# Rod-Airfoil Interaction Noise Reduction Using Gradient Distributed Porous Leading Edges
## 3 Results
### Effect of Gradient Properties on Noise Reduction  
Figure 9 compares the \(\Delta\)SPL values for different coverage percentages of the porous treatments for three typical operating conditions (i.e., \(\alpha=0^{\circ}\) at \(L=100\) mm and \(L=200\) mm, and \(\alpha=10^{\circ}\) at \(L=200\) mm). From left to right in Figure 9, all three interchangeable leading edge strips or only part of them were composed of 40 ppi porous material. These figures show that both the maximum noise attenuation and the range of noise attenuation at mid-to-high frequency decreased with decreasing porous coverage. The reason for this finding may be that a large porous coverage increases the flow penetrating into the porous media, which thus reduces the rod-airfoil interaction noise. Figure 9 shows that the noise-increasing effect at high frequencies slightly decreases with a lower porous coverage, which is consistent with the smaller porous surface. Figure 10 compares the \(\Delta\)SPL values when the upstream, middle, or downstream of the three interchangeable leading edge strip was composed of porous material. Figure 11 illustrates the typical noise spectra at a flow velocity of \(V_{\infty}\) = 50 m/s. From these figures, we can see that the position of the porous material had different effects on the noise attenuation, though the porous coverage was basically the same when the pores were located in different strips. Generally, the pores located on the middle strip (i.e., X00Y40Z00) produced the best noise attenuation, whereas the minimum noise reduction was achieved using the X40Y00Z00 configuration. This finding is relevant for applications in which the mean lift coefficient of the wing profile must be preserved. As proved [19], porous treatment of the airfoil can reduce lift and increase drag, which finding implies that we can substantially attenuate interaction noise with a lower aerodynamic penalty by introducing porous holes only a small chordwise area downstream of the leading airfoil edge. The Strouhal number corresponding to the maximum reduction in the mid- to high-frequency band increased with the upstream movement of the porous position. For example, the Strouhal number increased from \(S_{\text{f}}\) = 0.38 for X00Y00Z40 (Figure 10g) to \(S_{\text{f}}\) = 0.65 for X40Y00Z00 (Figure 10i) at the operating conditions of \(L\) = 200 mm and \(\alpha=10^{\circ}\). The underlying mechanism for these observations is not clear at this stage, but may be related to the characteristics of the shedding vortices (such as vortex intensity or vortex size) at different leading edge positions, which will be revealed by our ongoing work involving flow-field measurements and numerical simulations. Figures 12-14 show the effect of arrangement order of the porous leading edges on the rod-airfoil interaction noise reduction. In these figures, the porous leading edges represented in the upper rows were composed of gradually sparser porous materials (i.e., lower ppi value or larger pores, such as X80Y60Z40 and X80Y50Z20) from the upstream strip to the downstream strip, whereas the leading edges represented in the lower rows were composed of gradually denser porous materials. Figure 15 summarizes the difference in OASPL (i.e., \(\Delta\)OASPL = OASPL\({}_{p}\) - OASPL\({}_{b}\), where OASPL\({}_{p}\) and OASPL\({}_{b}\) denote the OASPL of the porous leading edge and the baseline leading edge, respectively). The \(\Delta\)OASPL of two homogeneous porous leading edges (X40Y40Z40 and X120Y120Z120) are also presented in Figure 15. Several observations were obtained from these figures. First, the noise reduced (whether \(\Delta\)SPL around and above the peak frequency or \(\Delta\)OASPL) by the gradually more sparsely distributed porous leading edges were generally larger than those of the corresponding gradually denser counterparts, though the denser ones had a slightly wider frequency range of \(\Delta\)SPL \(<\) 0. Second, the gradient-distributed porous leading edge could attenuate more noise than the homogeneous-distributed porous leading edge.