  In this paper we develop a physics-based model for the erosion of lining in
steel ladles. The model predicts the temperature evolution in the liquid slag,
steel, refractory bricks and outer steel casing. The flows of slag and steel is
due to forced convection by inert gas injection, vacuum treatment (extreme
bubble expansion), natural convection and waves caused by the gas stirring. The
lining erosion is due to dissolution of refractory elements into the steel or
slag. The mass and heat transfer coefficients inside the ladle, during gas
stirring, is modeled based on wall functions which take the distribution of
wall shear velocities as a critical input. The wall shear velocities are
obtained from CFD (Computational Fluid Dynamics) simulations for sample of
scenarios, spanning out the operational space, and using curve fitting a model
could be built. The model is capable of reproducing both thermal evolution and
erosion evolution well. Deviations between model predictions and industrial
data are discussed. The model is fast and has been tested successfully in a
"semi-online" application. The model source code is made available to the
public on https://github.com/SINTEF/refractorywear.
