Effect of Initial Bubble Temperature on the Temperature Filed

Figure 9 shows the temperature measurement position in industrial practice, and the numerical simulation of the temperature varies with the solution time at the temperature measurement position. In industrial practice, the temperature is 1759 K before the argon blow, and the temperature is 1740 K when the argon blow lasts for 22 min. The temperature drop rate is 0.0144 K/s. The bubble is injected from the ladle bottom, and then the bubble temperature is lower than that of the molten steel, which will decrease the molten steel temperature. Figure 9b shows the temperature variation with the solution time under different initial bubble temperatures. The temperature decrease rate is 0.0147 K/s, 0.023 K/s, and 0.0313 K/s when the initial bubble temperature is 800 ◦C, 400 ◦C, and 25 ◦C, respectively. The temperature decrease rate is increased when the initial bubble temperature decreases. The temperature decrease rate is similar to the industrial practice when the initial bubble injection temperature is 800 ◦C.

Figure 10 shows the iso-surface of the temperature under the different initial bubble temperatures when the argon blow simulation time lasts 150 s. The molten steel temperature is lower where the bubble is placed. The low-temperature area is diffused along the fluid flow direction.

**Figure 9.** (**a**) Temperature measurements position in the industrial practice; (**b**) temperature varies with solution time at the temperature measurements position.

**Figure 10.** The temperature iso-surface under different initial bubble temperatures: (**a**) 25 ◦C, (**b**) 400 ◦C, and (**c**) 800 ◦C.

Figure 11 shows the sliced contour of the temperature when the initial bubble temperature is 800 ◦C and the solution time is 150 s. The results show that the temperature in the ladle bottom is higher than those in the other slices. The temperature in the bubble plume area is lower than those in the different regions. The temperature distribution is asymmetric because the plugs distribution is asymmetric, which results in the flow being asymmetric. The high-temperature area is diffused to the low-temperature area.

Figure 12a shows the streamline in the top view of the ladle. The stream in the ladle is divided into two main circulations. Plug 1 is set at 0.67*R*<sup>m</sup> and plug 2 is set at 0.6*R*m. Figure 12b shows the schematic of the circulation, and the circulation is larger in plug 1. The circulation area is asymmetric, which results in the temperature field asymmetry. The temperature fields are diffused in the flow direction. The circulation area of plug 1 is larger than that of plug 2, then the molten steel temperature above plug 1 is higher, as shown in Figure 11f.

**Figure 11.** The temperature slice contour when the initial bubble temperature is 800 ◦C: (**a**) slice position, (**b**) slice position near the bottom, (**c**) slice position at Y = 0.3935, (**d**) slice position at Y = 0.787, (**e**) slice position at Y = 1.18, and (**f**) slice position at near the surface.

**Figure 12.** (**a**) The streamline in the top view; (**b**) the schematic of the streamline in the different plugs.

#### 3.2.3. The Steel–Slag Interface Shape

Figure 13a shows the argon-stirred process in a steel plant. The ladle contains 25 t of molten steel. There are two plugs used in the argon-stirred process, and there are two places called 'slag eyes' plotted by blue dash circles. Figure 13b shows the simulation results of the steel–slag interface shape during the argon-stirred process, and there are two 'peaks' formed above the two plugs. The argon bubbles drive the fluid upward, then push the slag away, which results in the two 'slag eyes' formed. Figure 13b shows that the maximum height of the steel–slag interface is 7.95 mm, and the simulation results of the position of the 'slag eyes' are similar to industrial practice.

**Figure 13.** (**a**) The molten steel and slag surface during the argon-stirred process, and (**b**) the numerical simulation results of the steel–slag interface position.

#### 3.2.4. Alloy Melting and Alloy Species Diffusion

Figure 14 shows the sliced contour of the dimensional concentration. Figure 14a–c show the alloy added in the 'slag eye' above plug 1. The results show that the alloy melts and releases the species of the alloy, then the species is diffused along the fluid flow direction. Figure 14d–f show that the alloy added above the 'slag eye' is above plug 2.

**Figure 14.** The contour of the slice of the dimensional concentration of the alloy species in the ladle when the alloy is added on the 'slag eye' above plug 1, after (**a**) 10 s, (**b**) 65 s, and (**c**) 120 s; when the alloy is added on the 'slag eye' above plug 2, after (**d**) 10 s, (**e**) 65 s, and (**f**) 120 s.

Figure 15a,b show the alloy melting position when the alloy is added in the 'slag eye' above plug 1 and plug 2. Figure 15a,b show that the alloy melting position is in a circle shape, near the 'slag eye'. Figure 15c shows the statistical results of the melting time, and the results show that the average melting time is 12.49 s and 12.71 s when the alloy added in the 'slag eye' is above plug 1 and plug 2, respectively. The melting time when the alloy is added in the 'slag eye' above plug 1 is less than that of plug 2. Figures 11f and 12 show that

the circulation area in plug 1 is higher than that of plug 2, the molten steel temperature in the 'slag eye' above plug 1 is higher than that of plug 2, and the melting time is decreased when the molten steel temperature increases. Figure 15d shows the average dimensional concentration varying with the solution time, and the average dimensional concentration is increased and reaches a maximum after the alloy is added after 20 s. The maximum of the average dimensional concentration is higher when the alloy is added on the 'slag eye' above plug 1, because the melting time is less, and the average dimensional concentration has fewer changes after the alloy is added after 100 s.

#### **4. Conclusions**

In this paper, a multi-physics numerical simulation model in an argon-stirred ladle was established, the random walk model was used in the bubble transport model, and the effect of *CL* on the fluid flow simulation was studied for the first time. In the temperature simulation, a heat flux transfer model in molten steel and bubbles was introduced for the first time. The effect of initial bubble temperature on the molten steel temperature simulation was discussed. The alloy melting and alloy concentration diffusion were simulated. The multi-physics simulation model was beneficial in the ladle design and the modification of the parameters.

(1) The random walk model needs to be applied to the bubble transport model. The velocity difference between the numerical simulation and the hydraulic model decreases when the *CL* decreases from 0 to 0.3 and increases when the *CL* increases from 0.3

to 0.45. The velocity difference between the numerical simulation and the hydraulic model is minimum when the *CL* is 0.3.


**Author Contributions:** Conceptualization, C.H. and Y.B.; Methodology, C.H.; Software, C.H.; Validation, C.H. and Y.B.; Formal Analysis, C.H.; Investigation, C.H.; Resources, Y.B.; Data Curation, C.H.; Writing—Original Draft Preparation, C.H.; Writing—Review and Editing, C.H., Y.B. and M.W.; Visualization, C.H.; Supervision, Y.B.; Project Administration, Y.B.; Funding Acquisition, Y.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Open Project of State Key Laboratory of Advanced Special Steel, Shanghai Key Laboratory of Advanced Ferrometallurgy, Shanghai University (SKLASS 2020-02), and the Science and Technology Commission of Shanghai Municipality (No. 19DZ2270200).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All the data are given in the manuscript.

**Conflicts of Interest:** The authors have declared no conflict of interest.

#### **Nomenclature**


