Effect of porosity on Curle's dipolar sources on an aerofoil in turbulent flow

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.