## 4 Results and Discussion
### Tangential Velocity Distributions  
To investigate the effect of the guide cone on the velocity distribution in the classification chamber, the points (P\({}_{i}\)) at the outer surface of the rotor cage (i.e., rotor's inlet), at the middle of the wall and the outer surface of the rotor cage, and near the wall region were taken from top to bottom in the axial direction, as indicated in Figure 5.  
Figure 4: The path line of the airflow inside the classifier, with \(d\) of 708, 808, 758, and 658 mm. Figure 3: Vortices of the airflow inside the classifier (vectors are colored according to velocity magnitude). (**a**) Vortices in the classification chamber and guide cone; (**b**) vortices in the coarse material cone. The arrows show the vortex rotation with the circles indicating the vortex location. The contour of the tangential velocity distribution at a vertical central plane in the classifier is shown in Figure 6. A comparative analysis of the above four cases reveals that the tangential velocity distribution almost achieved uniformity with the guide cone at a diameter of 808 mm. This uniformity was beneficial in improving the separation efficiency. Consequently, it was anticipated that the classification efficiency would be optimal in this case. Moreover, it is noteworthy that, in all four simulation cases, no vortices were observed in the blade zone. This absence of vortices created a stable airflow pattern within this critical region, which is essential for maintaining consistent and efficient particle classification processes. V\({}_{t1}\), V\({}_{t2}\), V\({}_{t3}\), and V\({}_{t4}\) are the tangential velocities corresponding to \(d\) = 708, 808, 758, and 658 mm, respectively. From Figure 7, it can be seen that the tangential velocities decreased significantly from the blade zone (I) (i.e., space between rotor blades) to the annular zone (II) (i.e., space between the rotor outer surface and the classification chamber wall). The tangential velocity in the annular zone (II) was much lower than that in the blade zone (I). As a result, the fine particles were likely to migrate to zone (II) under the influence of strong centrifugal forces and finally settle along the side wall to become a coarse powder. This phenomenon led to a decrease in both classification efficiency and accuracy. A comparison of the above cases shows that V\({}_{t3}\) was the highest in both (I) and (II). Conversely, V\({}_{t2}\) was the smallest and the most stable in these regions. After entering  
Figure 5: Points in the classification chamber are used for velocity determination. Figure 6: Contours of the tangential velocity distribution inside the classifier, with \(d\) of 708, 808, 758, and 658 mm, respectively. the rotor cage, V\({}_{11}\), V\({}_{12}\), V\({}_{13}\), and V\({}_{14}\) increased sharply, facilitating the transport of the fine particles. In this region, V\({}_{t1}\), V\({}_{t2}\), V\({}_{t3}\), and V\({}_{t4}\) were similar. In addition, the tangential velocities of the airflow near the wall were approximately zero, which is clearly presented in Figure 8c. This is why the particles lost their kinetic energy and fell, resulting in the formation of coarse products. From Figure 8a, it can be seen that the tangential velocities fluctuated across the points (Pi) from the top to the bottom face of the rotor cage under the four different guide cone structures. Specifically, V\({}_{t3}\) was the highest, whereas V\({}_{t2}\) was the smallest. V\({}_{t1}\) and V\({}_{t4}\) were similar. However, in the middle of the classification chamber, as presented in Figure 8b, V\({}_{t1}\), V\({}_{t3}\), and V\({}_{t4}\) increased slightly from the top face of the rotor cage. V\({}_{t2}\) was the smallest and increased slightly on the left side of the rotor, but it decreased significantly on the right. On this side, V\({}_{t2}\) attained its peak at point 2 in the upper half of the rotor cage, but it overcame  
Figure 8: Comparison of tangential velocity distribution at certain points (Pi).