Reflection of a weak discontinuity from an axis of symmetry in a uniform flow
This paper considers the steady supersonic axisymmetric flow of a non-viscous non-heatconductive perfect gas in the vicinity of a weakly discontinuous reflection point from an axis of symmetry. The boundary conditions on the incoming weak discontinuity to the axis of symmetry are formulated based on the compatibility conditions for the Prandtl Meyer function, the velocity vector inclination angle and its first derivatives along the flow line and the normal to it. The asymptotic form of the solution for the nondimensional gasdynamic parameters (the PrandtlMeyer function and the velocity vector inclination angle) in the vicinity of the reflection point is presented. It is shown that a reflected weak discontinuity is outgoing from the reflection point. The obtained solution has a logarithmic singularity of the first derivatives of the gasdynamic parameters with respect to the polar angle in the meridional plane in the vicinity of the reflected weak discontinuity.