## 3 Parametric Investigation
### Varying the TE Noise Source Location and/or Frequency  
The variability of the delta effects with respect to the sole TE noise source location (i.e., airfoil incidence) is assessed first. To do so, the previous case of a low frequency source (\(St=0.294\)) is considered again, the angle of attack being now varied from \(\alpha=0^{\circ}\) to \(\alpha=25^{\circ}\) by increments of \(\Delta\alpha=5^{\circ}\). Figure 7 depicts the corresponding deltas between the incident and total RMS pressure fields, as recorded along both the top and bottom walls. Of note, given the symmetry of the problem, cases of negative incidences (\(\alpha=0^{\circ}\rightarrow-25^{\circ}\)) would deliver identical outcomes, except that top and bottom walls results would be inverted. In other words, the delta effects to be recorded on the top (resp. bottom) wall for a negative \(\alpha\) would match those acquired on the bottom (resp. top) wall for its positive \(\mid\alpha\mid\) counterpart. As can be seen, the deltas exhibit similar albeit distinct patterns, depending on the incidence. One can first notice that only the case \(\alpha=0^{\circ}\) sees the deltas of its top and bottom walls perfectly mirroring each other. This naturally results from the combined effect of a perfectly symmetric configuration (uninclined airfoil) and a perfectly antisymmetric noise emission (dipolar source). Contrarily, all other cases (\(\alpha\
eq 0^{\circ}\)) are characterized by delta effects that do not mirror each other, which comes from the broken symmetry of the configuration (inclined airfoil). Figure 7: Low frequency (\(St=0.294\)) noise radiation from the trailing edge of an airfoil set at low to high incidences (\(\alpha=0^{\circ}\), \(5^{\circ}\), \(10^{\circ}\), \(15^{\circ}\), \(20^{\circ}\), \(25^{\circ}\)). Deltas (in dB) between the incident and total RMS pressure fields, as along the top (**a**) and bottom (**b**) walls. At moderate to high incidences (\(\alpha=15^{\circ}\) to \(25^{\circ}\)), one recovers the patterns previously observed for the \(\alpha=20^{\circ}\) case (which is reproduced here in grey color, for reference). In particular, one retrieves the delta peak of up to +60 dB impacting the top (resp. bottom) wall upstream (resp. downstream) the airfoil, whereas moving away from it as the incidence decreases. Again, this peak reflects the walls backscattering effect onto that shadow zone which initially characterized the incident field along the airfoil chord line (cf. Figures 4 and 5). Logically, as the airfoil incidence decreases, this peak travels away, up to disappearing beyond the \(\left\lvert\,x\,\right\rvert/c=12.5\) limit when \(\alpha\) gets down to \(10^{\circ}\). At lower incidences (\(\alpha=10^{\circ}\) to \(\alpha=0^{\circ}\)), whilst the +60 dB delta peak is no longer visible, a _negative_ delta peak is seen to appear at \(x/c\sim-4.75\) and \(x/c\sim 5.75\) on top and bottom walls, respectively. This peak is more importantly pronounced for an incidence of \(\alpha=5^{\circ}\), exhibiting an amplitude of approximately \(-10\) dB and \(-30\) dB on the top and bottom walls, respectively. Such a negative delta effect finds its origin in the reciprocal cause of the previous positive +60 dB peak; whereas the latter originated from the constructive interferences between the incident and reflected fields, here, it is rather their destructive counterparts that are at play, resulting in an overall pressure that is less than originally. This effect is especially more visible in Figures 8 and 9, which depict the corresponding incident and total pressure fields (cf. Figure 8), as well as their associated deltas (cf. Figure 9). There, one can clearly see how the confined acoustic field is driven by all constructive and destructive interferences (cf. Figure 8b), which then result in areas where the total RMS pressure is less than its incident counterpart (compare for instance Figure 8c,d). Subsequently, their delta turns negative over a few spatially distributed zones (cf.