A Simple Mathematical Model for Estimating Plume Hydrodynamics of Metallurgical Ladles

In secondary steelmaking, the refining operation is typically carried out in a metallurgical ladle that is commonly furnished with gas injection facilities. Since gas injection plays an intrinsic role in determining the efficiency of secondary steelmaking and thus the quality of final products, a great volume of work has been conducted mostly utilizing air-water systems at room temperature. Despite a portion of the air-water correlations have been adopted in the literature, their applicability to the real argon-metal system is still questionable. The main motivation behind this paper is to present a simple mathematical model for plume hydrodynamics of metallurgical ladles based on the characteristic phenomena and underlying mechanisms of a buoyant plume, where bubble breakup and coalescence occur simultaneously. The main assumptions/simplifications and governing equations are firstly introduced. After that, the accuracy of the model is demonstrated by comparing predicted plume velocities with the ones measured in an industrial ladle.