Natural convection and solidification of phase-change materials in circular pipes: A SPH approach

Smoothed Particle Hydrodynamics is used to model natural convection and solidification of a liquid material inside a cylindrical pipe, whose wall temperature is kept below the freezing point. The model is validated with two benchmark cases and a parametric study targeting the properties of the most common phase-change materials is carried out. The results show three hydrodynamic regimes: the static regime, the dynamic regime, and the pseudo-static regime. In the static regime, viscous forces overcome buoyancy forces; liquid motion is minimal and the solidification front proceeds axisymmetrically from the wall to the centre of the pipe. In the dynamic regime, the flow shows the typical recirculation vortices of natural convection. Density differences drive the colder liquid in the lower (or higher, in the case of water) part of the pipe, where it quickly solidifies. Solidification does not proceed symmetrically and the solidified shell around the wall is thicker in the lower region of the pipe. The pseudo-static regime is the result of two competitive processes: on one hand a buoyancy-driven boundary layer tends to form around the solid-liquid interface, on the other hand the advancing solidification front tends to halt the motion by freezing the boundary. As a result, a small velocity profile around the solid-liquid interface is observed, but, as the solidification front moves, it has no time to transfer enough momentum to set the rest of the liquid in motion. A criterion for predicting the regime based on two dimensionless groups is given, and, since the regime affect the freezing time, a correlation for calculating the freezing time based on the hydrodynamic regime is provided.