Various ways to take into account density change in solid-liquid phase change models: Formulation and consequences

In this paper, a classification of different methods for accommodating volume variations during solid-liquid phase change is presented. The impact of each method is analyzed with the help of a scale analysis. Neglecting fluid velocity at the interface or allowing fluid to enter/exit the domain may result in either local (at the solid-liquid interface) or global (within the system) mass imbalance. This can lead to significant differences in the transient phase change process itself (e.g., 19% more time and 9% more energy to completely solidify a given mass of water with models for which the total mass of the system is conserved). This paper aims at addressing this issue by deriving two new models of thermo-mechanical coupling between the PCM and its container. The first model is that of a PCM bounded by an elastic wall, whereas the second model assumes that a compressible air gap is adjacent to the PCM, which allows the PCM to expand more easily. Analytical expressions are developed for both models and can be used to predict important quantities at equilibrium, such as the position of the solid-liquid interface and the pressure rise within the system. Finally, the two thermo-mechanical coupling models are implemented numerically with a finite volume moving mesh method. Numerical simulations are performed to show the limits of the two models. It is observed that volume variations during phase change can have significant impacts on the evolution of the process.