A. Bourdon et P. Vervisch, ELECTRON-VIBRATION ENERGY-EXCHANGE MODELS IN NITROGEN PLASMA FLOWS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(4), 1997, pp. 4634-4641
This work presents an examination of the validity of the simple linear
Landau-Teller-type model proposed by Lee for the electron-vibration e
nergy exchange term in nitrogen [in Thermal Design of Aeroassisted Orb
ital 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 infl
uence of the anharmonicity of the molecule and of the initial vibratio
nal temperature T-v is studied. With a harmonic oscillator approximati
on, it is found that a linear Landau-Teller-type model is accurate to
describe the vibrational energy relaxation rate for electron temperatu
res T-e in the range 3000 K less than or equal to T less than or equal
to 20 000 R. When T-v <T-e, our results show that the initial model p
roposed by Lee overestimates by a mean factor of 3 the electron-vibrat
ion (e-V) relaxation time. When T-v>T-e, the relaxation time appears t
o depend on the initial vibrational distribution. When the anharmonici
ty 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 energ
y exchange term.