Unsteady motion of airfoils with boundary-layer separation

It is shown that the condition that determines circulation about an airfoil with boundary layers is identical with the usual inviscid-flow condition based on conservation of total circulation and the Kutta-Joukowski condition, in both steady and unsteady flow. This implies interesting relationships between the viscous and inviscid models, namely, between boundary-layer vorticity and bound-vortex strength, viscous-wake vorticity and freevortex strength, and vortex/vorticity fluxes, in both steady and unsteady flow. The unsteady aerodynamics of airfoils with rounded trailing edges is discussed in this light, and it is concluded that a dual model is needed, involving a boundary-layer calculation over a smooth body to determine circulation, and a vortex-sheet model to determine the perturbed potential flowfield needed in this calculation, as well as forces and moments on the airfoil.