Solidification Modeling: Evolution, Benchmarks, Trends in Handling Turbulence, and Future Directions

Abstract

A systematic evolution of the solidification modeling is presented in this article. An approach starting from the basic governing equations to the intricate modeling of the alloy solidification using different approaches has been reviewed. Important advantages and issues related to different formulations and the use of fixed/moving grids for the modeling of solidification have been discussed. This article outlines the important solidification modeling approaches used in the literature. The mathematical description of the most frequently employed methods for modeling of solidification has been presented providing adequate references for other solidification models. This article highlights an important subdomain of solidification modeling, namely, the modeling of solidification processes having significant turbulence (such as welding, casting, and Czochralski crystal growth). A review of the use of different turbulence models along with the state-of-the-art techniques in these areas is presented. The paper also describes the important benchmarking studies (both experimental and numerical modeling results) used for the validation of solidification of both pure metals and alloys. Finally, the physical and numerical complexities associated with the solidification modeling phenomena along with the important challenges and future directions are presented.