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Structure of shock waves in partially ionized argon

Published online by Cambridge University Press:  13 March 2009

V. Shanmugasundaram  and
S. S. R. Murty
V. Shanmugasundaram
Affiliation:
Department of Aeronautics, Indian Institute of Science, Bangalore 560012, India
S. S. R. Murty
Affiliation:
P.O. Box 47, Normal, Alabama 35762, USA
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Abstract

A unified picture of the structure of steady, one-dimensional shock waves in partially ionized argon, in the absence of external electric or magnetic field, is presented. The investigation is based on a two-temperature, three-fluid continuum approach, using the Navier–Stokes equations as a model and including non-equilibrium ionization. Quasi charge neutrality and zero velocity slip are assumed. The analysis of the governing equations is based on the method of matched asymptotic expansions and results in the following three layers: (1) a broad thermal layer dominated by electron thermal conduction, (2) an atom-ion (A-I) shock structured by the heavy particle (atoms and ions) collisional dissipative mechanisms and (3) an ionization relaxation layer (IRL) wherein electron- atom inelastic collisions dominate. Solutions have been obtained for the first two orders with respect to a small parameter, which is the ratio of energy fluxes due to heavy particle viscous dissipation and electron thermal conduction. Whereas only electron temperature and electric potential show any marked variation in the thermal layer, the changes in all the variables in both the A-I shock and the IRL are significant.

Inclusion of electron thermal conduction terms in the governing equations has been observed to introduce numerical instabilities in the analysis of the IRL. They are circumvented by adopting a regular perturbation scheme with respect to a local small parameter, which has been identified to be the ratio of the freestream degree of ionization to the nondimensional characteristic temperature for first ionization. Numerical results show that the effect of electron thermal conduction on the IRL profiles is significant. Results in the form of tables and figures are presented for five sets of equilibrium free-stream conditions.

Type
Research Article
Information
Journal of Plasma Physics , Volume 20 , Issue 3 , December 1978 , pp. 419 - 451
Copyright
Copyright © Cambridge University Press 1978

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References

REFERENCES

Appleton, J. P. & Bray, K. N. C. 1964 J. Fluid Mech. 20, 659.CrossRefGoogle Scholar
Bond, J. W., Watson, K. M. & Welch, J. A. 1965 Atomic Theory of Gas Dynamics, p. 452. Addison-Wesley.Google Scholar
Chubb, D. L. 1968 Phys. Fluids, 11, 2363.CrossRefGoogle Scholar
Greenberg, O. W., Sen, H. K. & Treve, Y. M. 1960 Phys. Fluids, 3, 379.CrossRefGoogle Scholar
Greenberg, O. W. & Treve, Y. M. 1960 Phys. Fluids, 3, 769.CrossRefGoogle Scholar
Grewal, M. S. & Talbot, L. 1963 J. Fluid Mech. 16, 573.CrossRefGoogle Scholar
Harwell, K. E. & Jahn, R. G. 1964 Phys. Fluids, 7, 214.CrossRefGoogle Scholar
Hoffert, M. I. & Lien, H. 1967 Phys. Fluids, 10, 1769.CrossRefGoogle Scholar
Jaffrin, M. Y. 1965 Phys. Fluids, 8, 606.CrossRefGoogle Scholar
Kamimoto, G., Teshima, K. & Nishimura, M. 1972 Kyoto University C.P.36.Google Scholar
Kelly, A. J. 1966 J. Chem. Phys. 45, 1723.CrossRefGoogle Scholar
Krishnamurthy, M. & Ramachandra, S. M. 1975 Acta Astronautica, 2, 367.Google Scholar
Morgan, E. J. & Morrison, R. D. 1965 Phys. Fluids, 8, 1608.CrossRefGoogle Scholar
Murty, S. S. R. 1969 Phys. Fluids, 12, 1830.CrossRefGoogle Scholar
Petschek, H. & Byron, S. 1957 Ann. Phys. 1, 270.CrossRefGoogle Scholar
Prasada, Rao G. S. H. K., Shanmugasundaram, V. & Murty, S. S. R. 1970 J. Aeronaut. Soc. India, 22, 71.Google Scholar
Romanelli, M. J. 1967 Mathematical Methods for Digital Computers (ed. Ralston, A. and Wilf, H. S.), vol. 1, p. 110. Wiley.Google Scholar
Shanmugasundaram, V. 1975 Ph.D. Thesis, Indian Institute of Science, Bangalore, India.Google Scholar
Shanmugasundaram, V. & Murty, S. S. R. 1976 Report 76FM8, Department of Aeronautics, Indian Institute of Science, Bangalore, India.Google Scholar
Sutton, G. W. & Sherman, A. 1965 Engineering Magnetohydrodynamics, p. 111. McGraw- Hill.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.Google Scholar
Vinolo, A. G. & Clarke, J. H. 1973 Phys. Fluids, 16, 1612.Google Scholar
Wong, H. & Bershader, D. 1966 J. Fluid Mech. 26, 459.CrossRefGoogle Scholar