## 4 Results
### Rotor Aerodynamics
The migration of the hub vortex close to midspan is motivated by the very high flow turning of this rotor (120\({}^{\circ}\)) and by the Coriolis force; corresponding to the hub vortex, a local loss increase is observed. Conversely, the tip passage vortex appears considerably weaker, and its trace into the loss distribution is entrained in the huge wake loss that affects the outer part of the channel. The map of unresolved unsteadiness (Figure 7d) confirms that the most relevant turbulent structures occur in vortex regions at the tip and at midspan. In particular, the highest turbulence is found on the left side of the tip leakage vortex, where the shear layer between the jet leaking through the cascade and the main flow rolls up in a vortex. When the stage is run in subsonic conditions, represented in Figures 8 and 9 for OP2 and OP3, respectively, the general flow configuration is similar to that found for OP1, even though the magnitude of the main flow structures changes significantly. Figures 8 and 9 show that the velocity deficit in the wake is now significant all along the span (at least above 20% span), while the tip leakage losses are less sensitive to the operating conditions. In OP2, the loss region extends up the hub, assuming an almost straight shape, even though a reduction of loss is observed from tip to hub. In OP3 the loss region enlarges significantly and appears bent towards the suction side of the channel below 30% span; this is probably connected to the over-turning measured in this region, that appears enhanced for OP3  
Figure 7: Rotor-exit relative flow field in OP1 (transonic), (**a**) relative total pressure coefficient; (**b**) deviation angle; (**c**) relative Mach number; (**d**) unresolved unsteadiness. with respect to OP1 and OP2. Correspondingly, the tip and secondary vortices grow progressively as the stage expansion ratio reduces. Where the vortices magnitude appears increased, corresponding loss cores are found in the \(C_{PT,R}\) distribution. As a result, for these conditions the wake and the tip leakage vortex are not the main loss mechanism, and the dissipation connected to the secondary flows contributes significantly to widen the low \(C_{PT,R}\) region. For OP3, in particular, the passage vortex regions identify exactly two loss cores; the very large passage vortices, migrated towards midspan, occupy entirely the central part of the channel and make the loss region to be wider in the midspan region. In terms of flow angle (Figures 8b and 9b), the tip leakage vortex retains the features observed in OP1, while the magnitude of the passage vortices appears enhanced in subsonic conditions, as commonly found in literature about the Mach and Reynolds number effects on secondary flows [26]. It is also of interest to note that the position of the wake and vortices slightly change with respect to those in OP1, as a consequence of the different flow evolution downstream of the rotor, already depicted in Figure 2.  
These phenomena appear dramatically amplified for the lowest expansion ratio tested, OP4. Given the specific features of the flow in this condition, all the relative quantities are shown in Figure 10. Except for the tip leakage vortex and its associated loss, that retain the character discussed for the other OP, the low relative total pressure and relative Mach number region in the central part of the channel are greatly enlarged, reducing the free-stream to a narrow area in-between the wakes. Secondary flows grow in both scale and magnitude, as a \(30^{\circ}\) variation of flow angle is measured in both the local passage vortex regions above and below midspan. In particular, the tip passage vortex undergoes the largest amplification passing from OP1 to OP4. This is consistent with the larger wake extension observed for all the OP above midspan, resulting in a huge loss core just above midspan. This peak loss area, combined with that of the tip leakage vortex, penaliz  
Figure 8: Rotor-exit relative flow field in OP2, (a) relative total pressure coefficient; (b) deviation angle.