Semi-analytical unsteady aerodynamic model of a flexible thin airfoil

This paper presents a geometrically exact semi-analytical approach to model the unsteady aerodynamics of a flexible thin airfoil in incompressible potential flow. The velocity field is described by a complex potential, which is developed by mapping the airfoil boundary onto a circle. This methodology, well established for small disturbances, is here generalized to evaluate the aerodynamic load on an airfoil subject to prescribed arbitrary rigid-body motion and deformation. The model also includes the effects of free wake, modeled by a large number of discrete vortices. A general semi-analytical solution for the aerodynamic pressure distribution is obtained, specialized to the case of curvature of constant sign along the airfoil chord, and validated with reference linearized results. Next, the model validity for large curvatures is discussed by comparing velocity fields around increasingly deformed airfoils with numerical solutions from suitable panel methods. Finally, results for a cantilevered flexible airfoil subject to prescribed deformation in a steady axial flow are presented to point out different unsteady mechanisms influencing the aerodynamic pressure distribution and responsible for its changes in time. This insight is peculiar of the semi-analytical nature of the present formulation and cannot be easily obtained through numerical handling of the problem. The paper ends by outlining future developments of the present work toward the ultimate goal of studying coupled fluid-structure interaction problems in presence of very large deformations.