Computation of Three-Dimensional Transonic Internal Flow in Cylindrical Coordinates

Abstract

Abstract : The Euler equations for the inviscid rotational flow of a perfect gas are solved for three-dimensional subsonic-transonic internal flow by use of a time-dependent numerical technique. The numerical approach, which is an extension and modification of that of Cline for two-dimensional flows, is based on the use of the MacCormack finite-difference method for the interior field points. The reference-plane method of characteristics is used for coupling the interior field solution to the boundary points. Both the basic equations and the numerical procedures are described, as is the computer program which was written in FORTRAN IV language for either the Cray-1 or the IBM 370/165 computer. As presently written, the program is applicable to the computation of three- dimensional flow in both axisymmetric and relatively simple three-dimensional nozzle geometries. The validity of the computer program was established by computing, in various ways, an axisymmetric nozzle flow as a three-dimensional flow; the numerical results are in good agreement with the results from a well- established computer program for axisymmetric flow.