Numerical Simulation of Particle Sedimentation in a 3D Rectangular Channel

LIU Ma-lin

doi:10.3879/j.issn.1000-0887.2011.09.006

Volume 32 Issue 9

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2011 > 32(9): 1071-1083

LIU Ma-lin. Numerical Simulation of Particle Sedimentation in a 3D Rectangular Channel[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1071-1083. doi: 10.3879/j.issn.1000-0887.2011.09.006

Citation:

LIU Ma-lin. Numerical Simulation of Particle Sedimentation in a 3D Rectangular Channel[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1071-1083. doi: 10.3879/j.issn.1000-0887.2011.09.006

Citation:

LIU Ma-lin. Numerical Simulation of Particle Sedimentation in a 3D Rectangular Channel[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1071-1083. doi: 10.3879/j.issn.1000-0887.2011.09.006

PDF( 3519 KB)

Numerical Simulation of Particle Sedimentation in a 3D Rectangular Channel

doi: 10.3879/j.issn.1000-0887.2011.09.006

LIU Ma-lin

Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, P. R. China

Received Date: 2010-11-24
Rev Recd Date: 2011-06-14
Publish Date: 2011-09-15

Abstract

Abstract

The 3D lattice Boltzmann method was used to simulate the particle sedimentation in a rectangular channel.The results of single particle sedimentation indicated that the last position of particle was along the center line of the channel,regardless of the initial position and the particle diameter,so as to the particle Reynolds number.The wall effect on the terminal velocity was in good agreement with experimental results quantitatively.The drafting,kissing and tumbling (DKT) process was reproduced and analyzed by simulating two particles cluster sedimentation.The diameter ratio,initial position and wall effect on the drafting,kissing and tumbling process were investigated.When two particles with equal diameter sediment in the rectangular channel,the periodical DKT process and the spiraling trajectory were found,the last equilibrium configuration was obtained from simulation results.Also,the interesting regular sedimentation phenomena were found when 49 particles fell down under the gravity.
- sedimentation,
- lattice Boltzmann method,
- particle-particle interaction

FullText(HTML)

References(22)

References

[1]	Shinbrot T. The brazil nut effect—in reverse[J]. Nature, 2004, 429(6990): 352-353.
[2]	Mobius M E, Lauderdale B E, Nagel S R, Jaeger H M. Size separation of granular particles[J]. Nature, 2001, 414(6861): 270. doi: 10.1038/35104697
[3]	邵雪明，刘杨，余钊圣. 不同大小颗粒之间相互作用的直接数值模拟[J].应用数学和力学， 2005, 26（3）：372-378.（SHAO Xue-ming, LIU Yang, YU Zhao-sheng. Interactions between two sedimenting particles with different sizes[J]. Applied Mathematics and Mechanics(English Edition）, 2005, 26(3): 407-414.）
[4]	Sun R, Chwang A T. Interactions between two touching spherical particles in sedimentation[J]. Physical Review E，2007, 76(4): 046316. doi: 10.1103/PhysRevE.76.046316
[5]	Subramanian G, Koch D L. Evolution of clusters of sedimenting low-Reynolds-number particles with Oseen interactions[J]. Journal of Fluid Mechanics, 2008, 603: 63-100.
[6]	Aidun C K, Ding E J. Dynamics of particle sedimentation in a vertical channel: period-doubling bifurcation and chaotic state[J]. Physics of Fluids, 2003, 15(6): 1612-1621. doi: 10.1063/1.1571825
[7]	Qi D W, Luo L S. Rotational and orientational behaviour of three-dimensional spheroidal particles in Couette flows[J]. Journal of Fluid Mechanics, 2003, 477: 201-213.
[8]	Feng Z G, Michaelides E E. The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems[J]. Journal of Computational Physics, 2004, 195(2): 602-628. doi: 10.1016/j.jcp.2003.10.013
[9]	Niu X D, Shu C, Chew Y T, Peng Y. A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows[J]. Physics Letters A, 2006, 354(3): 173-182. doi: 10.1016/j.physleta.2006.01.060
[10]	Singh P, Joseph D D. Sedimentation of a sphere near a vertical wall in an Oldroyd-B fluid[J]. Journal of Non-Newtonian Fluid Mechanics, 2000, 94(2): 179-203. doi: 10.1016/S0377-0257(00)00157-9
[11]	Feng J, Hu H H, Joseph D D. Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid—part 1：sedimentation[J]. Journal of Fluid Mechanics, 1994, 261: 95-134. doi: 10.1017/S0022112094000285
[12]	Patankar N A, Singh P, Joseph D D, Glowinski R, Pan T W. New formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows[J]. International Journal of Multiphase Flow, 2000, 26(9): 1509-1524. doi: 10.1016/S0301-9322(99)00100-7
[13]	Ladd A J C. Numerical simulations of particulate suspensions via a discretized Boltzmann equation—part 1：theoretical foundation[J]. Journal of Fluid Mechanics, 1994, 271: 285-309. doi: 10.1017/S0022112094001771
[14]	Feng Z G, Michaelides E E. Proteus: a direct forcing method in the simulations of particulate flows[J]. Journal of Computational Physics, 2005, 202(1): 20-51. doi: 10.1016/j.jcp.2004.06.020
[15]	Wu J, Shu C. Particulate flow simulation via a boundary condition-enforced immersed boundary-lattice Boltzmann scheme[J]. Communications in Computational Physics, 2010, 7(4): 793-812.
[16]	Ladd A J C, Verberg R. Lattice-Boltzmann simulations of particle-fluid suspensions[J]. Journal of Statistical Physics, 2001, 104(5/6): 1191-1251. doi: 10.1023/A:1010414013942
[17]	Nguyen N Q, Ladd A J C. Lubrication corrections for lattice-Boltzmann simulations of particle suspensions[J]. Physical Review E, 2002, 66(4): 046708. doi: 10.1103/PhysRevE.66.046708
[18]	Singh P, Joseph D D, Hesla T I, Glowinski R, Pan T W. Distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flows[J]. Journal of Non-Newtonian Fluid Mechanics, 2000, 91(2): 165-188. doi: 10.1016/S0377-0257(99)00104-4
[19]	Vasseur P, Cox R G. The lateral migration of a spherical particles sedimenting in a stagnant bounded fluid[J]. Journal of Fluid Mechanics, 1977, 80: 561-591. doi: 10.1017/S0022112077001840
[20]	Miyamura A, Iwasaki S, Ishii T. Experimental wall correction factors of singile solid spheres in triangular and square cylinders, and parellel plates[J]. International Journal of Multiphase Flow, 1981, 7(1): 41. doi: 10.1016/0301-9322(81)90013-6
[21]	王叶龙. 相互碰撞的圆离子在竖直通道中沉降的数值研究[J]. 应用数学和力学, 2006, 27(7):859-866.(WANG YE-Long. Simulation of sedimentation of two circular particles with collision considered in vertical channel[J]. Applied Mathematics and Mechanics(English Edition), 2006, 27(7): 983-991.)
[22]	Vanroyen C, Omari A, Toutain J, Reungoat D. Interactions between hard spheres sedimenting at low Reynolds number[J]. European Journal of Mechanics, B/Fluids, 2005, 24(5): 586-595. doi: 10.1016/j.euromechflu.2005.01.002