Size scaling relation of velocity field in granular flows and the Beverloo law

doi:10.1007/s10035-019-0872-z

	Size scaling relation of velocity field in granular flows and the Beverloo law
	Zhang, Yongwen 2,4; Hu, Gaoke 2,4; Chen, Xiaosong 2,4; Yang, Lei3 ; Li, Liangsheng 1; Lin, Ping 3
刊名	GRANULAR MATTER
	2019-05-01
卷号	21 期号:2 页码:6
关键词	Granular flow Beverloo law Size scaling relation
ISSN号	1434-5021
DOI	10.1007/s10035-019-0872-z
通讯作者	Chen, Xiaosong(chenxs@itp.ac.cn)
英文摘要	In a hopper with cylindrical symmetry and an aperture of radius R, the vertical velocity of granular flow v z depends on the distance from the hopper's center r and the height above the aperture z and v z = v z (r, z; R). We propose that the scaled vertical velocity v z (r, z; R)/v z (0, 0; R) is a function of scaled variables r/R r and z/R z, where R r = R - 0.5d and R z = R - k 2 d with the granule diameter d and a parameter k 2 to be determined. After scaled by v 2 z (0, 0; R)/R z, the effective acceleration a eff (r, z; R) derived from v z is a function of r/R r and z/R z also. The boundary condition a eff (0, 0; R) = - g of granular flows under earth gravity g gives rise to v z (0, 0; R). v g R - k 2 d 1/2. Our simulations using the discrete element method and GPU program in the three- dimensional and the two- dimensional hoppers confirm the size scaling relations of v z (r, z; R) and v z (0, 0; R). From the size scaling relations, we obtain the mass flow rate of D- dimensional hopper W. v g(R - 0.5d) D- 1 (R - k 2 d) 1/2, which agrees with the Beverloo law at R >> d. It is the size scaling of vertical velocity field that results in the dimensional R- dependence of W in the Beverloo law.
资助项目	National Magnetic Confinement Fusion Science Program of China[2014GB104002] ; Strategic Priority Research Program of the Chinese Academy of Sciences[XDA03030100] ; National natural Science Foundation of China[11421063]
WOS关键词	DISCHARGE ; HOPPER ; MODEL
WOS研究方向	Materials Science ; Mechanics ; Physics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000459976400001
资助机构	National Magnetic Confinement Fusion Science Program of China ; Strategic Priority Research Program of the Chinese Academy of Sciences ; National natural Science Foundation of China
内容类型	期刊论文
源URL	[http://119.78.100.186/handle/113462/134591]
专题	中国科学院近代物理研究所
通讯作者	Chen, Xiaosong
作者单位	1.Sci & Technol Electromagnet Scattering Lab, Beijing 100854, Peoples R China 2.Chinese Acad Sci, Inst Theoret Phys, Key Lab Theoret Phys, POB 2735, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Inst Modern Phys, 509 Nanchang Rd, Lanzhou 730000, Gansu, Peoples R China 4.Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Yongwen,Hu, Gaoke,Chen, Xiaosong,et al. Size scaling relation of velocity field in granular flows and the Beverloo law[J]. GRANULAR MATTER,2019,21(2):6.
APA	Zhang, Yongwen,Hu, Gaoke,Chen, Xiaosong,Yang, Lei,Li, Liangsheng,&Lin, Ping.(2019).Size scaling relation of velocity field in granular flows and the Beverloo law.GRANULAR MATTER,21(2),6.
MLA	Zhang, Yongwen,et al."Size scaling relation of velocity field in granular flows and the Beverloo law".GRANULAR MATTER 21.2(2019):6.