An enthalpy method based on fixed-grid for quasi-steady modeling of solidification/melting processes of pure materials

We propose a quasi-steady enthalpy method based on fixed-grid to consider the latent heat of phase change during a solidification/melting process of a pure material. The latent heat of phase change released or absorbed at the solid-liquid interface disperses into a region at the interface in the proposed method. It is validated through comparing to the solutions obtained with the adaptive mesh method which is commonly accepted for its accuracy in modeling solidification/melting processes for pure materials. The effects of the dispersed region size and the phase change rate on the simulation accuracy of the proposed method are investigated. Based on the proposed method, a general form of the distribution function of the latent heat of phase change is proposed. The distribution of the latent heat of phase change in the dispersed region is controlled by selecting different forms of distribution function to improve the simulation accuracy. The selecting principle of the distribution function is proposed on the basis of concentrating the latent heat of phase change at the solid-liquid interface. By following the selecting principle, the accuracy can be controlled and the size of the dispersed region does not need to be determined in advance. Two distribution functions of the latent heat of phase change are investigated. Results show that the proper concentration of the latent heat of phase change at the solid-liquid interface is favorable for the simulation accuracy.