# Rod-Airfoil Interaction Noise Reduction Using Gradient Distributed Porous Leading Edges
## 3 Results
### Noise Characteristics of Porous Leading Edges  
A comparison of the sound pressure reduction level (\(\Delta\)SPL = SPL\({}_{p}-\) SPL\({}_{b}\)) versus the frequency and flow velocity between the porous leading edge SPL\({}_{p}\) and the baseline case SPL\({}_{b}\) is shown in Figure 6 for different airfoil attack angles and in Figure 7 for different streamwise gaps. Positive and negative values in \(\Delta\)SPL represent a noise amplification and noise reduction effects, respectively. Comparisons of the noise spectra at a typical flow velocity of \(V_{\infty}\) = 50 m/s are plotted in Figure 8.  
These figures reveal several characteristic features associated with rod-airfoil interaction noise reduced by the porous leading edges: (1) Porous leading edges can reduce rod-airfoil interaction noise around the peak frequency and substantially suppress the mid-to-high frequency broadband noise above the peak frequency. The maximum noise reduction is 20.71 dB at \(L\) = 200 mm and \(\alpha=20^{\circ}\). However, low-frequency noise below the peak frequency generally increases due to the shifting of the main peak (Figure 8). Moreover, high-frequency noise above 2000 Hz also increases, and this noise amplification effect increases with the decrease in the ppi value of the porous materials. This phenomenon is consistent with published experimental observations and can be attributed to the surface roughness of porous materials [21; 26; 27]: lower ppi values indicate higher surface roughness noise, which is usually noticeable at high frequencies. (2) With the increase in the airfoil attack angle, the noise reduction effect becomes more considerable and the frequency range with \(\Delta\)SPL \(<\) 0 widens. For example, the upper limit increases from about 2000 Hz in Figure 8b to about 3000 Hz in Figure 8c. This phenomenon may be due to the enhanced flow communication across the pressure and suction sides of the porous airfoil and thus the decreased intensity of the impingement of the vortices onto the solid leading edge because of the increased pressure difference between the two sides of the downstream airfoil at a high attack angle. (3) With the increase in the streamwise gap, the frequency range with noise reduction capability (i.e., \(\Delta\)SPL \(<\) 0) is basically unchanged, and the variation in noise attenuation for different streamwise gaps is not as large as that at different attack angles of the downstream airfoil. (4) With the decrease in the ppi value of the porous materials, the noise reduction ability is enhanced and the peak frequency decreases. The reason for this is that lower-ppi materials have relatively bigger pores, which allows the shedding vortices and the impinging turbulence to permeate into the porous leading edge and thus reduces the intensity of the surface pressure fluctuations. This is in agreement with previous findings [19], because surface pressure fluctuations mitigation reduces sound source intensity; the latter is one of the mechanisms through which noise is attenuated.  
Figure 8: Typical noise spectra between the porous leading edges and the baseline configuration (\(V_{\infty}\) = 50 m/s): (**a**) \(L\) = 100 mm, \(\alpha=0^{\circ}\); (**b**) \(L\) = 200 mm, \(\alpha=0^{\circ}\); and (**c**) \(L\) = 200 mm, \(\alpha=10^{\circ}\).