A Comparison of Different Solution Methodologies for Melting and Solidification Problems in Enclosures

A comparison of two frequently used computational techniques for solving phase-change problems is presented. The governing equations for the conservation of mass, momentum, and energy are solved using a control-volume-based discretization scheme. In Ike first approach, the physical space is mapped onto a simpler domain and the moving boundary is immobilized using Landau transformation. The computations are carried out on a uniform orthogonal grid in the transformed space using the stream function-vorticity formulation. The need to retain all the terms in the governing equations arising from the transformation, for an accurate simulation, is investigated. Simplifications in the governing equations have been used in the literature and are discussed. Both implicit and explicit methods are used to track the phase front. In the second approach, the computations are carried out on a uniform fixed grid in the physical space with primitive variables. The enthalpy-porosity formulation, with appropriate source terms to account for the phase change, is employed. Numerical results yield the temperature distribution and the buoyancy-induced velocity field. The test problems used are the melting of gallium and tin in a rectangular cavity with isothermal side walls and adiabatic top and bottom walls. Comparisons are made between the numerical predictions and experimental data on the morphology and position of the phase front for cavities of different aspect ratios, and the computational times are recorded. Heat transfer rates and velocity field results obtained are also presented. The study indicates the range of applicability and computational complexity of the two approaches.