## 3 Results and Discussions
### Flow-Field Analysis  
The effect of the inclination angles of the diffuser vanes on the compressor aerodynamic performance was already evaluated with steady simulations in the previous work [11]. In steady calculations, while the impeller and diffuser locations are changed during the numerical simulation, the relative position of the impeller and diffuser across the interface is fixed (frozen rotor interface), which is known as clocking effect. Therefore, as it was shown in [11], the flow-field distributions within the diffuser passages are different at the design point. In addition, in the steady simulations, the transient effects between the impeller and diffuser are not taken into account. For these reasons, in order to have time-averaged and symmetric flow patterns within the compressor passages and also to realize the transient behaviors of the inclined leading edges on the flow physics, and clearly identify the radiated noise generated within the compressor, the unsteady simulations were carried out at the design point for five various cases, with \(\alpha\) = (0, \(\pm\)30, and \(\pm\)75)\({}^{\circ}\). Figure 13 compares the time-averaged static pressure and velocity contours at mid-span cutting plane for various inclination angles with those of the original diffuser vanes. The pressure and velocity magnitudes shown in Figure 13 are normalized by the inlet pressure and tip velocity, respectively. It is clearly observed that the highest pressure ratio within the diffuser passages is related to 30\({}^{\circ}\) inclined leading edge. However for \(-\)30\({}^{\circ}\) inclination angle, the magnitude of the static pressure is reduced compared to the original diffuser and 30\({}^{\circ}\). The lowest pressure ratio distribution was found for the \(-\)75\({}^{\circ}\) inclined leading edges. The velocity contours demonstrates that by using 30\({}^{\circ}\) hub-to-shroud inclined leading edge, the separated regions generated on the pressure sides of the diffuser vanes are reduced in comparison to other cases. However, for \(-\)30\({}^{\circ}\) inclined leading edge in diffuser vane, the separation and low-momentum flow zones are clearly identified within the diffuser passages, especially close to the trailing edges. Figure 13 showed that  
Figure 12: Flow-field distributions at mid-span near stall (at 4.16 kg/s mass flow rate); Mach number contour: (**a**) original diffuser, (**b**) 30\({}^{\circ}\) inclined leading edge, normalized pressure contour: (**c**) original diffuser, (**d**) 30\({}^{\circ}\) inclined leading edge. the hub-to-shroud inclination angles are more effective to improve the efficiency of the current centrifugal compressor. Moreover, in the case of 30\({}^{\circ}\) inclined leading edge, the high-momentum regions in the vaneless space are decreased compared to the original diffuser, and the flow-field is more uniform. In order to show the effect of inclined leading edges on the flow-field, the time-averaged meridional velocity profiles are shown in Figure 14a. The velocity profiles are circumferentially averaged close to the diffuser vane leading edge. Figure 14a shows that the magnitude of velocity is decreased near the shroud for the 30\({}^{\circ}\) case and the difference between minimum and maximum of the velocity signal is decreased in the spanwise direction compared to the original diffuser vane. For 75\({}^{\circ}\) and \(-\)75\({}^{\circ}\) inclination angles, the velocity magnitude is significantly reduced near the shroud and hub, respectively. Moreover, the time-averaged pressure profiles at the midspan along the streamwise direction from inlet to outlet of the diffuser are shown in Figure 14b. It is observed that for 30\({}^{\circ}\) case, the pressure recovery along the diffuser passage is increased compared to other cases due to reduction of separations and low-momentum regions. Figure 13: Time-averaged pressure and velocity distributions for different inclined leading edge at 50% span.