Flow around axisymmetric bodies with uniform-velocity zones

The appriori unknown shape of a thick axisymmetric body is determined from the streamlining pattern, on the assumption that such a body with a given volume has a small surface but also a sufficiently high critical Mach number to make nonseparation flow along its surface realizable. The body is furthermore assumed to be symmetric with respect to the r = 0 plane as well as with respect to the x = 0 plane. The velocity is uniform v sub 1 along the front nose and the back nose and uniform v sub 2 along the main lateral segment, but not uniform along the spherical transition segments between the main lateral surface segment and the nose segments. The boundary between a spherical transition and the main lateral surface segment is determined from the condition of zero velocity gradient. The problem is solved by regarding the body surface as a vortical one with unknown vortex intensity. The solution is obtained by a numerical method, the equivalent of Ryabushinskiy's scheme for axisymmetric jet flow, using a cubic spline with respect to the axial coordinate and subsequent approximating iterations with respect to the radial coordinate for the main lateral segment.