Direct numerical simulation of an evaporating turbulent diluted jet-spray at moderate Reynolds number

The evaporation of liquid droplets dispersed in jet-sprays is involved in many industrial applications and natural phenomena. Despite the relevance of the problem, a satisfactory comprehension of the mechanisms that regulate the process has still not been achieved. Indeed, a wide range of turbulent scales and an enormous number of droplets are typically involved, causing the numerical and theoretical tackling of the problem to be challenging. In this context, we address the Direct Numerical Simulation (DNS) of a turbulent jet-spray at a bulk Reynolds number Re= 10, 000. We focus on the effect of the jet Reynolds number on the evaporation process and the preferential segregation of droplets. The analysis is conducted by comparing the outcomes of the present DNS with that from a lower Reynolds number one in corresponding conditions, Re= 6, 000. The problem is addressed by employing the point-droplet approximation in the hybrid Eulerian-Lagrangian framework. We present detailed statistical analyses of both the gas and the dispersed phases. We found that the mean droplet vaporization length grows as the bulk Reynolds number is increased from Re= 6, 000 to Re= 10, 000, while keeping all the remaining conditions fixed. We attribute this result to the complex interaction between the inertia of the droplets and the dynamics of the turbulent gaseous phase. In particular, at the higher Reynolds number, the effect of the faster turbulent fluctuations of the jet mixing layer, which tend to fasten the process, is compensated by the slower mass transfer from the liquid droplets to the surrounding environment. We also observe intensive preferential segregation of the dispersed phase that originates from the entrainment of dry environmental air into the mixing layer and is intensified by small-scale clustering in the far-field region. We show how the preferential segregation is responsible for a strongly heterogeneous Lagrangian evolution of the dispersed droplets. All these aspects contribute to the Reynolds-number dependence of the overall droplet evaporation rate. Finally, we discuss the accuracy of the d-square law, often used in spray modelling, for present cases. We found that using this law based on environmental conditions leads to a relevant overestimation of the droplet evaporation rate.