Multiscale Mathematical Model with Discrete–Continuum Transition for Gas–Liquid–Slag Three-Phase Flow in Gas-Stirred Ladles

Gas–liquid–slag three-phase flow in a gas-stirred ladle is composed of both large-scale interfaces and discrete bubbles, making its modeling and study difficult. In the present work, a discrete–continuum transition model was incorporated into a hybrid Eulerian–Lagrangian model to comprehensively resolve the fluid flow in ladle metallurgy. The volume-of-fluid method was used to capture the large-scale interfaces, while a discrete bubble model was applied to simulate the small bubbles that cannot be resolved using the interface-capturing method. The transition between the small bubbles in Lagrangian coordinates and the large bubbles whose interfaces are captured is included using a newly developed algorithm to further reveal the bubble behaviors. Moreover, the complicated vortex structure is characterized using the large-eddy simulation approach. The present modeling framework enables the most complete analysis of gas–liquid–slag three-phase flow in ladles to date.