Reduced Order Modeling of Deflection of a Membrane Covered Airfoil in a Fluid Flow

Flow over a flexible membrane is different to that over a rigid object. Fluid stresses developed over a membrane create a deflection, which in turn affects the flow field and generates a new stress distribution, thereby altering the original deflection. The behavior of the membrane can be modeled using the Young-Laplace equation which links the pressure difference across the membrane and the surface tension force with the radius of curvature of the membrane surface. In this work a computational approach is developed to solve the Young-Laplace equation. The approach is validated with a simple case of simply supported membrane subjected to a pressure load and a pretension. The performance of a S825 airfoil whose upper surface is replaced with a membrane is studied for various angles of attack. It is noted that the deformed airfoils perform better than the S825 till α = 6°. Beyond this angle of attack it is observed that the drop in performance is small.