Transonic rotational flow over a convex corner

Abstract

A singularity is encountered in the flow field about two-dimensional and axisymmetric bodies characterized by a sharp corner, where the fluid velocity becomes sonic. Investigation shows that the problem in question belongs, as do many other discontinuity problems, to the family of asymptotic or ‘boundary-layer’ phenomena of mathematical physics. The solution of a first approximation to the flow equations is given by a series in powers of a variable measuring the distance from the corner, with coefficients depending on an appropriate similarity variable. The leading coefficient of the series is independent of three-dimensional and rotationality effects, in complete analogy to the well-known solution of the corner problem in supersonic flow. Detailed results are presented for the leading singularity and for the first two corrections due to rotationality and axial symmetry of the flow.