Steady Aerodynamics of Airfoils with Porosity Gradients with Nonlinear Boundary Conditions

This study determines the sectional lift coefficient of an airfoil with prescribed thickness, camber, and porosity distributions in a steady incompressible flow. A Darcy porosity condition on the airfoil surface furnishes a Fredholm integral equation, which permits an exact solution provided that the porosity distribution is Holder-continuous. However, a comparison of the lift prediction for a porous airfoil of type SD7003 indicates that for large values of the porosity parameter, the model completely departs from the experimental data suggesting a characteristic missing from the current model. Consequently, in this paper the Darcy porosity condition is replaced by the Forchheimer porosity condition to include nonlinear effects in the solution. The Forchheimer porosity condition (when simplified into a piecewise linear condition) on the airfoil surface provides a modified system of Fredholm integral equations, which permits an approximate solution by superposition. The Holder-continuous solution is verified against the SD7003 airfoil results. These results are to be integrated into a theoretical framework to optimize turbulence noise suppression with minimal impact to the aerodynamic performance of wing sections.