A three-dimensional mathematical model has been developed to predict the growth and removal of inclusions during gas stirring in a multi-tuyere ladle. In the model, the efficiency of inclusions removal have been investigated under three different collision mechanisms of Brownian collision, turbulent collision and Stokes collision. Importance of the three approaches of wall adhesion, Stokes flotation and bubbles adhesion to remove inclusions has been analyzed. The results indicated that inclusions growth resulting from turbulent collision is most important and that effect of Stokes collision is remarkable as size of inclusions and difference in size of two particles increase, while inclusion growth resulting from Brown collision is negligible. Removal by Stokes flotation is main manner for large inclusions, while inclusion removal by wall adhesion is negligible. The smaller bubbles contribute the higher efficiency of inclusion removal.KEY WORDS: mathematical model; inclusion growth; inclusion removal; multi-tuyere ladle; gas stirring; bubble flotation. iors of molten steel and inclusion are different in gas stirring ladle with one tuyere and two tuyeres. The object of this paper is to develop a current three-dimensional mathematical model to predict inclusion growth and removal in gas stirring ladle with multi-tuyere and investigate the factor of this process. Flow of molten steel and transfer behavior of inclusion have been studied in this model by use of CFD software package, CFX. Calculation of inclusion growth and removal were carried out by amending transport equation using FORTRAN code. As an application of this model, the distribution of alumina particle in a ladle with different position of tuyere has been calculated. Mathematical Model AssumptionsThe mathematical model of inclusion growth and removal in this investigation is based on the following assumptions: Assumptions concerning the molten steel:1 the liquid steel inside the ladle is incompressible Newtonian fluid and flow fluid is transient. 2 the effect of slag at top surface of molten steel on flow was not considered. 3 injected gas overflows the top surface of molten steel which was set as free surface, and gravitation and fluctuation of free surface are negligible. 4 the molten steel in a ladle is steady at initial time. 5 the effect of nature convection on flow of molten steel is negligible. 6 the flow of molten steel in a ladle is turbulence flow. 7 the heat flux values of 12 500 W/m 2 21) and 36 000 W/m 2 22) were respectively used for refractory bricks used in a ladle and free surface of molten steel. Assumptions concerning bubbles: 8 the bubbles generated at tuyere have the same sizes, and the frequency of bubbles can be calculated by conversation of volume. 9 the generated bubbles are spherical and rigid. 10 interactions of bubbles are negligible. Assumptions concerning inclusions:11 inclusions are spherical and uniformly distributed in molten steel at initial time. 12 the size of inclusion particles is so small that the effect of inclusio...

A three-dimensional mathematical model has been developed to predict steady flow field, pressure distribution inside the shroud and efficiency of inclusion removal in tundish after argon gas injection at the shroud. Effects of the different opening of the slide gate and gas injection on velocity and pressure have been analyzed. The results show that the molten steel velocity gradually decreases and the pressure increases as the opening of the slide plane becomes larger. The velocity increases and the pressure decreases after gas injection. Bubble adhesion plays an important role in inclusion removal. Smaller bubbles and larger inclusions are favorable for inclusions removal. The larger flow rate of gas is, the greater number of bubbles generated is. Thereby the amount of removed inclusion increases. But local boiling will occur in the case of larger rate of gas, so the flow rate of gas should be strictly controlled in practice.

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A three‐dimensional mathematical model has been developed to predict growth and removal of inclusions during gas stirring through eccentric tuyeres in a ladle. In the model, the efficiency of inclusion removal is investigated under three different collision mechanisms: Brownian, turbulent and Stokes collision. The Importance of the three approaches of wall adhesion, Stokes flotation and bubble adhesion on inclusion removal is analysed and the efficiency of inclusion removal through three types of tuyeres in central, eccentric and multi‐tuyere form is studied. The results indicate that inclusion growth resulting from turbulent collision is most important and the effect of Stokes collision is remarkable with increased inclusion size, while inclusion growth resulting from Brownian collision is negligible. Removal by Stokes flotation is the main mechanism for large inclusions, while inclusion removal by wall adhesion is negligible. The smaller the bubbles are, the higher the efficiency of inclusion removal is. The type of tuyere arrangement has a great effect on inclusion removal. Inclusion removal in a 135t ladle with one eccentric tuyere is more efficient than in a ladle with central tuyere or multi‐tuyere design.