Steady-state granular flow in a 3D cylindrical hopper with flat bottom: Macroscopic analysis

H. P. Zhu, A. B. Yu

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The information of a hopper flow at a particle scale, obtained from discrete particle simulation, is used to investigate the macroscopic dynamic behaviour of granular flow in a cylindrical hopper with flat bottom by means of an averaging technique. The macroscopic properties including velocity, mass density, stress and couple stress are quantified under the cylindrical coordinate framework, and an effort is made to link these variables to the microscopic variables considered. The velocity and density distributions are first illustrated to match qualitatively the experimental and numerical results, confirming the validity of the proposed averaging method. Four components of stress, T zz , T rr , T rz and T zr , and two dominant components of couple stress, M r θ and M z θ , are then investigated in detail. It is shown that large vertical normal stress is mainly observed in the region close to the bottom corner, large radial normal stress is observed within the particle bed as well as the bottom corner, and large shear stresses in the region adjacent to the vertical wall. The four stresses are relatively small in a region close to the orifice. Their magnitudes are mainly contributed by the interaction forces between particles and between particles and walls. However, the transport of particles also plays a significant role at the orifice, especially, in the vertical normal stress. The couple stress can be ignored except for the regions close to the vertical and bottom walls, where the most dominant components are M r θ adjacent to the vertical wall and M z θ close to the bottom wall. The magnitudes of these macroscopic variables depend on the geometric and physical parameters of the hopper and particles such as the orifice size and wall roughness of the hopper, and the friction and damping coefficients between particles although their spatial distributions are similar.

Original languageEnglish
Pages (from-to)97-107
Number of pages11
JournalGranular Matter
Issue number2-3
Publication statusPublished - 1 Jul 2005
Externally publishedYes


  • Continuum mechanics
  • Discrete particle simulation
  • Granular dynamics
  • Hopper flow

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