## 3 Prototype Performance Analysis
Figure 11 shows the flow diagram of the prototype fan with the different span, on which it can be seen that before the optimisation of the leaf shape, there is an apparent vortex coming off the trailing part of the moving blades in the A area on the 0.1 span, and the airflow is turbulent in the d dynamic-static coupling duct; as shown in the B area in the figure, there are vortices and backflow phenomena in the front abdomen of the OGVs on the 0.5 span, the airflow speed is deficient, there is flow separation at the trailing edge of the blade root, and the flow field condition is not good; as shown in the C area, the OGVs at 0.9 span are at the end of the same giant vortex. In summary, the fan has a poor flow field in the OGVs duct, shedding vortices and swirls, and the OGVs structure has a significant impact on the fan's performance and noise. Comprehensive analysis of the acceleration and vibration characteristics of the fan and internal flow analysis shows that the OGVs duct is the worst of the three ducts. To further analyse the impact of the OGVs on the fan's performance, the following analysis of the static pressure distribution and pressure pulsation at the different span of the OGVs was conducted. From Figure 12, it can be seen that the static pressure distribution of the different OGVs spans are the same; the separation points of the three spans of the OGVs are all at 0.25, very close to the front, while the gradient of the pressure surface static pressure curve is enormous, in 0.0-0.4 streamwise, and \(C_{p}\) decreases from 0.4 to \(-0.8\), indicating that there  
Figure 11: Original axial flow fan streamline diagram. (**a**) 0.1 span streamline. (**b**) 0.5 span streamline. (**c**) 0.9 span streamline. Figure 10: Schematic diagram of fan rotating surface and pressure pulsation monitoring points. is a large number of shedding vortices and apparent pressure pulsations in the flow field in this region. \(C_{p}\) is the pressure coefficient. The equation of the \(C_{p}\) is as follows:  
\[C_{p}=\frac{p}{0.5\rho u^{2}} \tag{7}\]  
where \(p\) is the static pressure in Pa; \(\rho\) is the density in m\({}^{3}\), and \(u\) is the leaf tip linear velocity in m/s. For the axial flow fan that increases the OGVs, the vortex, backflow, and other complex flow phenomena in the OGVs duct may lead to rapid changes in fluid pressure within the fan continuously over time, i.e., pressure pulsation. Vortex shedding noise and the pressure pulsation value related to the blade surface per unit area of the pulse of the lift can reflect the sound radiation pressure. Therefore, reducing the value of the pressure pulsation can effectively mitigate the acoustic radiation pressure. The relationship is as follows:  
\[P=\frac{x_{i}}{4\pi R^{2}C}\iint\limits_{S}\left\{-\frac{\partial F_{T}}{ \partial t}(y_{i},t)\right\}dS(y_{t}) \tag{8}\]  
where \(F_{\rm T}\) is the pressure pulsation value (or pulsation lift per unit area on the blade surface), \(x_{i}\) is the coordinates of the observation point, \(y_{i}\) is the coordinate value of the source point (\(i\) = 1, 2, 3), and R is the distance between the source and the observation point. Usually, R is much larger than the blade size, so \(R=|x_{i}-y_{i}|\approx|x_{i}|\); C is the acoustic velocity, and \(S\) is the blade surface area. The effect of the OGVs on the pressure pulsation over the OGVs duct is analysed below. Pressure pulsation monitoring points are set at the 0.1, 0.5, and 0.9 spans at the OGVs inlet, pressure surface, suction surface and outlet, respectively, and the monitoring points are set up as shown in Figure 13.  
Figure 12: Static pressure distribution at the different span of the OGVs before optimisation. From the time domain graph of pressure pulsation, information, such as the amplitude of pressure changes, can be analysed and the key locations of pressure changes can be determined. The following is an analysis of the pressure pulsation time domain diagram. Figure 14 shows the time-domain analysis of the pressure pulsation at each monitoring point over one cycle.