Improved modelling of disperse multi-phase transport based on numerical simulation and PDF analysis

Abstract

In this work probability density function (PDF) models are used as a method for studying the statistical distribution of particles in turbulent flows, which is of interest in many industrial and environmental processes. This approach involves derivation of a transport equation for describing the evolution of the joint PDF of particle variables. In different flow configurations the PDF approach identifies various contributions to the particle phase mass flux that act as additional drift and diffusion terms. These terms, which are critical in the formulation of two-fluid models, require closure. In order to evaluate the effect of the different flux contributions arising in the various flow configurations, these terms are considered in the context of both homogeneous and inhomogeneous flows. In the case of homogeneous flows the enhancement of the settling rate of inertial particles under an applied body force, specifically gravity, is investigated. Inhomogeneous turbulence is used to study the clustering of particles in a framework associated with the behaviour of particle pair dynamics in homogeneous flows. Existing closures based on simple local approximations are shown to neglect the contributions of interest to the particle phase mass flux, and an improved methodology is proposed which takes into account underlying physical mechanisms behind the observed behaviour, and consists of modelling various correlations that arise from the PDF formulation. The performance of this closure strategy is evaluated making use of particle trajectory simulations in a synthetic flow field generated using Kinematic Simulation (KS). The Eulerian two-point, two-time fluctuating velocity correlations for the continuous phase are central to the modelling, and these are determined in the specification of the flow field. Similarly the particle response tensor to perturbations in the continuous phase is computed allowing for exact evaluation of the unclosed terms. A linear drag law is used in the particle equation of motion, and the influence of both Stokes number and applied body forces on the increase in particle settling rate and clustering is investigated. In agreement with previous work it is seen that the mechanism responsible for these effects can be quantified in terms of the preferential sampling of strain over rotation by inertial particles due to interaction with the structures in the flow field.