On the effect of structure permeability on the sound of an airfoil

The effect of structure permeability on the far-field radiation of a thin airfoil is studied. Assuming low-Mach and high-Reynolds number flow, the near- and far-field descriptions are investigated at flapping-flight flow conditions. Analysis is carried out using thin-airfoil theory and compact-body-based calculations for the hydrodynamic and acoustic fields, respectively. Airfoil porosity is modeled via Darcy's law, governed by prescribed distribution of surface intrinsic permeability. Discrete vortex model is applied to describe airfoil wake evolution. To assess the impact of penetrability, results are compared to counterpart predictions for the sound of an impermeable airfoil. Considering the finite-chord airfoil as "acoustically transparent", the leading-order contribution of surface porosity is obtained in terms of an acoustic dipole. It is shown that, at all flow conditions considered, porosity causes attenuation in outcome sound level. This is accompanied by a time-delay in the pressure signal, reflecting the mediating effect of permeability on the interaction of fluid flow with airfoil edge points. To the extent that thin-airfoil theory holds (requiring small normal-to-airfoil flow velocities), the results indicate on a decrease of ~10% and more in the total energy radiated by a permeable versus an impermeable airfoil. The applicability of Darcy's law to model the effect of material porosity is discussed in light of existing literature.