## 4 Results
### Rotor Aerodynamics
Figure 9: Rotor-exit relative flow field in OP3, (a) relative total pressure coefficient; (b) deviation angle. aerodynamic efficiency in the outer part of the channel. Coherently with the general increase in secondary flows, the cross-flow/overturning at the hub is also larger and induces a further pitch-wise deformation of the wake. The unresolved unsteadiness (Figure 10d) also marks a general amplification with respect to the transonic case, with peaks in the wide loss regions in the central part of the channel, but also high levels in the free-stream all along the span (except below 20% span). The strengthening of the viscous and vortex structures with the reduction of the expansion ratio is only partially caused by a direct Mach and Reynolds number effects. As discussed previously, the rotor incidence angle grows significantly as the expansion ratio reduces (see Figure 6c), as a consequence of the constraint imposed on the stage-exit flow angle. The variation increases from hub to tip, and it is quantitatively relevant for the whole blade span, passing from 10\({}^{\circ}\) at the hub to 40\({}^{\circ}\) at the tip. For the transonic condition the rotor works with negative incidence all along the span, with a fairly uniform span-wise profile at \(-10^{\circ}\). This explains the relatively low magnitude of rotor secondary flows, especially the tip passage vortex, in OP1 with respect to the other conditions. For subsonic turbine operation, the incidence exhibits an increasing trend along the span, the profiles being roughly shifted with the OP2 condition centered to null incidence. The combined changes in the incidence trend and in the mean incidence values contribute to justify the growth of the tip passage vortex between, especially, OP1 and OP2 conditions, as most of the difference in incidence occurs passing from these two OPs. The average incidence variation between OP2 and OP3 is much smaller (\(\approx\)5\({}^{\circ}\)) and further reduces between OP3 and OP4 (\(<\) 5\({}^{\circ}\) on 110\({}^{\circ}\) of flow turning and a mean value of \(\approx\)10\({}^{\circ}\)). The comparison between the latter two subsonic conditions is particularly interesting as, for similar values of incidence, relatively large change in Reynolds and Mach numbers occur (the Mach number drops from 0.6 to 0.4 at the vane exit, and from 0.5 to 0.3 at the rotor exit; the midspan Reynolds number drops from 0.9 \(\times\) 10\({}^{6}\) to 0.55 \(\times\) 10\({}^{6}\) for the stator and from 0.5 \(\times\) 10\({}^{6}\) to 0.3 \(\times\) 10\({}^{6}\) for the rotor, see also Table 5). Hence, the differences between OP3 and OP4 mostly depend on Mach and Reynolds numbers of the rotor profile. Figure 10: Rotor-exit relative flow field in OP4, (**a**) relative total pressure coefficient; (**b**) deviation angle; (**c**) relative Mach number; (**d**) unresolved unsteadiness. Based on the present measurements, the impact of Reynolds/Mach numbers is shown to be large in the turbine under investigation. In fact, the general flow topology is preserved (see Figures 9 and 10), but both the extension of the loss region and the magnitude of the passage vortices are greatly amplified at low Reynolds/Mach numbers. In OP4 the higher relevance of viscous stresses and the lower flow acceleration connected to the nearly incompressible flow regime both contribute to enlarge the boundary layers, resulting in wider wake and secondary flows. The expansion ratio has also an extremely significant impact on the vane-rotor interaction, which is here discussed by resorting to the periodic fluctuations in the rotating frame. Figures 11 and 12 show the distribution of periodic unsteadiness (in terms of RMS) of \(\mathrm{C_{PT,R}}\) and \(\delta\) for OP1 and OP4 to provide a synthetic view of the flow regions affected by the highest unsteadiness. To aid the reader in the interpretation, the positions of the three main vortex structures are also marked in the figures.