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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 PublicationGRANULAR MATTER
AbstractIn 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.
Subject AreaMaterials Science ; Mechanics ; Physics
MOST Discipline CatalogueMaterials Science, Multidisciplinary ; Mechanics ; Physics, Applied
Indexed BySCIE
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Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.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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