*3.2. Surface Velocity and Boundary Layer Thickness of Silicon Rods*

In order to find ways to relieve the excessively high temperature in the upper bridge area of the silicon rods, the gas flow field in the same section in the three schemes is visualized, as shown in Figure 6. The flow velocity in designs B and C at each cross-section is larger than that of design A, especially at the upper part of the furnace body. The area with a flow velocity above 3.5 m/s increases significantly, while the area with flow velocity below 0.5 m/s decreases significantly, which can be called a gas stagnation zone. Although the gas flow rate decreases rapidly with the rise in the vertical height, the flow velocity of the latter two designs is mostly maintained at 1–1.5 m/s above the height of 1.7 m and even reaches a high flow velocity of 2 m/s at the top-most part. As a result, the gas stagnation zone is greatly reduced, indicating that designs B and C have a relatively stable flow structure on the vertical cross-section. Meanwhile, the flow velocity on the surface of the silicon rod is more noteworthy, since it directly determines the replenishment of reaction gas and the displacement of reaction tail gas. The calculation shows that the average velocity around the silicon rod surface is 1.19 m/s, 1.80 m/s and 2.53 m/s in designs A, B and C, respectively. The increase in flow rate and flow velocity can increase the gas flow velocity on the surface of the silicon rods, which will be more conducive to reducing the volume of the overheated gas area and supplementing the reaction gas in time.

**Figure 6.** Flow field distribution. (**a**) Design A; (**b**) design B; (**c**) design C (height of horizontal sections is the same as in Figure 4).

The boundary layer thickness in different schemes is plotted to better evaluate the velocity distribution on the surface of the silicon rods, as shown in Figure 7. The boundary layer refers to the thickness of the area with a large velocity gradient near the surface of the silicon rods. From the wall of the boundary layer, the velocity in this area decreases rapidly along the tangential direction of the wall. Different schemes have similar value distributions, and larger values appear in the upper part and bridge part of the silicon rods. The difference is that the values around the silicon rod bridge part in design A and design B is greater than those in design C, even reaching 7 mm, while the values in design C are mostly between 2–5 mm. In the middle position of the outer-ring silicon rods, designs B and C have smaller values than design A, which means that the boundary layer thickness of design A is larger than that of designs B and C. In order to compare the distribution uniformity, the deviations of the parameter on the surface of the silicon rods at different times in different schemes were obtained and are shown in Table 4. These values also evaluate the uniformity of the boundary layer thickness at different thicknesses of silicon rods (different deposition stages). The boundary layer thickness deviation in design A is the lowest, with an average of 46.6%. Meanwhile, the average values of design B and design C reach 50% and 48%, respectively. These values show that the increasing flow rate and increasing flow velocity achieve smaller boundary layer thickness but also improve the non-uniformity of the boundary layer on the surface of the silicon rods, especially when the diameter of the silicon rod is small. By comparison, design C has better uniformity than design B, and its boundary layer thickness deviation is closer to that of design A, which can provide both better gas flow structure and better polysilicon deposition conditions. Therefore, design C is determined as the base plate scheme for the reduction furnaces in coupled mode.

**Figure 7.** Boundary layer thickness along the rods. (**a**) Design A; (**b**) design B; (**c**) design C.

**Table 4.** Boundary layer thickness deviation (%).

