Quantitative criteria to design optimal permeable trailing edges for noise abatement

Abstract

An experimental study on broadband noise scattered by permeable trailing edges with different pore arrangements is performed. A NACA 0018 airfoil with chord c = 0.2 m is investigated at chord-based Reynolds numbers ranging from 1.4 × 10⁵ to 3.8 × 10⁵ and angles of attack of 0.2 and 5.4 degrees. Noise emission from five 3D-printed perforated trailing-edge inserts, with channels normal to the chord, is measured with a microphone antenna. For comparison, inserts manufactured with metallic foams, with comparable flow permeability K but more tortuous pore paths, are also analysed. All the inserts have a permeable extension s equal to 20% of the chord (s/c = 0.2). It is shown that noise mitigation ΔL_p, computed as the difference between far-field noise scattering from solid and permeable edges, collapse when nondimensionalizing frequency as Strouhal number based on the chord. From the collapsed data, it is observed that the maximum noise attenuation reported for each insert ΔL_p,max reaches an asymptotic value of 9.3 dB for increasing K. To parameterize such asymptotic behaviour, noise reduction levels are fitted to a newly proposed relation ΔL_p,max=γ₁tanh(γ₂K) (where γ₁ and γ₂ are fitting coefficients, that depend on the type of insert and angle of attack). Following this analysis, limit permeability values for perforated and metal foam inserts of K = 3.5 × 10⁻⁹ and 1 × 10⁻⁹ m² are found, respectively; above these thresholds, less than 1 dB additional noise mitigation is reported; below, a difference in ΔL_p,max of up to 4 dB for a given K is measured depending on the pore organization. Consequently, the tortuosity of the permeable structure is identified as an additional parameter (to K) controlling noise attenuation. It is also observed that the acoustic performance of lower-permeability edges is less sensitive to changes in the angle of attack. Tests for permeable lengths equal to s/c = 0.05 and 0.1 are performed: the change of ΔL_p,max with increasing s/c is also properly described with a hyperbolic tangent, evidencing equally good performance in noise reduction for all measured extents. Finally, for the most permeable insert with periodic pore arrangement, an extremely loud tonal noise caused by vortex shedding (+30 dB higher than broadband levels) from the blunt solid-permeable junction at s/c=0.8 is reported. Since applying a longer permeable surface, or increasing the permeability at the trailing edge decreases the aerodynamic performance of the blade, a permeable trailing edge with s/c = 0.05, K = 1 × 10⁻⁹ m² and tortuosity of 1.15 is recommended to optimize broadband noise abatement and avoid shedding-related tones for the conditions explored in the current study.