Steady injection of identical clusters of evaporating drops embedded in jet vortices

Abstract

A model has been developed that describes the evaporation of clusters of drops in a flowing gaseous jet. Each one of these clusters is embedded into a coherent vortex and the drops evaporate as the clusters convect downstream together with the vortex. Because there is a continuous injection of clusters, each cluster represents in fact a statistical average of clusters at that particular location. Thus, the formulation contains a conservation equation for the cluster number density, conservation equations for the gas in the jet, and conservation equations for the drops in the cluster and the vortex containing the cluster. The cluster and vortex models are coupled to the gaseous jet model through boundary conditions. The heat necessary to evaporate the drops comes from the surroundings of the gaseous jet, and this is described through a global, diffusive entrainment model. It is assumed that the turbulent diffusion coefficient is proportional either to the local vortex strength or to the cluster velocity and the multiplier is named the entrainment coefficient. Results are presented here for the stationary case representing the situation when identical clusters are continuously injected and the injection rate is constant. Thus, if a “snapshot” of the calculation is taken at any time, the cluster is observed at that time and the clusters in its wake represent the history of the cluster at previous times. Parametric studies cover the influence of the initial air/fuel mass ratio, the entrainment coefficient, and the initial drop and gas velocities inside the vortices. The results show that quantitative predictions of the evaporation time, the penetration of the clusters into the ambient, and the temperature of the jet depend on details of the entrainment of hot gas into the jet.