Ionizing argon boundary layers. Part 1. Quasi-steady flat-plate laminar boundary-layer flows

Details are given of an implicit six-point finite-difference scheme for solving two-temperature, laminar, boundary-layer flows not in chemical equilibrium in ionizing argon. The analysis extends previous work by considering the radiation-energy loss and the chemical reactions due to atom-atom and electron-atom collisions in the ionizing boundary-layer and free-stream flow. Also included are variations in transport properties based on known elastic-scattering cross-sections, effects of chemical reactions, radiation-energy loss and the electric-sheath wall boundary conditions. The results are compared with dual-wavelength interferometric boundary-layer data obtained by using a Mach-Zehnder interferometer 23 cm in diameter with the UTIAS 10 × 18 cm Hypervelocity Shock Tube for shocks of initial Mach numbers M s ∼ 13 and 16 moving into argon at a pressure p 0 ∼ 5 torr and temperature T 0 ∼ 297 °K. Considering the difficulties involved in solving such complex plasma flows, satisfactory agreement was obtained between analytic and experimental total-density profiles and electron-number-density profiles for the case M s ∼ 16 and good agreement for M s ∼ 13.

[1]  M. Jaffrin.  Shock Structure in a Partially Ionized Gas , 1965 .

[2]  Nelson H. Kemp,et al.  Theory of Stagnation‐Point Heat Transfer in Ionized Monatomic Gases , 1965 .

[3]  J. P. Appleton,et al.  The conservation equations for a non-equilibrium plasma , 1964, Journal of Fluid Mechanics.

[4]  R. C. Stabler,et al.  Electron-Ion Recombination by Collisional and Radiative Processes , 1962 .

[5]  S. Knöös.  Boundary-layer structure in a shock-generated plasma flow: Part 1. Analysis for equilibrium ionization , 1968, Journal of Plasma Physics.

[6]  Edward A. Mason,et al.  Properties of Gases at Very High Temperatures , 1958 .

[7]  J. Fay,et al.  Theory of heat transfer to a shock-tube end-wall from an ionized monatomic gas , 1965, Journal of Fluid Mechanics.

[8]  C. Su,et al.  Continuum Theory of Spherical Electrostatic Probes , 1963 .

[9]  B. Eu,et al.  On the energy dependence of reaction cross sections near threshold , 1975 .

[10]  L. Back.  Laminar Boundary‐Layer Heat Transfer from a Partially Ionized Monatomic Gas , 1967 .

[11]  Y. Tambour,et al.  Theory of thermodynamic coupling in surface reacting boundary layers , 1977 .

[12]  I. I. Glass,et al.  Effects of hydrogen impurities on shock structure and stability in ionizing monatomic gases. Part 1. Argon , 1978, Journal of Fluid Mechanics.

[13]  P. M. Chung.  Electrical Characteristics of Couette and Stagnation Boundary‐Layer Flows of Weakly Ionized Gases , 1964 .

[14]  Jim Douglas,et al.  On the numerical integration of quasilinear parabolic differential equations. , 1956 .

[15]  H. Petschek,et al.  Approach to equilibrium lonization behind strong shock waves in argon , 1957 .

[16]  I. I. Glass,et al.  Effects of hydrogen impurities on shock structure and stability in ionizing monatomic gases: 2. Krypton , 1977 .

[17]  M. Hoffert,et al.  Quasi‐One‐Dimensional, Nonequilibrium Gas Dynamics of Partially Ionized Two‐Temperature Argon , 1967 .

[18]  Y. Enomoto.  Wall Boundary Layer Effects on Ionizing Shock Structure in Argon , 1973 .

[19]  Joseph G. Hirschberg,et al.  Electron-Ion Recombination in Dense Plasmas , 1962 .

[20]  Harold Mirels,et al.  Flow Nonuniformity in Shock Tubes Operating at Maximum Test Times , 1966 .

[21]  J. Douglas,et al.  On Predictor-Corrector Methods for Nonlinear Parabolic Differential Equations , 1963 .

[22]  Stephen H. Crandall,et al.  An optimum implicit recurrence formula for the heat conduction equation , 1955 .