Numerical Investigations of Drop Solidification by a Front-Tracking Method

We present a front-tracking/finite difference method for simulation of drop solidification, where the melt is confined by its own surface tension. The problem includes temporal evolution of three interfaces, i.e. solid–liquid, solid–air, and liquid–air, that are explicitly tracked under the assumption of axisymmetry. The solid–liquid interface is propagated with a normal velocity that is calculated from the normal temperature gradient across the front and the latent heat. The liquid–air front is advected by the velocity interpolated from nearest bulk fluid flow velocities. Method validation is carried out by comparing computational results with exact solutions for two-dimensional Stefan problems, and with related experiments. We then use the method to investigate a drop solidifying on a cold plate in which there exists volume expansion due to density difference between the solid and liquid phases. Effects of the tri-junction in terms of growth angles on the solidification process are also investigated. Computational results show that a decrease in the density ratio of solid to liquid or an increase in the growth angle results in an increase in the height of the solidified drop. In addition, reducing the gravitational effect also increases the drop height after solidification.Copyright © 2014 by ASME