Particle Collisions in a Lumped Particle Model (Communications in Computational Physics, 2011)
This paper presents an extension of the lumped particle model in [1] to includethe effects of particle collisions. The lumped particle model is a flexible frameworkfor the modeling of particle laden flows, that takes into account fundamentalfeatures, including advection, diffusion and dispersion of the particles. In this paper,we transform a binary collision model and concepts from kinetic theory into acollision procedure for the lumped particle framework. We apply this new collisionprocedure to investigate numerically the role of particle collisions in the hindered settlingeffect. The hindered settling effect is characterized by an increase in the effectivedrag coefficient CD that influences each particle in the flow. This coefficient is given byCD =(1−φ)−nC∗D, where φ is the volume fraction of particles, C∗D is the drag coefficientfor a single particle, and n ≃ 4.67 for creeping flow. We obtain an approximation forCD/C∗D by calculating the effective work done by collisions, and comparing that to thework done by the drag force. In our numerical experiments, we observe a minimalvalue of n = 3.0. Moreover, by allowing high energy dissipation, an approximationfor the classical value for creeping flow, n = 4.7, is reproduced. We also obtain highvalues for n, up to n=6.5, which is consistent with recent physical experiments on thesedimentation of sand grains.