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On the decay of weak shock waves in axisymmetric non-equilibrium flow

Published online by Cambridge University Press:  29 March 2006

David C. Chou  and
Boa-Teh Chu
David C. Chou
Affiliation:
The University of Iowa, Iowa City, Iowa
Boa-Teh Chu
Affiliation:
Yale University, New Haven, Connecticut
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Abstract

The supersonic flight of a slender projectile in a fluid which may undergo internal non-equilibrium transformations is examined by a systematic perturbation scheme. In the frozen limit, the classical results of Whitham and his celebrated ‘rule’ are recovered. Unlike the classical theory, however, the shape of the nose shock can be expressed explicitly in terms of known functions when the relaxation decay length becomes of the same order as a characteristic length scale. The theoretically predicted shock angle, expressed as a function of the radial distance, is found to be in excellent agreement with the experimental measurements of Wegener and Klikoff.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 2 , 29 November 1971 , pp. 355 - 367
Copyright
© 1971 Cambridge University Press

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References

Chu, B. T. 1970 Weak nonlinear waves in non-equilibrium flow. In Non-equilibrium Flow, Part II (ed. by P. P. Wegener) p. 33. New York: Marcel Dekker, Inc.
Taylor, G. I. & Maccoll, J. W. 1933 Proc. Roy. Soc. A 139, 278.
Vincenti, W. G. & Kruger, C. H. 1965 Introduction to Physical Gas Dynamics. John Wiley.
Wegener, P. P. 1961 A review of investigations of stationary supersonic nozzle flow with a reacting gas mixture. Combustion and Propulsion—4th AGARD Colloquium. Pergamon.
Wegener, P. P., Chu, B. T. & Klikoff, W. A. 1965 J. Fluid Mech. 23, 787.
Whitham, G. B. 1952 Comm. Pure & Appl. Math. 5, 301.