Electron-vibration energy exchange models in nitrogen plasma flows

Abstract

This work presents an examination of the validity of the simple linear Landau-Teller-type model proposed by Lee for the electron-vibration energy exchange term in nitrogen [in Thermal Design of Aeroassisted Orbital Transfer Vehicles, edited by H. F. Nelson (AIAA, New York, 1985), Vol. 96, p. 3; in Thermophysical Aspects of Re-entry Flows, edited by J. N. Moss and C. D. Scott (AIAA, New York, 1986), Vol. 103, p. 197]. Plasma flow conditions encountered in high enthalpy wind tunnels are considered. The time-dependent relaxation of the vibrational energy of nitrogen due to electron inelastic collisions is calculated. The influence of the anharmonicity of the molecule and of the initial vibrational temperature ${\mathrm{T}}_{\mathrm{v}}$ is studied. With a harmonic oscillator approximation, it is found that a linear Landau-Teller-type model is accurate to describe the vibrational energy relaxation rate for electron temperatures ${\mathrm{T}}_{\mathrm{e}}$ in the range 3000 K\ensuremath{\leqslant}${\mathrm{T}}_{\mathrm{e}}$\ensuremath{\leqslant}20 000 K. When ${\mathrm{T}}_{\mathrm{v}}$${\mathrm{T}}_{\mathrm{e}}$, our results show that the initial model proposed by Lee overestimates by a mean factor of 3 the electron-vibration (e-V) relaxation time. When ${\mathrm{T}}_{\mathrm{v}}$>${\mathrm{T}}_{\mathrm{e}}$, the relaxation time appears to depend on the initial vibrational distribution. When the anharmonicity of nitrogen is taken into account, generally the relaxation rate of the vibrational energy deviates from a linear rate equation. In this case, it appears much more difficult to model accurately the e-V energy exchange term.