## 4 Conclusions  
In this paper, an experimental aeroacoustic study on reducing the tonal noise from laminar instability by using structured porous trailing edges was presented. Detailed acoustic measurements have been conducted on a symmetrical NACA 0012 airfoil with a solid trailing edge and seventeen structured porous trailing edges, under varying free-stream velocities and angles of attack. The key findings of this study are listed as follows:  
1. Structured porous trailing edges can reduce the noticeable tonal noise of the symmetrical NACA 0012 airfoil. Under the same pore coverage, larger noise reduction was generally obtained by structured porous edges with a larger diameter of sub-millimeter-scale pores and gradually sparsely arranged pores transiting from the solid body to that of the free flow.
2. Due to the sensitivity of airfoil tonal noise to changes in the free-stream velocity and the geometric angle of attack, as shown in Section 3.1, the design parameters for tonal noise reduction are slightly different at a zero angle of attack (\(\alpha=0^{\circ}\)) and a non-zero angle of attack (\(\alpha=10^{\circ}\)).
3. At \(\alpha=0^{\circ}\), the pressure difference between the pressure and suction sides close to the trailing edge is relatively small, especially at low free-stream velocities. Moreover, bluntness-related vortex shedding tonal noise and cavity tonal components are more likely to occur at this angle of attack. Therefore, larger airfoil tonal noise reduction is prone to the porous parameters of small pore coverage, small-to-moderate chordwise  
Figure 21: \(\Delta\)OASPL for structured porous trailing edges with different spanwise spacings: (**a**) \(\alpha=0^{\circ}\), (**b**) \(\alpha=10^{\circ}\).  
Figure 20: Typical noise spectra between the structured porous trailing edges and the baseline trailing edge with different spanwise spacings. (**a**) \(V_{\infty}=30\) m/s, \(\alpha=0^{\circ}\); (**b**) \(V_{\infty}=60\) m/s, \(\alpha=10^{\circ}\). Different colored circles in the zoomed inset figures illustrate the peak SPL of the different configurations.  
spacing, and moderate spanwise spacing. Meanwhile, structured pores are preferably distributed on the downstream of the airfoil.
4. At \(\alpha=10^{\circ}\), a sufficient pressure difference between the pressure and suction surfaces can easily drive airflow passing through both sides of the airfoil. Consequently, the optimal combination of the structured porous edge is a configuration with larger pore coverage, smaller chordwise spacing, and spanwise spacing.  
Due to the significant difference between the studied Reynolds number of \(10^{5}\) and the actual Reynolds number of \(10^{12}\) for full-scale wings (e.g., Boeing 747 [4]), further research is needed on noise reduction using structured porous trailing edges at comparatively higher Reynolds numbers in the future. Another direction for future research is to reveal the underlying noise reduction mechanisms of structured porous trailing edges via numerical simulations or PIV flow field measurements.  
Conceptualization, Y.W. and K.Z. ([PERSON]); methodology, Y.W.; validation, P.G. and K.Z. ([PERSON]); formal analysis, P.G.; investigation, Y.W.; resources, K.Z. ([PERSON]); data curation, V.F.K.; writing--original draft preparation, Y.W.; writing--review and editing, Y.W. and K.Z. ([PERSON]); visualization and experimental tests, P.G. and K.Z. ([PERSON]); supervision, K.Z. ([PERSON]); modification and English edit, V.F.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China, under grant numbers 12261131502 and 12102451. [PERSON] was supported by the Russian Science Foundation, grant no. RSF 23-41-00023.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors would like to thank the editor and anonymous referees for their helpful comments and suggestions.  
The authors declare no conflicts of interest.