A DEM-DLM/FD method for direct numerical simulation of particulate flows: Sedimentation of polygonal isometric particles in a Newtonian fluid with collisions

Abstract

An efficient direct numerical simulation method to tackle the problem of particulate flows at moderate to high concentration and finite Reynolds number is presented. Our method is built on the framework established by Glowinski and his co-workers [Glowinski R, Pan TW, Hesla TI, Joseph DD. A distributed lagrange multiplier/fictitious domain method for particulate flow. Int J Multiphase Flow 1999;25:755–94] in the sense that we use their Distributed Lagrange Multiplier/Fictitious Domain (DLM/FD) formulation and their operator-splitting idea but differs in the treatment of particle collisions. Compared to our previous works [Yu Z, Wachs A, Peysson Y. Numerical simulation of particle sedimentation in shear-thinning fluids with a fictitious domain method. J Non Newtonian Fluid Mech 2006;136:126–139; Yu Z, Shao X, Wachs A. A fictitious domain method for particulate flow with heat transfer. J Comput Phys 2006;217:424–52; Yu Z, Wachs A. A fictitious domain method for dynamic simulation of particle sedimentation in Bingham fluids. J Non Newtonian Fluid Mech 2007;145:78–91], the novelty of our present contribution relies on replacing the simple artificial repulsive force based collision model usually employed in the literature by an efficient Discrete Element Method (DEM) granular solver. The use of our DEM solver enables us to consider particles of arbitrary shape (at least convex) and to account for actual contacts, in the sense that particles actually touch each other, in contrast with the repulsive force based collision model. We validate GRIFF, 1 ▪ GRIFF stands for “GRains In Fluid Flow”. 1 our numerical code, against benchmark problems and compare our predictions with those available in the literature. Results, which, to the best of our knowledge, have never been reported elsewhere, on the 2D sedimentation of isometric polygonal particles with collisions are presented.