Modelling density variation due to phase change during droplet impact

A three-dimensional model of droplet impact and solidification has been modified to include the effects of density variation during phase change. The governing equations for conservation of mass, momentum, and energy, and a volume of fluid (VOF) equation are derived by assuming different but constant solid and liquid densities. A fixed-grid control volume discretization of the momentum and energy equations, combined with a volume-tracking algorithm to track free surfaces, has been developed.; The numerical model was validated against the Stefan problem and a planar solidification problem, for which analytical solutions are available. The numerical and analytical solutions were in good agreement. The numerical model was then applied to simulate solidification shrinkage of molten tin in a rectangular mold. Finally, the effects of density variation during phase change were studied during the impact and solidification of a tin droplet impinging onto a stainless steel substrate.