Inviscid separated flow over a non-slender delta wing

We consider inviscid incompressible flow about an infinite non-slender flat delta wing with leading-edge separation modelled by symmetrical conical vortex sheets. A similarity solution for the three-dimensional steady velocity potential Phi is sought with boundary conditions to be satisfied on the line which is the intersection of the wing-sheet surface with the surface of the unit sphere. A numerical approach is developed based on the construction of a special boundary element or 'winglet' which is effectively a Green function for the projection of del(2) Phi = 0 onto the spherical surface under the similarity ansatz. When the wing semi-apex angle gamma(0) is fixed, satisfaction of the boundary conditions of zero normal velocity on the wing and zero normal velocity and pressure continuity across the vortex sheet then leads to a nonlinear eigenvalue problem. A method of ensuring a condition of zero lateral force on a lumped model of the inner part of the rolled-up vortex sheet gives a closed set of equations which is solved numerically by Newton's method. We present and discuss the properties of solutions for gamma(0) in the range 1.3 degrees less than or equal to gamma(0) less than or equal to 89.5 degrees. The dependencies of these solutions on gamma(0) differs qualitatively from predictions of slender-body theory. In particular the velocity held is in general not conical and the similarity exponent must be calculated as part of the global eigenvalue problem. This exponent, together with the detailed flow field including the position and structure of the separated vortex sheet, depend only on gamma(0). In the limit of small gamma(0), a comparison with slender-body theory is made on the basis of an effective angle of incidence.