Aerodynamics of porous airfoils with nonlinear Forchheimer boundary condition

Owls have aero-acoustic advantages to fly silently due to the flexibility and porosity of their feathers. Researchers have shown that modeling the trailing edge with bio-inspired features is very effective for noise suppression. However, noise reduction and aerodynamic performance are in competition.

This study investigates the pressure distribution over porous airfoils in an incompressible flow. A Darcy-type porosity condition on the airfoil surface provides a Fredholm integral equation that can be solved exactly for Hölder-continuous porosity distributions. However, the generated lift predicted by the model diverges from the experimental data for highly-porous airfoils. To improve the mathematical model, we replace the linear Darcy porosity condition with the nonlinear Forchheimer boundary condition. The result indicates that the Forchheimer boundary condition performs better than the Darcy condition; the theoretical lift prediction for a porous SD7003 airfoil demonstrates better agreement with the available experimental data. The methodology will be combined with previous work on the aeroacoustics of a porous airfoil with a Forchheimer boundary condition to address the conflicting aims of improving aerodynamic performance but reducing unwanted aeroacoustic emissions.