4.1. Effect of the Rotor Cage Shape on Velocity Distribution near the Classification Surface
In order to clarify the distribution characteristics of the flow field in the classifier, multiple cross-sections were selected as the research object in the classifier, and velocity cloud diagrams and local vector diagrams of different cross-sections were obtained, as shown in
Figure 5. It can be observed from the figure that the airflow entered from the air inlet, entered the classification chamber through the guide cone, entered the rotor cage under the action of the central negative pressure, and finally discharged from the fine powder outlet. The velocity reached the maximum at the outlet of the fine powder, which was favorable to the output of fine powder, while the velocity was smaller in the near-wall area of the classification chamber, which was favorable to the fall of the coarse powder. According to the velocity vector diagram, it can be observed that after the air flow was rectified by the guide cone, most of the air flow smoothly entered the rotor cage and a small part of the air flow continued to move in the axial direction. Inside the rotor cage, the airflow moved upward at an angle of approximately 60°, causing part of the airflow to collide with the inner wall at the bottom of the rotor cage and deflect to form a vortex. This seriously affected the conveyance and classification of the material, which in turn compressed the effective classification area. While outside the rotor cage, the airflow continued to move in the axial direction, colliding with the wall at the top of the classification chamber and turning to form a vortex. Then, the vortex formed the secondary scouring for the material after classification, reducing the chance for fine particles to be collected as coarse powder.
In order to obtain a higher classification accuracy and efficiency, the "aerodynamic screen" must maintain the same mesh size, that is, to ensure a stable and evenly distributed airflow near the classification surface [
6]. According to the flow field distribution characteristics, since the high-efficiency rotor classifier was combined with the downward air inlet form, it remained difficult to ensure that the velocity distribution near the classification surface remained consistent along the axial direction. In order to determine the suitable rotor cage shape for the high-efficiency rotor classifier, the velocity distributions near the classifying surface of the column rotor cage and conical rotor cage were analyzed and compared.
The outer surface of the rotor cage was taken as the object of study. The radial and tangential velocity distributions of the airflow were obtained by taking points along the axial direction at the entrance of the rotor cage, as shown in
Figure 6. The cloud diagram for the radial and tangential velocity distributions corresponded to different rotor cage shapes, as shown in
Figure 7. From the figure, it can be observed that the radial and tangential velocities of the conical rotor cage decreased to different degrees, when compared to the column rotor cage, and that the velocity distribution was more uniform with smaller gradients. The decreases in radial and tangential velocities were mainly correlated to the rotor cage shape. Since the column rotor cage was combined with the downward air inlet form, most of the airflow moved to the upper part of the rotor cage. Meanwhile, a large vortex was formed at the bottom of the rotor cage, which made it difficult for the airflow to evenly enter the rotor cage. Hence, the radial velocity of the airflow presented a distribution of upper large and lower small. Influenced by the vortex, the tangential velocity of airflow also had a large velocity gradient. However, the conical rotor cage was combined with the downward air inlet form, which increased the cross-sectional area at the entrance of the rotor cage due to the structural characteristics of large upper and small lower, resulting in a decrease in radial velocity. The vortex at the bottom of the rotor cage was weakened by the structural limitation, thus decreasing the tangential velocity at the bottom of the rotor cage. Since the conical rotor cage was more catered to the airflow direction, the airflow could evenly enter the rotor cage, making the velocity distribution more uniform. The tangential velocity of the airflow at the entrance of the rotor cage was small, primarily because the tangential velocity of the airflow was mainly generated by the rotation of the rotor cage. However, as the airflow entered the rotor cage channel, the tangential velocity gradually increased until it remained stable. Hence, compared with the column rotor cage, the conical rotor cage made the flow field near the classifying surface more evenly distributed and the classifying force field more stable. Therefore, material particles were basically subjected to the same force at any position near the classification surface, which was conducive to improving the classification performance.
The results for the discrete phase simulation using the column and conical rotor cage at different operating conditions are presented in
Table 3. For each operation condition, the cut size using the column rotor cage was smaller than that using the conical rotor cage, with a decrease of 9.2–11.3%. In addition, K increased by 13.0–25.9%. According to the simulation results, it could be observed that the conical rotor cage could effectively improve the classification performance and had a better adaptability to different working conditions.
4.2. Effect of Blade Number on Classification Performance
The number of rotor cage blades is the key factor that affects the flow field between blades. When the number of blades increased and made the rotor cage channel narrower, the vortex intensity between blades was weakened and the flow field became more stable. However, an excessive number of blades could lead to a very narrow channel in the rotor cage, which would affect the material passage and thereby reduce the processing capacity of the classifier. Therefore, it is essential to select a reasonable number of rotor cage blades in real applications.
In order to investigate the effect of the number of rotor cage blades on classification performance, five different rotor cages with N = 24, N = 36, N = 48, N = 60, and N = 72 blade numbers were simulated and the radial velocity distribution cloud was obtained, as shown in
Figure 8. Due to the existence of vortices at the bottom of the rotor cage, only the cross-section within the effective classification area needed to be analyzed. Therefore, the velocity distributions at an XOY-plane with Z = −37.5mm and Z = −75 mm were discussed as follows.
As shown in the figure, the radial velocity between blades was distributed in a fusiform stepped manner, and a large velocity gradient generally existed. Mainly due to the limited number of rotor cage blades, the airflow in the channel was not completely in accordance with the movement of the blade profile. There was a relative axial rotational motion in addition to the relative motion between blades in the radial direction, and these two movements compounded the relative motion of the airflow in the channel. On the side of the blade proceeding surface, two kinds of motion in the same direction superimposed on each other, making the relative velocity increase. On the side of the blade receding surface, these two motions were in opposite directions, and these canceled each other out, thus causing the relative velocity to decrease. When N < 36, the blade spacing was larger. Furthermore, in the receding surface and the rotor cage inlet, there were different degrees of anti-vortex, and the flow field between blades was unstable. When N > 36, the blade spacing gradually decreased as the number of blades increased. Furthermore, the radial velocity increased and the velocity gradient in the channel became larger. Meanwhile, the increased pressure difference between the blades made the airflow on the receding side reverse, forming an inertial anti-vortex in the channel. When the number of blades was increased to 72, the rotor cage channel narrowed, the space for airflow movement was reduced, and the inertial anti-vortex between the blades was basically eliminated. However, excessively narrow channels would lead to an increased chance of collision between materials and blades, which would not be conducive for classification. When N = 36, the velocity gradient between blades was small, the radial velocity direction was basically the same, and the flow field was relatively stable.
According to the flow field distribution, it was observed that the flow field between the blades was relatively stable and uniform when N = 36. For further validation, the partial classification efficiency of the classifier was calculated by the DPM model. At different operating conditions, the partial classification efficiency curves that corresponded to different numbers of blades were obtained, as shown in
Figure 9. The cut size and classification accuracy were calculated according to the partial classification efficiency curve, as shown in
Table 4.
As shown in the chart, the cut size and classification accuracy had some fluctuations as the number of blades increased, indicating the existence of a better number of blades. When N < 36, the Tromp curve was flat, the classification accuracy was low, and the classifying effect of the classifier on material particles was poor. This was mainly due to the existence of an inertia anti-vortex between the blades, resulting in the phenomenon of back-mixing in the side of the receding surface. Hence, the material could not be classified in time. Meanwhile, due to the large blade spacing, the radial velocity in the channel was small. As the particle size increased, the effect of centrifugal force on the particles increased. Hence, the probability for material particles to enter the rotor cage and complete the classification decreased. When N > 36, with the increase in the number of blades, the classification efficiency of materials with a smaller particle size improved, but the classification efficiency of materials with a larger particle size rapidly decreased. Moreover, the greater the number of blades, the faster the decrease rate. Therefore, the classification accuracy decreased with the increase in the number of blades at different working conditions. This was mainly because as the number of blades increased, the blade spacing decreased, the radial velocity between blades increased, and the inertial anti-vortex strength became weakened. The fine particles were classified according to the better airflow carrying properties. Hence, the classification efficiency for the fine particles improved. However, a narrow rotor cage channel could lead to an increased chance of collision between materials and blades, which would increase the randomness of the material classification and decrease the classification efficiency of materials with a larger particle size. When N = 36, no polarization of the Tromp curve was observed, and a smaller cut size was obtained at higher classification accuracy, which was better for improving the classification performance and optimizing the particle grade.
4.3. Effect of the Blade Profile on the Flow Field Distribution between Blades
The movement of airflow in a rotor cage channel presents a typical forced vortex motion. On one hand, the airflow is driven by the rotor cage blade to do rotational movement; on the other hand, this moves inward under the action of the central negative pressure [
30]. In this case, the classification of material particles mainly relies on the air drag force and centrifugal force, and both of these forces come from the airflow. Therefore, achieving a high classification accuracy is necessary to ensure that the flow field between blades is uniform and stable. By analyzing the flow characteristics of the airflow in the rotor cage channel, the influence of the blade profile on the flow field distribution was investigated, and a blade profile suitable for the high-efficiency rotor classifier was designed.
Due to the existence of a vortex at the bottom of the rotor cage, two cross-sections at the axial positions of Z = −37.5 and −75 of the rotor cage were chosen as the object of study.
Figure 10 presents the cloud diagram for the radial velocity distribution and relative velocity streamline of airflow corresponding to the straight blade profile. The negative values of velocity in the figure indicate that the radial velocity direction pointed toward the center of the rotor cage, while the positive values of velocity indicate that the radial velocity direction pointed outward. As shown in
Figure 10a, the flow field in the channel was seriously polarized, and a large velocity gradient was present and could reach up to −6–0 m/s. Hence, the coarse particles could easily enter the rotor cage through the side of the proceeding surface, and these were collected as fine powder. The fine particles were easily carried by the airflow to deflect and collide with the blades, making it difficult to pass through the rotor cage. This was mainly due to the airflow in the channel induced by the rotor cage blade forced action, which formed a negative pressure area in the receding surface. This made it easy to form an inertia anti-vortex between the blades. As shown in
Figure 10b, the relative velocity of the airflow on the proceeding side was greater than that on the receding side at different axial positions of the rotor cage, and a partial inertial anti-vortex was formed on the side of the receding surface. Affected by the inertial anti-vortex and deflection, the airflow impacted the blade at a larger angle. This increased the chance for the material particles to hit the blades, which was not conducive for classification.
By analyzing the flow characteristics of the airflow in the rotor cage channel, the blade profile of the streamlined blade was determined. The movement of the airflow in the rotor cage channel exhibited a composite movement that could be decomposed into implicate and relative motion. The implicated velocity is represented by
, the relative velocity is represented by
, and the absolute velocity is represented by
. According to these three velocity vectors, the velocity triangle could be drawn at the blade inlet and outlet, as shown in
Figure 11. In the figure,
refers to the inlet installation angle, i.e., the angle between the tangent line at the airflow inlet and the tangent line of the blade;
refers to the relative velocity angle, which is the angle between the relative velocity vector and the tangent line at the airflow inlet; and
refers to the impact angle, which is the angle between the tangent line of the blade and the relative velocity vector.
Since a conventional rotor cage has a straight blade profile, the inlet installation angle
and outlet installation angle
were both 90°. The relative velocity angle was calculated using Fluent 19.0, in which the relative velocity angle
at the inlet and
at the outlet were 38° and 100°, respectively. Thus, the airflow impact angle
at the inlet and
at the outlet were determined to be 52° and −10°, respectively. According to the energy equation, it is clear that the greater the impact angle of airflow, the greater the resistance and energy loss. Therefore, the inlet angle of the streamlined blade was set to 38° in order to reduce the impact of airflow on the blade. In addition, the outlet installation angle was set to 90°, because the airflow in the blade end of the impact angle was small and the impact on the blade could be negligible. Meanwhile, the deflection of the blade profile could be reduced to facilitate the processing and manufacturing. According to the blade inlet and outlet installation angle, the streamlined blade was drawn using the single arc method, as shown in
Figure 12.
The cloud diagram for the radial velocity distribution and relative velocity streamlines corresponding to the streamlined blade is shown in
Figure 13. In
Figure 13a, it can be observed that the velocity gradient in the flow channel was significantly reduced and that the radial velocity basically stabilized from −5 to −1 m/s. Furthermore, the flow field distribution was more uniform and the inertial anti-vortex disappeared. In
Figure 13b, it can be observed that the streamlines in the different axial positions of the rotor cage were basically coincident with the blade profile. The airflow impact angle at the inlet was basically 0°, which reduced the impact of the airflow on the blade. The airflow at the outlet was also in good agreement with the blades, and there were no large deflection occurrences. The improvement of the inner flow field was mainly because the streamlined blade profile was more compatible with the flow characteristics of the airflow, reducing the aerodynamic resistance. This would be beneficial for the conveyance and classification of material particles, reducing the chance of particle back-mixing.
According to the discrete phase simulation results, d
50 and K are illustrated in
Table 5. For each operating condition, the simulation results indicated that the streamlined blade rotor cage reduced the cut size by 4.7–6.3%, while the classification accuracy remained basically unchanged. The cut size reduction was mainly due to the flow field in the rotor cage channel, which became more uniform, and the velocity gradient decreased. As a result, the drag force of the particles decreased and materials with a larger particle size had difficulties in passing through the rotor cage. However, a range of application exists for the inlet installation angle at simulated operating conditions. When the inlet air velocity and rotational speed greatly differed from the simulated working condition, the inlet installation angle and airflow incidence angle were no longer equal, which was not conducive for classification. Therefore, the application range of the streamlined blade rotor cage needs to be further studied.
4.4. Comparison of the Simulation and Experiment Results
In order to verify the reliability of the simulation results, powder classification experiments were conducted and the simulation results were compared with the experimental data. An optimized rotor cage (a conical rotor cage with 36 straight blades) was selected for the classification experiments. The experiment and simulation were performed at different inlet velocities and rotary speeds, including 13.8–500, 13.8–600, and 16.2–500. The particle size distribution when using calcium carbonate as the raw material is presented in
Figure 14. The blue line represents the cumulative distribution curve, while the red line represents the distribution frequency of the particles. After each test, the coarse and fine powders were weighed for mass balance. The samples were analyzed using a laser particle sizer, and then the partial classification efficiency of the high-efficiency rotor classifier was calculated.
The partial classification efficiency (Tromp curve) for the simulation and experiment is presented in
Figure 15. A certain difference between the simulated and experimental Tromp curves can be observed in the figure, mainly in the fishhook effect, but the overall trend was the same. The experimentally obtained Tromp curves exhibited the same S-shaped trend, presenting a fishhook effect. As the particle size increased, the partial classification efficiency curve presented a trend of initially decreasing and subsequently increasing, while the fishhook dip appeared at approximately 6 μm. This phenomenon could not be predicted by the DPM model, which was due to the neglect of particle interactions during the simulation, resulting in a higher classification accuracy for the simulation compared to that of the experiment. A comparison between the simulated results and the experimental data is presented in
Table 6. It can be observed that the cut size and classification accuracy obtained from the simulation were in better agreement with the experiment, with maximum errors of 9.4% and 9.8%, respectively. In addition, the variation of the pressure drop was well-predicted, with a maximum error of 6.0%. Since the relative errors were all within 10%, the computational model was correct and reasonable for predicting the performance of the classifier. However, the effect of the streamlined blades on the classification performance of the high-efficiency rotor classifier needs to be further verified. The application range of streamlined blades, as well as the effect on the fishhook effect and classification accuracy, are worthy of further studies.