Nonlinear aeroelastic modeling via conformal mappings for typical section in arbitrary motion

Although linearized approaches are typically applied in aeroelastic design, advanced nonlinear modeling capabilities are increasingly important to accurately analyze highly fexible or rapidly maneuvering aircraft congurations. On the other hand, high-fielity modeling requires huge computational resources, which preclude its extensive application in preliminary design, what-if analysis, and optimization processes. In this framework, the development of simplied analytical models may represent a compromise solution between accuracy and computational burden. The present work proposes a nonlinear unsteady aerodynamic model for a typical-section at-plate airfoil in arbitrary motion. The fluid is assumed to be inviscid and incompressible. The ow is assumed to be attached to the body, planar, and irrotational. The aerodynamic loads acting on the section are related to a complex potential of the ow and analytically evaluated via conformal-map approach. Free-wake kinematics is implemented by compacting the vorticity shed at the trailing edge in point vortices, which move according to Biot-Savart law. Numerical results are presented for both unsteady aerodynamics and aeroelastic response of the typical-section airfoil elastically connected to a support. These results demonstrate the ability of the present model to capture arbitrary motions and free-wake geometries without introducing additional simplifying assumptions, providing good physical insight and leading to relevant applications for aeroelastic design.