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The use of flows with uniform velocity gradient in modelling free expansion of a polytropic gas

Published online by Cambridge University Press:  09 March 2009

G. J. Pert
G. J. Pert
Affiliation:
Applied Physics Department, Hull University, Hull, UK
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Abstract

The free expansion of a heated mass of uniform gas (e.g. a laser produced plasma) can be modelled by self-similar motion with a linear velocity gradient. Using a series of numerical solutions we have shown that a reasonable representation is obtained by the use of a matching parameter relating the scale lengths in the prototype and its model, and that the representation improves as the ratio of the heating and disassembly times increases. In this paper we re-examine these two inferred results, and re-derive them on an analytic basis. The extension of the theory to multi-structured bodies shows that such systems of symmetric form allow self-similar motion, as does the particular case of an asymmetric one-dimensional foil. The case of isothermal foils is examined in detail to illustrate the derivation of the matching conditions.

Type
Research Article
Information
Laser and Particle Beams , Volume 5 , Issue 4 , November 1987 , pp. 643 - 658
Copyright
Copyright © Cambridge University Press 1987

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References

Dawson, J. M. 1964 Phys. Fluids, 7, 981.Google Scholar
Dawson, J. M., Kaw, P. & Green, B. 1969 Phys. Fluids, 12, 875.CrossRefGoogle Scholar
Englehardt, A. G., George, T. V., Hora, H. & Pack, J. L. 1970 Phys. Fluids, 13, 212.CrossRefGoogle Scholar
Fader, W. J. 1969 Phys. Fluids, 11, 2200.Google Scholar
Farnsworth, A. V. et al. 1979 Phys. Fluids, 22, 859.Google Scholar
Farnsworth, A. V. 1980 Phys. Fluids, 23, 1496.Google Scholar
Haught, A. F. & Polk, D. H. 1966 Phys. Fluids, 9, 2047.Google Scholar
Haught, A. F. & Polk, D. H. 1970 Phys. Fluids, 13, 2825.Google Scholar
Hora, H. 1964 Institute für Plasmaphysik, Garching Report IPP 6/23 (English Translation: U.S. Govern. Res. Rep NRC-TT-1193, 1965).Google Scholar
Hora, H. 1971 in Laser Interaction and Related Plasma Phenomena, ed Schwarz, H. J. and Hora, H., (Plenum Press, New York) Vol. 1, p. 365.CrossRefGoogle Scholar
London, R. A. & Rosen, M. D. 1986 Phys. Fluids, 29, 3813.Google Scholar
Lubin, M. J., Dunn, H. S. & Friedmann, W. 1969 Proc. Conf. Plasma Physics and Cont. Nuclear Fusion,Novosibirsk (IAEA Vienna) 945.Google Scholar
Nemchinov, , 1964 PMTF 5, 18 (translation by Sandia Corp).Google Scholar
Nemchinov, I. V. 1965 Appl. Math. Mech., 29, 143.CrossRefGoogle Scholar
Pert, G. J. 1976 J. Phys., 9, 3301.Google Scholar
Pert, G. J. 1980 J. Fluid. Mech., 100, 257.Google Scholar
Pert, G. J. 1983 J. Fluid. Mech., 131, 401.Google Scholar
Rosen, M. D. et al. 1985 Phys. Rev. Lett., 54, 106.CrossRefGoogle Scholar
Zeldovich, Ya. B. & Raizer, Yu. P. 1966 Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, Academic Press, New York.Google Scholar