## 5 Results and Discussion
### Aeroacoustic Results
This concealment effect is also exacerbated because noise is expressed in dB. Figure 8: Sound directivity of isolated rotor. Figure 7: Convention used to report the acoustic results on the sphere. The coordinate system is right-handed so that, on the left the Northern view is characterised by the \(z\)-axis outgoing whereas on the right the Southern view is characterised by the \(z\)-axis incoming. Finally, Figure 11 shows the variation of noise emitted by rotor #1 with respect to the isolated rotor in terms of \(\Delta\)dB, for the two configurations whose noise is more affected by the interaction phenomena (\(dist=0\) and \(dist=0.125d\)). The main effect is the change in the noise directivity in the forward direction on the southern hemisphere, which increases with the tip-clearance reduction (note that the logarithmic scale hides the variations in the high noise region). The noise level is globally increased, although some regions (located near the south pole) may present lower OASPL values. Furthermore, the three-propeller configuration, with tip-clearance equal to 0, is analysed. Figure 12 shows the directivity pattern on the 5-m sphere, in terms of SPL of the first three BPFs as well as in terms of OASPL, for the southern (first row) and northern (second row) hemispheres. From this analysis two important considerations may be drawn. First, the directivity of the southern hemisphere is practically identical to the northern one. This implies that rotor #2 affects the southern hemisphere of the rotor #1 as the rotor #3 affects the northern one, and _vice versa_. Besides, comparing southern hemispheres of the three-propeller case with those of the twin-propeller case shown in Figure 9, it is possible to observe that they are really similar, showing that the contribution of the rotor #3 on the southern hemisphere of the rotor #1 is negligible, as well as the contribution of the rotor #2 on the northern one. Hence, each adjacent rotor affects only one of the two hemispheres. Figure 10: Sound directivity (OASPL) of rotor #1 for the cases \(dist=\{0,\,0.125d,\,0.25d,\,0.5d\}\). The first row shows the noise sphere from below, the second one from above. Figure 9: Sound directivity of rotor #1 for the case \(dist=0\). The first row shows the noise sphere from below, the second one from above. Finally, Figure 13 shows, for the twin-propeller configuration with tip-clearance equals to 0.01\(d\) and for microphones located on circles in the propeller rotational plane with increasing radius, the comparison between the pressure field directivity pattern at the 1 st BPF normalised with the ratio between the reference circle radius (5 m) and the current one. This analysis is aimed at defining the far-field boundary, that is, the distance from the hub centre beyond which the pressure decreases as the inverse of the distance. As expected, in the near field, the directivity pattern is strongly affected by the distance. For hemisphere radii greater than 20-m, on the contrary, the directivity is almost the same with the magnitude decreasing proportionally to the observer distance. This is confirmed by Figure 14, which shows the trends of: (a) the difference between the azimuth position of the pressure peak evaluated at the current distance and that of the 160 meters circle (considered representative of the far-field conditions and identified by the subscript \"ref\"); (b) the ratio between the maximum normalised pressure and its value in the far-field conditions; (c) the ratio between the average normalised pressure and its value in the far-field. Once again, up to 20-m the three quantities remarkably change with the distance, whereas they become constant for higher distances. However, the differences between the far-field quantities and those evaluated on the sphere with a radius equal to 5 m (that considered for analyses in Figures 8-10 and 12) are quite small, lower than 3% on the pressure peak and average pressure, and about 10 \(deg\) for the azimuth position of the peak.