*2.3. Parameters of Blast Furnace and Assumptions of Calculation*

In order to combine the mathematical model with the radar data for a blast furnace, the relevant parameters of the charging system are listed in Tables 1–3.


**Table 1.** Parameters of the bell-less top blast furnace.

<sup>1</sup> Distance from throttle to chute suspension point. <sup>2</sup> Distance from the chute suspension point to the chute bottom plate. <sup>3</sup> Distance from the chute suspension point to the zero line.


**Table 2.** Parameters of rotating chute.

**Table 3.** Physical parameters of raw material.


Considering the influence of the charging parameters, burden distribution properties, and practical experience of blast furnace operators, the mathematical model combining the radar data was derived on the basis of the following assumptions [5,23]:

(1) Velocity of particles after collision with chute can be described by an attenuation factor without bouncing of particles in the chute.

(2) The chute rotates around the centerline of the blast furnace at any inclination angles with the revolution speed of 8 ring/min.

(3) There is no size distribution of particles in the raw material. The drag force of particles in the air after the chute and Coriolis force can be ignored.

(4) Burden is distributed in three dimensions, is uniform around the circumference, and is symmetrical around the centerline of the blast furnace.

(5) Burden keeps an alternate layer structure during the descent.

#### **3. Application of the Combined Model and Results**

#### *3.1. Mathematical Model Test*

The trajectory of the burden flow model was used to calculate the material flow path at different inclination angles of the chute as shown in Figure 13. With the increase of the inclination angle of the chute, the trajectory moves to the periphery. The drop point for a large inclination angle of the chute is farther away from the center line of the blast furnace. When the inclination angle of the chute is less than 15◦, the chute dumps the materials directly to the center of the furnace (called center-charged burden), which cannot be observed in Figure 13. Figure 14 shows the radial velocity of the burden descent calculated by the burden decent velocity model (Equations (19)–(21)). The descent velocity increases with the increase of the distance from the centerline.

**Figure 13.** Main trajectories of coke flow.

**Figure 14.** Burden descent velocity from the mathematical model.

Based on the parameters of Tables 1–3 and charge matrix of Table 4, the burden distribution of a multi-ring charging program was calculated by the burden profile model. The results are shown in Figure 15. Blue, green, and red lines express the initial material surface, and the ore and coke surface, respectively. An ore profile with a single ring is shown in Figure 15a. After the full burden matrix, the burden distribution of a batch of ore and coke can be calculated as shown in Figure 15b. The structure of multi-batch burden layers (two coke and two ore layers) was calculated by iterative calculation, as shown in Figure 15c. From the latter, the same type of material has a similar shape and the apexes of the burden profile move toward the periphery a little during the descent due to the effect of the shaft angle of the furnace.


**Table 4.** Charging matrix of a blast furnace.

**Figure 15.** Burden distribution by a multi-ring charging program based on Tables 1–4: (**a**) 1st ring of ore; (**b**) a full burden distribution of an ore and a coke layer with multi-ring; (**c**) 2 coke and 2 ore layers. Blue line: initial material surface. Blue dash-dotted line: wall. Green line: ore layer. Red line: coke layer.

In order to test the mathematical model, a number of cases are listed in Table 5. A comparison of the burden distributions for different charging matrixes is shown in Figure 16. Figure 16a shows burden profiles with central coke when the inclination angle of the chute is 12◦ and the number of coke rings is 5. Figure 16b shows the burden profile with exactly the same parameters as in Figure 16a but for four coke rings. Comparing Figure 16a,b, only one ring of coke moves to an angle of 27◦, which means the central coke becomes thinner and the thickness of the coke layer at an angle of 27◦ becomes bigger. With another ring of coke moving to 27◦ (Figure 16c), the thickness of the central coke becomes much thinner and the layer becomes much thicker than in Figure 16a. Figure 16d shows the burden distribution without the central coke and three rings moved to an angle of 20◦. Compared to Figure 16c, the central coke has disappeared and the layer thickness at an angle of 20◦ becomes bigger than in Figure 16d. a comparison of Figure 16d,e shows that only a ring of coke moves from an angle of 20◦ to 27◦. Therefore, the only difference between them is that the coke thicknesses at these two angles are somewhat different. Figure 16f shows the burden distribution with one ring less of coke at an angle of 27◦ compared to (e). Comparing Figure 16f,g, the burden distribution without two rings at an angle of 20◦ in the latter yields a thin layer at an angle of 20◦. In Figure 16h, every inclination angle of the chute decreased by 1◦ except 27◦ for coke. Therefore, the ore layers move toward the center. Figure 17 shows the effect of the ore batch on the burden distribution (a. with ore batch of 63 t and b. with ore batch of 55 t). When the ore batch decreased from (a) to (b), the ore layer thickness became smaller.


**Table 5.** Charging programs with different matrixes to test the mathematical model.

**Figure 16.** (**a**–**h**) are the comparison of burden distributions corresponding to the charging matrix of (**a**–**h**) in Table 5.

**Figure 17.** Comparison of the burden distribution with different ore batches: (**a**) Ore batch of 63 t; (**b**) Ore batch of 55 t.

Figures 16 and 17 shows the test of the sensitivity of the mathematical model. When the number of burden rings increased, the corresponding thickness of the burden layer increased. When the inclination angle of the chute changed, the structure of the burden layers changed accordingly. According to the conservation of volume, the burden distribution changes with the change of the burden batch. In short, changes in the inclination angle of the chute, ring of charging, and ore batch will cause corresponding changes of the layers predicted by the mathematical model.

The burden distribution with the charging matrix of Table 5a is shown in Figure 18a. The ratio of ore to coke (Equation (23)) is defined by the last two layers and is shown in Figure 18b. The ratio is zero at the center due to the central-coke layers and has a highest value at r = 1.3 m at the inclination angle of the chute of 31◦.

**Figure 18.** (**a**) Burden distribution; (**b**) ratio of ore to coke from (**a**) case.

#### *3.2. Combination of the Mathematical Model and Radar Data*

Radar data can work together with the mathematical model to support and guide the operation of blast furnace charging. Therefore, it is necessary to compile them into a visual interface. Based on the charging parameters and radar data from a plant in East China, a 2D simulation software of blast furnace charging was developed. The model was programed in Python and the visualization code was provided by JavaScript to give a friendly web interface.

A cloud map drawn by radar scanning data is shown in Figure 19a. Radar scanning data includes many points in an interval. After noise removal and feature extraction in the interval, 20 relatively stable points (green curve) were obtained. These points were used to calculate the burden distribution by the burden distribution model. The calculated burden layers' structure is shown in Figure 19b.

**Figure 19.** Burden profile: (**a**) Burden profile from radar data; (**b**) Burden profile from the mathematical model combined with radar data.

In order to display the radar data and the results of the mathematical model, we designed a user-friendly operator interface. Its main functions are shown in Figure 20. After logging into the software (Figure 20a), the left column is the function menu of the software. A column is designed to enter the parameter settings of the furnace in Figure 20b and includes blast furnace parameters, chute parameters, raw material properties parameters, charging matrix, and so on. The burden distribution display is the main page of the software and is drawn out by Echarts after radar data

processing in Figure 20c. After noise removal and feature extraction, the radar data combined with the mathematical model illustrate the structure of the material layers. The burden descent velocity and ratio of ore to coke are also drawn in the main interface. In addition, the system parameters of the radar are also monitored, such as the chip temperature, nitrogen temperature and nitrogen flow rate, valve pressure in radar system, and liquid flow rate.

**Figure 20.** Visualization of our software by the combination of the mathematical model and radar data: (**a**) Software login interface; (**b**) Parameter setting interface; (**c**) Burden distribution display and radar data monitor; (**d**) User management interface.

In order to guarantee the security of the data and analyze the data of different users and different furnaces, a user management system was designed for user administration, as shown in Figure 20d.
