Integrating a porous material into the structure of an aerofoil constitutes a promising passive strategy for mitigating the noise from turbulence–body interactions that has been extensively explored in the past few decades. When a compact permeable body is considered in the aeroacoustic analogy derived by Curle to predict this noise source, a dipole associated with the non-zero unsteady Reynolds stresses appears on the surface in addition to the dipole linked to the pressure fluctuations. Nevertheless, the relative contribution of this source to the far-field noise radiated by a porous wing profile has not been clarified yet. The purpose of the current research work is twofold. On the one hand, it investigates the impact of porosity on the surface-pressure fluctuations of a thick aerofoil immersed in the wake of an upstream circular rod at a Mach number of 0.09. On the other hand, it quantifies the relevance of the Reynolds-stresses term on the surface as a sound-generation mechanism. The results from large-eddy simulations show that the porous treatment of the wing profile yields an attenuation of the unsteady-pressure peak, which is localised in the low-frequency range of the spectrum and is induced by the milder distortion of the incoming vortices. However, porosity is ineffective in breaking the spanwise coherence or in-phase behaviour of the surface-pressure fluctuations at the vortex-shedding frequency. The Reynolds-stresses term is found to be considerable in the stagnation region of the aerofoil, where the transpiration velocity is larger, and partly correlated with the unsteady surface pressure, suggesting constructive interference between the two terms. This results in a non-negligible contribution of this term to the far-field acoustic pressure emitted by the porous wing profile for observation angles near the stagnation streamline. The conclusions drawn in the present study eventually provide valuable insight into the design of innovative and efficient passive strategies to mitigate surface–turbulence interaction noise in industrial applications.

A possible strategy for the reduction of the aeroacoustic noise generated by turbulence interacting with a wing profile, also referred to as leading-edge noise, is represented by the implementation of a porous medium in the structure of the airfoil. However, the physical mechanisms involved in this noise mitigation technique remain unclear. The present work aims at elucidating these phenomena and particularly how the porosity affects the incoming turbulence characteristics in the immediate vicinity of the surface. A porous NACA-0024 profile equipped with melamine foam has been compared with a solid baseline, both airfoils being in turn subjected to the turbulence shed by an upstream circular rod. The mean wall-pressure distribution along the airfoils shows that the implementation of the porous material mostly preserves the integrity of the NACA-0024 profile's shape. Results of hot-wire anemometry and large-eddy simulations indicate that the porous design proposed in this study allows for a damping of the velocity fluctuations and it has a limited influence on the upstream mean flow field. Specifically, the upwash component of the root-mean-square of the velocity fluctuations turns out to be significantly attenuated in the porous case in contrast to the solid one, leading to a strong decrease of the turbulent kinetic energy in the stagnation region. Furthermore, the comparison between the power spectral densities of the incident turbulent velocities demonstrates that the porosity has an effect mainly on the low-frequency range of the turbulent velocity power spectrum. This evidence is in line with the results of the acoustic beamforming measurements, which exhibit a noise abatement in an analogous frequency range. On the basis of these observations, an interpretation of the phenomena occurring in the turbulence-interaction noise reduction due to a porous treatment of the airfoil is finally given with reference to the theoretical inputs of the Rapid Distortion Theory.

The analysis of porous materials for aeroacoustic noise mitigation requires high-fidelity numerical tools to simulate the sound propagation and interaction in porous media. The manuscript presents the calibration and validation of a direct-hybrid LES/CAA method used to model the aerodynamically generated sound. The porous micro-structures are modeled with a volume-averaging approach. Additional terms, emerging in the governing equations, owing to the force exerted by the porous matrix on the fluid, are closed by means of Darcy's law and the quadratic Forchheimer term. The sound generation and propagation is predicted by a solution of the acoustic perturbation equations via a discontinuous Galerkin method. The model for the porous material is separately calibrated for the CFD and CAA with the parameters retrieved by the characterization of a melamine foam in experimental tests. The sound predicted by an absorbing layer of the material is compared with measurements performed in an impedance tube. Secondly, the transmission coefficient of the melamine foam placed in an acoustic liner configuration inside a duct is studied numerically. The results are then compared with experiments conducted in absence of a flow and also with a flow velocity of 30 m/s in order to assess the accuracy of the model calibration.