A multiple level-set approach for modelling containerless freezing process

Abstract

We propose a multiple level-set model to represent the physics governing the three-phase solidification problem. The model couples thermal characteristics of the freezing front with the dynamics of droplet interface. To deal with liquid, solid, and gas phases, two distinct level-sets are used. The liquid-gas interface which is represented by a level-set moves with an external velocity field that is obtained from the Navier-Stokes equations. The solid-liquid interface, on the other hand, evolves according to the freezing rate of the liquid. The solid-liquid level-set is comprised of an active and passive part. The active segment of the level-set evolves based on temperature gradients and the latent heat of fusion. The passive segment, however, is merely utilized to impose an angle at the tri-junction point. We propose a Hamilton-Jacobi type equation to impose constant or variable angles at the tri-junction point. In order to consider the effect of volume expansion we modify the continuity, and the energy equation. Importantly, in the case of expansion during solidification we can capture the pointy shape on top of the freezing droplet. For validation we compare numerical results with the analytical Stefan problem with and without the density expansion. In addition, we use experimental results of water droplet freezing, available in the literature, to examine the accuracy of the freezing rate, and the droplet morphological.