Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-07-01T20:42:51.501Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Johannesen, N.H., Ejector Theory and Experiments, Copenhagen (in the press).Google Scholar
2. Taylor, G.I., and Maccoll, J.W. (1935). Aerodynamic Theory (edited by Durand), Berlin, Vol. III, Div. H., Chap. IV, pp. 243–246, 1935.Google Scholar
3. Meyer, R.E. (1948). The Method of Characteristics for Problems of Compressible Flow Involving Two Independent Variables. Part I. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 1, pp. 196–219, 1948.Google Scholar
4. Meyer, R.E. (1948). The Method of Characteristics for Problems of Compressible Flow Involving Two Independent Variables.Part II.Quarterly Journal of Mechanics and Applied Mathematics, Vol. 1, pp. 451–469, 1948.Google Scholar
5. Herbert, P.J., and Older, S.J. (1946). Tables for Use in the Investigation of Supersonic Fields of Flow by the Method of Characteristics. A.R.C. 10261, 1946.Google Scholar
6. Meyer, R.E. (1949). Focusing Effects in Two-Dimensional, Supersonic Flow.Philosophical Transactions of the Royal Society, London, A, Vol. 242, pp. 153–171, 1949.Google Scholar
7. Holt, M. (1948). The Behaviour of the Velocity along a Straight Characteristic in Steady Irrotational Isentropic Flow with Axial Symmetry.Quarterly Journal of Mechanics and Applied Mathematics. Vol. 1, pp. 358–364, 1948.CrossRefGoogle Scholar