## 3 Numerical Calculation and Discussion
### Analysis of Stirring Effects and Impact Characteristics in Molten Bath Flow  
The evolution of the gas-liquid phase in a steel converter is the main factor that leads to stirring and splashing of the molten bath. Most of the kinetic energy of the blown gas is lost at the gas-liquid interface, and the energy conversion of oxygen impacting the molten bath is ineffective. Accordingly, tracking the evolution of the two-phase interface is important for analyzing the flow field characteristics in a molten bath and characterizing the top-blowing state. To explore the influence of the blown gas on the molten bath, we constructed a velocity vector diagram of the top-blowing with a conventional oxygen lance at the steel liquid level, as shown in Figure 9. In Figure 9a, the steel liquid near the wall had the maximum volume fraction and the center region had a minor volume fraction, which indicated that the shock effect range of the oxygen with high speed only focused on the center region of the molten steel. In addition, a great disparity is observed in the velocity of oxygen and molten steel. The gas flow rate is approximately 200-300 m/s, and the liquid steel flow rate is 0-3 m/s (Figure 9b). Therefore, the velocity vector diagram of molten steel is obtained by filtering the low velocity values (there may be some low-speed gas molecules) and filtering the high-speed molten steel, as shown in Figure 9c). To discuss the stirring effect in the molten bath, we need to analyze the velocity of various NTAs at different steel converter heights. Figure 10 shows the velocity vector (Y-plane projection) at the steel liquid level with different NTAs. In the surface layer, the velocity distribution and scale of 0\({}^{\circ}\), 5\({}^{\circ}\), and 8\({}^{\circ}\) oxygen lances are similar and all of them exhibit the phenomenon of high intermediate velocity and small surrounding velocity. However, the flow rate of the 13\({}^{\circ}\) oxygen lance is low, which is related to the large loss of kinetic energy in the blow process. In addition, the conventional and 5\({}^{\circ}\) nozzle form the vortex package in the area of the steel converter wall through several high-speed flow belts, resulting in molten flow at the surrounding area of the steel converter. The transition area of the 8\({}^{\circ}\) nozzle is annular, indicating that the stirring effects in the center and surrounding area are better; however, almost no flow occurs in the area near the wall. Two main reasons account for this phenomenon: (i) First, the tangential velocity component of the 8\({}^{\circ}\) nozzle is high, the molten steel exhibits stable swirling under the tangential force, and the peripheral velocity is relatively uniform because of the influence of the fluid viscous force. (ii) Second, the blow impingement of the conventional and 5\({}^{\circ}\) nozzles is intense and the local kinetic energy is high, which leads to a considerable impact depth. The splashing caused by impact increases the radial velocity of the molten steel, thus causing the aforementioned situation. To analyze the stirring effect of each NTA nozzle, we investigated the horizontal velocity at different molten steel depths, as shown in Figure 11. Although the conventional nozzle and 5\({}^{\circ}\) nozzle have advantages in some aspects, the 8  
Figure 8: Turbulence kinetic energy profiles in top-blowing steelmaking with different multi-nozzle oxygen lances. (**a**) NTA = 0\({}^{\circ}\) (**b**) NTA = 5\({}^{\circ}\) (**c**) NTA = 8\({}^{\circ}\) (**d**) NTA = 13\({}^{\circ}\). oxygen lance has a good stirring effect in various layers of the molten steel. In addition, the 13\({}^{\circ}\) nozzle is less effective at swirling, consistent with the previous theoretical prediction. Figure 10: Velocity vector of molten steel at the liquid level with different multi-nozzle oxygen lances. **(a)** NTA = 0\({}^{\circ}\) **(b)** NTA = 5\({}^{\circ}\) **(c)** NTA = 8\({}^{\circ}\) **(d)** NTA = 13\({}^{\circ}\). Figure 9: Velocity vector diagrams of molten steel at the steel liquid level.