## 3 Parametric Investigation
### Varying the TE Noise Source Location and/or Frequency
#### 3.2.1 Characterization of the Installation Effects  
Figure 12 depicts the corresponding RMS deltas, as recorded for three specific frequencies (\(St=0.294\), \(1.47\), \(2.94\)) and all five incidences (\(\alpha=0^{\circ}\) to \(25^{\circ}\)). Overall, it appears that there is no specific location for which the RMS deltas are minimum at all angles and frequencies considered. In particular, it is again confirmed that the top wall is somehow less impacted than the bottom wall (the opposite would hold for negative incidences). More precisely, for points that are located less than a chord away downstream the source (\(x/c<1.5\)), the top and bottom walls are affected in a similar manner. In particular, at low frequency (\(St=0.294\)), the delta is roughly constant whatever the airfoil incidence is, namely \(\Delta\sim+8\) dB for both walls. At moderate (\(St=1.47\)) and high (\(St=2.94\)) frequencies, this delta varies with the incidence whereas staying within similar bounds (\(\Delta\sim+3.5\) dB to \(+8\) dB for both walls). Oppositely, for points that are located further downstream (\(x/c>1.5\)), the top and bottom walls are impacted differently; whereas their deltas go on varying with the incidence (\(\alpha\)), such variation is less for the top wall (\(\Delta\sim 2\) dB to \(9\) dB) compared to its bottom counterpart (\(\Delta\sim-1\) dB to \(11\) dB). Based on the above observations, one can infer that a microphone should preferably be located on the \(x/c<1.5\) portion of either the top or the bottom wall, thereby being impacted less, overall. Oppositely, the worse location would correspond to a microphone located on the \(x/c>1.5\) portion of the bottom wall, thereby suffering from deltas with a higher variability, depending on the (positive) incidence and frequency. To further assess and illustrate this point, two pairs of microphones are considered; the first pair of microphones (M1\({}^{\pm}\)) is positioned such that \(x_{M}/c=0.5\), i.e., they are located right at the zenith of the airfoil TE location, on either the top or bottom wall (M1\({}^{+}\) and M1\({}^{-}\)  
Figure 12: Low to high frequency (\(St=0.294\), \(1.47\), \(2.94\)) noise radiation from the trailing edge of an airfoil set at low to high incidences (\(\alpha=0^{\circ}\), \(5^{\circ}\), \(10^{\circ}\), \(15^{\circ}\), \(20^{\circ}\), \(25^{\circ}\)). From left to right: \(St=0.294\) (**a**,**d**), \(St=1.47\) (**b**,**e**), \(St=2.94\) (**c**,**f**). Deltas (in dB) between the incident and total RMS pressure fields, as recorded along the top (up: **a**–**c**) and bottom (down: **d**–**f**) walls. respectively). The second pair of microphones (M2\({}^{\pm}\)) is located approximately 1.5 chord downstream the TE, i.e., \(x_{M}/c=2\), being also positioned on either the top or bottom wall (M2\({}^{+}\) and M2\({}^{-}\), respectively). For each microphone, Figure 13 depicts the delta between the incident and the total RMS pressure fields, plotted here as a function of both the airfoil incidence (\(\alpha\)) and the source frequency (\(St\)). From a qualitative viewpoint, both pairs of microphones exhibit an identical pattern, namely a regular oscillation of their associated RMS delta as the source frequency (\(St\)) increases. Notably, for the two microphones located on the top wall (M1\({}^{+}\) and M2\({}^{+}\)), these oscillations get slightly slower when the incidence increases, whereas the opposite is true for their bottom wall counterparts (M1\({}^{-}\) and M2\({}^{-}\)). From a quantitative perspective, the downstream microphones (M2\({}^{\pm}\)) appear to exhibit higher deltas than their upstream counterpart (M1\({}^{\pm}\)), although this depends on the airfoil incidence (i.e., source location). To illustrate this point better, Figure 14 depicts again the RMS delta recorded at each four microphones, this delta being now plotted as a function of the sole source frequency (\(St\)), for either a nil (\(\alpha=0^{\circ}\)) or a high (\(\alpha=25^{\circ}\)) incidence.