Development and validation of a stabilized immersed boundary CFD model for freezing and melting with natural convection

Numerous processes in the automotive, additive manufacturing or energy storage industries require an accurate prediction of the solidification (freezing) and melting (thawing) dynamics of substances. The numerical modeling of these phase changes is highly complex because it includes sharp moving interfaces and strong discontinuities in the material properties. This complexity is often exacerbated by the occurrence of natural convection, which induces a strong coupling between the motion of the liquid and the position of the solid–liquid interface. This leads to strongly coupled non-linear thermo-fluid problems which have to be solved in complex geometries.
In this work, we introduce two novel stabilized finite element models to predict the phase change with natural convection. The first model uses a more classical viscosity approach to impose stasis in the solid region whereas the second one is based on an immersed boundary formulation to accurately describe the solid–fluid interface.
The efficiency of the stabilization is first demonstrated by studying the Stefan problem. The two approaches to impose stasis are then compared using 2D test cases before they are both used to study melting in a rectangular (2D) and prismatic (3D) cavity. Significant differences are observed in the flow profiles and the solid–liquid interface position between the 2D and the 3D simulations.