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Axially-symmetrical supersonic flow near the centre of an expansion

Published online by Cambridge University Press:  07 June 2016

N.H. Johannesen  and
R.E. Meyer
N.H. Johannesen
Affiliation:
Mechanical Engineering Laboratory, The Technical University of Denmark
R.E. Meyer
Affiliation:
Department of Mathematics, The University of Manchester
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Summary

When a uniform, two-dimensional supersonic flow expands suddenly round a corner in a wall it forms a pattern known as a Prandtl-Meyer expansion or centred simple wave. If the flow is two-dimensional but not initially uniform, or if it is axially-symmetrical, the expansion is still centred, but is not a simple wave. An approximate solution is given in this paper for the isentropic, irrotational, steady two-dimensional or axially-symmetrical flow of a perfect gas in the neighbourhood of the centre of such an expansion. The solution is designed to replace the conventional method of characteristics in such a region.

The main application is to a jet issuing from a nozzle that discharges into a container with a pressure lower than that in the nozzle; in particular, a formula is derived for the initial curvature, at the lip of the nozzle, of the boundary of the jet. The solution also applies to the flow near an edge in a boundary wall, and a formula is derived for the velocity gradient on the wall immediately downstream of the edge.

Type
Research Article
Information
Aeronautical Quarterly , Volume 2 , Issue 2 , August 1950 , pp. 127 - 142
Copyright
Copyright © Royal Aeronautical Society. 1950

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References

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