## 4 Optimization and Analysis of Multi-Blade Centrifugal Fan
### Optimization Results and Analysis
The maximum static pressure position is closer to the outlet compared to before optimization in the sections of z = 50 mm and z = 25 mm, which weakens the backflow phenomenon near the tongue, improving the impeller efficiency and reducing the fan noise. The maximum and minimum static pressure difference after optimization has increased by approximately 187 Pa compared to before, indicating an improvement in the pneumatic performance. Figures 17 and 18 illustrate the velocity-streamline nephograms of the fan. Analysis shows that the airflow acceleration effect of each section of the fan is significantly promoted. Based on the turbulence kinetic energy diagram (Figures 19 and 20), it can be inferred that the matching between the airflow inlet angle and the blade inlet angle has been improved, the flow separation effect in the blade channel has been weakened, and the flow loss inside the fan has decreased. The average velocity of the airflow at the impeller outlet position has increased by about 8 m/s compared to before optimization, which means that the airflow is receiving more energy, and the fan efficiency has improved by 0.67%. Figures 19 and 20 show the nephograms of turbulent kinetic energy before and after optimization. It can be seen that during the operation of the fan, the positions with strong turbulent kinetic energy are concentrated near the tongue, in the blade channel, and inside the impeller, all of which are the main sources of fan noise. By comparison, it can be found that the flow situation near the solute tongue with the section of z = 75 mm has significantly improved, as the tongue radius near the front disc of impeller is larger, and the unsteady interference between the tongue and airflow is weakened, manifested by a decrease in the overall fan noise. After optimization, the turbulent kinetic energy in the blade channel of the fan at the main work area z = 50 mm and z = 25 mm sections significantly decreased  
Figure 16: Static pressure nephogram of each section after optimization. Figure 15: Static pressure nephogram of each section before optimization. To further illustrate the optimization effect, three monitoring points p1, p2, and p3 near the volute tongue (Figure 2) are selected for pressure pulsation analysis, as shown in Figure 21. From the figure, it can be seen that there are obvious peaks at the rotating frequency (70 Hz) and blade frequency (2871 Hz) at each pressure pulsation monitoring point before and after optimization, indicating the accuracy of the simulation results. The optimized fan has a varying reduction in the peak pressure pulsation at three monitoring points. The reduction effect of pressure pulsation is most significant in the middle and rear disc positions of the impeller: the amplitude of the middle and rear discs decreased by 32.12 Pa and 55.82 Pa at 70 Hz, while the amplitude decreased by 30.03 Pa and 2.6 Pa at 2871 Hz, respectively. Figure 21: Pressure pulsation at detection points near the volute tongue before and after optimization. (a) p1 pressure pulsation. (b) p2 pressure pulsation. (c) p3 pressure pulsation. After increasing the tongue radius at the front disc, the interference between the airflow and the tongue is weakened, and the periodic impact on the volute tongue is weakened. Moreover, due to the change in the radius of volute tongue, there is a phase difference in the unsteady force on the volute tongue at different heights. After superposition, the overall effect is weakened compared to before optimization, which is manifested as a decrease in the noise of the optimized fan (Figure 22). In order to observe the noise performance of the optimized fan, the noise sound pressure level of the remote field monitoring points before and after optimization are compared (Figure 22). According to the curves, it can be observed that the sound pressure level of the optimized fan has decreased to a certain extent in most frequency bands, and at the one- and two-time blade frequencies, the noise has significantly decreased by 10.24 dB and 6.46 dB, respectively.