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Unsteady expansions into vacuum with spherical symmetry

Published online by Cambridge University Press:  29 March 2006

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

In this paper time dependent expansions of monatomic gases with spherical symmetry are discussed. For the particular case of Maxwellian molecules closed expressions for the moments up to second order are obtained in regions of the flow where the inviscid solution is no longer valid. These solutions are derived in a general form using the particle path function as a parameter. The structure of the inviscid solution is such that this simplification can be made. The novelty of the present approach is that solutions already derived in previous papers can be obtained from the general solution in various limits; both the results for steady flow and the expansion of a fixed mass of gas can be derived in this manner. Finally, a particular example is constructed in order to illustrate the general theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 39 , Issue 3 , 27 November 1969 , pp. 529 - 546
Copyright
© 1969 Cambridge University Press

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