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- Title
Size scaling relation of velocity field in granular flows and the Beverloo law.
- Authors
Hu, Gaoke; Lin, Ping; Zhang, Yongwen; Li, Liangsheng; Yang, Lei; Chen, Xiaosong
- Abstract
In a hopper with cylindrical symmetry and an aperture of radius R, the vertical velocity of granular flow vz depends on the distance from the hopper's center r and the height above the aperture z and vz=vz(r,z;R). We propose that the scaled vertical velocity vz(r,z;R)/vz(0,0;R) is a function of scaled variables r/Rr and z/Rz, where Rr=R-0.5d and Rz=R-k2d with the granule diameter d and a parameter k2 to be determined. After scaled by vz2(0,0;R)/Rz, the effective acceleration aeff(r,z;R) derived from vz is a function of r/Rr and z/Rz also. The boundary condition aeff(0,0;R)=-g of granular flows under earth gravity g gives rise to vz(0,0;R)∝gR-k2d1/2. 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 vz(r,z;R) and vz(0,0;R). From the size scaling relations, we obtain the mass flow rate of D-dimensional hopper W∝g(R-0.5d)D-1(R-k2d)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.
- Subjects
GRANULAR flow; VELOCITY; FLOW velocity; DISCRETE element method; EARTHFLOWS
- Publication
Granular Matter, 2019, Vol 21, Issue 2, p1
- ISSN
1434-5021
- Publication type
Article
- DOI
10.1007/s10035-019-0872-z