Numerical simulations, performed with a new two-phase bi-projection scheme, of the collapse of columns of glass beads with aspect ratios equal to 0.7 and 2 over a horizontal plane are reported and comparison with experiments are presented. A level-set formulation for the Navier-Stokes equations is used, so that the interface between the granular material and the ambient air is tracked. The granular flow is modeled with a viscoplastic rheology, derived from the mu(I)-rheology, resulting in a Drucker-Prager plasticity criterion combined with a spatio-temporal variable viscosity depending on the pressure and on the shear rate. The computational effort is reduced by using instead a constant viscosity. The dependence of the results upon the value of the constant viscosity, which has been reduced by two orders of magnitude, is very weak suggesting that these granular flows are mainly governed by the Drucker-Prager plasticity criterion. The rheology is formulated as a projection, allowing for an efficient computation of the plastic part of the stress tensor. Coulomb friction conditions are applied on the walls. The dynamics of the collapse and the morphology of the final deposit are accurately reproduced. Sensitivity of the results, with respect to the resolution and the basal friction coefficient, is also studied. During the collapse, the granular material consists of a basal deposit overlain by a flowing layer, which are separated by an interface that migrates upwards until the flowing layer is consumed. The time evolution of this static-mobile interface is quantified and a good agreement is found with experiments. To the best of our knowledge this is the first simulation of internal flow dynamics validated by experiments. We also report results obtained with a viscoplastic model where the dynamic pressure in the yield is replaced by the hydrostatic pressure, depending on the granular flow height. This model produces non-physically relevant solutions. Nevertheless, from a numerical point of view, it provides interesting and challenging test cases for two-phases viscoplastic simulations as the interface rolls up before the head of the granular mass falls on the bottom wall.
Plan de classement
Sciences fondamentales / Techniques d'analyse et de recherche [020]
