Evaluation of the Eulerian and Lagrangian Approaches to model the dispersed phase in non-uniform turbulent particle-ladens flows

Abstract

This paper deals with non-uniform turbulent particle-laden jet flows. These flows are frequently found in industry and are characterized by a large value of the particle fluctuating-velocity anisotropy, much larger than the one corresponding to the carrier phase. As the classical Eulerian and Lagrangian approaches to the description of the dispersed phase fail in the estimation of such anisotropy, two extended Eulerian models for the particle phase are introduced in this work; one of them is algebraic [the Algebraic Particle Stress (APS) model] and the other one is differential [the Particle Reynolds Stress (PRS) model]. The performance of these two Eulerian models and a classical Lagrangian approach is evaluated against some experimental measurements available in the literature. The PRS model provides results in good agreement with the experiments for all available variables, including the particle fluctuating-velocity anisotropy. The differential equations that describe the dispersed phase in the PRS model are decomposed into their basic terms and analyzed separately. In the case of high inertia particles, it is shown that modeling of the so-called interaction terms is the crucial point, as these terms govern the existing equilibria in the Eulerian equations that describe the dispersed phase.