A COMPARISON OF DIFFERENT SOLUTION METHODOLOGIES FOR MELTING AND SOLIDIFICATION PROBLEMS IN ENCLOSURES

A comparison of two frequently used computational techniques for solvi ng 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 the first approach, the physica l space is mapped onto a simpler domain and the moving boundary is imm obilized using Landau transformation. The computations are carried out on a uniform orthogonal grid in the transformed space using the strea m function-vorticity formulation. The need to retain all the terms in the governing equations arising from the transformation, for an accura te simulation, is investigated. Simplifications in the governing equat ions 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 fo rmulation, with appropriate source terms to account for the phase chan ge, 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 si de walls and adiabatic top and bottom walls. Comparisons are made betw een the numerical predictions and experimental data on the morphology and position of the phase front for cavities of different aspect ratio s, and the computational times are recorded Heat transfer rates and ve locity field results obtained are also presented The study indicates t he range of applicability and computational complexity of the two appr oaches.