## 3 Numerical Calculation and Discussion  
### Analysis of Supersonic Coherent Jets with Multi-Nozzle Oxygen Lance  
The analysis of blow characteristics plays a key role in research on oxygen top-blown converter steelmaking. A pressure gradient is the main factor causing the flow field variation, where the dynamic pressure can reflect the kinetic energy characteristics of the jetted gas. On the basis of the LSM, the dynamical pressure profiles of a top-blow in the steelmaking process were obtained (Figure 4). In the first 0.002 s, the oxygen was blown from the nozzles and the molten bath showed no obvious disturbance by the high-speed gas. In Figure 4b, the oxygen with high speed was injected vertically to the molten steel, wherein the dynamic pressure took on a high aggregate state. This produced an intensive shock force that was acting on the gas-liquid interface, as shown in Figure 4c,d. Apparently, the dynamic pressure distribution was stable, and the kinetic energy of oxygen was transferred to the molten bath through the gas-liquid interface, resulting in a series of complex physical phenomena such as dimpling, penetration, and splashing. Thereafter, the dynamic pressure and swing velocity of the molten steel gradually increased and the nozzle-twisted lance began working. In Figures 5a and 6a, it can be found that the shock morphology of the oxygen took on a concentration state, which induced the molten steel to be spattered, and the gas-liquid interface had apparent sunken, as shown in Figure 7a,b. However, with the increment of the swirl angle, the dynamic pressure of the oxygen had an apparent decrease, as shown in Figure 5c,d, and the morphology of the shock velocity had changed from concentrated state to the dispersive state. It is indicated that the vertical energy reduces, and circumferential energy increases, as shown in Figure 6c,d. Meanwhile, the spattering phenomenon was vanished, as shown in Figure 7d. To investigate the working efficiency of the nozzle-twisted lance, the physical parameters of the flow field, such as the dynamic pressure, blow velocity, and volume fraction, were compared. Figures 5-7 show the influence of different NTAs on the flow characteristics, especially the dynamic pressure, blow velocity, and two-phase interface evolution. The interference in the dynamic pressure field and velocity field of a conventional nozzle is weak. Therefore, large kinetic energy is generated, which results in a considerable impact depth and area in the molten pool. From the blow characteristics, the swirl effect of the oxygen lance with a 5\({}^{\circ}\) NTA is more obvious. Both the dynamic pressure and velocity show substantial swirling motion. Meanwhile, the kinetic energy transfer area of the gas-liquid two-phase interface was relatively concentrated and the top-blowing effect was distinct. By contrast, the impact of the 8\({}^{\circ}\) oxygen lance was not substantial. However, the tangential velocity component increased and less kinetic energy was lost at the two-phase interfaces. For the 13\({}^{\circ}\) oxygen lance, despite the increase of the NTA, the mutual interference of supersonic coherent jets between the nozzle exits was relatively large, which resulted in a large loss of kinetic energy in the collision between the jets, which in turn  
Figure 4: Dynamic pressure profiles in the blowing process with multi-nozzle oxygen lance (NTA = 0\({}^{\circ}\)). (**a**) Flow time = 0.002 s, (**b**) flow time = 0.008 s, (**c**) flow time = 0.1 s, (**d**) flow time = 1 s.  
affected the top-blowing efficiency, which is undesirable in oxygen top-blown converter steelmaking. On the basis of the aforementioned discussion, the following four points are inferred:  
1. The dynamic pressure and velocity of the conventional oxygen lance are the largest, and the impact depth is considerable. However, most of the kinetic energy is lost at the two-phase interface. 2. The 5\({}^{\circ}\) nozzle-twisted lance exhibits good performance in both impact kinetic energy and swirl of the blow gas. 3.