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Shock compression of a perfect gas

Published online by Cambridge University Press:  28 March 2006

Cerda Evans  and
Foster Evans
Cerda Evans
Affiliation:
Los Alamos Scientific Laboratory of the University of California, Los Alamos, New Mexico
Foster Evans
Affiliation:
Los Alamos Scientific Laboratory of the University of California, Los Alamos, New Mexico
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Abstract

The compression of a perfect gas between a uniformaly moving piston and a rigid wall is discussed in the one-dimensional case. If the piston moves with a finite speed, it will initiate a shock in the gas which will reflect successively from rigid wall and piston and cause the compression process to deviate from a reversible adiabatic process. Expressions are derived for the relative changes in pressure and density at each shock reflection. Then values of density and pressure after any number of shock reflections are computed relative to their initial values, and, in terms of these, the corresponding values of temperature and entropy, as well as shock speeds, are determined. The limiting value of the entropy change, as the number of reflections goes to infinity, is obtained as a function of the ratio of specific heats of the gas and the strength of the initial shock. Hence it is possible to estimate an upper limit to the deviation of the shock compression process from a reversible adiabatic process. Some illustrative numerical examples are given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 1 , Issue 4 , October 1956 , pp. 399 - 408
Copyright
© 1956 Cambridge University Press

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References

Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves, New York: Interscience Publishers.
Davis, H. T. 1933 Tables of the Higher Mathematical Functions, Indiana: Principia Press.
Evans, C. & Evans, F. 1953 Los Alamos Scientific Lab. Rep. no. LA-1334.
Grad, H. 1952 Comm. Pure Appl. Math. 5, 257.
Sachs, R. G. 1946 Phys. Rev. 69, 514.