ARTICLE:

• RADIATIVE EQUILIBRIUM OF AN HYDROGEN-HELIUM MIXTURE WITHIN AN ELLIPSOIDAL SHELL USING THE DISCRETE ORDINATES METHOD AND A SPECIFIC FREQUENCY INTEGRATION METHOD  download article

Rodolphe Vaillon
Centre de Thermique de Lyon (CETHIL, CNRS/INSA Lyon/UCBL), Domaine Scientifique de La Doua, 20 av. A. Einstein, 69621 Villeurbanne Cedex, France

M. Lallemand
LET, UMR CNRS 6608, ENSMA, 86960 Futuroscope, FRANCE

D. Lemonnier
LET, UMR CNRS 6608, ENSMA, 86960 Futuroscope, FRANCE

C. Stehle
DARC, UPR CNRS 176, Observatoire de Paris, 92195 Meudon Cedex, FRANCE

ABSTRACT

The radiative equilibrium of an hydrogen-helium ellipsoidal gas layer confined between an internal black surface at prescribed temperature and an external one either transparent or black is investigated. The temperature field is calculated by considering the coupling between the chemistry and the optical properties of the reactive medium in the range [3000 — 30000] K. The theoretical determination of the hydrogen-helium mixture absorption properties is performed under the assumption of local chemical and thermodynamical equilibria in the working temperature range, at a pressure of one atmosphere and a given initial molar fractions of the mixture. Absorption cross-sections calculations are presented for the following processes: bound-free and free-free electronic transitions of the negative hydrogen ion, bound-free, free-free and bound-bound transitions of the hydrogen atom. The determination of the lines shapes is carried out by means of the Model Microfield Method. Since total radiative quantities have to be calculated, a specific frequency integration method suitable for the hydrogen-helium absorption coefficient spectrum is presented. It is based on the constitution of a spectral data bank that makes total radiative quantities integration fast and accurate. Finally, the proposed method is used to solve the radiative equilibrium of such a system. The spectral directional intensity and incident energy fields are determined by using the Discrete Ordinates Method extended to orthogonal curvilinear coordinates.

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