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Metallurgical Flows

In a gas-stirred molten metal bath quite a few phases require thorough modelling. Liquid metal and slag which floats on top of it both need a proper description of a substance whose mass transfer between slag and metal and vice versa should be calculated. These phases are modelled by the Volume of Fluid (VOF) method in combination with the Large Eddy model of turbulence.

Besides the phases mentioned above, gas bubbles released at the converter bottom induce recirculation flow in the molten metal thus improving the mixing quality. Bubbles are simulated by the Discrete Phase Model, which calculates particle trajectories in a Lagrangian reference frame.

The reaction rate of a substance X strongly depends on the concentration difference between slag and steel and on the interfacial area. In this model the difference is made between area size in the “stratified” and in the “emulsification”-regime. The difference between these regimes is made upon the vorticity magnitude at the slag-metal interface (Fig. 1). In the areas where bubbles are rising up through molten metal and slag the mixing quality is the highest, thus the “emulsification”-regime with greater interfacial area can be applied. In the outer region the slag floats horizontally stratified on the metal, and the interfacial area is smaller.

Fig. 1: Vorticity magnitude (1/s) at the slag-metal interface

Simulation results clearly show the difference between the regimes (Fig. 2 and 3). The substance in the slag is depleted faster in the middle, leaving relatively large outer region where the substance needs much more time to react. Due to the recirculation flow induced by bubbles, this substance is moving in the molten metal towards outer walls of the converter.

Fig. 2: Mass fraction of substance X in molten metal after 30 sec. (Planes from left to right: converter bottom, vertical profile, slag-steel interface)

Fig. 3: Mass fraction of substance X in slag after 30 sec. (Planes from left to right: slag-steel interface, vertical profile, slag-air interface)

(Damir Kahrimanovic)