# Investigation on Aerodynamic Noise Characteristics of Coaxial Rotor in Hover
## 3 Results and Discussion  
### Noise at Different Observation Points  
Figure 5 presents the sound pressure time histories of thickness noise for the coaxial and single rotors at different observation points of case A3. Here, the single rotor means the isolated upper rotor without the lower one, which adopts the same collective pitch as the upper rotor. It can be seen from the three observation points in the rotor plane (#1, #2, and #3) that, for the single rotor, different azimuth angles only affect the phases of the sound pressure, but have no effect on the amplitudes and waveforms. There are two troughs in one resolution, as each rotor has two blades. For a coaxial rotor, the sound pressure history is the superposition of those caused by the twin rotors. As the rotation directions of them are opposite, the sound pressure fluctuations of the two rotors are opposite along the azimuth angle. At #1 point, the troughs are superimposed, which forms larger troughs. At #2 and #3 points, there are four troughs, but the amplitudes are slightly smaller than the single rotor, due to the superposition. Through the three observation points in the longitudinal plane (#1, #4, and #5), it can be found that, as the location moves downward from the rotor plane, the fluctuation amplitudes caused by thickness noise gradually decrease, while the waveform and phase have no change. For the coaxial rotor, the amplitudes of troughs are roughly twice those of the single rotor, due to the superposition effect of rotor noise sources. Figure 6 shows the temporal \(C_{\rm T}\) and its first-order time derivative of the coaxial and single rotors for case A3. For the single rotor, the thrust is almost constant at different azimuths, while for the dual rotors, the thrusts show periodic unsteady fluctuations. A detailed explanation of the thrust fluctuations has been given in Ref. [18]. It is important to note that there are pulse-type fluctuations at the locations where the blades meet, which can be called the blade-meeting interaction. Thrust of the upper rotor spikes down, but for the lower one, it spikes up. Moreover, the pulse amplitude of the upper rotor is much larger than the lower rotor. Referring to Equation (4), considering that rotor azimuth has no influence on \(M_{i}\), it means that \(\dot{M}_{i}\) is equal to 0. Thus, the first-order time derivative of load (\(\dot{p}\)) is dominant in the noise source term. As seen in Figure 6b, for the time derivative of \(C_{\rm T}\), the unsteady fluctuations mainly occur at the blade-meeting azimuths, and the fluctuation amplitudes of the upper rotor are obviously higher than those of the lower rotor. Figure 4: Comparison of calculated sound pressure and experimental data. (a) #3 point; (b) #9 point. Figure 7 shows the sound pressure histories of loading noise at different observation points for case A3. For the single rotor, blade loads are almost same at different azimuths. Thus, at #7 point, there is little load fluctuation, which corresponds to little sound pressure. According to Equation (4), the terms of \(\dot{p}\) and \(\dot{M}_{i}\) both are theoretically equal to 0. At other points, the sound pressures have periodic fluctuations, which is due to the changes in rotor position relative to the observation point and the radiation direction of the loading noise. Figure 5: Sound pressure histories of thickness noise. (**a**) Points in the rotor disk plane; (**b**) Points in the longitudinal plane. Figure 6: Comparison of temporal rotor performance. (**a**) \(C_{\mathrm{T}}\); (**b**) \(\mathrm{d}C_{\mathrm{T}}/\mathrm{dt}\). For the coaxial rotor, fluctuations in sound pressure are more complex. At #7 point, \(\dot{M}_{i}\) remains 0, and the sound pressure is mainly caused by the unsteady interaction loads, corresponding to a large value of \(\dot{p}\). This causes a new kind of impulsive loading noise, compared with the single rotor. As rotors meet every other 90\({}^{\circ}\), the main fluctuation period is also around 90\({}^{\circ}\).