*3.3. Results of Coupling Scheme*

In coupling mode, several reduction furnaces are connected in series to maximize the utilization of raw materials, which also provides the possibility to make full use of the heat of exhaust gas. Since the conversion rate of raw materials is generally about 10%, the influence of the difference in the contents of gas components on the composition of raw materials is ignored in the calculation, and attention is paid to the inlet gas temperature of furnace #1 and furnace #2. With the help of the calculation platform, the pipe between the coupled reduction furnaces with different silicon rod diameters was modeled. With reference to the actual process, the interlayer cooling water temperature was set to 413 K, and the corresponding silicon rod diameter inside the furnace body was 50 mm. The temperature field distribution in the pipe was obtained and is shown in Figure 8. The tail gas of furnace #1 is discharged from the base plate and transported to the inlet nozzles

of furnace #2 through pipes. The outlet temperature of furnace #1 reaches 780 K. From the base plate outlet, the channel is connected to the annular pipeline viaa1m vertical pipeline. At this time, the gas temperature reaches 622 K, and the temperature decreases by about 158 K. Before the tail gas enters furnace #2, it needs to be cooled by water cooling through a 4 m long pipe, and the temperature drops to 523 K. After the water-cooled pipe, combined with the actual distance, the outlet temperature can be maintained at around 523 K through the thermal insulation pipeline and then connected to reduction furnace #2.

**Figure 8.** Temperature distribution of tail gas.

The gas temperatures corresponding to the different silicon rod diameters at the outlet of furnace #1 are between 534 K and 745 K, so the inlet temperature of furnace #2 is set according to these values. Further, gas temperature and pipe outlet gas temperature corresponding to different diameters of the silicon rods of coupled reduction furnace #1 and furnace #2, including 30 mm, 50 mm, 90 mm and 125 mm, were calculated, as shown in Table 5. With the increase in diameter, the gas temperature at the outlet gradually increases, and the tail gas temperature gradually rises. However, when the rod diameter reaches more than 90 mm, temperatures remain basically unchanged, and the temperature at the outlet of the pipeline also has similar trends. The pipe outlet temperature of furnace #2 is higher than that of furnace #1, ranging from 170 K to 450 K, which can be easily explained because fresh gas as raw material is heated twice in two furnaces.



In order to calculate the process characteristics of coupling mode, design C was used in both coupled reduction furnaces #1 and #2. The internal physical fields of the two furnaces with different silicon rod diameters were modeled and calculated, and the thickness deviation of the boundary layer is shown in Table 6. The data show that the difference in the thickness deviations of the boundary layer between the two furnaces is very small, which means that the performance of the two reduction furnaces is similar in coupling mode. Design C provides approximate gas flow conditions and ensures the consistency of the deposition conditions of the two furnaces to a certain extent. At the same time, the boundary layer deviation decreases rapidly and then increases slightly with the increase in the silicon rod diameter. The consistency of deposition conditions is best when the silicon rod diameter is 90 mm, which means that the gas flow structure of design C plays the largest role when silicon rods grow to this diameter. Therefore, the base plate scheme in design C was adopted for the two reduction furnaces, i.e., furnace #1 and furnace #2. The coupling reduction process can adopt single-direction feeding, and the feeding switching step is no longer required.


**Table 6.** Boundary layer thickness deviation (%).

When the diameter of the silicon rods is 90 mm, the flow field and temperature field of the two reduction furnaces are shown in Figure 9. The gas flow rate near the bridge position is still high; an area of more than 2.5 m/s in the 2.3 m height section accounts for more than 50%, and the area of a gas flow rate of less than 0.5 m/s accounts for less than 5%: that is, the gas stagnation area is greatly compressed. Although the temperature in the furnace is high at this growth stage, due to the strong gas flow circulation, the temperature distribution near the silicon rod with the same section in the upper section of the overall reduction furnace is relatively uniform, and the excessive-temperature area in design A no longer exists. Due to the increase in flow velocity and the improvement in flow structure, the surface temperature distribution of the silicon rods is relatively uniform in the upper area of the silicon rods. Only the temperature near the bridge of the silicon rods in the inner ring is slightly higher than 1450 K, and the temperature distribution is mostly concentrated between 1350–1450 K. Compared with furnace #1, the overall gas temperature of furnace #2 is higher for higher inlet temperature. As the diameter of the silicon rod becomes larger, the outer-ring silicon rods have a greater shielding effect on the radiation of the inner silicon rods, and the gas near the inner-ring silicon rods is about 50 K higher than that near the outer-ring silicon rods. In summary, the temperature distribution of the silicon rod is uniform, and the temperature at the bridge is also maintained at an appropriate level, which is conducive to improving the deposition rate and reducing energy consumption while maintaining the uniformity of deposition.

The modeling of the deposition process was also carried out using PolySim software, and the quasi-steady-state method was used to approximate the silicon rod growth process. Based on the former calculated results of different deposition times, including silicon rod surface temperature, boundary layer thickness and its deviation, silicon rod surface flow velocity, inlet gas composition and other parameters, process characteristic parameters such as deposition rate were obtained using the built-in model. While maintaining similar deposition quality between the two reduction furnaces, the expected process characteristics were obtained and are shown in Table 7. The deposition rate in coupling mode reaches 20.8 kg/h, which is 44.9% higher than that of the two single reduction furnaces. The unit energy consumption is 17.2% lower than it was in the original scheme, reaching 74.2 kWh/kg. Although a single furnace in coupling mode has a lower conversion rate of raw materials of about 7%, this parameter increased by 17.5% to 14.1% from 12%. This means that the coupling scheme achieves a significant improvement in the characteristics of the deposition process, significantly reducing the reaction time from about 80 h to 53 h, and the optimization range is obvious.

**Figure 9.** Temperature and velocity distributions. (**a**) Cross-sections of gas velocity; (**b**) cross-sections of temperature; (**c**) rod surface temperature (the height of cross-section is 0.5 m, 1.1 m, 1.7 m and 2.3 m, respectively).

**Table 7.** Process characteristics.

