密集剪切颗粒流中速度波动和自扩散特性的离散元模拟

孟凡净; 刘焜

doi:10.7498/aps.63.134502

摘要

分析了平行板间密集剪切颗粒流的平均速度、速度波动、区域划分和自扩散特性. 为了分析以上问题，建立了平均固体体积分数为0.80剪切平行板间密集颗粒流的离散元物理模型. 研究结果表明：间隙间颗粒的平均速度从上到下逐渐增大，波动速度恰好相反；纵向的平均速度、波动速度较小，这一点稀疏剪切颗粒流正相反；根据剪切率和平均速度大小把间隙间纵向区域依次划分为类固体、振荡和类流体区域，并得出了波动速度对剪切率的依赖关系；间隙间颗粒的自扩散主要集中在横向，而稀疏剪切颗粒流在纵向的自扩散同样较突出. 通过对流变和扩散特性的模拟分析，直观地反映了颗粒的微观流变特性，有益于密集剪切颗粒流的流变机理的研究.

关键词:

密集颗粒流 /
离散元 /
流变 /
自扩散

Abstract

The distribution of average velocities, fluctuation of velocities, regional definition, and granular self-diffusion characters in dense granular flows between sheared parallel plates are discussed. In order to study the above problems, we use computer-established discrete element model with an average solid fraction of 0.80. Theoretical results show that the average velocities decrease with increasing height, and are larger for the case of lower plate with greater velocity; the average velocities in y direction are close to 0 because there is no bulk motion in y direction. Flows of the lower plate with a greater velocity induce relatively greater fluctuation of velocities in the x and y directions, the fluctuation of velocities increases with the height and is larger in the area close to the upper plate. The flows consist of a “solid-like” area in the lower test region, but a “fluid-like” region in the upper, and an “oscillating” region in the middle of the channel. By tracking the movements of granules continually, variations of the mean-square self-diffusion relative displacements with square time are plotted, and the mean self-diffusion relative coefficients are determined. As the fluctuation and self-diffusion analysis directly reflect the macroscopic properties of granules and provide bases and references for researching the flow mechanisms of “dense granular sheared flows”.

Keywords:

作者及机构信息

孟凡净,
刘焜

1.
合肥工业大学摩擦学研究所, 合肥 230009

基金项目: 国家自然科学基金（批准号：51375132，51175136，51005067）资助的课题.

Authors and contacts

1.
Institute of Tribology, Hefei University of Technology, Hefei 230009, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51375132, 51175136, 51005067).

参考文献

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施引文献

[1]	Hsiau S S, Shieh Y M 1999 J. Rheol. 43 1049
[2]	Majmudar T S, Behringer R P 2005 Nature 43 1079
[3]	Ji S Y, Li P F, and Chen X D 2012 Acta Phys. Sin. 61 184703 (in Chinese)[季顺迎, 李鹏飞, 陈晓东 2012 物理学报 61 184703]
[4]	Peng Z, Li X Q, Jiang L, Fu L P, Jiang Y M 2009 Acta Phys. Sin. 58 2090 (in Chinese) [彭政, 李湘群, 蒋礼, 符力平, 蒋亦民 2009 物理学报 58 2090]
[5]	Peng Y J, Zhang Z, Wang Y, Liu X S 2012 Acta Phys. Sin. 61 134501 (in Chinese)[[彭亚晶, 张卓, 王勇, 刘小嵩 2012 物理学报 61 134501]
[6]	Leonard A, Daraio C 2012 Phys. Rev. Lett. 108 214301
[7]	Eugenio H, Franco T, Francisco M 2011 Phys. Rev. E 84 041304
[8]	Seguin A, Bertho Y, Martinez F, Crassous J 2013 Phys. Rev. E 87 012201
[9]	Lehane B M, Liu Q B 2013 Geotech. Geol. Eng. 31 329
[10]	Wang W, Liu X J, Liu K 2012 Tribol. Lett. 48 229
[11]	Yi C H, Liu Y, Miao T D, Mu Q S, Qi Y L 2007 Granular Matter 9 195
[12]	Shojaaee Z, Roux J N, Chevoir F, Wolf D E 2012 Phys. Rev. E 86 011301
[13]	Azèma E, Estrada N, Radjaï F 2012 Phys. Rev. E 86 041301
[14]	Zhen H P, Jiang Y M, Peng Z 2013 Chin. Phys. B 22 040511
[15]	Elkholy K N, Khonsari M M 2008 J. Eng. Tribo. 222 741
[16]	Bose M, Kumaran V 2004 Phys. Rev. E 69 061301
[17]	Bocquet L, Losert W, Schalk D, Lubensky T C, Gollub J P 2001 Phys. Rev. E 65 011307
[18]	Johnson P C, Jackson R 1987 J. Fluid Mech. 176 67
[19]	Kondic L, Fang X, Losert W, O'Hern C S, BehringerR P 2012 Phys. Rev. E 85 011305
[20]	Tordesillas A, Walker D M, Lin Q 2010 Phys. Rev. E 81 011302
[21]	Cai Q D, Chen S Y, Shen X W 2011 Chin. Phys. B 20 024502
[22]	Zhou G G D and Sun Q C 2013 Powder Technology 239 115
[23]	Bei Z W, Sun Q C, Liu J G, Jin F, Zhang C H 2011 Acta Phys. Sin. 60 034502 (in Chinese) [毕忠伟, 孙其诚, 刘建国, 金峰, 张楚汉 2011 物理学报 60 034502]
[24]	Ragione L L, Magnanimo V 2012 Phys. Rev. E 85 031304
[25]	Lu L S, Hsiau S S 2008 Particuology 6 445
[26]	Utter B, Behringer R P 2004 Phys. Rev. E 69 031308
[27]	Meng F J, Liu K, Wang W 2013 Applied Mathematics and Mechanics 34 7 14 (in Chinese). [孟凡净, 刘焜, 王伟 2013 应用数学和力学 347 14]
[28]	Han X M, Gao F, Fu R, Song B W, Nong W H 2009 Materials China 28 8 ( in Chinese) [韩晓明, 高飞, 符蓉, 宋宝韫, 农万华 2009 中国材料进展 28 8]
[29]	Zhang B P 2011 MS Thesis (Hefei: Hefei University of Technology) (in Chinese) [张柏平 2011 硕士学位论文(合肥: 合肥工业大学)]
[30]	Chun C L, Shu S H, Wen J Y 2012 Inter. J. Multi. Flow 46 22
[31]	Giulio B 2007 Nature Physics 3 222
[32]	Zhang Y, Campbell C S 1992 J. Fluid Mech. 237 541
[33]	Wang W, Liu X J, Jiao M H, Liu K 2009 J. Mech. Eng. 45 101 (in Chinese) [王伟, 刘小君, 焦明华, 刘焜 2009 机械工程学报 45 101]
[34]	Campbell C S 1990 Annu. Rev. Fluid Mech. 22 57

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