Vortical singularities in conical flow.

In this paper, we investigate the behavior of inviscid supersonic conical flow fields near crossflow stagnation points by constructing coordinate expansions of the exact equations of conical flow. The local cross-flow streamline pattern is shown to be determined primarily by the curvature of the surface pressure distribution (P and by the direction of the surface velocity near the stagnation point. The local streamline pattern at a maximum of the surface pressure is shown to be either a saddle point or a nodal point with cross-flow streamlines normal to the body. The solution corresponding to the node changes to a saddle point at a critical value, (P == — 8, which thus signals the liftoff of the vortical singularity first suggested by Ferri. The streamline pattern at a minimum of the pressure distribution is a node with streamlines tangent to the body if (P is less than a critical value, (P = 1, and does not exist if (P > 1. The local solutions are used to infer the general characteristics of the cross-flow streamline pattern generated by yawed circular cones and flat plates. They are also used to analyze the nonuniformity of the small yaw and thin-shock-layer expansions at vortical singularities.