**5. Conclusions**

A complete 3D integrated model including the coherent jet modeling, the jet penetration cavity estimation and the decarburization modeling was proposed in this study and the validations for three parts were conducted respectively. The 3D integrated model can avoid the direct simulation of the supersonic coherent jet interacting with the liquid steel bath and provide a possible method to simulate the liquid steel-oxygen two-phase reacting flow system for the decarburization prediction with acceptable computational time. The conclusions made by adopting this 3D integrated model in EAF refining simulation are listed below:


**Author Contributions:** Conceptualization, Y.C.; methodology, Y.C.; software, Y.C.; validation, Y.C.; formal analysis, Y.C.; investigation, Y.C.; resources, Y.C.; data curation, Y.C.; writing—original draft preparation, Y.C.; writing—review and editing, Y.C. and A.K.S.; supervision, C.Q.Z.; project administration, C.Q.Z.; funding acquisition, C.Q.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Steel Manufacturing Simulation and Visualization Consortium (SMSVC).

**Acknowledgments:** The authors would like to thank the Steel Manufacturing Simulation and Visualization Consortium (SMSVC) members for funding this project. The Center for Innovation through Visualization and Simulation (CIVS) at Purdue University Northwest is also gratefully acknowledged for providing all the resources required for this work. The authors also appreciate the great help from Yury Krotov (Steel Dynamics, Inc.), Joseph Maiolo (Praxair) and Hamzah Alshawarghi (Praxair).

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript or in the decision to publish the results.
