## 4 Results
### Aeroacoustics Measurements and Predictions
#### 4.2.4 Overall Sound Pressure Level and Directivity  
To combine the acoustic results across the multitude of cases run, the directivity of the total sound is addressed in this section. The overall sound pressure level (OASPL) is used as a metric for the total sound across both tonal and broadband components and is defined here as the integral of the PSD in the frequency band of 50 Hz to 10 kHz.  
The polar directivity of both dual rotor configurations is shown in Figure 19. The experimental values are shown as lines, the combined Helios/PSU-WOPWOP and UCD-Quietfly results are shown as squares, and the standalone Helios/PSU-WOPWOP results are shown as circles. It is obvious from the results in previous sections, including the acoustic spectra, that the OASPL of the experiments would be much greater than that of the single rotor computation due to the impact of other effects, including recirculation, unsteady motor vibration, motor noise, and any potential structural dynamics. These factors, in addition to installation effects, may explain the lack of trend across the different tip separation distances of the dual rotor measurements. The factors make it particularly difficult to see the expected trend between single and dual rotor experimental results. Validation of the computational predictions with the experimental data is not possible. If one has some faith that the computations provide good predictions for rotors in a free field environment void of motor noise, etc., then a few conclusions follow. (1) Rotor-rotor interactions lead to higher harmonics that are on the order of, or greater than, higher harmonics caused by recirculation. (2) The polar directivity between \(-15\) deg and \(15\) deg is symmetric for the single rotor, but greater above-plane for the dual rotor. In general, the largest OASPL is seen near the rotor plane. (3) Both configurations show similar directivity. (4) The contribution of the trailing edge broadband noise to the OASPL is proportionally greater for the single rotor than the dual rotor, due to the relative amplitude of the BPF. (5) The decreasing tip distance between the dual rotors barely affects the noise from \(-15\) degrees to \(25\) degrees and increases the noise by a few dB at a higher elevation. The influence of rotor proximity has a greater impact on above-plane noise than thrust, highlighting the fact that the noise is more susceptible to interactions than interaction.  
Figure 18: Direct comparison of computational and experimental acoustic spectra of the dual rotors with a separation distance of \(t=0.04\) at Mic 3 of the linear array.  
Next, the azimuthal directivity of the noise is plotted in Figure 20. The authors again refer the reader to Appendix A for insight into the asymmetry of the experimental OASPL. The predicted acoustic magnitude is lower than experiment as expected, given the aforementioned environmental effects. The co-rotating configuration demonstrates a uniform directivity around the azimuth, while the counter-rotating configuration shows a reduction in OASPL between 120 deg and 150 deg, even beyond the magnitudes of the single rotor. The reduction is due to destructive interference of the tones of in-phase counter-rotating rotors. These results are in agreement with those of [PERSON] et al. and [PERSON] et al., who compared computations and experiments of counter-rotating and co-rotating side-by-side rotors and found interesting directivity patterns in-plane depending on the phasing [68; 69]. They concluded that exact rotor phasing and less than 0.5% variation in the RPM were required to produce the destructive interference. It is not surprising then that the experiments, which are not phase locked, do not show as dramatic of a reduction in the OASPL from 120 deg to 150 deg for the counter-rotating case.