A Lifting Surface Theory for Wings Experiencing Leading-Edge Separation

This report describes a nonlinear lifting surface theory for a wing with leading-edge vortices in a steady, incompressible flow. A numerical scheme has been developed from this theory and initial runs have been made for the delta wing and arrow wing planforms. A general procedure for other planforms is also described. The present formulation is the result of an extensive modification of the work of Nangia and Hancock, in which a model of the leading-edge vortex is added to a vorticity representation of the wing and wake. This lifting surface theory program is based on the kernel function formulation, in that the vorticity distribution is described by continuous functions with unknown coefficients. The vortex location is similarly described by functions with unknown coefficients. These unknowns are found by satisfying the downwash condition and the no-force condition on the leading-edge vortex representation. Due to the nonlinear nature of the boundary conditions with respect to the vortex position, the solution is obtained from an iterative scheme based on Newtons method. Results for the delta wing and arrow wing are presented and compared with experiment and other theories.