Abstract
Granular flows of 200 μm particles and the pile formation in a flat-bottomed hopper and bin in the presence of air and in a vacuum were predicted based on three-dimensional numerically empirical constitutive relations using Smoothed Particle Hydrodynamics and Computational Fluid Dynamics methods. The constitutive relations for the strain rate independent stress have been obtained as the functions of the Almansi strain including the large deformation by the same method as Yuu et al. [1]. The constitutive relations cover the elastic and the plastic regions including the flow state and represent the friction mechanism of granular material. We considered the effect of air on the granular flow and pile by the two-way coupling method. The granular flow patterns, the shapes of piles and the granular flow rates in the evolution are compared with experimental data measured under the same conditions. There was good agreement between these results, which suggests that the constitutive relations and the simulation method would be applicable for predicting granular flows and pile formation with complex geometry including free surface geometry. We describe the mechanisms by which the air decreases the granular flow rate and forms the convergence granular flow below the hopper outlet.
Highlights
Granular flows through a hopper and granular piles subsequently formed on the bottom of a storage vessel have been topics of extensive research for several decades
The calculated and the experimental flow patterns shown in these figures indicate that the granular flow reaches the bottom of the bin and the granular material begins to pile on the bottom of the bin
We have obtained the numerically empirical constitutive equations for the strain rate-independent stress as the functions of the Almansi strain including the large deformation by the same method as
Summary
Granular flows through a hopper and granular piles subsequently formed on the bottom of a storage vessel have been topics of extensive research for several decades. The constitutive relations needed for closure in the continuum approach have been derived by many kinds of models Many of these studies have been reviewed by Yuu and Umekage [1]. Some other recent studies using the continuum model are as follows: Aranson and Tsimring presented the flows in inclined chutes, avalanches, rotating drums, simple shear cells and some unsteady flows without many fitting parameters using the continuum theory of partially fluidized granular flows [2,3]. They applied dissipative dynamics for the order parameter. The calculated stress ratio and the volumetric strain versus the axial strain in tri-axial test were compared with experimental results and fairly good agreements were observed between them
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