This paper presents a lumped particle model for simulating a large number of particles. The lumped particle model is a flexible framework in modeling particle flows, embodying fundamental features that are intrinsic in particle laden flow, including advection, diffusion and dispersion. In this paper, the particles obey a simplified version of the Bassinet-Boussinesq-Oseen equation for a single spherical particle. However, instead of tracking the individual dynamics of each particle, a weighted spatial averaging procedure is used where the external forces are applied to a "lump" of particles, from which an average position and velocity is derived. The temporal evolution of the particles is computed by partitioning the lumped particle into smaller entities, which are then transported throughout the physical domain. These smaller entities recombine into new particle lumps at their target destinations. For particles prone to the effects of Brownian motion or similar phenomena, a symmetric spreading of the particles is included as well. Numerical experiments show that the lumped particle model reproduces the effects of Brownian diffusion and uniform particle transport by a fluid and gravity. The late time scale diffusive nature of particle motion is also reproduced.

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AbstractFirst introduced in, the lumped particle framework is a flexible and numerically efficient framework for the modelling of particle transport in fluid flow. In this paper, the framework is expanded to simulate multicomponent particle-laden fluid flow. This is accomplished by introducing simulation protocols to model particles over a wide range of length and time scales. Consequently, we present a time ordering scheme and an approximate approach for accelerating the computation of evolution of different particle constituents with large differences in physical scales. We apply the extended framework on the temporal evolution of three particle constituents in sandladen flow, and horizontal release of spherical particles. Furthermore, we evaluate the numerical error of the lumped particle model. In this context, we discuss the Velocity-Verlet numerical scheme, and show how to apply this to solving Newton’s equations within the framework. We show that the increased accuracy of the Velocity-Verlet scheme is not lost when applied to the lumped particle framework.

This paper presents an extension of the lumped particle model in [1] to include the effects of particle collisions. The lumped particle model is a flexible framework for the modeling of particle laden flows, that takes into account fundamental features, including advection, diffusion and dispersion of the particles. In this paper, we transform a binary collision model and concepts from kinetic theory into a collision procedure for the lumped particle framework. We apply this new collision procedure to investigate numerically the role of particle collisions in the hindered settling effect. The hindered settling effect is characterized by an increase in the effective drag coefficient CD that influences each particle in the flow. This coefficient is given by , where ϕ is the volume fraction of particles, is the drag coefficient for a single particle, and n ≃ 4.67 for creeping flow. We obtain an approximation for CD/CD by calculating the effective work done by collisions, and comparing that to the work done by the drag force. In our numerical experiments, we observe a minimal value of n = 3.0. Moreover, by allowing high energy dissipation, an approximation for the classical value for creeping flow, n = 4.7, is reproduced. We also obtain high values for n, up to n = 6.5, which is consistent with recent physical experiments on the sedimentation of sand grains.