Abstract

This talk considers the lift coefficient of an aerofoil with non-zero prescribed thickness and camber, along with a prescribed porosity distribution in a steady incompressible flow. In similar prior work, a Darcy porosity condition on the aerofoil surface furnishes a Fredholm integral equation, which permits an exact solution provided that the porosity distribution is Hölder-continuous. However, a comparison of that lift prediction for porous aerofoils versus experimental measurements indicates that for large values of the porosity parameter, the model diverges from the experimental data. This indicates a fundamental characteristic is missing in the mathematical model. Consequently, in this paper the (linear) Darcy porosity condition is replaced by the (non-linear) Forchheimer porosity condition. The Forchheimer porosity condition is decomposed into linear sections and provides a modified system of Fredholm integral equations, which permits an approximate solution by superposition. The new Höldercontinuous solution is verified against the SD7003 aerofoil results, and the comparison shows better agreement rather than considering the Darcy porosity condition. The methodology and results presented here may be combined with previous work on the aeroacoustics of porous aerofoil with a Forchheimer boundary condition to address the conflicting aims of improving aerodynamic performance but reducing unwanted aeroacoustic emissions