1993 Volume 33 Issue 6 Pages 664-671
Solid descending flow due to gravity is frequently applied to industrial processes. Several kinds of models have been proposed like the plug flow model, the potential flow model, the kinematic model, etc. In this study, a viscous flow model based on the Navier-Stokes equation has been developed and was compared with the potential flow and the kinematic models. Both two and three dimensional experimental apparatuses have been constructed to observe the velocity fields.
The concept of solid viscosity was quoted to describe the friction between particles and the value was obtained from the experimental data. Slip boundary condition was used at the wall and the friction between particles and the wall or the dead zone was expressed by the Fanning equation.
Navier-Stokes equation was applied to simulate the solid flow. The good agreement between the observed and computed results was obtained in different scale apparatuses at different solid descending velocities. The computation results gave about 0.07 Pa·s as the solid viscosity of sand particles with the diameter of 0.001-0.002 m. The solid-gas countercurrent flow was also simulated by the Navier-Stokes equation with the same value of solid viscosity.