Front tracking method in modeling transport phenomena accompanying liquid–solid phase transition in binary alloys and semitransparent media

Abstract

The paper presents the potential of an efficient front tracking method on a fixed control-volume grid in micro–macroscopic numerical modeling of both binary alloy solidification and a solid–liquid phase transition of single-component or doped optically functioning materials. In the former case, the method, basing on the assumption that an envelope of columnar dendrite tips moves locally according to a single crystal growth law, allows more precise identification of zones of different dendritic structures developing within the two-phase region, and thus more detailed analysis of some closing models. It is shown, by exploiting the commonly used benchmark problem that a porous medium model of the columnar mush must be carefully chosen since it strongly affects the predicted macro-segregation pattern. In the case of solidification of a single-component or doped semi-transparent material the combination of the front tracking method with the immersed boundary technique provides a new simulation method, which can handle different thermo-physical and optical properties of liquid and solid phases, processes of emission, absorption, reflection and refraction or transmission of thermal radiation at a diffusive or specular distinct solid–liquid interface detected by the front tracking technique. The method has been used in a detailed parametric analysis where the impact of different optical configurations of both phases and their various optical properties as well as variable transmissivity of solid–liquid interface on the phase change process development has been addressed.