Time Dependent Numerical Simulations of Solidification Processes

摘要

This work was aimed at developing and applying a new methodology for the efficient and accurate computation of problems involving several phases of matter. In particular. solidification processes typically involve melt/solid and sometimes melt//gas interfaces, whose location and shape is unknown a priori. This class of problems is called free or moving boundary problem, and the numerical approaches for its solution to date are inaccurate, inefficient, and can not be readily extended to multi-dimensions or to time dependent phenomenon. Ongoing research on welding at ONR and on crystal growth at NASA and other institutions all fall into the category of free boundary problems. It is exactly the accurate determination of the process dynamics and the shape and location of the interface between the phases which is responsible for the ultimate chemical segregation and the mechanical properties in the solid. This work developed the Triad Field Formalism approach for the computation of general multi-dimensional and time dependent free boundary problems. The particular subject addressed is solidification phenomena. All the relevant boundary conditions on the developing interface were exactly resolved. Several computer programs were developed during the course of this research, enabling us to determine for the first time the interplay among the various fields operating in tandem to produce the phenomena observed during solidification processes in weld pools and during crystal growth.