## 4 Results of Traveling Wave Mode Simulations
A detail of central blade trailing edge is depicted. Analogous results are obtained on the other two plasma-equipped blades of the cascade. The alternate switching of the PS and SS actuation is clearly visible. It is also worth noting that, differently from the assessments at a constant angle of attack, the recirculating flow areas on the pressure and on the suction side are almost equally extended. This is due to the application of a larger body force on the suction side, relative to the pressure side. It will be highlighted hereinafter that now the affection on the positive and negative oscillations in the pitching moment is almost symmetrical. This means that the effects provided by PS and SS actuation are expected to be more similar, when the SS body force is larger than the PS counterpart. Figures 14-16 show the fluctuation of the mid-chord pitching moment coefficient versus the non-dimensional time, for the last simulated period. Several IBPAs, ranging from \(-180\) to \(180\) deg., are shown. The time on the \(x\)-axis is made dimensionless by the oscillation period of the blade. Figure 12: Time history of lift, drag and moment coefficient for the complete simulation (**a**) and for the last three periods (**b**); Re \(\sim\)195,000; IBPA = \(-51.43\) deg. ; \(\alpha=2+\sin 2\pi ft+4\times\mathrm{IBPA}\pi/180\) deg. ; f = \(19.17\) Hz, T = \(1/\)f.  
Figure 13: Trailing edge detail of velocity magnitude, normalized by the freestream velocity, at four time instants of the oscillation cycle; plasma actuation on; Re \(\sim\)195,000; IBPA = \(-51.43\) deg. ; \(\alpha=2+\sin 2\pi ft+4\times\mathrm{IBPA}\pi/180\) deg. ; f = \(19.17\) Hz, T = \(1/\)f.  
An effective reduction of the unsteady peaks on the pitching moment is observed for each of the interblade phase angles. As a result, two major benefits can be achieved: (i) vibratory loads, responsible for fatigue phenomena are alleviated; and (ii) the blade aeroelastic stability is potentially increased, as the energy transfer from the flow to the blade is reduced [23]. It is worth remarking that plasma seems to have a greater affection on the pitching moment for negative IBPAs than for positive values of the interblade phase angle. According to the convention employed in this work, for IBPA < 0, the pressure wave travels from the pressure side of a blade to the suction side of the neighbouring one. On the contrary, for IBPA > 0, the pressure wave travels from the suction side of a blade to the pressure side of the neighbouring one. A higher body force is employed on the SS for travelling wave mode simulations. Even though the recirculating flow areas generated on PS and SS with asymmetric actuation have comparable extensions, the affection on unsteady loads might be slightly higher on the suction side. This may be one of the causes for the better affection of the actuation for negative IBPAs which--according to [24; 26]--feature lower aerodynamic damping, and therefore are the most critical. The differences in actuation effectiveness encountered among the negative IBPAs are probably due to local effects that are not detectable when integrating pressure to obtain the resulting loads. In Ref. [2], [PERSON] et al. investigate the effects of the IBPA on the pressure distribution on a cascade of blades oscillating in pitch. The reduced frequency of oscillation is comparable to the ones of this work, therefore the findings of [2] can be considered valid also for this manuscript. [PERSON] et al. [2] show that, whereas the phase of the pressure distribution along the chord on the suction side is close to zero for all the IBPAs, a large excursion of this quantity is observed on the pressure side. Specifically, they point out that the \"average phase lead on the pressure surface varies [with the IBPA] in steps of 45 deg. for every 45 deg. change in [IBPA]\" [2]. That is, the pressure peaks on the pressure side change remarkably their chord-wise location, according to the IBPA. This shifts change the interaction between blade-induced and plasma-induced pressure distribution.