Nowadays, depending on the steel grade, Ca treatment with the aim of modifying the morphology and melting temperature of non-metallic inclusions is performed in the secondary steelmaking process. The addition of calcium to steel melts rises a technological challenge because at steelmaking temperatures Ca has the tendency to vaporize from the ladle. Efforts are actively pursued in developing solutions that increase Ca yield and improve repeatability of results from treatment to treatment. This work presents a two-phase Euler-Euler flow model of a steel ladle with gas stirring through bottom porous plugs. The model considers that before gas exits through the ladle top, some Ca is transferred from the gas to the liquid steel. The yield is thus defined as the ratio between the Ca transferred to the steel and the total calcium injected into the ladle. The fluid-dynamic calculations are coupled with ArcelorMittal thermodynamic software CEQCSI to get the evolution of the local concentration of dissolved species and non-metallic inclusions assuming local thermodynamic equilibrium. Industrial trials have been performed at one of ArcelorMittal’s facilities with the aim of obtaining data to validate the model. Samples of steel were taken before, during, and after the Ca injection treatment. The total Ca content and the inclusion populations in the steel samples can be compared against the results given by the model, as well as the measured and calculated Ca yield.
Existence of a conjugate point in the incompressible Euler flow on an ellipsoid
