A cell-by-cell thermally driven mushy cell tracking algorithm for phase-change problems

The finite volume based numerical approach is used to simulate phase-change processes including natural convection. This approach is based on a cell-by-cell, thermally driven mushy cell tracking equation, developed in Part I [20], to trace the front at which phase-change occurs. A mushy cell is a specialized cell where the interface between liquid and solid phases is located. In this paper, the mushy cell tracking equation and the associated boundary condition around the mushy cells are derived in a general manner and shown to have the same form as that used in Part I. The SIMPLE algorithm is adopted to solve the flow, including pressure field, as well, in the liquid phase and a conjugate gradient method is used when solving the system of discretized equations. To reduce computational time, an acceleration technique, based on a justified quasi-steady state assumption, is adopted. The proposed numerical method is applied to simulate the solidification and melting of Tin with natural convection. The numerical predictions are compared well with the available experimental data and previously published numerical results. Specifically, these comparisons demonstrate that the proposed methodology is capable of predicating the location of moving fronts and the temperature distributions for phase-change processes with natural convection.