Computational model of flexible membrane wings in steady laminar flow
A computational procedure is presented that models the interaction of a two-dimensional flexible membrane wing and laminar, high-Reynolds-number fluid flow. The membrane wing model is derived by combining a spatial-coordinate-based finite difference formulation of the equilibrium statement for an elastic membrane with a pressure-based control volume formulation of the incompressible Navier-Stokes equations written in general curvilinear body-fitted coordinates. The model is applied to initially flat membrane wings of both vanishing and finite material stiffness as well as to flexible inextensible wings with excess length. Computational results are presented for Reynolds numbers between 2 x 10 3 and 10 4 . The results from the viscous-flow-based membrane wing model are compared with predictions using a potential-flow-based model as well as with experimental data for membrane wings in turbulent flow. Although the assumption of laminar flow precludes a quantitative comparison with the available experimental data, the solutions obtained capture many of the significant features of the aeroelastic interaction that are unaccounted for with a potential flow description of the fluid dynamics.