*4.4. The E*ff*ects of Ca, La1, Njm,* δ*, Hi and hi*

The position of the tracer feeding position and the insertion depth of the side nozzle are also important variable parameters. The expression of the dimensionless group of mixing time was studied after adding these two dimensionless groups. On the basis of the above dimensionless groups, the dimensionless group related to the tracer feeding position and the dimensionless group related to the insertion depth of the side nozzle was added unceasingly into the equation of mixing time dimensionless group. After substituting the parameters such as the flow velocity of upper side nozzle and the insertion depth of upper side nozzle into the Equation (14), multiple linear regression was performed through the origin, and the results are shown in in Table 9:



As can be seen from Table 9, the equation of the dimensionless group of the mixing time of the upper side nozzle is as follows in Equation (21):

$$\tau = \frac{D\_{\rm s}}{V\_{\rm us}} (\text{Ca}^{-1.87} \text{La}\_{1}^{-2.72} \text{N}\_{\rm jur} \, ^{5.35} \delta^{0.12} \left(\frac{H\_{\rm i}}{H\_{\rm oil+w}}\right)^{-0.36} \left(\frac{h\_{\rm us}}{H\_{\rm oil+w}}\right)^{0.01}) \tag{21}$$

*Processes* **2020**, *8*, 129

$$\tau = \frac{D\_s}{V\_{ls}} (\text{Ca}^{-1.84} \text{La} \text{ }^{-2.61} \text{N}\_{\text{jm}} \text{ }^{4.77} \text{\ $}^{-0.40} \left(\frac{H\_i}{H\_{oil+w}}\right)^{-0.36} \left(\frac{h\_{ls}}{H\_{oil+w}}\right)^{0.01} \text{\$ } \tag{22}$$

Similarly to the upper side nozzle, Table 9 can also be obtained after the injection velocity and insertion depth of the lower side nozzle are replaced in the Equation (14) by multiple linear regression. According to the data in Table 9, the equation of the dimensionless group of mixing time of lower side nozzle can be obtained in Equation (22).

By comparing the dimensionless group calculated by the dimensionless Equations (21) and (22) with the dimensionless groups measured in the experiment, the correctness of the above dimensionless group can be verified. Figure 11a shows the relationship between the experimental value and the calculated value of the mixing time dimensionless group for the upper side nozzle, while Figure 11b shows the relationship between the experimental value and the calculated value of the mixing time dimensionless group for the lower side nozzle. It can be seen from Figure 11a,b that the fitting effect of a dimensionless group of mixing time is good. At the same time, in order to further verify its accuracy, Figure 12a–f shows the fitting curves of the three mixing time monitoring points at the respective operating conditions of the upper side nozzle and the lower side nozzle, respectively. It can also be seen that the distribution of the showcases 1, 2, and 3 has a relatively high degree of fitness. Therefore, it can be concluded that the equation of the mixing time dimensionless group of the upper side nozzle and the equation of the mixing time dimensionless group of the lower side nozzle have practical reference value.

**Figure 11.** Comparison of experimental lgτ*Vs*/*Ds* with calculated ones for upper side nozzle (**a**) and lower side nozzle (**b**), respectively, using proposed Equations (21) and (22).

**Figure 12.** Comparison of experimental lgτ*Vs*/*Ds* with calculated ones for upper side nozzle (**a**–**c**) and lower side nozzle (**d**–**f**), respectively, using τ1, τ2, τ3.

### **5. Conclusions**

Based on the experimental research and data analysis, the dimensionless groups of mixing time and kinetic viscosity, the surface tension, the tracer feeding position, the insertion depth of the side nozzle, etc., were obtained. In this paper, the expressions between the dimensionless group of mixing time and dimensionless groups such as Ca and La1 were obtained by multiple linear regression. It can be seen from the expressions that the indexes of the dimensionless groups have a higher identity when they have more than three dimensionless groups. By verifying the calculated and experimental values of the dimensionless group of mixing time, it can be seen that both have a good positive correlation. At the same time, it can also be seen from the comparison between the calculated values of τ1, τ2, τ<sup>3</sup> and the experimental values that they are in good agreement with the corresponding τ, which indicates that the fitting expressions have higher reliability. Because density, surface tension, and other parameters of the medium have not been changed in this study, Equations (15) and (16) are more suitable for the study of the side nozzle velocity and related angle. Equations (21) and (22) will be of great significance when the density, viscosity, surface tension, and furnace diameter of the medium are changed in further work. This conclusion will better provide help for the control of key parameters, help to establish the design standard of C-H2 smelting reduction furnaces, and lay a foundation for the optimization of side nozzle parameters of C-H2 smelting reduction furnaces.

**Author Contributions:** Conceptualization, J.X. and J.Z.; Data curation, J.X. and J.Z.; Formal analysis, J.X.; Funding acquisition, J.Z.; Investigation, J.X. and J.Z.; Methodology, J.X., B.W., and J.Z.; Project administration, J.Z.; Resources, J.X., B.W., and J.Z.; Supervision, J.Z.; Validation, J.X., B.W., and J.Z.; Writing—original draft, J.X.; Writing—review and editing, J.X., B.W., and J.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was funded by the National Science and Technology Support Program for development of smelting reduction iron smelting process based on hydrogen metallurgy (2006BAE03A12).

**Acknowledgments:** The authors gratefully acknowledge the resources partially provided by the State Key Laboratory of Advanced Special Steel, Shanghai University of Materials Science and Engineering.

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

### **References**

1. Tylecote, R.; Hua, J. *History of Metallurgical Development in the World*, 1st ed.; Beijing Science and Technology Literature Publishing House: Beijing, China, 1985; pp. 576–582.


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