Enthalpy porosity model for melting and solidification of pure-substances with large difference in phase specific heats

A modified enthalpy porosity formulation is introduced to capture melting and solidification of pure substances. When melting and solidification of pure substances are addressed by the fixed grid based volume averaging technique, it is possible to obtain two equivalent and interchangeable mathematical formulations of the energy conservation equation if the governing equation is expressed in terms of temperature as the primary dependent variable. Between these two formulations, only one form is shown to provide physically consistent numerical solutions when very large difference in specific heats for liquid and solid phases is involved. A modified enthalpy updating scheme is proposed to predict the solid/liquid fraction during melting and solidification process of pure substances having large difference in phase specific heats. The results from the proposed scheme are validated with the existing results from literature involving numerical prediction of freezing of water. The physical consistency of the simulation results obtained by solving two interchangeable forms of energy conservation equation is tested and compared considering a case study involving melting of ice. While one of the conservation forms fails to predict the melting process, the other conservation form successfully predicts physically consistent result. The proposed formulation is capable of predicting melting and solidification of all pure substances including those with large difference in phase specific heats such as water and paraffin wax.