Hostname: page-component-7c8c6479df-p566r Total loading time: 0 Render date: 2024-03-29T00:39:44.811Z Has data issue: false hasContentIssue false

Structure of shock waves at re-entry speeds

Published online by Cambridge University Press:  13 March 2009

V. Shanmugasundaram
Affiliation:
Department of Aeronautics, Indian Institute of Science, Bangalore 560 012, India
S. S. R. Murty
Affiliation:
906, Roll Tide Lane N.W., Huntsville, Al. 35805, USA

Abstract

The unified structure of steady, one-dimensional shock waves in argon, in the absence of an external electric or magnetic field, is investigated. The analysis is based on a two-temperature, three-fluid continuum approach, using the Navier—Stokes equations as a model and including non-equilibrium collisional as well as radiative ionization phenomena. Quasi charge neutrality and zero velocity slip are assumed. The integral nature of the radiative terms is reduced to analytical forms through suitable spectral and directional approximations. The analysis is based on the method of matched asymptotic expansions. With respect to a suitably chosen small parameter, which is the ratio of atom-atom elastic collisional mean free-path to photon mean free-path, the following shock morphology emerges: within the radiation and electron thermal conduction dominated outer layer occurs an optically transparent discontinuity which consists of a chemically frozen heavy particle (atoms and ions) shock and a collisional ionization relaxation layer. Solutions are obtained for the first order with respect to the small parameter of the problem for two cases: (i) including electron thermal conduction and (ii) neglecting it in the analysis of the outer layer. It has been found that the influence of electron thermal conduction on the shock structure is substantial. Results for various free-stream conditions are presented in the form of tables and figures.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Chubb, D. L. 1968 Phys. Fluids, 11, 2363.CrossRefGoogle Scholar
Clarke, J. H. & Ferrari, C. 1965 Phys. Fluids, 8, 2121.CrossRefGoogle Scholar
Foley, W. H. & Clarke, J. H. 1973 Phys. Fluids, 16, 375.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
Jones, N. R. & McChesney, M. 1966 Nature, London. 209, 1080.CrossRefGoogle Scholar
Kamimoto, G. & Teshima, K. 1972 Trans. Japan Soc. Aeronaut. Space Sci. 15, 141.Google Scholar
Kelly, A. J. 1966 J. chem. Phys. 45, 1723.CrossRefGoogle Scholar
Merilo, M. & Morgon, E. J. 1970 J. chem. Phys. 52, 2192.CrossRefGoogle Scholar
Neloson, H. F. 1974 J. Quant. Spect. Rad. Trans., 14, 873.CrossRefGoogle Scholar
Petschek, H. & Byron, S. 1957 Ann. Phys. 1, 270.CrossRefGoogle Scholar
Shanmugasundram, V. & Murty, S. S. R. 1976 a Report 76FM8, Department of Aeronautics, Indian Institute of Science, Bangalore.Google Scholar
Shanmugasundram, V. & Murty, S. S. R. 1976 b Report 76FM21, Department of Aeronautics, Indian Institute of Science, Bangalore.Google Scholar
Shanmugasundram, V. & Murty, S. S. R. 1978 J. Plasma Phys. 20, 419.CrossRefGoogle Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.Google Scholar
Wong, H. & Bershader, D. 1966 J. Fluid Mech. 26, 459.CrossRefGoogle Scholar