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 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 Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS] 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 China2.Chinese Acad Sci, Inst Modern Phys, 509 Nanchang Rd, Lanzhou 730000, Gansu, Peoples R China3.Sci & Technol Electromagnet Scattering Lab, Beijing 100854, Peoples R China4.Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China Recommended CitationGB/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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