Studies of Three-Dimensional Boundary Layers on Bodies of Revolution. III. Cones at Incidence in Supersonic Flow

摘要

An investigation is carried out into the properties of a nonsimiliar boundary layer on a cone at incidence with special reference to the flow near the leeside line of symmetry. The nonsimilarity is induced by allowing suction near the vertex of the cone and the external velocity is given by supersonic inviscid theory. The principal new results of the theory may be expressed in terms of a parameter -k, which is approximately equivalent to the angle of attack of the cone. Three ranges of k have been identified. For small negative values of k, the three-dimensional boundary layer on the cone is smooth everywhere and, once the suction is removed, rapidly approaches a semi-similarity form as the distance from the vertex increases. For more negative values of k the boundary layer is not smooth near the leeside of the cone but can be computed everywhere. The nature of this singularity is partially explained in terms of a collision phenomenon. If k decreases further, separation occurs in computations from the windward side of the cone. The solution develops a singularity along this line provided sufficient care is taken in the calculations. An apparent nonuniqueness in the solution prevents integration from the leeside over the remainder of the region of accessibility.