# A Computational Study on the Aeroacoustics of a Multi-Rotor Unmanned Aerial System
## 3 Results and Discussion  
### Sound Pressure Level  
#### 3.1.1 Interaction Effects  
The noise sources of CRC-3 include propeller-tip vortices and the interaction of the four propellers with each other as well as with the wings and the fuselage. In order to clarify how each of these sources contribute to the noise, simulations at \(U_{0}=7\) m/s and RPM \(=6000\) were carried out for four different configurations as follows: (i) isolated propeller, (ii) a single propeller-wing system, (iii) only four propellers and (iv) CRC-3, for two pitch angles of \(\theta=0^{\circ}\) and \(\theta=75^{\circ}\). A comparison is made between the four configurations on their SPL spectra at a microphone located in the downstream \(\Phi=180^{\circ}\) (defined in Figure 2), SPL directivity at the first harmonic and the OASPL directivity, as shown in Figure 7. The isolated propeller spectrum shows peaks at BPF harmonics as expected, with some humps in the broadband noise part of the spectra, which is ascribed to the vortex shedding noise and flow separation on the blades [22]. It should be noted that, in the present work, the relative position of the microphones and the configurations studied were kept fixed with the changing pitch angle (\(\theta\)), as shown in Figure 2. The isolated propeller spectrum in Figure 7 is independent from the pitch angle in BPF and experiences a slight growth in broadband noise as \(\theta\) increases. For the propeller-wing configuration, increase in \(\theta\) results in 3 dB increase in noise level at BPF, which is in contrast with the finding of [PERSON] [33], in whose work the noise at BPF was not affected by the interaction between the propeller tip vortex and the wings. This is probably because the microphones were located at a distance of about 4\(D_{p}\) in that study comparing to 1.5\(D_{p}\) in this study. With increase in the pitch angle, case (ii) also experiences a larger increase in some other tonal harmonics, but broadband noise decreases. In addition, a new peak at BPF/2 appears. The appearance of this peak agrees with the findings [PERSON] [36] reported to the literature. The case with four-propellers also experiences 4-5 dB noise increase at BPF and a smaller level of increase in other tonal harmonics, except BPF/2, in which a 6-7 dB growth may be observed. The case with four-propellers also shows a negligible increase in  
Figure 6: Validation: (**a**) Thrust for CRC-3 propeller; (**b**) position of the microphone in acoustics validation simulation; (**c**) SPL spectrum for APC 10 \(\times\) 7E at RPM = 4660 and static condition.  
broadband harmonics. Nevertheless, the noise level is significantly higher in the case of four propellers than that of the isolated propeller. It was previously reported that when the spacing between the tip of the adjacent propellers in a quadrotor is small, the degree of fluctuation they impose on each other's loads becomes significant [35]. Unlike the first three configurations, CRC-3 experiences a large growth in noise by increasing pitch angle, i.e., a 21 dB increase in noise at BPF and BPF/2 and almost the same at other harmonics. The major cause of growth in CRC-3 noise from \(\theta=0^{\circ}\) to \(\theta=75^{\circ}\) is due to the interaction of the propellers with the wings and the fuselage.  
Figure 7: Variation of SPL spectra and directivity of SPL and OASPL versus pitch for various configurations: (**a**) \(\theta=0^{\circ}\); (**b**) \(\theta=75^{\circ}\).