Prandtl-Meyer-Expansion in rotationssymmetrischer Strömung.

If a gas, flowing at supersonic speed, expands into a vacuum, a singularity occurs which, for two dimensional flow, is known under the name of 'Prandtl-Meyer Expansion' and can be described mathematically by means of simple relations since all properties are constant along straight lines radiating from the corner. For axial symmetric flow this is only approximately true in the neighbourhood of the singularity. In order to continue the parallel flow into the field of expansion with the aid of the method of characteristics, the velocity distribution in the vicinity of the singularity must first be determined to obtain the data from which one can start the computation. This is done by means of a series expansion, whereby the coefficients have to be determined by a system of differential equations. The resulting coefficients are numerically calculated for different flow Mach numbers and, finally, the expansion of an axially symmetric jet into the vacuum is determined as an example. The present work forms part of a report [1] in which, after deriving some algorithms pertaining to the method of characteristics especially suitable for electronic computers, three typical examples for the application of this method for the solution of problems in gas dynamics are described, namely the axially symmetric Laval nozzle, the Prandtl-Meyer expansion and the non-stationary shock wave in a tube. The mathematical investigations were carried out on the electronic computer of the ETH (ERMETH) at the Institute for Applied Mathematics of the ETH. [ABSTRACT FROM AUTHOR]