Mathematical modeling of multiphase flow in steel continuous casting

This paper reviews multiphase flow models for continuous casting of steel from classical models to recent methods. These multiphase flow models are classified into six groups in this paper: quasi-multiphase models, multi-fluid models, moving grid methods, interface tracking methods, particle based models/ methods and hybrid models. For each model, the governing equations are summarized and the inherent advantages and disadvantages are discussed. Example applications of each model are presented from previous literature, illustrating typical results and accuracy that can be obtained. The objective of this paper is to guide readers to choose an appropriate multiphase flow model for their application. Argon gas bubble effects on the flow pattern can be modeled with simple mixture models, Eulerian-Eulerian models, Multiple size group models which also track bubble size distributions, and Discrete-Phase Models (DPM). Gas pockets and slug flow, which can occur inside the nozzle are more complex, and hybrid models which combine different models together, such as Eulerian-Eulerian, level-set, Volume of Fluid (VOF), and DPM, appear promising. The shape of the slag/steel interfacial profile, level fluctuations, and slag entrainment can be modeled with free surface methods, such as moving grid, VOF, or other interface tracking methods. Particle transport and entrapment, including inclusions and gas bubbles can be added via DPM models and also require a capture criterion model. Solidification and meniscus phenomena require flow models coupled with heat transfer and solidification.