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Self-similar flows with uniform velocity gradient and their use in modelling the free expansion of polytropic gases

Published online by Cambridge University Press:  19 April 2006

G. J. Pert
G. J. Pert
Affiliation:
Department of Applied Physics, University of Hull, Hull HU6 7RX
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Abstract

The self-similar motion of a polytropic gas with a linear velocity distribution is considered in an arbitrary ν-dimensional space. It is shown that if the initial state of the gas is isotropic the flow has a characteristic ellipsoidal form. Both expanding and compressing flows are shown to exist. The application of such flows as models for the expansion of an initially uniform mass of gas into vacuum is considered by comparison with computationally modelled expansions in one-dimensional cylindrical and spherical geometries. It is found that the accuracy of the representation increases when the heating time is long compared with the characteristic time of expansion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 100 , Issue 2 , 25 September 1980 , pp. 257 - 277
Copyright
© 1980 Cambridge University Press

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References

Book, D. L. 1979 J. Fluid Mech. 95, 779.
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. Wiley-Interscience.
Dawson, J., Kaw, P. & Green, B. 1969 Phys. Fluids 12, 875.
Fader, W. J. 1969 Phys. Fluids 11, 2200.
Haught, A. F. & Polk, D. H. 1970 Phys. Fluids 13, 2825.
Imshennik, V. S. 1960 Sov. Phys. Dokl. 5, 253.
Keller, J. B. 1948 Comm. Pure Appl. Math. 1, 275.
Keller, J. B. 1956 Quart. Appl. Math. 14, 171.
Kidder, R. E. 1974 Nuclear Fusion 14, 53.
Korobeinikov, V. P. & Ryazanov, E. V. 1959 Sov. Phys. Dokl. 4, 40.
Kulikovskii, A. G. 1958 Sov. Phys. Dokl. 3, 501.
Molmud, P. 1960 Phys. Fluids 3, 362.
Nemchinov, I. V. 1961 PMTF 1, 17 (translation Foreign Technology Division, Air Force Systems Command, USAF: FTD-MT-24-375-69).
Nemchinov, I. V. 1964 PMTF 5, 18 (translation by Sandia Corporation).
Nemchinov, I. V. 1965 Appl. Math. Mech. 29, 143.
Pert, G. J. 1974 Plasma Phys. 16, 1051.
Pert, G. J. 1976 J. Phys. B 9, 3301.
Pert, G. J. 1979 J. Phys. B 12, 2067.
Richtmyer, R. D. & Morton, K. W. 1967 Difference Methods for Initial Value Problems. Wiley-Interscience.
Sedov, L. V. 1957 Similarity and Dimensional Methods in Mechanics. Academic.
Zel'dovich, YA. B. & Raizer, YU. P. 1966 Physics of Shock Waves and High Temperature Hydrodynamic Phenomena. Academic.