HEAT-CONDUCTION WITH PHASE-CHANGE IN A PURE SUBSTANCE - RESOLUTION FORMULATED WITH TEMPERATURE TERMS

Heat conduction with phase change in a pure substance: resolution formulated with temperature terms. Many studies are devoted to the numerical simulation of phase change phenomenon, and particularly of solidification phenomenon that occurs during foundry processes. The main difficulty of such a simulation is to find an efficient numerical treatment of the enthalpy discontinuity at solidification temperature for pure metals or eutectic alloys. Many softwares, particularly industrial softwares, ave based upon the resolution of the heat diffusion equation formulated with enthalpy terms, but this method is heavy and tedious. Other methods have been developed, which solve the heal equation formulated with temperature terms or use a fictitious heat source, but these methods only allow an approached treatment of the enthalpy discontinuity. In this paper, we propose an algorithm for the resolution of the heat equation formulated with temperature terms which needs no approximation concerning the enthalpy discontinuity. This method, which uses a fictitious heat source, can be applied to the solidification of pure metals or eutectic alloys. It exhibits different advantages: a) the enthalpy discontinuity is accurately taken into account; b) at any point, the solidified metal fraction can be obtained from the heat production released during the solidification; c) its implementation is easy and independent of the numerical model (FEM, FDM,... ID, 2D, 3D); d) finally, it can be applied in association with any standard subroutine for heat equation resolution. Following the presentation of the method, we propose a monodimensional example of solidification front progression; this allows to validate the method compared to the analytical solution of stefan's problem and to characterize the influence of the parameters. The bidimensional validation is controlled with the reference to the results of Lazaridis applied to an example of infinite corner.