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On the unsteady expansion of a gas into a near vacuum

Published online by Cambridge University Press:  29 March 2006

R. E. Grundy
R. E. Grundy
Affiliation:
Applied Mathematics Department, University of St Andrews, Fife, Scotland
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Abstract

This note intends to clarify the way in which the expansion of an initially uniform gas into an ambient atmosphere degenerates into an expansion into a perfect vacuum. The starting-point is a paper by Greenspan & Butler (1962) in which certain tentative remarks are made reprding this question. We show that the flow consists of an infinite-strength contact front coinciding with the gasvacuum interface of the perfect-vacuum expansion, driving an infinite-strength shock into the vacuum ahead of it. The ga,s-vacuum interface and the shock are separated a t all times even though the density of the gas through which the shock travels vanishes in the vacuum limit.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 56 , Issue 1 , 14 November 1972 , pp. 97 - 100
Copyright
© 1972 Cambridge University Press

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References

Freeman, N. C. 1965 In Research Frontiers in Fluid Dynamics (ed. R. J. Seeger & G. Temple), pp. 284–307. Interscience.
Greenspan, H. P. & Butler, D. S. 1962 J. Fluid Mech. 13, 101.
Taylor, G. I. 1946 Proc. Roy. Soc. A 186, 273.