## 3 Results and Discussion
### Far-Field Noise  
A comparison of far-field noise spectra from porous and solid trailing edges is displayed in Figure 7 to demonstrate the frequency region in which noise mitigation occurs. The SPLs are calculated according to Equation (6) for two different flow speeds and \(1/3\)-octave band levels are plotted against the frequency. In agreement with previous campaigns [14; 15; 16; 31], low-frequency noise is effectively reduced by up to \(10\,\mathrm{dB}\) within the lowest evaluated frequency band centered around \(630\,\mathrm{Hz}\). Above a frequency of \(1.3\,\mathrm{kHz}\) for \(U=15\,\mathrm{m}\,\mathrm{s}^{-1}\) and \(2\,\mathrm{kHz}\) for \(U=25\,\mathrm{m}\,\mathrm{s}^{-1}\), the use of a porous trailing edge leads to noise increase. The occurrence of excess noise is commonly attributed to the higher surface roughness of porous materials [14; 15]. Above a frequency of \(1.25\,\mathrm{kHz}\), the slope of the porous trailing edge noise spectra changes with respect to the linear trend at lower frequencies. The deviation between far-field spectra from homogeneous, porous inserts and porous inserts equipped with heating wires is depicted in Figure 7 to show wire installation effects. In addition to absolute SPL levels, the difference between the homogeneous baseline and the porous inserts fitted with wires is plotted in the form of  
\[\Delta SPL_{1/3}=SPL_{Wire}-SPL_{Hom.}. \tag{7}\]  
The installation of heating wires inside the P800 metal foam affects the porosity \(\varphi\) of the material since a certain volume of air is replaced by the non-permeable wires. Far-field noise levels increase by approximately \(1\,\mathrm{dB}\) in the low-frequency range upon heating wire installation while high-frequency bands are less affected. Based on an aeroacoustic characterization of porous materials, [PERSON] et al. [15] reported high-frequency excess noise which occurred when large rigid structures were embedded in porous materials and the use of solid wires in this study is expected to reduce the communication between suction and pressure side, hence deteriorating noise abatement performance. Results from the acoustic measurements confirm that active change of TBL-TE noise characteristics can be achieved by changing the temperature of the porous trailing edge. Far-field noise spectra for two different flow speeds are included in Figure 7. A broadband increase in noise levels is observed for increasing trailing edge temperature except for the case of higher flow velocity in the range between \(f_{c}=2\,\mathrm{kHz}\) and \(f_{c}=2.5\,\mathrm{kHz}\). Effects from changing temperatures are more pronounced at \(U=15\,\mathrm{m}\,\mathrm{s}^{-1}\) where a maximum noise increase of almost \(2.5\,\mathrm{dB}\) can be observed. Given the maximum heating input of \(210\,\mathrm{W}\), measurements at higher flow speeds are stronger affected by cooling effects due to forced convection and achievable far-field noise level changes are lower. The maximum activation effect is observed in the frequency band centered around \(f_{c}=1\,\mathrm{kHz}\) and \(f_{c}=1.25\,\mathrm{kHz}\) for \(U=25\,\mathrm{m}\,\mathrm{s}^{-1}\) and \(U=15\,\mathrm{m}\,\mathrm{s}^{-1}\), respectively. The dominant activation mechanism which leads to the variation in far-field noise levels is assumed to be the resistivity change of the trailing edge material upon heating. Cross-flow through the permeable trailing edge is required if communication between the suction and pressure side occurs. Assuming that this seepage flow is effectively heated while penetrating the porous material, pressure communication is influenced. The decrease in noise abatement performance upon activation is in agreement with the increase in resistivity with temperature reported in Section 3.1. The far-field noise spectra of heated trailing edges indicate that the frequency bands around \(2\,\mathrm{kHz}\) and \(2.5\,\mathrm{kHz}\) are less affected by resistivity changes.