## 3 Results and Discussions
### Flow-Field Analysis
Figure 16: Time-averaged streamlines on the diffuser vane pressure side for different inclination angles: (**a**) \(75^{\circ}\), (**b**) \(30^{\circ}\), (**c**) original diffuser, (**d**) \(-30^{\circ}\), (**e**) \(-75^{\circ}\). Figure 19 shows the time/space dimensionless pressure distributions on the 50% span of the suction and pressure sides of diffuser vanes, for various inclined leading edge during one impeller rotational period. It should be noted that the y axis is normalized by the diffuser vane chord length. It is evident that in all cases, the unsteady pressure fluctuations are well captured. Figure 19a shows that in the case of the original diffuser vanes, from the leading edge (LE) to trailing edge (TE), the magnitude of pressure is increased due to the diffuser effects. As shown in the figure, the transient effects of the pressure fluctuations are identified near the diffuser inlet on the suction side in \(-0.3<x/c_{D}<0\), which are generated by the reattached and separated flows within the diffuser passages. In addition, near the leading edge of the diffuser van, there are high-pressure regions, which are caused by the stagnation point and interaction of the impeller and diffuser blades. The generated pressure disturbances by the impeller-diffuser interactions are clearly observed in Figure 19, and are extended from the leading edges toward the trailing edges of the diffuser vanes [40; 41; 42]. Fifteen main blade pressure waves are clearly visible on the each side of the diffuser van. Moreover, between these pressure waves, there are other fifteen pressure waves with lower pressure magnitude, which are generated by the splitter blades. As shown in Figure 19, the slope of these generated waves by interactions between the impeller blades and diffuser vanes is constant along the diffuser channel, and is well-known as the convective velocity. From leading edge toward the trailing edge of the diffuser van, as the main flow travels toward downstream, the magnitude of the pressure waves is decreased, and near the vane trailing edge, the magnitude of these waves is almost uniform. It should be noted that these pressure fluctuations inside the diffuser channels reveal the strong connections between the aerodynamic and acoustic fields, which are called as the dominant discrete noise sources in the centrifugal compressors. In addition, the existence of these pressure waves, which are periodically generated inside the diffuser channels with respect to time confirms the flow pulsation inside the diffuser passages. Figure 17: Instantaneous iso-surface of \(Q_{criterion}\) near the leading edge for one impeller full passing period for various inclined leading edges: (**a**) original diffuser vane, (**b**) \(30^{\circ}\), (**c**) \(-30^{\circ}\) (\(Q_{criterion}=95,\)000 s\({}^{-2}\)). It is interesting to note that there are also some other waves with different slopes compared to those of the impeller blades, which are generated along the streamwise direction on the pressure and suction sides of the diffuser vane, as indicated by the arrows in Figure 19. These waves are caused by the unsteady movements of the separated flow regions within the diffuser passages (see Figure 17), which are named as separation pressure waves. These waves are related to shear layer motions inside the diffuser channels as well as the enlargement and concentration of the separation bubbles toward the diffuser exit. The maximum and minimum values of the static pressure contours were obtained in \(30^{\circ}\) and \(-75^{\circ}\) inclined leading edges, respectively, which are in a good agreement with Figure 13; Figure 13:0 Moreover, in the case of \(30^{\circ}\) inclination angle in the leading edge, no significant separation wave is observed at the pressure and suction sides of the diffuser vane (see Figure 19b).