A three-dimensional numerical model for incompressible two-phase flow of a granular bed submitted to a laminar shearing flow

Julien Chauchat (1) , Médale Marc (1)

1 IUSTI - Institut universitaire des systèmes thermiques industriels

A numerical model for the simulation of incompressible two-phase flows of a flat granular bed submitted to a laminar shearing flow is presented, considering a two-fluid model and a mixed-fluid one. The governing equations are discretized by a finite element method and a penalisation method is introduced to cope with the incompressibility constraint. A regularisation technique is used to deal with the visco-plastic behaviour of the granular phase. Validations are carried out on three flow test cases: a Bingham fluid between two infinite parallel planes, a Bingham fluid in a square lid-driven cavity and a Newtonian fluid over a granular bed in a two-dimensional configuration, for which we compare our numerical results with existing analytical or numerical results. The accuracy and efficiency of the numerical models have been compared for the two formulations of the two-phase flow model. It turns out that the two-fluid model requires ten times more CPU time than the mixed-fluid one for a comparable accuracy, which can be achieved provided one takes a smaller regularisation parameter in the latter model. Finally, three-dimensional computations are presented for the flow of a Newtonian fluid over a granular bed in a square and circular cross-section ducts.

Mots clés: Two-phase flow model; Fluid-particle coupling; Visco-plastic flow; Regularisation technique; Quadratic finite element

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Julien Chauchat, Médale Marc. A three-dimensional numerical model for incompressible two-phase flow of a granular bed submitted to a laminar shearing flow. Computer Methods in Applied Mechanics and Engineering, 2009, 199 (9-12), pp.Pages 439-449. ⟨10.1016/j.cma.2009.07.007⟩. ⟨hal-00619372⟩