Two-Dimensional Irrotational Transonic Flows of a Compressible Fluid

摘要

The method developed in NACA TN No. 995 has been slightly modified and extended to include flaws with circulation. The essential feature of the modified method is that in analytic continuation of the solution the alteration of the singularities of the incompressible solution due to the presence of the hypergeometric functions has been taken into account. It was found that for finite Mach number the only case in which the nature of the singularity of the incompressible solution can remain unchanged is for a ratio of specific heats equal to -1. Two particular flows, one having a finite circulation and the other having zero circulation, have been studied. Both flows were derived from the incompressible flow about an elliptic cylinder of thickness ratio 0.60. The free-stream Mach number for both cases was taken to be 0.60 in order to avoid the appearance of limiting lines. The pressure distribution for the flow without circulation has been compared with that of incompressible flow over approximately the same body. The discrepancies between the exact results and those predicted by the approximate Von Karman-Tsien and Glauert-Prandtl formulas are so wide as to show definitely that in this case the effect of geometry cannot be ignored, as is done in both approximate formulas. In general, it seems that the effect of geometry cannot be neglected and the conventional 'pressure correction' formulas are not valid, even in the subsonic region if the body is thick, especially if there is a supersonic region in the flow.