Journal of Plasma Physics

Research Article

Structure of shock waves at re-entry speeds

V. Shanmugasundarama1 p1 and S. S. R. Murtya2

a1 Department of Aeronautics, Indian Institute of Science, Bangalore 560 012, India

a2 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.

(Received December 06 1978)

(Revised August 31 1979)

Correspondence:

p1 Present address: Department of Mechanical Engineering, University of Edinburgh, Edinburgh EH9 3JL, UK.