**3. Results**

#### *3.1. Verification of the Model*

To show the feasibility and effectiveness of the proposed mathematical model, a comparison between the model prediction and the results of a physical experiment is conducted. Two important parameters, the radial coal/ore ratio and burden surface profile, are compared and analyzed. Table 2 shows the mixed charging pattern of Case 1 used in the physical experiment, where the time period of charging is 300 s (the same as the physical experiment), and the volumes of coal and DRI in one charging period (including two coal dumps and two DRI dumps) are 14.5 m<sup>3</sup> and 8.6 m<sup>3</sup> respectively.


**Table 2.** Data of charging pattern in Case 1.

According to the similarity principle, the scale ratio of the physical model to the actual furnace is 1:7.5, so the width of burden pile in the actual process should be expanded by 7.5 times. Therefore, the results for burden piles of coal and DRI in the mathematical model are listed in Table 3, including the inner end and outer end positions of the consecutive piles.

**Table 3.** Results for the burden piles of coal and DRI in mathematical model of Case 1 (Units: mm).


The burden surface profile of Case 1 obtained by the mathematical model is shown in Figure 7. As can be seen from Figure 7a, the height of the burden surface varies from 12.9 m to 14.5 m, and the burden surface is higher in the middle area and lower in the edge area. Figure 7b is an enlarged part view of the burden surface. By comparing with the result of the physical experiment (cf. Figure 7c), it can be seen that the profile calculated by the model is similar to the result of the physical experiment, showing that the mathematical model based on the burden flow width has a certain accuracy for predicting the burden profile. Both the results of the physical experiment and mathematical model show that the height of burden surface near the furnace center is lower than that in the middle region, and it then decreases along the radial direction but slightly rises near the wall. In this case, because the coal and DRI particles were charged from 2.0 m and 3.0 m outwards respectively, less particles reach the center and more particles were charged to the wall region. But the descent rate of the wall region is higher than that of the center region, and thus a lower burden bed profile was formed.

To further validate the mathematical model, the radial distribution of radial ore/coal mass ratio is compared. Figure 8 shows a comparison of the ore/coal mass ratio in the radial direction between model prediction and experimental measurement. In the physical experiment, eight samples (about 2 kg each) are collected from the layer formed in the last charging cycle at the locations of every 100 mm from center to wall. The ore/coal mass ratio is calculated based on the mass of coal and DRI particles of each sample.

Both the model prediction and experimental measurement in Figure 8 show that the ore/coal mass ratio increases first and then decreases, attaining a maximum at a radial position of about 5 m for the present charging matrix. The charging region of coal is in the radial range of 2~4.5 m, and that of DRI is in the range of 3~4.5 m. Therefore, the volume of coal distributed before the radial distance of 2 m is more than that of ore, and the mass ratio of ore/coal is close to zero. In the radial range of 2.0~4.5 m, the increase rate of coal is lower than that of DRI (cf. Table 1), so the mass ratio of ore/coal is increased. However, due to that larger size and lighter mass, coal particles tend to roll and easily be pushed to the descending region near the wall, the ore/coal mass ratio is decreased near the furnace wall.

**Figure 7.** Comparison of burden profile between model prediction and experimental measurement. (**a**) Overall schematic of model prediction; (**b**) partially enlarged view of model prediction; and (**c**) burden profile of experimental measurement.

**Figure 8.** Comparison of ore/coal ratio distribution between model prediction and experimental measurement.

Comparing the results of the mathematical model and physical experiment, it can be found that the trend is basically the same, but the value of ore/coal mass ratio calculated by the mathematical model is smaller than that measured in the physical experiment, which is mainly caused by the shape of DRI-flap in the physical experiment. In a previous work [12], it was observed that DRI particles were unevenly distributed in the circumferential direction due to the effect of DRI-flap shape, and the relative quantity of DRI distributed in the area between two adjacent flaps is somewhat more than that in the other areas. The sampling in the physical experiment is exactly in the points between the two DRI-flaps, and thus the ore quantity is somewhat large. In the mathematical model, however, it is assumed that the DRI is evenly distributed in the circumferential direction. In other words, the circumferential segregation is not considered, so the overall ore/coal ratio is somewhat smaller than the experimental value.

Since the burden distribution is determined according to its flow width (measured at a horizontal level), and do not consider the rolling of the particles at a horizontal level in the mathematical model, no material reaches the central area of the furnace (especially DRI). This is somewhat different from the results of the physical experiments. The model should thus be further improved in future studies to make it more consistent with the results of physical experiments. Overall, although the model calculation results are slightly different from the physical experiment results, the overall trend is consistent, which further proves that the mathematical model can effectively predict the mass ratio of ore/coal and the burden profile.
