Potential flow near conical stagnation points

Abstract

Flow patterns near conical stagnation points in supersonic flow have been investigated on the basis of potential flow. Near the conical stagnation point the nonlinear equation for the conical velocity potential reduces to the equation of Laplace. Solutions of the equation of Laplace for incompressible plane flow are then used as a guide to generate conical stagnation-point solutions. Apart from known types of streamline patterns, such as nodes and saddle points, new types are found. Among them are oblique saddle points, saddle-nodes, topological nodes and topological saddle points. They may be used to clarify certain questions in a number of practical conical-flow problems. The oblique saddle point may be used to describe the inviscid flow associated with flow separation and also certain features of the flow over an external corner. The saddlenode, being structurally unstable, may fall apart into a saddle and a node. It may then be used to interpret the lift-off phenomenon of the singularity in the flow around a circular cone at incidence as a bifurcation. Similarly, this may be done for the appearance of a dividing streamline in the same flow at still higher angles of incidence, where a vortex system is formed at the leeward side of the cone.

Numerical study of flowfields about asymmetric external conical corners

“…The asymmetry comes about because, in the predictor level of the scheme, the ^derivatives of a point next to the cross-flow sonic line on wedge 5 2 are computed using the values on the sonic line; for the point next to the cross-flow sonic line on wedge 6 7 , the values used are those on the second mesh point to the left of the sonic line. The opposite occurs in the corrector level.…”

“…One of these wedges rests on the xz plane (see Fig. 1) and is defined in terms of a compression angle 6 7 and a leading-edge sweep angle A 7 . The other wedge rests on a plane that is inclined fl deg measured clockwise from the yz plane and is defined in terms of a compression angle d 2 and a leading-edge sweep angle A 2 .…”