Modelling of spheroidal drop evaporation with non-uniform temperature conditions

Abstract

The heating and evaporation of single component spherical and spheroidal drops in gaseous quiescent environment are predicted, accounting for the effect of a non-uniform distribution of the temperature at the drop surface. The analytical solution of the species conservation equations in the proper coordinate system (spherical/spheroidal) is implemented to numerically solve the energy equation in a rectangular domain. The effect of temperature non-uniformity on the local Nusselt number and global heat and evaporation rates is calculated for different species, drop deformation and gaseous temperature. KeywordsDrop evaporation, spheroidal coordinates, non-uniform Dirichlet Boundary conditions. IntroductionMost of the models predicting the drop heating and evaporation to be implemented in CFD codes for dispersed phase applications rely on the assumption that drops are spherical, thus allowing a simpler solution in spherical coordinates of the energy and species conservation equations. However, experimental investigation on liquid drops in multi-particle systems has revealed that they are subject to significant shape deformations while interacting with the carrier phase [1-3], due to the interaction of surface tension and fluid-dynamic stresses on the drop surface [3]. Numerical investigations on oscillating drops [4,5] have shown that the vapour and heat fluxes on the drop surface are not uniform and they were empirically correlated to the local mean curvature of the surface [1,6]. Analytical modelling of the heating and evaporation of spheroidal drops have shown that the local vapour and heat flux scale with the fourth root of the Gaussian curvature [7,8] and later the same result was extended to a wider class of drop shapes [9]. When dynamical simulation of droplet heating and evaporation is necessary, uniform drop temperature is often assumed, on the basis of a commonly accepted belief that the internal recirculation would maintain uniform conditions. However a more accurate simulation can be obtained by using the concept of effective conductivity, firstly introduced by [10], to account for the effect of recirculation (see also [11] and [12]) and, although this cannot properly describe the temperature field inside the droplet, it can give a better estimation of the droplet surface temperature [13] . Recent modelling of heating and evaporation of spheroidal droplets [14] revealed that the uneven distribution of fluxes on the drop surface causes a corresponding uneven distribution of temperature on the drop surface, during most of the drop lifetime. This non-uniform temperature distribution affects the heat and vapour flow fields in a non neglectful way. The motivation of the work reported here is to investigate, through a combined analytical-numerical solution of the species and energy conservation equations, the effect of non-uniform Dirichlet boundary conditions at the drop surface (for spheroidal liquid drops) on the local heat and mass transfer coefficients.