cunha, G. C. Abade, A. J. Sousa and E. J. Hinch, J. Fluid Eng-T ASME, 124, 957 (2002).

    Article  Google Scholar 

  15. J. M. Stockie, Comp. Structures, 87, 701 (2009).

    Article  Google Scholar 

  16. J. T. Padding and A. A. Louis, Phys. Rev. E, 77, 011402 (2008).

  17. T. Kajishima, S. Takiguchi, H. Hamasaki and Y. Miyake, JSME Int. J. B-Fluid T, 44, 526 (2001).

    Article  Google Scholar 

  18. J. A. Simeonov and J. Calantoni, Int. J. Multiphase Flow, 46, 38 (2012).

    Article  CAS  Google Scholar 

  19. P. A. Cundall and O. D. L. Strack, Geotechnique, 29, 47 (1979).

    Article  Google Scholar 

  20. R. Beetstra, M. A. Van der Hoef and J. A. M. Kuipers, AIChE J., 53, 489 (2007).

    Article  CAS  Google Scholar 

  21. Y. Tsuji, T. Kawaguchi and T. Tanaka, Powder Technol., 77, 79 (1993).

    Article  CAS  Google Scholar 

  22. M. Hartman, D. Trnka and V. Havlin, Chem. Eng. Sci., 47, 3162 (1992).

    Article  CAS  Google Scholar 

  23. J.M. Ham and G. M. Homsy, Int. J. Multiphase Flow, 14, 533 (1988).

    Article  CAS  Google Scholar 

  24. M. A. Alnaafa and M. S. Selim, AIChE J., 38, 1618 (1992).

    Article  CAS  Google Scholar 

  25. R. H. Davis and K. H. Birdsell, AIChE J., 34, 123 (1988).

    Article  CAS  Google Scholar 

  26. R. Di Felice, Int. J. Multiphase Flow, 25, 559 (1999).

    Article  Google Scholar 

  27. J. F. Richardson and W.N. Zaki, Trans. Inst. Chem. Eng., 32, S82 (1954).

    Google Scholar 

  28. J. Garside and M.R. Aldibouni, Ind. Eng. Chem. Proc. Dd., 16, 206 (1977).

    Article  CAS  Google Scholar 

  29. T. Kajishima, Int. J. Heat Fluid Flow, 25, 721 (2004).

    Article  Google Scholar 

  30. T. Kajishima and S. Takiguchi, Int. J. Heat Fluid Flow, 23, 639 (2002).

    Article  CAS  Google Scholar 

  31. T. Doychev and M. Uhlmann, Proc. of the 8th Int. Conf. on Multiphase Flow, May 2013, 320.

    Google Scholar 

  32. G. K. Batchelor, J. Fluid Mech., 52, 245 (1972).

    Article  Google Scholar 

  33. A. F. Fortes, D.D. Joseph and T. S. Lundgren, J. Fluid Mech., 177, 467 (1987).

    Article  CAS  Google Scholar 

  34. Y. M. Chen, C. S. Jang, P. Cai and L. S. Fan, Chem. Eng. Sci., 46, 2253 (1991).

    Article  CAS  Google Scholar 

  35. L. Talini, J. Leblond and F. Feuillebois, J. Magn. Reson., 132, 287 (1998).

    Article  CAS  Google Scholar 

  36. H. J. Herrmann, D. C. Hong and H. E. Stanley, J. Phys. A, 17, L261 (1984).

    Article  Google Scholar 

  37. J. J. Wylie and D. L. Koch, Phys. Fluids, 12, 964 (2000).

    Article  CAS  Google Scholar 

  38. Q. G. Xiong, B. Li, F. G. Chen, J. S. Ma, W. Ge and J. H. Li, Chem. Eng. Sci., 65, 5356 (2010).

    Article  CAS  Google Scholar 

  39. E. Thiele, J. Chem. Phys., 39, 474 (1963).

    Google Scholar 

  40. M. S. Wertheim, Phys. Rev. Lett., 10, 321 (1963).

    Article  Google Scholar 

  41. A. Hamid and R. Yamamoto, Phys. Rev. E, 87, 022310 (2013).

  42. G. Bossis and J. F. Brady, J. Chem. Phys., 87, 5437 (1987).

    Article  CAS  Google Scholar 

  43. D. L. Koch, Phys. Fluids A, 5, 1141 (1993).

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Osaka University, Suita, 565-0871, Japan

    Ali Abbas Zaidi, Takuya Tsuji & Toshitsugu Tanaka

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  1. Ali Abbas Zaidi
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  2. Takuya Tsuji
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  3. Toshitsugu Tanaka
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Correspondence to Ali Abbas Zaidi.

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Zaidi, A.A., Tsuji, T. & Tanaka, T. Direct numerical simulations of inertial settling of non-Brownian particles. Korean J. Chem. Eng. 32, 617–628 (2015). https://doi.org/10.1007/s11814-014-0241-x

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  • DOI: https://doi.org/10.1007/s11814-014-0241-x

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