On the computation of steady hopper flows III: Model comparisons

Gravity flows of granular materials through hoppers are considered. For hoppers shaped as general nonaxisymmetric cones, i.e., “pyramids”, the flow inherits some simplified features from the geometry: similarity solutions can be constructed. Using two different plasticity laws, namely Matsuoka–Nakai and von Mises, those solutions are obtained by solving first-order nonlinear partial differential algebraic systems for stresses, velocities, and a plasticity function. dospectral discretization is applied to both models and the resulting flow fields are examined. Some similarities are found, but important differences appear, especially with regard to velocities near the wall and normal wall stresses. Preliminary comparisons with recent experiments [J.F. Wambaugh, R.P. Behringer, Asymmetry-induced circulation in granular hopper flows, in: R. Garcia-Rojo, H.J. Herrmann, S. McNamara (Eds.), Powders and Grains, 2005, pp. 915–918] based on the present results indicate that for slow granular flows the lesser known Matsuoka–Nakai plasticity law yields better results than more common models based on a von Mises criterion.