Development of a three-dimensional Eulerian model of droplet-wall interaction mechanisms

A wide variety of engineering applications involve the flow of particulate multiphase systems, featuring discrete liquid droplets dispersed in a continuous gas phase. Specific industrial examples range from fuel injection technologies over the optimization of multiphase segregation processes commonly encountered in petrochemical applications to aircraft in-flight icing control. A detailed understanding of dispersed phase characteristics such as local droplet velocity and volumetric fraction is required for design purposes and may be obtained from a numerical solution of the equations governing droplet motion.;A fundamental choice between Lagrangian and Eulerian reference frames presents itself in the formulation of the governing equations. While the physically intuitive Lagrangian approach treats the dispersed phase as a set of discrete particles that are individually tracked through the computational domain, the Eulerian formulation considers the dispersed phase as a continuum. The use of an Eulerian formulation to describe the evolution of discrete particles may appear counter-intuitive from a physical standpoint; however, advantages with respect to computational effort, numerical accuracy and accommodation of geometric complexity strongly suggest the use of an Eulerian formulation.;In order to accurately predict droplet behavior in the vicinity of a solid system boundary, droplet-wall interactions must be accounted for in the governing mathematical model. Due to current limitations in computational capacity, an industrially viable simulation is necessarily based on a semi-empirical description of the droplet-wall interaction process. Since empirical correlations are inherently Lagrangian in nature, the associated information must be transformed from a Lagrangian to an Eulerian frame of reference. This transformation, however, is not obvious and as a consequence no Eulerian impact models have been reported in the published scientific literature to date. A detailed derivation of an Eulerian model of the droplet-wall interaction process is presented along with a comparison of numerical and experimental results demonstrating the model's current simulation capabilities and suggested future improvements.