A combined enthalpy-level-set approach for melting/solidification within two immiscible fluids

This paper develops a numerical model combining enthalpy and level-set methods to study melting and solidification within two immiscible fluids. The melting and solidification interface is predicted through enthalpy method while the interface between two immiscible fluids is captured by the level-set method. The current model is validated against both semi-analytical solution and experimental data via different cases. With those obtained, the model is then applied to two different cases including water solidification and ice melting in water-oil stratified flow. The effects of different parameters involving with gravity force, surface tension force, latent heat and the viscosity ratio between water and the immiscible fluid are investigated. These corresponding parameters are Fr, We, Ste and μ_f/μ₊, respectively. It is found that Ste and μ_f/μ₊ have more significant effects on both solidification and melting process compared with Fr and Wenumbers. No obvious differences are observed without considering gravity and surface tension forces in the solidification process. However, the amount of melted ice increases without considering gravity and surface tension forces.