## 4 Results and Discussion  
### Verification of Landing Gear Calculation Model  
Figure 10 shows the iso-surface map of the vortex formed by the flow around the landing gear based on the \(Q\) criterion when the incoming flow velocity is 75 m\(\cdot\)s\({}^{-1}\). The color indicates the change of Mach number. It can be seen from the figure that complex vortical structure is formed at the tail of the landing gear, thereby forming a complex flow field change, which generates aerodynamic noise. Figure 11 shows the comparison of the SPL (Sound Pressure Level) evolution with the frequency between test and numerical simulation under different wind speeds. Figure 11a-c are the result of microphone 13, and Figure 11d-f are the result of microphone 15. Table 2 is the comparison the OASPL (Overall Sound Pressure Level) between test and simulation. Figure 10: \(Q\) iso-surface map (\(Q\) = 3000 s\({}^{-1}\)). From Figure 11, it can be concluded that the difference of spectrum amplitude between the experimental and simulation are minor, but there are some differences in the wave peaks corresponding to the frequency, mainly due to the complex flow of the landing gear and the fact that the model is not scaled, so more grids are needed to accurately analyze the flow field. Moreover, LES can capture small flow structures, which makes it difficult to extract sound source, resulting in multiple wave peaks in the numerical results. It can be seen from Table 2 that the total far-field sound pressure level difference of landing gear at different wind speeds is within 5%, which meets the research on the amplitude characteristics of landing gear aerodynamic noise at different wind speeds. Figure 12 shows the comparison of sound pressure levels under different wind speeds. According to Figure 12, it can be concluded that with the increase of wind speed, the fluctuation frequency and amplitude of sound pressure increase, but the amplitude increment of 34 m\(\cdot\)s\({}^{-1}\)\(\sim\)55 m\(\cdot\)s\({}^{-1}\) is greater than that of 55 m\(\cdot\)s\({}^{-1}\)\(\sim\)75 m\(\cdot\)s\({}^{-1}\). In order to further analyze the relationship between the velocity and the acoustics, scaling was used to predict the effects on acoustic performance from other factors in addition to \(U_{\infty}\). The Scaled SPL is as follows:  
\[SPL_{scaled}=SPL-10\times n\times\log(U_{\infty}/U_{ref}) \tag{9}\]  
where \(U_{ref}\) = 65 m\(\cdot\)s\({}^{-1}\) is the reference velocity of incoming flow, \(n\) is the power index of the scaling proportionality. It is generally known that the landing gear is a dipole-like source due to unsteady pressure forces so \(n\) = 6 is preferred. However, it is inferred that \(U_{\infty}\)\({}^{7}\) only works for a compact model and a higher order of scaling is required due to the existence of smaller geometric details in a real landing gear [9]. Therefore, \(n\) = 6, 7 were utilized. The scaled spectra of experiment using proportionality of \(U_{\infty}\)\({}^{6}\) and \(U_{\infty}\)\({}^{7}\) is shown in Figure 12(a),b. It is observed that scaling proportionality of \(U_{\infty}\)\({}^{7}\) shows better performance for the frequency over 150 Hz. For the low frequency range below 150 Hz, \(U_{\infty}\)\({}^{6}\) appears to be slightly better. In contrast, Figure 12(c),d are the scaled spectra of simulation. It can be conducted that the \(U_{\infty}\)\({}^{7}\) performs better than \(U_{\infty}\)\({}^{6}\). In conclusion, the model here is much larger, and with minor details. Therefore, the seven-power law is more appropriate for the scaling of large-size, while the six-power law is appropriate for the small-size.