## 4 Results
### Rotor Aerodynamics  
In this Section, the rotor aerodynamics are discussed on the basis of flow measurements at the rotor-exit for the different OP. To highlight the rotor flow features, the analysis is developed in terms of time-mean and fluctuating relative quantities, as perceived by a rotating observer integral to the rotor blades. This allows identifying the loss mechanisms and the vortex structures generated within the rotor blade row. On the methodology ground, it is worth noting that for time-mean rotor flow measurements an unsteady probe is required (the FRAPP), as the probe does not rotate integral to the rotor. In practice, the time-mean rotor-exit flow field perceived by a rotating observed was reconstructed starting from phase-averaged measurements taken in the stationary frame, converting them in rotating frame data and averaging them in phase (which means, averaged with respect to the different stator-rotor relative positions). The periodic unsteady fluctuations of the flow quantities are here defined as the differences between the mean and the instantaneous flows reconstructed in the rotating frame. For a rotating observer, any fluctuation over the mean value can be caused by the vane-rotor interaction only, and its magnitude marks the relevance of the unsteady coupling between the blade rows. To quantify the interaction, the root mean square of this fluctuation (RMS) was evaluated and it is shown in the present Section for different OP and reference as periodic unsteadiness. Coupled to the periodic unsteadiness, also the unresolved unsteadiness of the relative total pressure (\(I_{PT,R}\)) was calculated according to the methodology presented in [30]. This quantity is defined for each stator-rotor interaction phase and for each grid point and it has been shown to be a proficient marker of high turbulence intensity regions, such as wakes and vortex structures (see [13; 20] as application examples). The discussion on the rotor aerodynamics starts from the mean rotor-exit flow field for transonic operating condition (OP1, Figure 7), in terms of relative total pressure coefficient, rotor deviation angle, relative Mach number and unresolved unsteadiness. Low relative total pressure marks loss regions, while strong span-wise gradients in relative flow angle allow for the identification of the whirling structures (by resorting to the Rankine vortex model). For transonic condition (OP1, Figure 7), some general features of the flow in this rotor can be recognized. First considering the distribution of relative total pressure coefficient, a large loss region affects the top half of the channel: in particular, the huge loss core close to the tip is consistent with the  
Figure 6: (**a**) Reaction coefficient, (**b**) _Kp_ and (**c**) incidence span-wise profiles downstream of the stator. leakage flow, which originates from a tip gap equal to 1.3% of the blade height. Below midspan the gradients connected to the wake are significantly smeared, resulting in an almost uniform flow field. This general feature is even more evident in the Mach number distribution, which is almost wake-free below 60% span. The distribution of the rotor deviation angle exhibits large local spanwise gradients, with significant under-turning (\(\delta>0\)) above 40% span and a weak over-turning (\(\delta<0\)) in the hub region. Superimposed to this trend, three local regions of high flow angle variation are clearly visible, corresponding to three vortex structures placed on the suction side of the wake. The tip vortex centered at 90% span, where the maximum velocity deficit is found, is by far the largest structure appearing on the measurement plane and it is caused by the leakage flow. Below this structure two counter-rotating vortices are found, centered at 70% and 40% span, which can be identified as the tip and hub rotor passage vortices, respectively.