A Unified Approach to the Fluid Dynamics of Gas–Liquid Plumes in Ladle Metallurgy

The paper focuses on the fundamental aspects of the fluid mechanics of unconstrained gas–liquid plumes relevant to Ladle Metallurgy Practice. A mathematical model previously proposed by the authors is justified by comparison with Eulerian–Lagrangian models. Further, a unified analytical framework is proposed to describe the fluid dynamic and similarity characteristics of two-phase plumes. Despite the apparent complexity of the system, the analysis demonstrates that the plume cross-sectional area, void fraction and gas and liquid velocities can be quantified in terms of two parameters: a dimensionless gas flow rate and the normalized axial height. The analysis clarifies the proper form of the Froude number similarity which is important for process design and scale-up.