Ladle Eye Formation Due to Bottom Gas Injection: A Reassessment of Experimental Data

Abstract

The ladle furnace was a watershed in the evolution of steelmaking when it was invented in the 1980s. Both the BOF and the EAF were assigned a more specialized role. The ladle furnace assumed the function to provide for the final steel chemistry with the lowest concentration of sulfur and non-metallic inclusions. Both functions are possible with the use of bottom gas injection. Through many years of intense research work it has been possible to identify conditions to improve the mixing conditions in liquid steel; however those conditions result in another problem, the ladle eye. The ladle eye has been extensively investigated in the past and the results have been reported in many relationships because, it has been argued that the previous ones cannot accurately predict the new experimental values. There are several reasons why the existing relationships cannot predict all the experimental data; the experimental conditions are different or the number of variables is also different. The current work has made a re-assessment of most of the existing experimental data on ladle eye using dimensional analysis. It was possible to unify all experimental data for thin slags, thick slags, different nozzle diameters, nozzle and porous plugs, cold model results and industrial plant results, etc., using the following two correlations, for single and double injection elements:

$\begin{gathered} \frac{{A_{{\text{e}}} }}{{H^{2} }} = 0.3076\left( {\frac{{h_{{\text{s}}} }}{H}} \right)^{ - 1.019} \left( {\frac{{Q^{2} }}{{gH^{5} }}} \right)^{0.408} \left( {\frac{\Delta \rho }{{\rho_{{\text{l}}} }}} \right)^{ - 1.238} \left( {\frac{{\nu_{s} }}{{g^{0.5} H^{1.5} }}} \right)^{ - 0.084} \left( \frac{D}{H} \right)^{ - 0.197} \left( {\frac{{r_{1} }}{H}} \right)^{0.014} ;N = 1 \hfill \\ \frac{{A_{{\text{e}}} }}{{H^{2} }} = 0.204\left( {\frac{{h_{{\text{s}}} }}{H}} \right)^{ - 0.702} \left( {\frac{{Q^{2} }}{{gH^{5} }}} \right)^{0.317} \left( {\frac{{r_{3} }}{{r_{1} }}} \right)^{ - 0.056} \left( {\frac{{r_{3} }}{{r_{2} }}} \right)^{0.061} \left( {\frac{\Delta \rho }{{\rho_{l} }}} \right)^{ - 1.012} \left( {\frac{{\nu_{{\text{s}}} }}{{g^{0.5} H^{1.5} }}} \right)^{ - 0.09} \left( \frac{D}{H} \right)^{0.431} ;N = 2 \hfill \\ \end{gathered}$

where A_e is the slag eye area, Q is the gas flow rate, H is the height of liquid steel or water, h_s is the slag or oil thickness, ${\rho}_{\text{l}}$ is the density of liquid steel or water, ${\Delta}{\rho}$ is the density difference between the two liquids, D is the ladle diameter, r₁ and r₂ represent the nozzle or porous plug distance from the center, r₃ is the distance between nozzles or porous plugs, ${ \nu }_{\text{s}}$ is the slag or oil kinematic viscosity, N is the number of nozzles or porous plugs, and g the gravity force. These equations include all the relevant variables that affect the formation of ladle eye and can be used to predict its formation on both laboratory and industrial scales. The exponents in the dimensionless variables also provide information on their impact factor and can be used to define conditions that decrease the ladle eye area. For comparison purposes, it is suggested to report the dimensionless ladle eye with respect to the cross-sectional area of the ladle.