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A Short Proof of the Prandtl-Meyer Expansion Formula

Published online by Cambridge University Press:  04 July 2016

A. R. Collar
A. R. Collar*
Affiliation:
Sir George White Professor of Aeronautical Engineering, University of Bristol
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Extract

Most teachers of gasdynamics with whom the writer has discussed the Prandtl-Meyer analysis find difficulty in giving a lucid exposition to students; the standard treatment tends to be long, and mathematical rather than physical, so that steps in the process of integration are difficult to remember. Lockwood Taylor gives a short treatment; but he begins from Ackeret's formula, which is in effect the differential equation to be treated; and he avoids the actual integration. These considerations have prompted the writer to publish the following treatment, which though self-contained is quite short, and—being mostly graphical—gives some insight into the physics of the problem.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 70 , Issue 669 , September 1966 , pp. 885 - 886
Copyright
Copyright © Royal Aeronautical Society 1966

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References

1.LockwoodTaylor, J. Taylor, J.Derivation of the Prandtl-Meyer Expansion Solution from the Linear Approximation. Journal of the Royal Aeronautical Society, p. 64, Jan. 1956.Google Scholar
2.Collar, A. R.An Iteration Process for the Solution of the Prandtl-Meyer Expansion. Journal of the Royal Aeronautical Society, pp. 357–359, May, 1961.CrossRefGoogle Scholar
3.Houghton, E. L. and Brock, A. E.Tables for the Compressible Flow of Dry Air. Arnold, 1961.Google Scholar
4.Prandtl, L.The Essentials of Fluid Dynamics, p. 281. Blackie, 1952.Google Scholar