Modeling of Gas-Steel-Slag Three-Phase Flow in Ladle Metallurgy: Part II. Multi-scale Mathematical Model

Gas stirring ladle is a complex three-phase reactor which contains phases whose interfaces are in different scales. The bubble-liquid interaction also leads to multi-scale eddy structures. The present work proposes a multi-scale mathematical model to simulate the multiphase flow in ladle, which directly captures large phase interfaces and eddies, while models sub-grid scale interfaces and eddies using respectively discrete bubble model (DBM) and one equation eddy viscosity model (OEEVM) in large eddy simulation (LES) approach. By this way, the mesh resolution can be defined relatively coarse to save computational resources. The volume of fluid (VOF) model coupled with the compressive interface capturing scheme for arbitrary meshes (CICSAM) is adopted for the slag surface, while the DBM is used for handling the dynamics of discrete bubbles. The bubble coalescence is considered using the O'Rourke's algorithm to solve the bubble diameter redistribution and it is found that aggregation mostly occurs below 0.2 m from the inlet. Moreover, bubbles are removed after leaving the air-liquid interface and the mass is transferred to air. The flow with multi-scale eddies induced by bubble-liquid interaction is solved using LES. The slag droplet entrainment and the slag-eye size fluctuation related with the pressure fluctuation on gas inlet are well revealed. The time-averaged spout eye size and the bubble diameter evolution are validated against the experimental data. The results show that the multi-scale VOF-DBM-LES model provides an effective modeling framework to predict the intrinsically unsteady flow behaviors in ladle.