Aeroelastic Characteristics of Porous Membrane Airfoils

Membrane compliance is known to increase lift in steady flow conditions, while airfoil porosity reduces the wing load due to velocity seepage through the wing surface. These seemingly contradicting effects highlight the importance of the combined contribution of wing compliance and porosity when seeking an understanding of the aerodynamic performance of bats in steady flow. To this end, we derive a theoretical framework to study the aerodynamic characteristics of a two-dimensional porous membrane airfoil in steady inviscid incompressible flow. The airfoil model is constructed of a porous membrane that is attached to solid impermeable edges at both ends and is free to passively deform to accommodate the flow. The membrane shape and its aerodynamic characteristics are obtained by incorporating Darcy’s porosity law in the thin airfoil theory and solving the coupled fluid-structure interaction problem, assuming small membrane camber, small angles of attack, and constant tension along the membrane. Various values of the constant porosity parameter are considered, and its effect on the membrane stability limits are examined in terms of the minimum tension coefficient required to obtain a stable membrane profile, the corresponding airfoil shape, and its aerodynamic characteristics.