Direct numerical simulations of inertial settling of non-Brownian particles

Ali Abbas Zaidi; Takuya Tsuji; Toshitsugu Tanaka

Korean Journal of Chemical Engineering, Vol.32, No.4, 617-628, April, 2015

DOI10.1007/s11814-014-0241-x Export Citation

Direct numerical simulations of inertial settling of non-Brownian particles

Ali Abbas Zaidi^†, Takuya Tsuji, and Toshitsugu Tanaka

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

E-mail:

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.

Keywords:Hindered Settling Velocity;Sedimentation;Particle Structuring;Moderate Reynolds Number;Direct Numerical Simulation

[References]

Nicolai H, Guazzelli E, Phys. Fluids, 7, 3 (1995)
Nicolai H, Herzhaft, Hinch EJ, Oger L, Guazzelli E, Phys. Fluids, 7, 12 (1995)
Nicolai H, Peysson Y, Guazzelli E, Phys. Fluids, 8, 855 (1996)
Caflisch RE, Luke JHC, Phys. Fluids, 28, 759 (1985)
Brenner MP, Phys. Fluids, 11, 754 (1999)
Nguyen NQ, Ladd AJC, J. Fluid Mech., 525, 73 (2005)
Ladd AJC, Verberg R, J. Stat. Phys., 104, 1191 (2001)
Padding JT, Louis AA, Phys. Rev. Lett., 93, 220601 (2004)
Padding JT, Louis AA, Phys. Rev. E, 74, 031402 (2006)
Swan JW, Brady JF, Phys. Fluids, 19, 113306 (2007)
Koo S, Korean J. Chem. Eng., 28(2), 364 (2011)
Nishiura D, Shimosaka A, Shirakawa Y, Hidaka J, Kag. Kog. Ronbunshu, 32(4), 331 (2006)
Hoogerbrugge PJ, Koelman JMVA, Europhys. Lett., 19, 5 (1992)
Cunha FR, Abade GC, Sousa AJ, Hinch EJ, J. Fluid Eng-T ASME, 124, 957 (2002)
Stockie JM, Comp. Structures, 87, 701 (2009)
Padding JT, Louis AA, Phys. Rev. E, 77, 011402 (2008)
Kajishima T, Takiguchi S, Hamasaki H, Miyake Y, JSME Int. J. B-Fluid T, 44, 526 (2001)
Simeonov JA, Calantoni J, Int. J. Multiph. Flow, 46, 38 (2012)
Cundall PA, Strack ODL, Geotechnique, 29, 47 (1979)
Beetstra R, van der Hoef MA, Kuipers JAM, AIChE J., 53(2), 489 (2007)
Tsuji Y, Kawaguchi T, Tanaka T, Powder Technol., 77, 79 (1993)
Hartman M, Trnka D, Havlin V, Chem. Eng. Sci., 47, 3162 (1992)
Ham JM, Homsy GM, Int. J. Multiphase Flow, 14, 533 (1988)
Alnaafa MA, Selim MS, AIChE J., 38, 1618 (1992)
Davis RH, Birdsell KH, AIChE J., 34, 123 (1988)
Di Felice R, Int. J. Multiph. Flow, 25(4), 559 (1999)
Richardson JF, Zaki WN, Trans. Inst. Chem. Eng., 32, S82 (1954)
Garside J, Aldibouni MR, Ind. Eng. Chem. Proc. Dd., 16, 206 (1977)
Kajishima T, Int. J. Heat Fluid Flow, 25, 721 (2004)
Kajishima T, Takiguchi S, Int. J. Heat Fluid Flow, 23, 639 (2002)
Doychev T, Uhlmann M, Proc. of the 8th Int. Conf. on Multiphase Flow, May 2013, 320. (2013)
Batchelor GK, J. Fluid Mech., 52, 245 (1972)
Fortes AF, Joseph DD, Lundgren TS, J. Fluid Mech., 177, 467 (1987)
Chen YM, Jang CS, Cai P, Fan LS, Chem. Eng. Sci., 46, 2253 (1991)
Talini L, Leblond J, Feuillebois F, J. Magn. Reson., 132, 287 (1998)
Herrmann HJ, Hong DC, Stanley HE, J. Phys. A, 17, L261 (1984)
Wylie JJ, Koch DL, Phys. Fluids, 12, 964 (2000)
Xiong QG, Li B, Chen FG, Ma JS, Ge W, Li JH, Chem. Eng. Sci., 65(19), 5356 (2010)
Thiele E, J. Chem. Phys., 39, 474 (1963)
Wertheim MS, Phys. Rev. Lett., 10, 321 (1963)
Hamid A, Yamamoto R, Phys. Rev. E, 87, 022310 (2013)
Bossis G, Brady JF, J. Chem. Phys., 87, 5437 (1987)
Koch DL, Phys. Fluids A, 5, 1141 (1993)

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

[2] Nicolai H, Herzhaft, Hinch EJ, Oger L, Guazzelli E, Phys. Fluids, 7, 12 (1995)

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

[4] Caflisch RE, Luke JHC, Phys. Fluids, 28, 759 (1985)

[5] Brenner MP, Phys. Fluids, 11, 754 (1999)

[6] Nguyen NQ, Ladd AJC, J. Fluid Mech., 525, 73 (2005)

[7] Ladd AJC, Verberg R, J. Stat. Phys., 104, 1191 (2001)

[8] Padding JT, Louis AA, Phys. Rev. Lett., 93, 220601 (2004)

[9] Padding JT, Louis AA, Phys. Rev. E, 74, 031402 (2006)

[10] Swan JW, Brady JF, Phys. Fluids, 19, 113306 (2007)

[11] Koo S, Korean J. Chem. Eng., 28(2), 364 (2011)

[12] Nishiura D, Shimosaka A, Shirakawa Y, Hidaka J, Kag. Kog. Ronbunshu, 32(4), 331 (2006)

[13] Hoogerbrugge PJ, Koelman JMVA, Europhys. Lett., 19, 5 (1992)

[14] Cunha FR, Abade GC, Sousa AJ, Hinch EJ, J. Fluid Eng-T ASME, 124, 957 (2002)

[15] Stockie JM, Comp. Structures, 87, 701 (2009)

[16] Padding JT, Louis AA, Phys. Rev. E, 77, 011402 (2008)

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

[18] Simeonov JA, Calantoni J, Int. J. Multiph. Flow, 46, 38 (2012)

[19] Cundall PA, Strack ODL, Geotechnique, 29, 47 (1979)

[20] Beetstra R, van der Hoef MA, Kuipers JAM, AIChE J., 53(2), 489 (2007)

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

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

[23] Ham JM, Homsy GM, Int. J. Multiphase Flow, 14, 533 (1988)

[24] Alnaafa MA, Selim MS, AIChE J., 38, 1618 (1992)

[25] Davis RH, Birdsell KH, AIChE J., 34, 123 (1988)

[26] Di Felice R, Int. J. Multiph. Flow, 25(4), 559 (1999)

[27] Richardson JF, Zaki WN, Trans. Inst. Chem. Eng., 32, S82 (1954)

[28] Garside J, Aldibouni MR, Ind. Eng. Chem. Proc. Dd., 16, 206 (1977)

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

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

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

[32] Batchelor GK, J. Fluid Mech., 52, 245 (1972)

[33] Fortes AF, Joseph DD, Lundgren TS, J. Fluid Mech., 177, 467 (1987)

[34] Chen YM, Jang CS, Cai P, Fan LS, Chem. Eng. Sci., 46, 2253 (1991)

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

[36] Herrmann HJ, Hong DC, Stanley HE, J. Phys. A, 17, L261 (1984)

[37] Wylie JJ, Koch DL, Phys. Fluids, 12, 964 (2000)

[38] Xiong QG, Li B, Chen FG, Ma JS, Ge W, Li JH, Chem. Eng. Sci., 65(19), 5356 (2010)

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

[40] Wertheim MS, Phys. Rev. Lett., 10, 321 (1963)

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

[42] Bossis G, Brady JF, J. Chem. Phys., 87, 5437 (1987)

[43] Koch DL, Phys. Fluids A, 5, 1141 (1993)