The Attachment Angle of a Sonic Line to the Streamlined Surface

This work considers the angle of the sonic-line attachment to the surface in flows with uniform fields of entropy and total enthalpy. A rigorous study of the Euler equations (without the use of asymptotic, numerical, and other approximate methods) is carried out. Plane-parallel and nonswirling axisymmetric flows are considered. It is shown that the attachment angle of the sonic line depends on the curvature of the surface. If the surface is convex towards the flow, then the attachment angle on the subsonic side is strictly greater than 90°. If the surface is concave towards the flow, then the attachment angle on the subsonic side is strictly less than 90°. The attachment to a straight section of the surface in a plane-parallel flow always occurs along the normal. Similarly, only the attachment along the normal is possible if the sonic line attaches to a straight generatrix parallel to the axis of symmetry in nonswirling axisymmetric flows. For the case when the straight generatrix is not parallel to the axis of symmetry, it is shown that the attachment angle from the sonic side can only be either 90° (attachment along the normal) or 0° (attachment along the tangent).