*3.2. Turbulence Modeling*

Figure 6 shows the simulated profiles of turbulent kinetic energy (*k*) at the same operating conditions of Figure 2 (see Table 2 for the sequence of the experiments). A reasonable agreement can be seen in Table 4 between the experimental and numerical results of turbulence, showing that the *k*-ε realizable turbulence model was an appropriate choice to represent turbulence in the three-phase fluid flow system implemented in this study. Due to the turbulence promoted by the bubbles, high turbulence zones corresponding to the two plume zones were observed. By increasing the gas flow rate (Figure 6b,d) the values of turbulent kinetic energy *k* in the circulation loops increase. A thicker slag reduces turbulence and the interaction between the loops. Although the magnitudes of the turbulent kinetic energy *k* in the plane overestimated the experimental results in almost all cases (in comparison with Figure 4 of Jardón-Pérez et al. [15]), the above-mentioned main effects of the three variables on *k* were successfully predicted with the numerical model. However, some features were not captured by the model, such as the drag effect (comparing Figure 2h with Figure 3h), where the smaller plume zone was not attracted to the center due to the influence of the loop.

**Figure 6.** Contours of turbulent kinetic energy (*k*) 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].

**Table 4.** Mean values of turbulent kinetic energy *<sup>k</sup>* (<sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>m</sup>2/s2) for the experimental and numerical model along the longitudinal plane (symmetry plane) for the eight cases presented in this study.

