Evaluation of equilibrium and non-equilibrium evaporation models for many-droplet gas-liquid flow simulations

Abstract

A variety of liquid droplet evaporation models, including both classical equilibrium and non-equilibrium Langmuir–Knudsen formulations, are evaluated through comparisons with experiments with particular emphasis on computationally efficient procedures for gas–liquid flow simulations. The models considered are those used in droplet laden flow calculations such as direct numerical simulations for which large numbers of individual (isolated) droplet solutions are obtained. Diameter and temperature evolution predictions are made for single-component droplets of benzene, decane, heptane, hexane and water with relatively large initial sizes ∼1 mm vaporizing in convective air flows. All of the models perform nearly identically for low evaporation rates at gas temperatures significantly lower than the boiling temperature. For gas temperatures at and above the boiling point, large deviations are found between the various model predictions. The simulated results reveal that non-equilibrium effects become significant when the initial droplet diameter is <50 μm and that these effects are enhanced with increasing slip velocity. It is additionally observed that constant properties can be used throughout each simulation if both the gas and vapor values are calculated at either the wet-bulb or boiling temperature. The models based on the Langmuir–Knudsen law and a corrected (for evaporation effects) analytical heat transfer expression derived from the quasi-steady gas phase assumption are shown to agree most favorably with a wide variety of experimental results. Since the experimental droplet sizes are all much larger than the limit for non-equilibrium effects to be important, for these conditions the most crucial aspect of the current Langmuir–Knudsen models is the corrected analytical form for the heat transfer expression as compared to empirical relations used in the remaining models.