Unsteady Lift Model for Morphing Airfoil Based on Potential Flow Theory

This paper describes the study of unsteady forces acting on a two-dimensional morphing airfoil under the assumption of incompressible, inviscid flow. Through conformal mapping, the flow over a morphing airfoil was mapped to the flow over a movable, variable radius circle, and a mathematic analytic model of unsteady lift was derived. To verify the unsteady lift model, it was then simplified for the case of a thin airfoil whose camber changes with time, and numerical simulations were conducted for the flow over the deformable thin airfoil. The unsteady lift caused by airfoil deformation is equivalent to the quasisteady lift added to the corresponding additional unsteady lift. The additional unsteady lift is linearly correlated with the first time derivative and second time derivative of the airfoil surface displacement. When the airfoil surface undergoes a vibration with a large reduced frequency, the additional unsteady lift is mainly decided by the second time derivative of the surface displacement.