Parametric study of a two-dimensional membrane wing in viscous laminar flow

A computational study of a two-dimensional membrane at low Reynolds numbers is presented. The membrane is assumed to be linearly elastic, massless and practically of zero thickness. A parametric study of the effects of membrane properties, tension, and How conditions is presented for both steady and unsteady cases. The membrane shape and aerodynamic forces are computed by a fully viscous flow model and compared to those computed with a potential model. Steady results, obtained for small angles of attack (AoA), show that the membrane AoA and tension coefficient uniquely define the membrane equilibrium shape for both potential and viscous flow (for prescribed Reynolds number). Thus, the membrane initial slack, elasticity and pretension, which are used to compute the tension coefficient, do not play an independent role in the steady cases. In these cases the parametric study concentrates 0n the effect of the membrane tension coefficient, angle of attack, Reynolds number and shear stress. Results show that the tension coefficient highly affects the membrane camber, while the AoA mostly influences the chordwise location of the maximum camber point. The shear stress effect on the equilibrium shape was found to be negligible, and an increase in Reynolds number resulted in stall conditions at smaller AoA. The unsteady solutions, computed for large AoAs, present oscillations of the membrane structure which are due to vortex shedding. In these cases the effects of membrane elasticity, slack, pretension, angle of attack and Reynolds number are studied.