### AUTHOR(S)

J.K. Spelt, K. Hashemnia

### SOURCE

Chemical Engineering Science

### ABSTRACT

Discrete element modeling of granular flows is effective, but requires large numerical models. In an effort to reduce computational effort, this paper presents a finite element (FE) continuum model of the vibrationally fluidized granular flow produced by a tub vibratory finisher. The constitutive equations governing the continuum model were calibrated using the discrete element method (DEM). A constant stiffness was used for the normal contact of the polyurethane tub wall and the spherical steel media, and an effective coefficient of Coulomb friction was obtained by studying the variation of the shear and normal forces at different points along the tub wall using DEM simulations. The DEM predictions of the ratio of the tangential to normal contact forces showed that rolling of the media on the tub wall was much more common than sliding, and the average effective coefficient of friction was relatively uniform over the wall. Average values of the equivalent elastic and plastic properties of the media were used in the continuum model, neglecting the small local variations that existed within the vibrationally-fluidized bed. The bulk flow behavior of the equivalent continuum media was then studied using both Lagrangian and Eulerian FE formulations. The bulk flow velocities predicted by the Lagrangian approach were in good agreement with those obtained using DEM simulations over a wide range of tub wall amplitudes. The qualitative trend of the local impact velocity distribution at various locations in the tub predicted by the DEM agreed with the trend predicted by the continuum model using the shear rate as a measure of the granular temperature and hence local velocity. The FE simulations required approximately 8 times less computing time than the equivalent DEM.

### KEYWORDS

Continuum modeling, Discrete element modeling, Granular flow, impact, Vibrationally-fluidized, Vibratory finishing