Heat flux and forces acting on a vaporising droplet in a superheated vapor flow

Abstract

In this paper, we present Direct Numerical Simulations of the interaction between a vaporising spherical droplet and a high-temperature vapour flow. The numerical simulations investigate on the Nusselt number and drag force when varying the Reynolds, Prandtl and Spalding numbers. Classical correlations based on experimental and numerical approaches, are revisited by performing simulations with interface capturing methods. The parametric study carried out by varying Reynolds and Spalding numbers, shows a quantitative agreement with previous correlations on the Nusselt number for a given Prandtl number. However, new trends are obtained by varying the Prandtl number. In particular, it is observed that the Nusselt number variations depend only on the Péclet number. Regarding the total force, we present an analysis on the three components acting on a vaporising droplet, i.e., the forces related to viscous effects, pressure effects and vaporisation effects. Our numerical investigations enable to clarify the impact of the component related to phase change, and a simple semi-empirical model is proposed to describe this force. It is shown that the three components of the total drag force depend on all the dimensionless numbers, if considered one by one, whereas the sum of their contributions is almost independent on the Prandtl and Spalding numbers, unlike what suggests usual correlations. The importance of a new dimensionless number based on the ratio between the Spalding and the Prandlt numbers is also highlighted to describe the flow around the droplet.