Exact solutions for flow of a perfect gas in a two-dimensional Laval nozzle

Abstract

A family of exact solutions is found for the problem of steady irrotational isentropic shockfree transsonic flow of a perfect gas through a Laval nozzle in two dimensions. The hodograph method is used, whereby the position co-ordinates x , y are expressed in terms of the velocity variables; the expressions are infinite series in the subsonic part of the flow field, infinite integrals (analytic continuations of the series) in the supersonic part. An inversion is required to get the velocity as a function of position; in general, this requires detailed numerical calculations, but approximate formulae (62) are found for the neighbourhood of the sonic point on the axis.