The Effect of Temperature Dependence of Density and Mass Diffusion Coefficient on the Mass Transport From a Drop Evaporating in Hot Gaseous Environment

Species, energy and momentum conservation equations are solved in spherical symmetry and under ideal gas approximation, to yield an analytical model capable to evaluate the heat transfer and the evaporation rate from a drop under quasi-steady conditions, accounting for the temperature dependence of mixture density and diffusion coefficient. The model is applied to predict the evaporation rate from water and hydrocarbon droplets under pressure and temperature conditions of interest for applicative fields, like fire control and combustion. The results obtained by the proposed model are compared with those from the most commonly used ones where mass diffusion coefficient and gas density are kept constant to an average value. INTRODUCTION Drop evaporation in a hot gaseous environment is of fundamental importance for a wide range of engineering applications, like in spray combustion, spray cooling, spray drying, fire suppression, etc. The evaporation process involves simultaneous heat and mass transfer and a wide literature is available on the modelling of the complex physical phenomena involved (see [1] for a thorough review). To numerically simulate evaporating spray using CFD methodologies, detailed models based on single drop analysis have to be simplified to be CPU efficient and this forced the introduction of many simplifying hypotheses to develop the nowadays available evaporation models. Constant properties of the gas mixture, quasi-steadiness, drop sphericity are among the most common approximations, and the most frequently used models (see for example [2]) are based on these assumptions, although recently, attempts to relieve some of them became available in the open literature [3-4]. Modelling of mass transfer and thermal phenomena occurring within the liquid phase in an evaporating drop has been object of deep investigation and an extensive literature became available in the latest years (see [1,5] for reference). The most simplified models, used in many conventional CFD codes for spray applications, assume infinite liquid thermal conductivity when modelling the drop heating, neglecting temperature gradient inside the drop [5]. There exists experimental evidence [6,7] that contradicts this assumption and to cope with these findings this issue has been addressed introducing a finite effective thermal conductivity, which takes into account also the effect of liquid recirculation inside the drop [1,5]. The totality of the analytical evaporation models implemented in commercial CFD codes neglects moving boundary effect due to radius shrinking; this hypothesis has been removed by Sazhin et al. in [8,9], who included the effect of a moving boundary to solve the conservation equations in the liquid phase. The comparison with previous models shows that drop shrinking has a non neglectful effect on liquid temperature prediction, yielding longer evaporation times compared to the conventional approach and reaffirming that such effect cannot be ignored when accurate predictions are needed. When a drop is injected into a hot gas, large temperature gradients are achieved and the previously mentioned constant property approximation becomes questionable since at least gas density and diffusion coefficient have a strong dependence on temperature. The use of an average value for all those properties that are expected to significantly change with temperature, commonly obtained by the ‘1/3-rd rule’ [10], may not be enough to correctly catch the main features of the phenomenon. Recently it was shown that a model that takes into account gas temperature and density gradient effects may yield significant differences respect to the classical ones, and it may better perform when compared with available experimental results obtained under high gas temperature conditions [3]. Among other parameters, the diffusion coefficient of a vapour in a gaseous mixture shows a significant temperature dependence, statistical thermodynamics [11] predicts a power law dependence on the absolute temperature with exponent equal to 3/2, while the widely used FuellerScheller-Giddings correlation [12] suggests a value of 7/4 for the same exponent. Numerical models for drop evaporation studies have been deeply refined over the decades including more complex physical aspects like drop composition, shape, interaction with other drops and/or solid surfaces (see [13,14] for reference) and obviously also detailed model to evaluate the temperature 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics