# Rod-Airfoil Interaction Noise Reduction Using Gradient Distributed Porous Leading Edges
## 3 Results  
### Noise Characteristics of the Baseline Case  
Figure 3 shows the typical noise spectra generated by the baseline rod-airfoil case (i.e., all the three leading edge strips were made of aluminum) at different airfoil attack angles. The noise spectra of the isolated rod and the flow only are plotted in Figure 3. As trends were similar for all flow velocities, only the values for \(V_{\infty}=50\) m/s are presented. Figures 4 and 5 compare the magnitude of the main peak (i.e., peak SPL) and the corresponding Strouhal number of the peak frequency based on the rod diameter. Because the validation and comparison of the presented experimental results with data from the literature are compulsory steps before performing any parametric study, Figure 5c also provides the Strouhal numbers of the rod-airfoil configuration and the rod-only configuration obtained by [PERSON] et al. [5] and [PERSON] et al. [12] for the benchmark case (\(d/c=0.1\), \(L/d=10\) and \(\alpha=0^{\circ}\)). Figure 2: Illustration of the tested model (not to scale). Several interesting points were drawn from these figures: (1) The measured spectra for the isolated \(d\)= 20 mm rod featured a strong tonal component and a substantial broadband part around the main peak, corresponding to the frequency of Karm\(\acute{\text{a}}\)n vortices shed by the rod (the Strouhal number was about 0.195). The presence of the airfoil embedded in the wake of the isolated rod increased the level of emission peak of about 10 dB and the broadband spectra around the main peak, which we attributed to the impingement of the periodic shedding vortices onto the airfoil leading edge, as proved in [12,13]. The spectra for frequencies above 8-9 kHz were dominated by rod noise, which implied that the noise in these frequency bands may have been caused by small-scale turbulent vortices, which do not strongly interact with the leading airfoil  
Figure 4: The main peak value of the acoustic spectra at different airfoil attack angles: \(L\) = (a) 100 mm, (b) 140 mm, and (c) = 200 mm. Figure 5: Strouhal number corresponding to the main peak at different airfoil attack angles: \(L\) = (a) 100 mm, (b) 140 mm, and (c) 200 mm. Figure 3: Acoustic spectra of the baseline rod–airfoil configuration at different airfoil attack angles (\(V_{\infty}\) = 50 m/s): \(L\) = (a) 100 mm, (b) 140 mm, and (c) 200 mm. edge. (2) As the streamwise gap increased, the peak SPL of the rod-airfoil configuration generally reduced, in good with prior experimental findings of various rotor-stator configurations [24] where the tonal noise levels reduced with larger rotor-stator spacing. The phenomenon can be understood because the energy of the shedding vortices and the corresponding impingement intensity onto the airfoil gradually weakened as the shed vortices moved and dissipated downstream. (3) The main peak somewhat shifted to a lower frequency in the presence of the downstream airfoil, which could be ascribed to a possible weak hydrodynamic-acoustic feedback of the airfoil onto the vortex shedding of the rod, as suggested by [PERSON] et al. [1], [PERSON] et al. [5], and [PERSON] et al. [25]. Moreover, the shifting became more obvious as the streamwise gap decreased, which may have occurred due to the enhancement in the aforementioned hydrodynamic-acoustic feedback because the spacing between the rod and the airfoil reduced. Additional evidence of this conclusion is that splitter plates close to the rod could completely suppress vortex shedding and tonal noise, as experimentally demonstrated by [PERSON] et al. [22] and [PERSON] et al. [23]. (4) The sound pressure level of the main peak slightly reduced as the angle of attack of the downstream airfoil increased, which is similar to the experimental observations of [PERSON] et al. [13], whose flow visualization tests proved that it is due to the weaker vortex entrainment. On the contrary, the broadband part of the spectrum far away from the main peak (both the low- and mid-to-high-frequency range) substantially increased as the angle of attack increased.