Elsevier

Acta Astronautica

Volume 2, Issues 5–6, May–June 1975, Pages 367-389
Acta Astronautica

Ionizing shock waves in monatomic gases through a kinetic theory approach

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Abstract

The paper discusses the structure of a normal shock wave in monatomic gases at high Mach numbers when ionization effects become important. The atom gas is represented by a trimodal distribution function while Maxwell distributions are used for the ion and electron species. Inverse-power force law models have been used to calculate the elastic collisions between the different species, while for the inelastic collisions, involving atom-atom and atom-electron encounters, experimental cross sections have been used. The resulting system of Boltzmann equations including their cx2-moment, along with the Saha equation and the appropriate boundary conditions, has been evaluated numerically to obtain the jump conditions across the shock wave. A numerical solution of the shock structure equations has been obtained for shock wave profiles in argon, krypton, and xenon gases for a range of Mach numbers from 15 to 40 over a range of initial pressures. The shock thickness and the thickness parameter defined by Petschek and Byron have been computed. These show good agreement with the experimental results of Wong and Bershader.

References (23)

  • H.E. Petschek et al.

    Approach to equilibrium ionization behind strong shock waves in argon

    Ann. Phys.

    (1957)
  • J.W. Bond

    Structure of a shock front in argon

    Phys. Rev.

    (1957)
  • E.J. Morgan et al.

    Ionization rates behind shock waves in argon

    Phys. Fluids

    (1965)
  • H. Wong et al.

    Thermal equilibration behind an ionizing shock

    J. Fluid Mech.

    (1966)
  • K.E. Harwell et al.

    Initial ionization rates in shock-heated argon, krypton, and xenon

    Phys. Fluids

    (1964)
  • A.J. Kelly

    Atom-atom ionization cross sections of the noble gases—argon, krypton, and xenon

    J. Chem. Phys.

    (1966)
  • M.I. Hoffert et al.

    Quasi-one-dimensional, nonequilibrium gas dynamics of partially ionized two-temperature argon

    Phys. Fluids

    (1967)
  • D.L. Chubb

    Ionizing shock structure in a monatomic gas

    Phys. Fluids

    (1968)
  • H.M. Mott-Smith

    The solution of the Boltzmann equation for a shock wave

    Phys. Rev.

    (1951)
  • S. Chapmann et al.

    The mathematical theory of nonuniform gases

    (1964)
  • I. Amdur et al.

    Scattering of high-velocity neutral particle III. Argon-argon

    J. Chem. Phys.

    (1954)
  • Paper presented at the Fourth International Colloquium on Gasdynamics of Explosions and Reactive Systems, La Jolla, California, 10–13 July, 1973.

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