1988 Volume 74 Issue 12 Pages 2262-2269
A mathematical model, capable of describing the macroscopic movement of an assembly of discs in a hopper, was developed based on the constitutive equations described by Voigt-Kelvin rheological model with a slider and on the equations of motion for translation and rotation of each disc. The validity of the present model was confirmed by comparing the results, such as the order of discs discharged from the hopper, arrangement of discs after charging in the hopper and stress distribution at the wall, obtained from calculations with the corresponding ones obtained by experiments as well as JANSSEN'S equation.
The present model was successfully applied to the macroscopic flow of the assembly of granular materials of different disc size, subjected to gravitational force in a hopper.
The installation of a repulsion box in the upper part of the hopper was also simulated and resulted in the decrease in the variation of disc size during discharge through the suppression of small disc segregation during charge, while it had insignificant effect on the deposit profile and the order of discharge.
The present model was found to precisely describe frictional wall effect in solid flow and abnormal flow behavior, such as bridge formation, in comparison with the conventional continuous potential flow model.