## 4 Conclusions  
The static pressure drop that is experienced by constant flow through permeable materials is a function of geometrical and fluid properties. In this work, the focus lies on actively changing the flow resistivity of porous metal foams by means of flow heating. Based on a simple power-law relation between fluid temperature and viscosity, the material resistivity increases with fluid temperature according to \(R/R_{0}\approx(T/T_{0})^{0.6}\). Using a resistivity rig with built-in heating unit, this relation is observed in good approximation.  
The emitted TBL-TE noise levels of a NACA0018 airfoil with different trailing edge inserts are measured in the anechoic wind tunnel at TU Delft. Equipping the porous trailing edge with heating wires results in increased broadband noise levels of up to \(1.5\,\mathrm{dB}\). Upon heating, active change of noise mitigation characteristics is observed. For an average trailing edge surface temperature of \(57\,\mathrm{\SIUnitSymbolCelsius}\) above ambient conditions and an inflow velocity of \(U=15\,\mathrm{m\,s^{-1}}\), far-field noise band levels increase by up to \(2.5\,\mathrm{dB}\). Strong temperature gradients along the trailing edge surface and inside the foam indicate effective heat transfer between the metal foam and the penetrating fluid. Having shown that the flow resistivity increases with the fluid temperature, it is concluded that hampered flow communication across the permeable inserts is a main factor for observed active change of TBL-TE noise emissions.  
Figure 7: Comparison of far-field noise spectra of different heated and unheated trailing edge cases for \(U=15\,\mathrm{m\,s^{-1}}\) and \(U=25\,\mathrm{m\,s^{-1}}\). SPLs as observed at a distance of \(1\,\mathrm{m}\) from the airfoil are depicted (**a**) as well as a comparison between selected measurement cases (**b**).  
The increase of broadband noise levels with rising fluid temperature shows similar characteristics compared to the wire installation effects. It is therefore argued that not only a uniform change of material resistivity accounts for the magnitude of noise increase but also a non-uniform resistivity distribution with peak values close to the wires. Further sources of excess noise upon heating, such as the change in density experienced by convected pressure fluctuations over the heated trailing edge, could play an additional role in the observed activation behavior.  
Embedding heating wires in porous trailing edges of aircraft wings or wind turbine blades might not be feasible due to the high complexity it adds to the design. Future experiments could focus on uniform trailing edge heating which would provide the ability to actively influence flow resistivity _independently_ of the microscopic pore structure. This would allow identifying beneficial pore geometry effects while keeping the material resistivity constant.  
Conceptualization, methodology as well as experimental investigation was performed by [PERSON] and [PERSON]. Responsible author was [PERSON] while original draft preparation was supported by [PERSON] and [PERSON]. Topic proposer and main supervisor of the project was [PERSON].  
The authors would like to thank the technical staff in the low-speed wind tunnel lab for their support during the experimental campaign. Special thanks to [PERSON] from the Novel Aerospace Materials department for his advice in the field of porous materials. The evaluation of beamforming results was a crucial part of this project and we would like to thank [PERSON] from the Aircraft Noise and Climate Effects department for his help. This work was carried out within the IPERMAN project group and many thanks go to the multidisciplinary team members and their technical advice.  
The authors declare no conflict of interest. The funders had no role in the design of the study: in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations are used in this manuscript: