*4.2. Stirring Mechanism*

Generally, there are different stirring mechanisms that affect the flow characteristics of the molten bath, including the momentum stirring, the bubble stirring and the electromagnetic stirring. In addition, the buoyancy force arising from the bath temperature gradient and the bath concentration gradient will also make contributions to stir the bath. In the present study, the electromagnetic stirring is assumed to be neglected in this alternating current (AC) EAF since the electromagnetic field induced is limited to the small region around the arcs and has a minor effect on the molten bath flow [28–30]. The stirring caused by the buoyancy-driven flow is always included in the model by applying the Boussinesq hypothesis for the liquid steel phase since it is a natural phenomenon built in any thermal system. As for the rest two stirring mechanisms, that is, the momentum stirring and the bubble stirring, they are the main stirring power provided by the supersonic coherent jet to the refining process, which are valuable and feasible to be investigated using the 3D integrated model proposed above.

In the actual steel refining process, the distance between the burner nozzle exit and the liquid steel bath surface is usually controlled to be within the jet potential core length to guarantee the coherent jet can maintain a relatively high kinetic energy when reaching the liquid steel bath. In this case, the coherent jet is able to push the liquid steel aside to form a cavity and transfer the momentum to the bath simultaneously. Generally, only a portion of the jet momentum can be transferred to a liquid steel bath and further used to generate the stirring. Sano et al. [23] reported that only 6% of the total jet momentum is transferable to the liquid steel and this value has also been proved to be suitable for the current simulation under the given burner operating condition. The stirring generated by this direct momentum transfer is called the momentum stirring. Another critical stirring mechanism during the refining process is the bubble stirring. The decarburization reaction will generate the CO bubbles that float upward together with oxygen bubbles quickly, creating a strong stirring power inside the liquid steel bath due to the bubble-liquid drag force. The CO bubbles will eventually be absorbed by the slag layer and subsequent chemical reactions will occur there. It has been reported that bubble stirring plays a key role in the homogenization of the flow field, therefore the corresponding investigation conducted below is aimed to reveal the impact of those two stirring mechanisms on the development of the flow field.

The comparison of the flow filed with and without the bubble stirring is given in Figure 8. Figure 8a shows the case only considering the momentum stirring. It can be seen that the high momentum transferred from the surface of the jet penetration cavity pushes the liquid steel downward, resulting in a high-speed liquid steel flow in the axial direction of the cavity together with vortexes generated on both sides. The volume-averaged liquid steel velocity in the bath fluctuates most frequently around a value of 0.01425 m/s. Figure 8b shows the case considering both the momentum stirring and the bubble stirring. Because of the bubble stirring, the high-velocity region occurs surrounding the jet penetration cavity instead and the direction of the vortex changes significantly. This is mainly due to the intensive oxidation reactions in that region generating a large number of oxides and the stirring intensity of the momentum transfer became much weaker compared to that of the floating CO and oxygen bubbles. In addition, significant turbulence is generated through bubble stirring in the liquid steel bath as well, which can lead to a better mixing. The volume-averaged velocity of the liquid steel bath is approximately 0.1485 m/s, which is about 10 times as much as the case only considering the momentum stirring. From this comparison, it can be seen that bubble stirring greatly promotes the homogenization of the liquid steel bath and is one of the most important stirring mechanism in the EAF refining stage.

**Figure 8.** (**a**) Momentum stirring without bubble stirring; (**b**) Momentum stirring together with bubble stirring.

The bath mixing efficiency evaluation for both cases was conducted as well and the results are given in Figure 9. A tracer is introduced in the center of the liquid steel bath and the simulations stop once the tracer is fully diffused inside the bath. During the simulation, the area-averaged concentration of the tracer is monitored at three different horizontal planes in the bath to evaluate the mixing time. The vertical distance between those three horizontal planes and the bottom of the furnace is 0.07 m (plane monitor 1), 0.47 m (plane monitor 2) and 0.57 m (plane monitor 3), respectively. Noticed that, plane monitor 1 is close to the furnace bottom surface, which is aimed to avoid the dead zone and guarantee the full diffusion of the tracer in the domain. Figure 9a shows the contours of the in-bath tracer mass fraction variation over time. Figure 9b,c show the molar concentration variation of the tracer over time. When the variation in the molar concentration of the tracer is negligible, the mixing time required for the liquid steel bath to reach full diffusion can be obtained. It can be seen that without the bubble stirring, the mixing time is estimated to be 1665.3 s, which is almost 9.5 times longer than the time needed for the case with the bubble stirring. Therefore, the bubble stirring needs to be considered in the stirring mechanism for the future simulation of the liquid steel flow field.

**Figure 9.** (**a**) In-bath tracer mass fraction over time (with momentum transfer and bubble stirring); (**b**) Mixing time of flow field without bubble stirring; (**c**) Mixing time of flow field with bubble stirring.
