Exact Solutions for Flow of a Perfect Gas in a Two-Dimensional Laval Nozzle

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 expre...

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Bibliographic Details
Published in:Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1950-10, Vol.203 (1075), p.551-571
Main Author: Cherry, Thomas Macfarland
Format: Article
Language:English
Subjects:
Analytic functions
Branch lines
Critical points
Cylinders
Hodographs
Hypergeometric functions
Ideal gas
Infinite series
Series convergence
Sine function
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Summary: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.
ISSN:1364-5021
0080-4630
1471-2946
2053-9169
DOI:10.1098/rspa.1950.0156