In a previous paper (Cherry 1947), the author has established a family of exact solutions for steady two-dimensional flow of a compressible fluid past a cylinder; the final formulae are given in theorem 6, equations (5.17) to (5.21). These formulae have now been evaluated (taking γ = 1.405) for the value
T
1
= 0.05, corresponding to a free-stream Mach number of 0.510, and the streamlines are shown in figure 1. The cylindrical obstacle has a thickness ratio 0.93, but is markedly different from an ellipse, being almost exactly circular over its up- and downstream quadrants. The Mach number a t the ends of its transverse axis is 1.39. The flow is everywhere regular, but a small increase in the free-stream Mach number would be critical; a shock-line would begin to appear near the points on the surface where the tangent is inclined at about 25 or 30° to the direction of the free-stream.
Some numerical solutions of local fractional tricomi equation in fractal transonic flow
