## 4 Results
### Rotor Aerodynamics
OP1 condition does not exhibit any visible effect of interaction above midspan, where a wide wake, a strong tip leakage flow, and a weak tip passage vortex determine the flow topology. Conversely, the effects of the vane-rotor interaction are well visible below midspan, and especially in the core of the hub passage vortex. Relative total pressure fluctuations affect most of the channel between 30%  
Figure 11: RMS of periodic unsteadiness for OP1 (transonic), (**a**) RMS of the relative total pressure coefficient; (**b**) RMS of the deviation angle. Figure 12: RMS of periodic unsteadiness for OP4, (**a**) RMS of the relative total pressure coefficient; (**b**) RMS of the deviation angle. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**OP** & \(\mathbf{\beta_{\mathrm{TS}}}\) & \(\mathbf{n_{\mathrm{TT}}}\) & \(\mathbf{Y_{\mathrm{stat}}\%}\) & \(\mathbf{R_{\mathrm{stat}}\times 10^{6}}\) & \(\mathbf{Y_{\mathrm{stat,MID}}\%}\) & \(\mathbf{M_{\mathrm{stat,MID}}}\) & \(\mathbf{I_{\mathrm{R}}\ @\ MID}\) & \(\mathbf{R_{\mathrm{R}}\times 10^{8}}\) \\ \hline OP1 & 1.95 & 0.906 & 5.79 & 1.37 & 4.33 & 0.79 & \(-9.7\) & 8.2 \\ OP2 & 1.65 & 0.896 & 5.77 & 1.11 & 4.38 & 0.71 & 1. & 6.6 \\ OP3 & 1.4 & 0.864 & 5.93 & 0.87 & 4.52 & 0.59 & 6. & 5.0 \\ OP4 & 1.155 & 0.837 & 6.62 & 0.56 & 5.32 & 0.40 & 11.2 & 3.2 \\ OPLL & 1.385 & 0.840 & 5.90 & 0.85 & 4.50 & 0.56 & 14 & 5.5 \\ OPLR & 1.385 & 0.867 & 5.90 & 0.85 & 4.50 & 0.56 & 5.5 & 4.9 \\ OPLU & 1.385 & 0.881 & 5.90 & 0.85 & 4.50 & 0.56 & \(-3.2\) & 4.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Stage efficiency and stator total pressure loss for all the tested operating conditions. and 50% of the span; this indicates that the rotor wake below midspan, even though appearing weak on a time-averaged basis, is actually a highly unsteady structure. The high RMS level in the free-stream region in-between the adjacent wakes (\(\theta/\Delta\theta_{\rm R}=1\)), is probably connected with the convection of the stator wake within the rotor. The periodic RMS of the flow angle shows a similar trend with a peak value in the core of the hub passage vortex and a second interesting peak in the free-stream at midspan. This feature was already observed in previous investigations on this turbine [11; 13], and marks the presence of vortex-blade interaction, namely the transport of the vane secondary vortex filament throughout the rotor channel and its release at the rotor exit. OP4 condition exhibits a completely different amplitude and pattern of periodic unsteadiness. At first, large fluctuations are found also above midspan, thus affecting the whole viscous/loss region identified on a time-averaged basis. Interestingly, below 30% span, where the rotor wake/loss region is mixed-out (see Figure 10a), also the unsteadiness decays completely. This suggests that, beside wake-blade interaction effects, for OP4 condition the rotor wake in itself is pulsating. Considering the flow angle unsteadiness, in this case all the three vortices undergo periodic fluctuations (even though the tip leakage vortex exhibits the lowest unsteadiness). The tip passage vortex now exhibits the largest unsteadiness, while being virtually steady in transonic condition (OP1). Vortex-blade interaction features are still visible in the free-stream, but the corresponding flow angle oscillations are much weaker than that detected in the core of the passage vortices. As a result, the dominating source of unsteadiness is not the transport of vane-exit vortex structures, but the pulsation of the rotor vortices, as already observed for the wake. The periodic pulsation of rotor viscous structures arises as a consequence of the pitch-wise gradients in vane-exit flow field, which act as periodic fluctuations in the rotor-inlet flow field. As the blade sweeps in front of the stator wake and potential field, the rotor incidence angle and the rotor inlet relative Mach number fluctuate modifying periodically the rotor aerodynamic loading.