A Cell-by-Cell, Thermally Driven, Mushy Cell Tracking Algorithm for Phase-Change Problems in Dendritic Solidification

Abstract

A cell-by-cell, thermally driven, mushy cell tracking method for predicting the time-evolving phase front under stable or unstable phase-change condition is developed. Discontinuous material properties and interfacial anisotropies across the solid and liquid phases are easily modeled by the developed tracking algorithm, which is applied together with a flux discretization developed within the unstructured, cell-centered, variable-collocating finite-volume method. Two analytic benchmark problems are investigated, without considering heat convection, to validate the proposed mushy tracking algorithm. Problems of tin melting and solidification with natural convection taken into account are also investigated. Finally, the dendritic solidification simulation, which involves curvature and kinetic mobility, is also studied for the sake of completeness. Our validation demonstrates that the proposed methodology is capable of capturing moving melt and solidification fronts under stable or unstable phase-change condition.

Yih-Jena Jan thanks the National Science Council of Taiwan for funding this research (Project NSC 95-2221-E-022-016).