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The expansion of a wedge of gas into a vacuum

Published online by Cambridge University Press:  24 October 2008

Lawrence Elliott Levine
Lawrence Elliott Levine
Affiliation:
Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Maryland
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Abstract

The front from the expansion into a vacuum of an infinite wedge of polytropic gas initially at rest at constant pressure is studied in detail. It is shown how the shape of that part of the gas-vacuum interface resulting from the presence of the sharp corner changes with the wedge angle and the adiabatic index of the gas. In addition to analytic results for wedges of arbitrary angle, numerical results substantiating the analysis are given for the special case of 90°. Finally, explicit formulae for the path of a particle initially part of a 60° wedge of water allowed to collapse at time t = 0 are derived from an exact linear solution obtained by Suchkov and interpreted through the hydraulic analogy for adiabatic index 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 4 , October 1968 , pp. 1151 - 1163
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Courant, R. and Friedrichs, K. O.Supersonic flow and shock waves, pp. 259–261 (New York: Interscience, 1948).Google Scholar
(2)Greenspan, H. P. and Butler, D. S.On the expansion of a gas into vacuum. J. Fluid Mech. 13 (1962), 101–119.CrossRefGoogle Scholar
(3)Mackie, A. G.Two-dimensional quasi-stationary flows in gas dynamics. Proc. Cambridge Philos. Soc. 64 (1968), 1099–1108.CrossRefGoogle Scholar
(4)Pogodin, I. A., Suchkov, V. A. and Ianenko, N. N.On travelling waves of gas dynamic equations. J. Appl. Math. Mech. 22 (1958), 256–267.CrossRefGoogle Scholar
(5)Suchkov, V. A.Flow into a vacuum along an oblique wall. J. Appl. Math. Mech. 27 (1963), 1132–1134.CrossRefGoogle Scholar