Experimental and Theoretical Investigation of Airfoil Noise Mitigation Using Biologically-Inspired Porosity

Porosity presents a practical strategy for reducing aeroacoustic noise on the airfoil surface. This study investigates the aeroacoustic performance of an SD7003 airfoil with a chord-wise varying porosity distribution. While previous studies have applied Darcy's law to model porous media at low Reynolds number cases, this linear model becomes inaccurate when the pore-based Reynolds number exceeds unity, Re > 1. To account for the resulting nonlinear inertial effects, we incorporate the Forchheimer condition which improves the accuracy of the model. The current study focuses on both the nonlinear theoretical analysis and experiments to evaluate the acoustic performance. Theoretically, the Mathieu function expansion is employed, with the Darcy and Forchheimer coefficients incorporated, to predict the acoustic pressure field for potential porosity cases. To validate the model, wind tunnel experiments were conducted using SLA-printed airfoils, including a non-porous baseline and three different porous configurations tested at air speeds ranging from 20 mph to 100 mph. The near-field acoustic measurements were taken using a 48LX1 microphone. The results show that the porous airfoils-particularly those with owl-inspired porosity distributions-demonstrate the highest effectiveness in noise reduction. At higher Reynolds numbers, the noise reduction is especially significant in the low-frequency range between 2 kHz and 5 kHz. These findings are consistent with trends reported in previous literature and provide a foundation for optimizing porosity-gradient distributions that achieve an effective balance between lift generation and noise reduction.