# A Computational Study on the Aeroacoustics of a Multi-Rotor Unmanned Aerial System
## 3 Results and Discussion
### Local Flow
#### 3.2.2 Level of Unsteadiness  
As mentioned before, for aerial systems relying on propulsion, the periodic motion of the propellers transmits noise through the system by exciting the skin panels of the structure [33], which eventually results in structure-born noise. To evaluate the level of unsteadiness on various conditions, the distribution of root-mean-square (RMS) of the static pressure (\(p_{RMS}\)) on propeller-3, wings and the fuselage of CRC-3 are represented in this section. The labels assigned to the eight cases in Table 2 are used in the pressure RMS figures. Figure 16 demonstrates \(p_{RMS}\) on propeller-3 for various conditions and as expected, the blade tips experience the maximum unsteadiness. From C1 to C5, the level of  
Figure 14: Snapshot of dilatation field on a slice passing through the propeller hub: (**a**) \(\gamma=45\); (**b**) \(\gamma=135^{\circ}\). Figure 15: Snapshot of iso-surface of pressure time-derivative: (**a**) CRC-3 at \(\gamma=45^{\circ}\); (**b**) CRC-3 at \(\gamma=45^{\circ}\); (**c**) Isolated propeller at an arbitrary phase angle. unsteadiness increases on the propeller as \(\theta\) grows. Interestingly, the percentage of increase at high \(\theta\) range is smaller than that of the low \(\theta\) range (\(\sim\) 28% versus \(\sim\) 50%), which is consistent with the trend depicted in Figure 7.  
The same agreement may be found on the inflow velocity effect on noise by comparing the level of unsteadiness between cases C2 (\(U_{0}=7\) m/s), C6 (\(U_{0}=4\) m/s) and C7 (\(U_{0}=13\) m/s) with Figure 10. Based on the OASPL trend shown in Figure 10, \(OASPL_{C7}>OASPL_{C6}>OASPL_{C2}\), and the maximum level of unsteadiness shows \(RMS_{C7}>RMS_{C6}>RMS_{C2}\). This confirms the importance of unsteady loading noise over steady loading noise in the CRC-3's noise generation mechanism, as mentioned in the discussion of Figure 10. In fact, the unsteadiness on propellers is significantly influenced by their interaction with the structure, which confirms that the wings and fuselage are the major cause of increase in noise due to increasing pitch angle. The RPM effect on unsteadiness of the propeller may be evaluated by comparing cases C2 and C8 which have similar condition except different RPM values of 6000 and 12,000, respectively. Although RPM results in doubling the maximum pressure fluctuation level, it can be seen that the  
Figure 16: Dimensionless \(P_{RMS}\) contour on propeller-3 of CRC-3 for various cases: C1 (RPM = 6000, \(U_{0}=7\) m/s, \(\theta=0\)), C2 (RPM = 6000, \(U_{0}=7\) m/s, \(\theta=15\)), C3 (RPM = 6000, \(U_{0}=7\) m/s, \(\theta=35\)), C4 (RPM = 6000, \(U_{0}=7\) m/s, \(\theta=55\)), C5 (RPM = 6000, \(U_{0}=7\) m/s, \(\theta=75\)), C6 (RPM = 6000, \(U_{0}=4\) m/s, \(\theta=15\)), C7 (RPM = 6000, \(U_{0}=13\) m/s, \(\theta=15\)), C8 (RPM = 12,000, \(U_{0}=7\) m/s, \(\theta=15\)). cases with \(\theta=55^{\circ},75^{\circ}\) at RPM = 6000 (C4 and C5) experience a higher unsteadiness level than case C8 with RPM = 12,000 and \(\theta=15^{\circ}\). It may be inferred that the pitch angle can increase the unsteadiness of the propellers significantly, and the amount it adds to the CRC-3 noise level may even become more important than noise originated solely from the propellers' tips. Figure 17 depicts dimensionless \(P_{RMS}\) contours on the fuselage and wings for various cases. Unlike the RMS contours on propellers, in which the case with maximum pitch (C5) demonstrates the maximum unsteadiness on the propeller, here the case with \(\text{RPM}=12,000\) (C8) experiences the maximum unsteadiness on the rest of the structure. This is in agreement with the fact that structure-born noise is mainly due to the propeller loading [29], which is maximal for the case C8. In addition, this indicates existence of a two-way unsteady mechanism between the propellers and the structure of CRC-3. The body imposes maximum unsteadiness on the propellers at large pitch, while the propellers cause maximum fluctuation on the body at large RPM.