## 3 Analysis of the Impeller-Diffuser Interaction
### Unsteady Analysis at 2M  
In this section, the results from the transient analysis are discussed to understand the effect of the non-uniform rotating flow pattern coming from the impeller on the vaned diffuser. The analysis is focused on plane 2M for operating point P1 to get a direct comparison with the experimental data. Because of random sampling inherent to the L2F technique and due to the need for a constant time-step in the simulations, there is a minor shift between numerical and experimental instants (with absolute errors between 0.1% and 2.6%). The analysis is performed using the same rotor-stator positions from measurements. Figures 15 and 16 are diffuser-sided views in the absolute frame of reference: the impeller moves from right to left. The numerical results have been obtained from the transient simulation approach HR-KO discussed in the previous section. A good matching between the numerical and the experimental data can be observed with very similar flow patterns. The main difference takes place in the velocity distribution at the unsteady position \(\varphi_{\text{ID}}/\varphi_{\text{UI}}=0.595\). At that instant, experimental results show a high velocity zone extending clearly from right to left along the front wall and spreading towards the rear wall; this stretching is not completely detected with the numerical simulation. On the other hand, a velocity pattern similar to the experimental data has been obtained for the two transient simulations using the SST model for the operating points M and P1. Nevertheless, in the operating point P1, the results with SST are shifted because of the stall appearing downstream in the diffuser channel, so consequently the flow is slower and more tangential at plane 2M. The results using the SST model are not used for further discussion because of the instability produced by the stalled channel in the diffuser, as previously discussed. Figure 14: Absolute velocity and angle at impeller exit in the relative frame of reference, point P1. Figure 15: Unsteady absolute velocity at 2M in the absolute frame of reference, point P1, comparison between numerical results of HR-KO (left) and experimental results (right). Many of the effects studied separately in the previous sections using steady analysis can now be seen in the single unsteady analysis. Flow incidence at the diffuser is positive (i.e., absolute flow is more tangential with respect to the diffuser vane camber line) almost exclusively near the front wall where the wake generates a highly tangential absolute flow. On the other hand, the incidence angle becomes lower (and negative) towards the rear wall (jet zone). Furthermore, a thicker positive-incidence zone can be seen from the right to the left in the center of the wake zone moving with the impeller channel. The flow has a higher velocity close to the front wall because of the jet-wake flow pattern. The absolute velocity maximum values are located at about z/b = 70% as shown by the monitoring points and by the vortical structures analysis. The absolute velocity becomes lower and the flow more radial (negative incidence) at the diffuser vane leading edge on the right side because of the diffuser vane blockage; the opposite occurs on the left side, with respect to the vane leading edge. A velocity maximum can therefore be seen close to the front wall on the diffuser vane suction side, while a minimum is found at the opposite corner (between the rear wall and the pressure side). The velocity peak is more evident when the high-velocity zones in the impeller flow (Figure 13) are aligned with those caused by the potential flow field: this occurs at \(\varphi_{\text{ID}}/\varphi_{\text{tl}}=0.093\). A zone with high negative incidence values appears along the rear wall towards the vane diffuser pressure side (see instants corresponding to \(\varphi_{\text{ID}}/\varphi_{\text{tl}}=0.093-0.843\)). It is clearly distorted by the passage of the impeller blade trailing edge (see instants \(\varphi_{\text{ID}}/\varphi_{\text{tl}}=0.342-0.595\)) with high flow incidence.