Marginal separation in three-dimensional flows

Abstract

The boundary layer in the vicinity of the zero skin-friction point on the leeward symmetry line of a prolate spheroid placed at an angle of attack is considered. The existence of this flow was established by Cebeci et al. (1980) for an angle of attack α=40°. The current study is based on the results of Brown (1985) who described the marginal separation in the symmetry plane for a zero skin-friction point and on the results of Zametaev (1989) who included the spatial extension of Brown's solution but without interaction between the boundary layer and the outer flow. It is found that the three-dimensional boundary-layer equations in the vicinity of the zero skin-friction point are reduced to a single nonlinear partial differential equation of hyperbolic type which governs the longitudinal skin-friction component. Smooth solutions of this equation may be found which contain separation lines as well as double-valued regions. It is likely that the latter regions are related to the tip of the separation line obtained as a result of calculations of the full boundary-layer equations. The influence of interaction is also considered, in which case the flow is governed by a partial integro-differential equation. Numerical solutions are given for each of these problems.