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On the breakdown of characteristics solutions in flows with vibrational relaxation

Published online by Cambridge University Press:  28 March 2006

B. S. H. Rarity
B. S. H. Rarity
Affiliation:
Department of the Mechanics of Fluids, University of Manchester
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Abstract

The breakdown of the characteristics solution in the neighbourhood of the leading frozen characteristic is investigated for the flow induced by a piston advancing with finite acceleration into a relaxing gas and for the steady supersonic flow of a relaxing gas into a smooth compressive corner. It is found that the point of breakdown moves outwards along the leading characteristic as the relaxation time decreases and that there is no breakdown of the solution on the leading characteristic if the gas has a sufficiently small, but non-zero, relaxation time. A precise measure of this relaxation time is derived. The paper deals only with points of breakdown determined by initial derivatives of the piston path or wall shape. In the steady-flow case, the Mach number based on the frozen speed of sound must be greater than unity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 27 , Issue 1 , 11 January 1967 , pp. 49 - 57
Copyright
© 1967 Cambridge University Press

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References

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