The transonic flow in the throat region of a two-dimensional nozzle with walls of arbitrary smooth profile

Abstract

A solution is presented for the flow in the throat region of a two-dimensional nozzle with an arbitrary smooth profile. The velocity components are determined as series expansions in ascending powers of Rpower-0.5 where R is the mean radius of curvature of the profile at the throat measured in throat half-heights. The first three terms of the series solution are given, and some properties of the flow are determined for two special cases, namely the configurations in which the nozzle is asymmetric about the longitudinal axis and in which the nozzle profile is described by a cubic equation. The solution of the indirect problem is also discussed. An axial velocity distribution of arbitrary form is assumed and the velocity components are obtained as series expansions in terms of the non-dimensional velocity gradient b1 along the axis at the throat. The coefficients of each power of this parameter are determined as closed expressions. The parameters which describe the shape of the nozzle walls (streamlines) are calculated.