On the nonlinear theory of the wing in a plane unsteady flow

The main aspects of the nonlinear theory of the wing in a plane unsteady fluid flow are generalized on the basis of the author’s previous results. An initial-boundary problem for complex velocity is formulated. A system of differential equations with conditions at points of vortex wake shedding is presented, which allows a large class of problems to be solved correctly. The Cauchy problem is solved by using a standard discretization procedure. The boundary-value problem is reduced at each time step to singular integral equations of the first and second kind. The accuracy of solving these equations by the method of discrete vortices and by the method of panels is compared. Specific features of pressure calculations in the case of a separated flow around the airfoil contour are discussed.