DNS and assessment of the D²-law for evaporation in turbulent diluted sprays

In many natural and applicative environments, the evaporation of dispersed droplets within high Reynolds number turbulent sprays plays an important role whose significance has been further emphasized during the outbreak of the COVID-19 pandemic.  Actually, the virus SARS-CoV-2 is transmitted among human subjects through respiratory droplets expelled from an infected source during spasmodic events, such as talking, coughing, and sneezing. To better understand and model the basic mechanisms governing this phenomenon, we conducted numerical studies of a dilute turbulent spray at Re=10,000 using a Direct Numerical Simulation approach, performing a detailed statistical analysis. We firstly observed intensive preferential segregation of the dispersed phase which originates from the entrainment of environmental dry air into the mixing layer and is intensified by small-scale clustering in the far-field region, contributing to extend the spray vaporization length. On the other hand, we showed that employing the classical D²-law, often used in modeling spray evaporation, would lead to an extreme overestimation of the droplet evaporation rate, a phenomenon also recently reported in unsteady respiratory flows. From our DNS dataset, we noted that the model inaccuracy was mainly induced by the assumed value for the droplet temperature. Based on that, we propose a revision of the classical D²-law capable to accurately determine droplet evaporation rate in dilute conditions by a proper estimate of the asymptotic droplet properties. Finally, our revised D²-law model has been tested against DNS of diluted turbulent evaporating sprays showing very good agreements.