STEADY INJECTION OF IDENTICAL CLUSTERS OF EVAPORATING DROPS EMBEDDED IN JET VORTICES

A model has been developed that describes the evaporation of clusters of drops in a flowing gaseous jet. Each one of these clusters is embed ded into a coherent vortex and the drops evaporate as the clusters con vect downstream together with the vortex. Because there is a continuou s injection of clusters, each cluster represents in fact a statistical average of clusters at that particular location. Thus, the formulatio n contains a conservation equation for the cluster number density, con servation equations for the gas in the jet, and conservation equations for the drops in the cluster and the vortex containing the cluster. T he cluster and vortex models are coupled to the gaseous jet model thro ugh boundary conditions. The heat necessary to evaporate the drops com es from the surroundings of the gaseous jet, and this is described thr ough a global, diffusive entrainment model. It is assumed that the tur bulent diffusion coefficient is proportional either to the local vorte x 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 continuou sly 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 c luster at previous times. parametric studies cover the influence of th e initial air/fuel mass ratio, the entrainment coefficient, and the in itial drop and gas velocities inside the vortices. The results show th at quantitative predictions of the evaporation time, the penetration o f the clusters into the ambient, and the temperature of the jet depend on details of the entrainment of hot gas into the jet.