On the formation of shock-waves in supersonic gas jets: Two-dimensional flow

Abstract

When a jet of gas issues from an orifice as a parallel stream with a given supersonic velocity and flows in a steady state through an outer medium at rest, its behaviour is governed by the ratio between the exit pressure of the jet and the pressure of the outer medium. If this ratio is only a little greater than unity, the jet has a periodic structure to a first approximation. This state has been examined by earlier workers; it is discussed here from the point of view of the 'characteristics' of the hyperbolic second-order partial differential equation of potential flow. The periodic structure ceases to give an adequate representation of the jet as the pressure ratio is increased, and shock-waves occur on account of the compressive effect of the outer medium. A method is given for computing the conditions in a steady two-dimensional supersonic jet. It is shown how the point of origin of a shockwave and the shape of the shock-wave formation may be obtained by theoretical means. The results of two calculations, given graphically, are discussed and compared, as far as possible, with experimental work.An expression is obtained for the nninimiiTin pressure in a jet.From the general behaviour of a jet with increasing chamber pressure it is found possible to infer the initial direction of the shock-wave arising at or near the muzzle of a gun after firing. © 1948 Oxford University Press.