*3.1. Model Validation*

Figure 2 shows the flow patterns obtained through the PIV technique reported in Jardón-Pérez et al. [15] at different operating conditions listed in Table 2, whereas Figure 3 shows the flow patterns obtained with the numerical model presented in this study. As seen in these figures, a reasonable agreement is observed between experimental and numerical results for all the cases. For equal (50%:50%) dual gas injection, two symmetric toroids are formed at each side of the plume, whereas for unequal (25%:75%) injection, symmetry vanishes and the high flow rate circulation expands at the expense of the low flow rate circulation loop. An increase in the gas flow rate increases the expansion of the plume in general, and for unequal injection further expands the high-flow rate circulation loop. The increment in (slag) oil thickness mitigates the inertia of the plumes, reducing the velocities of the liquid, and diminishes the loop expansions. An increase in (slag) oil thickness lowers the velocity of the liquid in the vicinity of the oil layer at the top of the ladle. In general, the experimental results were predicted successfully with the model, but some differences were also perceived. The numerical predictions using CFD do not account for the expansion of the bigger loop for unequal injection as occurs in PIV-measured flow patterns. As an illustration, Figure 4 shows measured

(a) and calculated (b) streamlines obtained for experiment b (see Table 2) under equal dual gas injection, showing good agreement between both predicted and measured streamlines; however, under unequal dual gas injection for experiment g (see Table 2), calculated (d) streamlines do not capture the expansion of the strong plume and the contraction of the small loop as seen in the measured (c) streamlines. In general, the magnitudes of the liquid velocity were slightly underestimated. Mean value was overestimated (see Table 3), but the distribution is quite different, especially in differentiated injection, since the model does not accurately predict the interaction of the plumes. In the case of differentiated dual gas injection, the interaction between the recirculation loops was not observed. This is probably due to the drag effect, which was not successfully implemented, and represents a challenging issue in numerical modeling, from the hydrodynamic point of view, of the more complex multiple differentiated dual gas injections, compared to the traditional equal dual gas injection. Despite the differences, the numerical model of the ladle furnace in steady state showed good results, with a reasonable agreement with the experimentally measured liquid flow patterns reported in Jardón-Pérez et al. [15]. A more quantitative validation is shown in Figure 5 by comparing experimental (continuous line) and numerical (dotted line) mean velocity radial profiles at h/H = 0.8 for experiments b (a) and g (b); axial profiles at r/R = −0.75 for experiments b (c) and g (d); and axial profiles at r/R = 0.75, for experiments b (e) and g (f). In all these cases, a good agreement between prediction and measurement is achieved, with, in general, the numerical velocity profiles slightly over-predicting the measured results, but with the simulations capturing the measured liquid motion in the plumes.

**Figure 2.** Flow patterns of the eight case studies obtained with the experimental model (particle image velocimetry (PIV) technique) in the longitudinal plane. (**a**) through (**h**) are the experiments described in Table 2.

**Figure 3.** Flow patterns of the eight case studies obtained with the numerical model and shown along the same longitudinal plane. (**a**) through (**h**) are the experiments described in Table 2. The cases presented in this study are in the same order as in the experimental study of Jardón-Pérez et al. [15].

**Figure 4.** Streamlines obtained for experiment b (Table 2), measured (**a**) and calculated (**b**); and for experiment g (Table 2), measured (**c**) and calculated (**d**).


**Table 3.** Mean values of velocity *v* (<sup>×</sup> 10−<sup>2</sup> m/s) for the experimental and numerical model along the longitudinal plane (symmetry plane) for the eight cases presented in this study.

**Figure 5.** Comparison of experimental (continuous line) and numerical (dotted line) mean velocity radial profiles at h/H = 0.8 for experiments b (**a**) and g (**b**); axial profiles at r/R = −0.75 for experiments b (**c**) and g (**d**); and axial profiles at r/R = 0.75 for experiments b (**e**) and g (**f**).
