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Two-phase turbulent recirculating flows generated by air injection to a ladle with or without throughflow are simulated using a Lagrangian-Eulerian approach. Two turbulent models, the conventional k-$\varepsilon$ (isotropic model) and Reynolds Stress models (anisotropic model) are employed to predict swirling flow fields and the predictions are compare with experimental data. The location of the air injection nozzle is varied for the throughflow case: at the bottom center, at the left corner (same side as the water inlet port) of the bottom, and at the left side wall. For the no throughflow case, predictions obtained by these turbulent models agree qualitatively well with measured data for most regions of the ladle. However, it is shown that the predictions of the turbulent kinetic energy by the k-$\varepsilon$ model are higher than those by the Reynolds Stress model. The effects of size and flow rate of bubbles on the dispersion rate of the two-phase plume are investigated. It is shown that the dispersion rate is more dependent on bubble flow-rate than on bubble size. For the throughflow configuration, it is shown that the k-$\varepsilon$ model is not suitable even for predicting the mean flow field, even though it yields results which are in agreement with measurements in less swirling flow. It is also revealed that air injection from the left bottom nozzle is more effective in reducing the zone of zero turbulent kinetic energy which results in poor mixing. The behaviors of a slag layer are simulated using the Volume of Fluid approach in various conditions such as density differential between the upper and lower phases, air injection velocity, and thickness of the slag layer. The goal of this investigation was to develop an understanding of the ways that the upper slag layer interacts with the bulky liquid metal during the gas injection operation to improve the design of the metallurgical processes. It is revealed that the presence of the overlying slag layer reduces the mean and turbulent kinetic energy significantly which results in poor efficiency in mixing and that the density differential ($\Delta\rho$) might be a critical factor in determining where and when the inclusions form for a given flow rate. It is also shown that an initial formation of the inclusions is not sensitive to the thickness of the slag layer but is sensitive to the density of the slag.