## 1 Introduction  
The reduction in an airfoil's self-noise level is one of the practical advantages of reducing the community noise impact of airports that are close to densely populated residential areas. Tonal noise from instabilities is an important airfoil self-noise mechanism at the trailing edge [1; 2; 3], especially on airfoils operating at low-to-moderate Reynolds numbers and angles of attack, e.g., small, unmanned air vehicles. To reduce the tonal noise from instabilities, a number of bio-inspired aerodynamic noise control techniques have been investigated in the past few decades [4], which can be classified into trailing edge serrations, brush-type extensions, and porous edges. [PERSON] et al. [5; 6; 7] investigated the capability of trailing edge serrations in reducing noise from airfoil instabilities. They found that trailing edge serrations could alter the length of the laminar separation bubble and inhibit the formation of a separated boundary layer at the pressure surface of the airfoil's trailing edge, which in turn reduces the amplitude of the tonal noise from the instability. Time-resolved PIV (Particle Image Velocimetry) measurements of instantaneous flow evolution by [PERSON] et al. [8] confirmed another noise reduction mechanism of serrated trailing edges, as the authors observed that they could strongly reduce the coherence of the shed Tollmien-Schlichting waves as they advected past the airfoil trailing edge. [PERSON] and [PERSON] [9; 10] demonstrated that brush-typeextensions could reduce both the broadband noise from a turbulent boundary layer and quasi-tonal vortex shedding noise if the edge modifications exceeded the minimum fiber length and had small fiber spacing. More recently, [PERSON] et al. [11; 12] conducted detailed aeroacoustic measurements on a set of porous edges, which were made of open-cell metallic foams with a piecewise gradient-distributed property in terms of pores per inch (ppi). They showed that the gradient-distributed porous edges could noticeably reduce the tonal noise from airfoil instabilities, and the performance was enhanced when the porous edges could gradually sparsely transition from the solid main body to that of the downstream air flow. [PERSON] et al. [13] numerically captured the noise reduction and increase caused by a micro-tube porous trailing edge and its effect on the wavenumber-frequency spectrum. An in-depth analysis of the dynamic structures of the trailing edge flow and surface pressure fields linked the noise reduction to 'cross-jet-like' flow permeation through the micro-tube structures. With the development of 3D printing technology (in terms of further meeting airworthiness requirements, such as maintainability, strength, and costs) and for the convenience of measuring the internal flow field of the pores, there is a tendency to replace traditional metal foam or polyurethane porous materials, which typically possess a randomized internal structure, with customized structured porous designs. [PERSON] et al. [14] validated that a 3D-printed porous coated cylinder can be used as a passive noise control method to reduce the cylinder vortex's shedding tone. [PERSON] et al. [15] demonstrated that an asymptotic value of up to 9.3 dB of broadband noise attenuation from the turbulent boundary layer was obtained by using 3D-printed perforated trailing edge inserts for increasing the flow permeability. They also reported that an extremely loud shedding-related tonal noise is generated from the blunt solid-permeable junction section, so it is recommended to optimize the physical parameters of the structured porous inserts to achieve better broadband noise abatement. [PERSON] and [PERSON] found that the most optimized 3D-printed porous trailing edge could obtain a maximum turbulent broadband noise reduction of 7 dB at an \(\alpha=0^{\circ}\) angle of attack [16], and the reduction in the broadband noise was more significant when \(\alpha\leq 0^{\circ}\)[17]. They also observed an unwanted bluntness-related tonal shedding noise at a high Reynolds number.