Direct numerical simulation of an evaporating turbulent diluted jet

The evaporation of dispersed, liquid droplets in jet-sprays occurs in several industrial applications and in natural phenomena. Despite the relevance of the problem, a satisfactory comprehension of the mechanisms involved has not still be achieved because of the wide range of turbulent scales and the huge number of droplets involved. In this context, we address a DNS of a turbulent jet spray at relatively high Reynolds number, i.e. Re=10,000. We focus on the effect of the jet Re on the evaporation process and the preferential segregation of droplets, comparing the outcomes also with a DNS at lower Reynolds number, Re = 6,000, in corresponding conditions. The problem is addressed in the hybrid Eulerian-Lagrangian framework employing the point-droplet approximation. Detailed statistical analysis on both the gas and dispersed phases are presented. We found that the droplet vaporization length grows as the bulk Re is increased from Re = 6,000 to Re = 10,000 keeping other conditions fixed. We attribute this result to the complex interaction between the inertia of the droplets and the turbulent gaseous phase dynamics. In particular, at higher Re, the slower droplet mass transfer is not able to comply with the faster turbulent fluctuations of the mixing layer that tend to fasten the process. We also found an intense droplet clustering which is originated by entrainment of dry air in the mixing layer and intensified by the small-scale clustering mechanism in the far-field region. We will show how clustering creates a strongly heterogeneous droplet Lagrangian evolution. All these aspects contribute to the Re dependence of the overall droplet evaporation rate. Finally, we discuss the accuracy of the d-square law, often used in spray modeling, for present cases. We found that using this law based on environmental conditions the droplet evaporation rate is overestimated.