**5. Conclusions**

The fluid-particle flow inside a bifurcated SEN is studied to evaluate flow oscillations through the LBM model. From the results, the following conclusions are drawn:


This work represents our further efforts towards fluid-particles flow, vortices structures and their effects on turbulence inside bifurcated SEN flow. Further studies are needed to study the behaviour of introduced particles or bubbles under the framework of LBM model, the interaction between vortex structure and bubbles as well as their interactions (aggregation and breakdown).

**Author Contributions:** Software, P.Z.; validation, P.Z.; investigation, Z.Z.; writing—original draft preparation, P.Z.; writing—review and editing, R.P.; funding acquisition, R.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (No. 51174122), and Anhui University of science and technology introduction of talent research start-up fund project (No. 13200456).

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** National Engineering Laboratory for Vacuum Metallurgy, Kunming University of Science and Technology for the supports.

**Conflicts of Interest:** The authors declare no conflict of interest.
