Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T12:15:15.977Z Has data issue: false hasContentIssue false
  • English
  • Français

Model computations of the influence of carbon impurities on the ionization relaxation in krypton shock waves

Published online by Cambridge University Press:  26 April 2006

D. Klages  and
F. Demmig
D. Klages
Affiliation:
Institut für Plasmaphysik, Universität Hannover, Callinstraße 38, D-3000 Hannover, Germany
F. Demmig
Affiliation:
Institut für Plasmaphysik, Universität Hannover, Callinstraße 38, D-3000 Hannover, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Chemical reactions in shock waves can be strongly affected by minute impurity concentrations. Thus it is not adequate to take into account the additional impurity electron production in relaxation studies simply by global adjustment of the atom—atom excitation cross-section constant to the measured electron density.

A definite improvement, however, can only be achieved if the ionization relaxation model is extended to include all relevant impurity atom reactions. Consequently we treated the real test gas as a mixture of krypton and impurity carbon atoms. For the carbon model it is important to take the lower real excitation levels into consideration. Carrying out a sensitivity analysis we were able to reduce the number of reactions substantially. A comparison with experimental electron density profiles yielded 3.0 × 10−6 m2/J for the Kr—Kr excitation cross-section constant as well as values for the C—Kr constants.

For a temperature of about 8000 K and an impurity concentration of about 40 p.p.m. it is shown that the impurity reactions dominate the electron production in the initial relaxation zone. This effect causes a pronounced decrease of the relaxation time with increasing concentration.

By comparing computational results of the Kr–C model with those of the simplistic pure Kr model it is possible to explain the dependence of the Kr–Kr excitation cross-section constant on the impurity concentration and the plasma temperature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 232 , November 1991 , pp. 455 - 467
Copyright
© 1991 Cambridge University Press

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

Demmig, F. 1978 The computation of one-dimensional unsteady non-equilibrium flows with a method of characteristics utilizing exponential fitting. Comput. Phys. Commun. 14, 7.Google Scholar
Demmig, F. 1983a Models for non-equilibrium flows in real shock tubes. Proc. 14th Intl Symp. on Shock Tubes and Waves, Sydney (ed. R. D. Archer & B. E. Milton), p. 51.
Demmig, F. 1983b Investigation of ionization relaxation in shock tubes; merits and limitations. Proc. 14th Intl Symp. on Shock Tubes and Waves, Sydney, p. 744.
Devoto, R. S. 1969 Transport coefficients of partially ionized Krypton and Xenon. AIAA J. 7, 199.Google Scholar
Ernst, G. 1982 Absorption spectroscopic investigations for the reaction kinetics of excited Krypton atoms in shock waves using a single-mode dye laser (in German). Doctorial thesis, University of Hannover.
Fröbe, U. 1981 Investigation of ionization relaxation in shock heated Krypton using an HCN- Laser-Interferometer (in German). Doctorial thesis, University of Hannover.
Fröbe, U., Müller, B.-H. & Bötticher, W. 1983 Ionization relaxation in shock-heated Krypton at electron densities from 1–50 × 10 19 m-3. J. Phys. B: Atom. Molec. Phys. 16, 4259.Google Scholar
Ganas, P. S. 1981 Electron impact excitation cross sections for Carbon. Physica C 104, 411.Google Scholar
Glass, I. I., Liu, W. S. & Tang, F. C. 1977 Effects of Hydrogen impurities on shock structure and stability in ionizing monoatomic gases: 2. Krypton. Can. J. Phys. 55, 1269.Google Scholar
Hoffert, M. I. & Lien, H. 1967 Quasi-onedimensional, nonequilibrium gas dynamics of partially ionized two-temperature Argon. Phys. Fluids 10, 1769.Google Scholar
Hoskin, N. E. 1964 Solution by characteristics of the equations of one-dimensional unsteady flow. Meth. Comput. Phys.: Adv. Res. Applies 3, 265.Google Scholar
Igra, O. 1972 Impurities effects on the ionization zone behind strong normal shock waves in monoatomic gas. Israel J. Technol. 10, 153.Google Scholar
Itikawa, Y. 1974 Momentum-transfer cross sections for electron collisions with atoms and molecules. Atom. Data Nucl. Data Tables 14, 1.Google Scholar
Jones, N. R. & McChesney, M. 1966 Ionization relaxation in slightly impure Argon. Nature 209, 1080.Google Scholar
Krauß-Varban, D. 1985 Radiation transport in rare gas shock waves and the model description of excitation and ionization in the precursor (in German). Doctorial thesis, University of Hannover.
Krauß-Varban, D. & Demmig, F. 1984 Model calculations of the ionization relaxation and radiative cooling in unsteady Krypton and Xenon shock waves. J. Fluid Mech. 149, 375.Google Scholar
Lifshitz, A. & Bidani, M. 1981 The effect of minute quantities of impurities on shock tube kinetics. Proc. 13th Intl Symp. on Shock Tubes and Waves, Niagara Falls (ed. C. E. Treanor & J. G. Hall), p. 602.
Meißner, J. 1988 The computation of a two dimensional non-equilibrium flow afflicted with friction behind an unsteady plane shock wave (in German). Doctorial thesis, University of Hannover.
Meyer-Prüssner, R. & Demmig, F. 1979 Ionization relaxation in shock tubes taking into account a non-maxwellian electron velocity distribution. Proc. 12th Intl Symp. on Shock Tubes and Waves, Jerusalem (ed. A. Lifshitz & J. Rom), p. 197.
Schneider, J. M. 1984 Particle density and collision frequency of electrons during the ionization relaxation in shock heated Krypton—Helium mixtures. A comparison of model computations and measurements using HCN– and CO2-lasers (in German). Doctorial thesis, University of Hannover.
Scraton, R. E. 1981 Some L-stable methods for stiff differential equations. Intl J. Comput. Maths B 9, 81.Google Scholar
Shaw, J. F., Mitchner, M. & Krueger, C. H. 1970 Effects of nonelastic collisions in partially ionized gases; I. Analytical solutions and results. Phys. Fluids 13, 325.Google Scholar
Thomas, L. D. & Nesbet, R. K. 1976 Low-energy electron scattering by atomic Carbon. Phys. Rev. A 12, 2378.Google Scholar
Vriens, L. & Smeets, A. H. M. 1980 Cross-section and rate formulas for electron-impact ionization, excitation, deexcitation, and total depopulation of excited atoms. Phys. Rev. A 22, 940.Google Scholar