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. Furthermore, the dissipation of the gas momentum in the vicinity of the injector is shown to be consistent with the present analysis.