*3.3. Slag Eye Modeling*

Tang et al. [14] compared the change in slag eye area between equal and differentiated flows at various gas injection parameters, including the angle between the dual plugs from 45◦ to 180◦ and its radial position from r/R = 0.5 to r/R = 0.7 and the gas flow rate. They found that in most cases the proportion of slag eye in the differentiated flow system is smaller than that in the equal flow system. Their results show that the proportion of slag eye in differentiated flow first decreases and then increases with the increasing relative angle of plugs at the same flowrate, and the exposed areas of the slag eyes of the two modes generally decrease with plug position from 0.55R to 0.70R, apparently due to the obstacle of the ladle wall and its absorption of the stirring energy. The slag eye is the smallest at 0.7R–90◦ and 0.7R–135◦. Conejo et al. [19] measured the change in the slag eye area between equal and differentiated flows for two nozzle radial positions (0.7R/0.7R and 0.7R/0.5R) and two angles (45◦ and 90◦). Their results show that the use of differentiated flow increases the area of slag eye for an angle of 45◦ and equal plug positions, whereas there is a decrease in the eye when using unequal plug positions and an angle between plugs of 90◦. From these results, it can be seen that the change in slag eye becomes rather complex in the presence of multiple variables.

Figure 7 presents the time-averaged predicted slag eye of the eight experiments (see Table 2) using the developed numerical model. The effect of the three variables, namely, gas flow rate, dual gas injection ratio and (slag) oil thickness on the size of the slag eye was predicted. As seen in the experiment, an increase in gas flow rate increases the extent of slag eye area in all cases, whereas the opposite effect is obtained with an increase of (slag) oil thickness. A good agreement between the experimental results (see Figure 5 of Jardón-Pérez et al. [15]) and the numerical results can be seen in Table 5, with slag eye area as a percentage of the total surface. Again, the drag effect generated with a differentiated gas injection was not captured completely by the model, i.e., the smaller slag eye is not attracted to the center as observed in the experimental results, but the shapes of the slag eye were correctly predicted. For example, for the case with 5% (slag) oil thickness and differentiated 2.22 L/min gas flow rate, presented in Figure 8, the numerical size of the big eye is slightly under-predicted, whereas the small eye is over-predicted, when compared against the measured eyes. As mentioned earlier, the velocity field near the water–oil (steel–slag) interface and the slag eye size features are not properly captured by the numerical model, which opens an opportunity for improvement of the physical description of the interaction between the two phases through the modification of forces such as drag and surface tension.

**Figure 7.** Time-averaged prediction of slag eyes at different operating conditions obtained with the numerical model. (**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 5.** Slag eye area as a percentage of the total surface area for different operating conditions experimentally obtained through image analysis from both experimental and numerical models.

**Figure 8.** Comparison of the time-averaged photograph of the slag eye obtained with the (**a**) experimental model (operating condition of differentiated dual gas injection with 5% (slag) oil thickness and 2.22 L/min gas flow rate) and the corresponding time-averaged (**b**) numerical model prediction. Dimensions of measured and predicted open slag eyes are also indicated.

#### *3.4. Mixing Time Modeling*

Mixing phenomena in metallurgical steel ladles by bottom gas injection involve three phases, namely, liquid molten steel, liquid slag and gaseous argon. Mixing time is the time needed for an established constant flow field to disperse an injected non-reactive tracer until the required mixing criterion is achieved. This criterion is generally set to 95%, although 99% and 99.5% [23,24] can be used as well. Typically, the mixing efficiency of a ladle is qualified as the mixing time (τ*m*) and is an important indicator for the hydrodynamic performance to quantify the degree of agitation, which influences secondary refining treatment in a ladle through desulphurization. Lou and Zhu [25] modeled desulfurization and inclusion removal in a ladle with multiple nozzle configurations. They concluded that dual nozzle configurations have a higher desulfurization rate than single nozzle configurations for the same flow rate. Zhu et al. [26] investigated the mixing phenomena in argon-stirred ladles with six types of tuyere arrangement. They concluded that mixing time is greatly influenced by the position of the tracer, and that mixing time decreases with increasing gas flow rate, although the effect is not so remarkable. Haiyan et al. [13] studied the effect of gas flow rate on the mixing phenomenon in a bottom-stirring ladle with dual plugs. They found that compared with the same flowrate for the two plugs, the mixing time is lower with different flow rates when the plug positions are located at 0.64R. This is mainly due to the strong gas plume, which produces a larger circulation flow to stir the ladle. A weaker plume forms a smaller one, which weakens the interference and collision from the two plumes, thus reducing the mixing time. Recently, Ramasetti et al. [27] calculated the mixing time of tracer addition into the metal bath of a ladle, which decreased when the argon flow rate was increased.

Nunes et al. [28] were among the earliest to use a dye tracer to determine the mixing time in a ladle, thus eliminating the dependence on the monitoring position. For the measurement of mixing time, techniques such as using a pH meter or conductivity meter are the most common, although more recently dye tracers and laser-induced fluorescence (LIF) have been used. To measure the time needed to reach a stable state, usually a criterion of ± 5% of variation of property is used, which can be measured by pH in a pH meter, conductivity in a conductivity meter, and tracer concentration and luminescence in LIF. In the experimental study of Jardón-Pérez et al. [15], mixing time in a gas-stirred ladle was measured by means of the novel technique of planar laser-induced fluorescence (PLIF) that uses Rhodamine 6G as a tracer. PLIF determinations were performed at two different planes and pH probe determinations were performed at two different locations. The results were then compared, which showed not only the accuracy of the PLIF method, but also that it is less sensitive to the location of the measurement than the pH probe method. A detailed explanation of the technique can be found in Jardón-Pérez et al. [29]. Ascanio [30] does not recommend the technique for highly aerated flows, because the presence of bubbles complicates the calibration and the measurement of the obtained concentration contour.

From the experimental study of Jardón-Pérez et al. [15], it was found that all cases gave smaller mixing times with the same conditions of (slag) oil thickness and dual gas injection ratio. The increase in the thickness gave slightly higher mixing times. The numerical model of the mixing time presented in this study gave very similar results to the experimental mixing time for both 50%:50% equal flow and 25%:75% dual differentiated flow. As with the experimental study, the effect of a 25%:75% dual injection ratio is slightly less significant with conditions of high gas flow rate (2.22 L/min) as compared with conditions of low gas flow rate (1.54 L/min) for 3% (slag) oil thickness than with 5% (slag) oil thickness (see Table 6). The deviation from the experimental mixing time was found to be the greatest for 25%:75% dual differentiated flow at a high gas flow rate (2.22 L/min), whereasthe deviation was found to be the lowest for 25%:75% dual differentiated flow at low gas flow rate (1.54 L/min) both at 5% oil thickness. The difference between experimental and predicted mixing times can be explained by comparing the experimental (Figure 2) and numerical (Figure 3) flow patterns. As can be seen, the area of the low-velocity zone with dual injection is higher for the numerical model than the physical model, mainly due to the difficulty of simulating the interaction between both the gas plumes, especially when a differentiated injection is used. This is because the interaction between the low-injection and the high-injection plumes (see Figure 3c,d,g,h) shows a large deformation in both plume structures due to the drag force that the high-injection plume exerts on the low-injection plume.


**Table 6.** Mixing time in seconds for different operating conditions experimentally (obtained through the planar laser-induced fluorescence (PLIF) method) and compared with the numerical model.

Figure 9 shows the trend in the model predictions and the experimental results reported in Jardón-Pérez et al. [15] based on all the cases implemented in this study. In this Figure, it is seen that the model is able to capture the more important issues regarding the behavior of the system under different experimental conditions. Considering that differences between predicted and experimental measurements increase for differentiated gas injection and high slag thickness (Cases 7 and 8 in Figure 9 and Table 2), the results suggest that these are places in which to seek improvements in the numerical model, especially in high slag thickness. This is probably because with a higher slag thickness the influence of slag emulsification on mixing time becomes prominent, since the numerical model does not consider the emulsified droplets. This is also shown clearly in Figure 10, which depicts the difference in the model prediction compared with the experimental results reported in Jardón-Pérez et al. [15] for the cases of low gas flow rate (Figure 10a) and high gas flow rate (Figure 10b), thus exploring the ability of the numerical model to capture the two limit cases analyzed in this study.

**Figure 9.** Comparison between the model prediction (dotted line) and experimental mixing time (black dots) obtained by Jardón-Pérez et al. [15].

**Figure 10.** Effect of the gas flow rate on the mixing time predicted by the model and experimental measurements for (**a**) low gas flow and (**b**) differentiated gas flow.

In both figures, the best match is obtained for the case of low gas flow rate and low slag thickness. At a high flow rate, the differences between experimental and predicted results increase for all cases (see Table 6) and these differences are bigger for differentiated gas injection, independently of the gas flow rates. The results suggest that modeling efforts must be focused on the improvement of the turbulence model, as well as finding approaches to simulate the effect of the slag layer (mainly the slag emulsification) on the flow dynamics of the stirred melt and to simulate changes in the flow plume linked to the change in the mode of gas injection.

However, even if numerical values of both slag eye area and mixing time show differences between numerical and experimental values (see Tables 5 and 6), the effect of the studied variables is correctly predicted by the mathematical model, i.e., an increase in gas flow rate causes an increase in the exposed area and a decrease in the mixing time, an increase in slag height causes a decrease in the slag eye area and an increment in the mixing time, and finally, the use of differentiated gas injection causes a slight increment in the exposed area but also a decrement in the mixing time compared with equal injection. Therefore, the CFD numerical model could be used to study the main effects of operation variables on both mixing time and slag eye area.
