Abstract

This thesis focuses on numerical simulation of the freezing process of liquid droplets on cold substrates. Solidification of droplets is one of the most challenging phenomenon for numerical modelling since various complicated physical mechanisms are involved. Dealing with the jump conditions at interfaces has been a long-term concern in numerical simulations. Moreover, the tri-junction point where three-phases come into contact requires special treatment. Furthermore, density expansion during freezing process should be taken into account.

In this thesis, we propose a level-set based model to represent three-phase solidification physics. Liquid and solid interfaces are represented by two different level-sets in order to deal with the phases separately. The liquid-gas interface is advected under an external velocity field obtained from solving Navier-Stokes equations. The solid-liquid level-set, on the other hand, evolves according to the freezing rate of the liquid. The level-set associated with the solid-liquid interface is comprised of two segments: active, and passive. The active part of the level-set evolves based on temperature gradients and latent heat of fusion. While, the passive part is merely utilized for imposing the angle at the tri-junction point. We solve a Hamilton-Jacobi type equation in the passive part of the liquid-solid interface to impose a constant or variable angle at the tri-junction point.

Furthermore, to consider the effect of density expansion, we added a source term into the continuity equation. The source term induces velocity in the domain by which the liquid-gas interface evolves. Moreover, a source term is added to the level-set advection equation to impose mass conservation in the liquid phase. The effect of density variation is included in the energy equation as well.

The proposed numerical approach is validated using benchmark problems. In addition, we compared numerical results of water droplet freezing on a cold substrate with experimental results available in the literature. Through the comparison, we prove that the proposed model is capable of accurately predicting solidification behavior.