The steady aerodynamics of aerofoils with porosity gradients

This theoretical study determines the aerodynamic loads on an aerofoil with a prescribed porosity distribution in a steady incompressible flow. A Darcy porosity condition on the aerofoil surface furnishes a Fredholm integral equation for the pressure distribution, which is solved exactly and generally as a Riemann-Hilbert problem provided that the porosity distribution is Hölder-continuous. The Hölder condition includes as a subset any continuously differentiable porosity distributions that may be of practical interest. This formal restriction on the analysis is examined by a class of differentiable porosity distributions that approach a piecewise, discontinuous function in a certain parametric limit. The Hölder-continuous solution is verified in this limit against analytical results for partially porous aerofoils in the literature. Finally, a comparison made between the new theoretical predictions and experimental measurements of SD7003 aerofoils presented in the literature. Results from this analysis may be integrated into a theoretical framework to optimize turbulence noise suppression with minimal impact to aerodynamic performance.