Spectral gas properties

The absorption coefficient $\kappa$ of the combustion products is highly dependent on the wavenumber $\nu$ as shown by line spectra of radiative gases (H$_2$ O, CO$_2$ and CO). To take into account this spectral dependency, the absorption coefficient of each species is here represented by the SNB-ck model [#!Sou97!#,#!Liu00b!#,#!Liu01!#]. For the gas mixture composed of different species, the same model is used, building data according to the mixing model exposed by Liu [#!Liu01!#]. The radiative solutions are obtained by computing $N_{bands} \times N_{quad}$ independent calculations where $N_{bands}=367$ is the number of narrow bands of spectral width $\Delta \eta = 25 \, cm^{-1}$ , describing the spectral properties in the range $150-9300 \, cm^{-1}$ , and $N_{quad}=5$ is the number of the Gauss-Legendre quadrature points used for the spectral integration over each narrow band. For non-gray media, introducing spectral dependencies in Eq. (), gives for the source term :

$$S_{r,DOM}=\sum_{i=1}^{N_{band}}\sum_{j=1}^{N_{quad}} \Delta \nu_i w_{ij} \kappa_{ij}(4\pi \overline{I}_{b,ij}-G_{ij})$$ (1.13)

where $G_{ij}$ is obtained from Eq.().
The computational efficiency of such a model is strongly linked to the number of bands $N_{bands}$ , that has to be optimized depending on the studied case.

Other models called global models have been developed : WSGG (Weighted Sum of Gray Gas) [#!Sou94!#] and FS-SNBcK (Full Spectrum SNBcK) [#!Poi09!#].