## 6 Conclusions  
On the basis of results obtained in this work, it can be concluded that the aerodynamic and the aeroacoustic interaction between small propellers may have a significant impact on the emitted noise in terms of intensity, directivity pattern, and spectral content. The first specific observation that can be made is that the presence of a second rotor introduces a low-frequency disturbance (approximately at 1/rev) on blade pressure which does not exist in a single-rotor signal. This causes the noise signal to include a relevant amount of loading contribution in addition to the dominant thickness term. In addition, there are significant variations when the distance between the rotors tips is closer than one half of the rotor radius. The main modifications concern an increase of the noise that propagates in the forward direction, a noticeable widening of the high-noise region and the increase of the noise peak. The differences are more relevant when the considered frequency is increased. In particular, when the distance between the propellers is lower than 0.25\(d\), the differences between the noise emitted by the isolated rotor and that emitted in presence of the other one are significant. In the high-noise region of the southern hemisphere, an increase up to 10 dB is observed (depending on the tip-distance). Furthermore, in the region where lower OASPL values are present, the aerodynamic interaction produces an increase of the noise emitted up to 50 dB. Concerning the characteristics of propagation, it can be observed that the far-field condition, where the pressure field decreases proportionally to the distance, is achieved at about 20-m, thus slightly closer than thirty radii. Then, the three-rotors configuration exhibits a symmetric emission which can be advantageously exploited to reduce the computational burden. Indeed, the effect of each side rotor on the noise emitted by the central one is only limited by the hemisphere where the blades of the two propellers approach. As a consequence, the three-propeller directivity pattern can be obtained from the twin-propeller one by mirroring the equatorial plane of the hemisphere affected by the presence of the side rotor. Finally, the numerical investigation confirms the possibility of performing the aeroacoustic analysis of a multi-propeller configuration by characterising each propeller of a three-propeller array and using the central one as an equivalent source for each internal propeller of the multi-propeller array. In this work, the only design variable considered in the parametric analysis is the distance between consecutive rotors. However, in order to have a wider exploration of the design space (i.e., also in terms of number of blades, chord length, rotational speed and rotational direction for assessing also co-rotating propellers noise), a second numerical campaign has just started. Conceptualization, F.C., M.R. and J.S. ; methodology, G.B., F.C., C.Pa., C.Po., M.R. and J.S. ; software, G.B., F.C., M.G., U.I., C.Pa., C.Po., M.R. and J.S. ; validation, F.C., C.Pa., C.Po., M.R. and J.S. ; formal analysis, F.C., C.Pa., C.Po., M.R. and J.S. ; investigating, F.C., C.Pa., C.Po., M.R. and J.S. ; resources, G.B., M.G. and U.I. ; data curation, F.C., C.Pa., C.Po., M.R. and J.S. ; writing-original draft preparation, F.C., C.Pa., C.Po., M.R. and J.S. ; writing-review and editing, G.B., F.C., M.G., U.I., C.Pa., C.Po., M.R. and J.S. ; visualization, C.Pa., C.Po. and M.R. ; supervision, G.B., F.C., U.I. and J.S. ; project administration, U.I. ; funding acquisition, U.I. All authors have read and agreed to the published version of the manuscript. This work has been partially supported by the European Union's Horizon 2020 research and innovation programme under project ARTEM (Aircraft noise Reduction Technologies and related Environmental iMpact) grant agreement No. 769350. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: