*4.1. Model Validaiton*

The validation of the coherent jet modeling in ambient air with and without shrouding flame was conducted based on the research works done by Anderson et al. [2]. The simulation was set up according to the reported experiment. The comparison of the jet axial velocity distribution between the present study and the measurement data is given in Figure 6a. The jet with the shrouding flame can maintain its initial velocity for a longer distance compared with the jet without the shrouding flame. The coherent jet with Mach 2.1 at nozzle exit has the potential core length around 48 De (where De is the diameter of the converging-diverging nozzle exit), which is 2.5 times longer compared with the conventional jet in this validation. On the contours given in Figure 6b, the entrainment of the ambient air is blocked by the shrouding combustion flame, which significantly reduces the turbulence effect around the primary oxygen jet leading to the great increase of the potential core length. The average difference in this validation is 5.9% compared with experimental data, which shows good accuracy of current supersonic coherent jet modeling.

**Figure 6.** (**a**) Jet axial velocity distribution with & without shrouding flame; (**b**) Velocity, temperature, density field distribution of the supersonic coherent jet.

The validation of the jet penetration cavity estimation was done by comparing the predicted jet penetration depth with the measurement data provided by Praxair under the same burner operating conditions. It should be noted that the burner configuration of the coherent jet used for current validation differs from the above-mentioned coherent jet validation. The key parameters of bath for jet penetration cavity estimation are given in Table 2. The jet penetration depth is measured under the fixed burner operating conditions. The distance between the jet nozzle exit and the liquid steel bath surface is successively increased to reach different penetration depths, thereby obtaining six sets of available data for the validation as shown in Figure 7a. The parity plot of the jet penetration depth inside the liquid steel bath is given in Figure 7b showing the comparison of the estimation in the present study and the experimental data by Anderson, et al. The jet penetration reduces exponentially as the nozzle moves away from the liquid surface. This is because when the nozzle-liquid surface distance is greater than the jet potential core length, no doubt increasing the distance (cases #4 to #6 in Figure 7a) will decrease the jet penetration depth since smaller momentum the jet will have when reaching the liquid bath surface. On the other hand, if the nozzle-liquid surface distance is less than the jet potential core length, the jet maintains the same axial velocity but the area of the jet mixing zone

in the radial direction increases with the increase of the nozzle-liquid surface distance (cases #1 to #3 in Figure 7a). This results in a reduction of the jet maximum pressure gradient in the mixing zone, thereby reducing the jet penetration ability inside the liquid steel bath. The tendency of the estimation in the present study meets the above description and the error compared with measurement data is less than 5% showing a good accuracy of the estimation.


**Table 2.** Key parameters of bath for jet penetration cavity estimation.

**Figure 7.** (**a**) Different nozzle-liquid surface distance for specific burner configuration; (**b**) Parity plot of penetration depth inside liquid steel bath.

The current 3D integrated model was adjusted accordingly to predict the decarburization process of the industrial electric arc furnace for model validation. Under the same furnace operating conditions, the percentage error of the decarburization rate prediction given by the model is less than 7% compared with industrial data.
