Knowledge Management System of Institute of Theoretical Physics, CAS
Hu, GK; Lin, P1; Zhang, YW; Li, LS; Yang, L1; Chen, XS | |
Size scaling relation of velocity field in granular flows and the Beverloo law | |
Source Publication | GRANULAR MATTER |
Language | 英语 |
Keyword | DISCHARGE HOPPER MODEL |
Abstract | 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. |
2019 | |
ISSN | 1434-5021 |
Volume | 21Issue:2Pages:21 |
Subject Area | Materials Science ; Mechanics ; Physics |
MOST Discipline Catalogue | Materials Science, Multidisciplinary ; Mechanics ; Physics, Applied |
DOI | 10.1007/s10035-019-0872-z |
Indexed By | SCIE |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.itp.ac.cn/handle/311006/23444 |
Collection | SCI期刊论文 |
Affiliation | 1.Chinese Acad Sci, Inst Theoret Phys, Key Lab Theoret Phys, POB 2735, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Inst Modern Phys, 509 Nanchang Rd, Lanzhou 730000, Gansu, Peoples R China 3.Sci & Technol Electromagnet Scattering Lab, Beijing 100854, Peoples R China 4.Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China |
Recommended Citation GB/T 7714 | Hu, GK,Lin, P,Zhang, YW,et al. Size scaling relation of velocity field in granular flows and the Beverloo law[J]. GRANULAR MATTER,2019,21(2):21. |
APA | Hu, GK,Lin, P,Zhang, YW,Li, LS,Yang, L,&Chen, XS.(2019).Size scaling relation of velocity field in granular flows and the Beverloo law.GRANULAR MATTER,21(2),21. |
MLA | Hu, GK,et al."Size scaling relation of velocity field in granular flows and the Beverloo law".GRANULAR MATTER 21.2(2019):21. |
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