A reference formulation for computing mass transfer rates of multi-component droplets undergoing general phase-change

Abstract

Mass diffusion is one of the key physical mechanisms inherent to the phase change of multi-component droplets. Modeling strategies often rely on simplifying assumptions such as Fick's law or the Hirschfelder and Curtiss' approximation. This work seeks to propose a droplet mass transfer formulation based on the Stefan-Maxwell equations without simplifying assumptions for diffusion closures. Such an option has already been investigated by Tonini and Cossali (Int. J. Heat and Mass Transfer, 2016). However, critical simplifications were employed in the analytical developments. In this work, we relax these simplifications with a final model that handles any number of species in general phase-change scenarios (evaporation and/or condensation), applicable to convective environments, and with no hypotheses for the diffusion coefficients' structure, such that it can be regarded as a reference. To show the impact of diffusion simplifications, this formulation is compared with two other approaches representing most mass transfer models used by the literature. In particular, the model originally proposed by Law (Combust. and Flame, 1976) is detailed here since its core results are still among the most used. The proposed formulation is validated with experimental data, and simulations are conducted for droplets of multiple fuel compositions with fixed or varying conditions at the far-away state to map diverse scenarios.