## 5 Conclusions  
To address the low efficiency of the slagging reaction and energy transfer in the BOF process, we proposed an optimized scheme for the oxygen lance based on the CFD and fuzzy control method. The corresponding theoretical modeling and self-adjustment strategy were carried out to achieve the research goals, and the main conclusions are summarized as follows:  
1. On the basis of the standard \(k\)-\(\omega\) turbulence model and LSM, a fluid dynamics model for a BOF was set up and the four key factors (i.e., supersonic coherent jet behavior, stirring effect, energy transfer mechanism, slag-metal-gas emulsion) were obtained. The results show that 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. In comparison, the coherent jet not only induces tangential velocity but also causes a decrease of the blown kinetic energy. Therefore, appropriate tangential velocity can improve the stirring effect and accelerate the slagging reaction. However, excessive cohesion will cause serious energy loss and cannot promote the slag-metal-gas emulsification.
2. To confirm the optimal design scheme for the slagging reaction, the stirring effect of different NTA oxygen lances was investigated. The comparison indicated that the 5\({}^{\circ}\) nozzle has apparent advantages over the conventional oxygen lance at the liquid level, but the improvement in the whole molten bath is not obvious. The 8\({}^{\circ}\) oxygen lance has a substantial stirring effect, but the near-wall velocity was weak. The results suggested that a uniform slagging reaction was achieved when the 8\({}^{\circ}\) oxygen lance was used. Otherwise, the optimal design scheme can improve the energy transfer efficiency and reduce the spray of the molten bath.
3. With respect to lance height, the self-adjustment control strategy for a multi-nozzle oxygen lance was adopted. The predictions indicated that the optimal NTA was within the range from 7.2\({}^{\circ}\) to 7.8\({}^{\circ}\), and the superior NIA distribution from 9.0\({}^{\circ}\) to 12.5\({}^{\circ}\). When the lance is at a low height, the optimal NIA is inversely proportional to the lance height. Within the lance height range of 1400-1800 mm, the optimal NTA and NIA are relatively stable. With the continued increasing of lance height, the optimal NTA decreases. It is in good agreement with previous studies, theoretical analyses, and simulations. The results presented here can provide support for saving and refining energy, improving top-blowing efficiency, and accelerating slagging reactions.  
[PERSON] and [PERSON] conceived and designed the research; [PERSON] and [PERSON] performed the simulations; [PERSON], [PERSON] and [PERSON] analyzed the data; [PERSON] and [PERSON] contributed analysis tools and provided research platform; [PERSON], [PERSON], and [PERSON] wrote the paper. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of China (NSFC), grant number 51775501, and the Zhejiang Provincial Natural Science Foundation for Distinguished Young Scientists, grant number LR16E050001.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
LSM Level Set Method  
CFD Computational Fluid Dynamics  
NTA Nozzle Twist Angle  
RANs Reynolds Averaged Naiver-Stokes  
FVM Finite Volume Method  
PRESTO Pressure Staggering Option  
CFL Courant-Friedrichs-Lewy  
NIA Nozzle Inclination Angle