A Critical Review of the Modified Froude Number in Ladle Metallurgy

"The modeling of gas-liquid plumes in steelmaking ladles has been the subject of many investigations. In most studies, the “modified” Froude number, based on the momentum of the injected gas, has been employed to characterize two-phase plumes. This approach has several shortcomings and is critically reviewed in the present work. Based on an extensive review of previous work and theoretical considerations, it is demonstrated that the injected momentum and consequently, the modified Froude number has no significance to gas blowing operations in Ladle Metallurgy. Instead, an approach based on the “plume” Froude number, previously shown by the authors as the proper form for Froude similarity, is extended as a simpler alternative.IntroductionGas injection is central to most Ladle Metallurgy operations. During ladle processing, the steel melt is usually stirred by an inert gas like Argon through porous plug(s) fitted in the bottom of the ladle or a lance inserted deep into the melt. The purging serves several purposes viz., homogenizing the melt, flotation of inclusions, enhancing the rates both of refining reactions and dissolution of alloying elements and promoting inter-phase interactions in the ladle.The topic of gas injection into liquid baths has been the subject of several investigations in the past. A great deal of this work, both experimental and computational, was devoted to describing the structure and properties of two-phase plumes as reviewed recently [1]. Generally, the ascending two-phase mixture is sub-divided into three distinct regions [2]: the jet core, transition and the bubble plume, respectively. The jet region, where the momentum of the injected gas is transferred to the bulk liquid, is also called the ‘momentum region’. In a similar manner, the plume is called the ‘buoyancy region’ where the motion of liquid is caused by the buoyancy force exerted by the bubbles. The proper characterization of these regions is important for the analysis and modeling of stirring operations in Ladle Metallurgy. Although many mathematical correlations exist for this purpose, some issues of theoretical and practical interest to the modeling of gas-liquid plumes need further attention."