# Investigation on Aerodynamic Noise Characteristics of Coaxial Rotor in Hover
## 3 Results and Discussion
### Noise at Different Observation Points
The amplitude of impulse increases as the observation point moves down from the rotor disk plane; see #1 to #7. Moreover, for #4 and #5 points, the waveforms and phases are both different from #7 point. This will be discussed in detail below. Figure 8 shows the comparison of loading noise sound pressures in a half rotor revolution. By comparing Figures 8b and 6b, it can be found that the characteristics of sound pressure are very close to the time derivative of \(C_{\rm T}\). The main period of fluctuation is around 90\({}^{\circ}\), and the amplitude of the upper rotor is larger than that of the lower rotor. As seen in Figure 8a, the wave marked as No. 2 is much weaker than No. 1, and the interval between the two troughs of the upper rotor is less than 90\({}^{\circ}\). A possible explanation for the sub-sound pressure fluctuations (No. 2) is the result of the interaction between the upper rotor tip vortex and the blade of the lower rotor. This is unreasonable, considering that the vortex interaction of a coaxial rotor in hover is a kind of vertical interaction, which has little effect on the blade load. In order to illustrate the phenomenon of the No. 2 wave, the sound pressure of loading noise at different points in the longitudinal plane is given in Figure 9. As the observation point gradually deviates from the position directly below the rotor (#7 point), the amplitude of the No. 2 wave gradually weakens, and the phase also changes. According to the position diagram of a rotor and two observation points (Figure 10), the #7 point is located directly  
Figure 8: Loading noise sound pressures at #5 and #7 points. (**a**) #5 point; (**b**) #7 point. Figure 7: Loading noise at different observation points. (**a**) Single rotor; (**b**) Coaxial rotor. below the rotor, and different azimuth angles have no effect on its vector distance from the rotor, which contain \(r\) and \(\theta\) in Equation (4). The #5 point is located diagonally below the rotor. When the rotor is at the longitudinal azimuth, for the #5 point, the distances from blades at \(0^{\circ}\) and \(180^{\circ}\) are different from the #7 point. By comparison, for blades at \(90^{\circ}\) and \(270^{\circ}\), their distances from #5 and #7 points are almost same. It can be concluded that the No. 1 wave is caused by the load fluctuations of blades at \(90^{\circ}\) and \(270^{\circ}\); for different observation points, the phases are almost the same, while the amplitude and waveform have some change due to the radiation direction of the loading noise. The No. 2 wave is caused by load fluctuations at \(0^{\circ}\) and \(180^{\circ}\), leading to the differences in the waveform and phase among different observation points. Figure 11 shows the sound pressure level (SPL) frequency spectrum of loading noise at different observation points. The fundamental frequency corresponds to the rotor rotation speed, i.e.,\(f_{0}=15.915\) Hz. As the rotors are two-bladed, the blade-pass frequency (BPF) is twice \(f_{0}\). At the #1 point, the thickness noise of the coaxial rotor is similar to the single rotor. The strong magnitude frequencies are mainly integer multiples of BPF. For the single rotor, the total noise is dominated by the thickness noise, and the amplitude of loading noise in the high-frequency band decreases rapidly. For the coaxial rotor, the total noise is dominated by the thickness noise before the 20 th harmonic, while, above this, the total noise is dominated by the loading noise. At the #5 point, the thickness noise is much weaker than the loading noise, as it mainly transmits in the rotor disk plane. Compared with the single rotor, the loading noise of the coaxial rotor has a stronger magnitude in a larger range of the frequency band. The total noise is mainly dominated by the loading  
Figure 10: Schematic diagram of distances between observation points and blades (\(\psi=0^{\circ}\)). Figure 9: Comparison of loading noise at different observation points. (**a**) Upper rotor; (**b**) Lower rotor. noise, both in low-frequency and high-frequency bands.