Direct comparison of Eulerian–Eulerian and Eulerian–Lagrangian simulations for particle‐laden vertical channel flow

Abstract

Particle‐laden flows in a vertical channel were simulated using an Eulerian–Eulerian, Anisotropic Gaussian (EE‐AG) model. Two sets of cases varying the overall mass loading were done using particle sizes corresponding to either a large or small Stokes number. Primary and turbulent statistics were extracted from these results and compared with counterparts collected from Eulerian–Lagrangian (EL) simulations. The statistics collected from the small Stokes number particle cases correspond well between the two models, with the EE‐AG model replicating the transition observed using the EL model from shear‐induced turbulence to relaminarization to cluster‐induced turbulence as the mass loading increased. The EE‐AG model was able to capture the behavior of the EL simulations only at the largest particle concentrations using the large Stokes particles. This is due to the limitations involved with employing a particle‐phase Eulerian model (as opposed to a Lagrangian representation) for a spatially intermittent system that has a low particle number concentration.

A Lagrangian probability-density-function model for turbulent particle-laden channel flow in the dense regime

“…Depending on the volume fraction of the particle phase within the flow, different regimes have been identified with totally different mechanisms of energy production and transfer between the phases. 1,2 Several pioneering works [3][4][5] have investigated the so-called dilute regime, where interphase coupling can be null or negligible, and the majority of the fluid-phase turbulence is generated by mean shear. In this regime, the particles exhibit several features caused by their interaction with turbulent structures.…”

“…Namely, a stochastic particle model has been developed for the case of homogeneous fully developed cluster-induced turbulence (CIT) based on the exact mesoscopic equations derived from the kinetic theory of collisional fluid-particle flows. In the present work, we test this model for an inhomogeneous application, i.e., a channel flow, comparing our results with a EL-DNS, 1 a EE-DNS, 2 and a Reynolds-stress model (RSM), 39 with a mass loading in the range 0 u 2, therefore from dilute to moderately dense flows. It is worth remarking that for the lower mass loading tested, simpler versions of the particle model 20 with only two-way coupling and without particle collisions could equally be valid.…”

Reynolds-stress modeling of cluster-induced turbulence in particle-laden vertical channel flow

“…The geometry used in the simulation cases is a vertical rectangular channel [24,32]. The dimensions of the EE-AG and EL simulations can be seen in Table I.…”

“…The low-mass-loading cases with large particles corresponding to a mass loading of 0.2, 1, and 2 using the EE-AG model are also omitted due their extremely small particle number density. The EE-AG model does not accurately capture the behavior of spatially intermittent systems such as these [32].…”

“…The application of steadystate equations to the full channel cannot capture this transient behavior, and its results would be indistinguishable from that seen in [19]. Additionally, turbulent statistics collected from both the previously applied EL model [13] and a highly refined EE anisotropic-Gaussian (EE-AG) model [30,32] of the channel are used as points of comparison and to inform the turbulent closures chosen for the model developed in this work.…”