## 3 Analysis of the Impeller-Diffuser Interaction
### Impeller Flow Analysis  
Figure 9 shows the meridional velocity contours at five hub-to-shroud sections of the impeller and Figure 10 presents the corresponding turbulent kinetic energy contours. At surface 1, the meridional velocity is clearly influenced by blade loading (with a faster relative flow at SS) and by different curvatures of the walls (which are the cause for the hub to shroud gradient). The meridional velocity distribution is progressively distorted downstream by the increasing thickness of the shroud boundary layer; this can be seen at surface 3 of Figure 11. The growth of this low momentum region corresponds to the increase of the high turbulence zone at the casing shown in Figure 10. A better knowledge of the complex phenomena inside the rotor can be achieved through the analysis of the vorticity contours of Figure 11. The different contributions to secondary flows can be seen clearly in surface 1: two blade surface vortices along the blade height (at SS: BVS, at PS: BVP, i.e., blade surface vortices at the respective sides) and a strong vortex near the casing. This last vortex results from the merging of the passage vortex at shroud (PVS) and the Coriolis vortex (CV), as discussed by [PERSON] [26]. The blade vortex is stronger at the SS, due to the greater velocity gradient of the boundary layer, and tends to vanish towards the radial exit, as shown in Figure 11. This is consistent with the conservation equation of the vorticity along a streamline derived by [PERSON] [27] and developed by [PERSON] [28]. The blade vorticity carries low energy fluid along the blade, from the hub to the  
Figure 8: Mach number and pressure at 2M and P1 point. tip. PVS (passage vortex at shroud) and CV (Coriolis vortex) contribute to the transport of low energy fluid from PS to SS along the shroud wall. The passage vortex is typically stronger in the first half of the impeller (because of higher blade-to-blade curvature) and at the shroud, while in the radial portion, the Coriolis force prevails ([PERSON] and [PERSON], 2001) [(29)]; in this case, the effect at the hub is not clearly visible. The Coriolis vortex (CV) and the passage vortex (PV) have the same effect and are not always distinguishable one from the other: they are often referred to as passage vortices. The overall effect is a low energy fluid transport towards the shroud wall and the SS. Moreover, at the casing, the above secondary flows interact with the tip vortex (TV). The passage vortex is well-defined in the first part of the impeller (Figure 11, surface 1) but it is clearly distorted by the trailing vortex downward and tends to move towards midspan. [PERSON] [(30)] described this phenomenon for the same compressor. The overall result is a thick high-turbulence region in the upper half of the channel (shown in Figure 10 for surface 5) that corresponds to the low relative velocity region in Figure 12 (wake). The remaining portion of the section has low turbulence level with high flow velocity and identifies the jet zone in the jet-wake model. Figure 10: Turbulence kinetic energy in the impeller, point P1. Figure 9: Meridional velocity in the impeller, point P1. The velocity contours in the relative frame are shown in Figure 12 in a plane close to the mixing-plane interface on the impeller side. On the same plane, the relative flow angle distribution shows a thin stripe near the casing; here, the relative flow is completely tangential because of the tip leakage vortex and the fixed (counter-rotating in the relative frame) shroud wall. Close to the blades, the relative angle becomes more and more affected by the trailing edge local distortion. The relative flow near PS is more tangential, while the relative flow near SS is more radial and they join downstream the trailing edge. Towards the channel midspan, the flow in the wake zone has a more radial character than in the jet zone, due to the low energy transport from pressure side to suction side caused by the passage vortex.