Numerical modeling of solid-liquid phase change in a closed 2D cavity with density change, elastic wall and natural convection

In this paper, the solidification of water near its density extremum is simulated while taking into account the expansion of the phase change material resulting from the different density of the solid and liquid phases. A thermo-mechanical coupling is achieved through one of the boundaries of the cavity behaving as an elastic wall. A methodology is introduced in which the problem is adapted in order to be solved with commercial CFD software (ANSYS Fluent 17.0). It is shown that when both the density variations and interaction of the phase change material with its boundaries are taken into account, significant differences may be observed in the flow pattern and the thermal behavior of the system, as opposed to an approach where a free ceiling or a constant density would be used. The pressure buildup inside the cavity resulting from the expansion of the phase change material as it pushes against the elastic wall causes the melting temperature to drop, which hinders solidification. It is shown that this effect becomes more pronounced as the spring constant of the elastic wall increases. It is also demonstrated that, with the assumptions made in the present model, the pressure rise may significantly influence the buoyancy forces within the cavity and change the relative size of the two counter rotating convective cells in the liquid phase. In some cases, when the pressure rises very quickly, the density extremum in the cavity disappears which strongly changes the flow pattern, i.e., only a single counter-clockwise convective cell is present in the cavity. This, in turn, changes the shape and position of the solidification front considerably.