# ABOUT MATHEMATICAL MODEL OF SLAG FOAMING IN CONVERTOR

### Abstract

The main factor of the foam formation in oxygen convertor is gas blowing so the aim of this work is to find an optimal amount of injected gas avoiding overflow of the convertor. Researches and experiments can be very expensive in plant conditions. On the other hand such experiments give important data about real process. A mathematical model can considerably decrease costs of mentioned process prediction and helps in finding of rational parameters. However for a good adequacy the model needs to take into account melt flow and gas movement. Conservation laws of impulse and mass are used in form of Navier-Stokes equations and convection-diffusion equation. Cylindrical coordinate system fits geometry of problem and axis symmetry can be used to simplify the model with two-dimensional statement (r-axis and z-axis).

### References

2. Repossi E., Rosso R., Verani M. A phase-field model for liquid-gas mixtures: mathematical modelling and discontinuous Galerkin discretization // Modeling and scientific computing. – 2016, № 27, pp. 1–36.

3. Cai X., Wörner M., Marschall H., Deutschmann O. CFD simulation of liquid back suction and gas bubble formation in a circular tube with sudden or gradual expansion // Emission control science and technology. – 2017, № 3, pp. 289–301. doi: 10.1007/s40825-017-0073-3.