Phase change process with free convection in a circular enclosure: numerical simulations

A numerical study of unsteady natural convection flow during freezing of water in a circular enclosure is presented. Mathematical model for phase change is based on apparent capacity method formulation and the governing equations are discretized on a fixed grid by means of finite element method. Water’s temperature is initially higher than its freezing temperature. Then, the temperature of the enclosure’s boundary is dropped to a temperature lower than freezing temperature. Ice forms at the enclosure boundary while natural convection flow is induced in the liquid region. Calculations have been made for the rate of change of solid fraction and temperature distributions, for conduction and conduction plus convection modes of heat transfer, and density inversion near freezing temperature phenomenon of water is considered. High resolution capturing of solid/liquid moving boundary as well as the details of flow structure is presented. The results indicate that the effect of natural convection is dominant over conduction if the Rayleigh number is higher than 5 × 10⁶ and relatively insignificant if the Rayleigh number is less than 1 × 10⁶.