Fast approximate technique for the cumulative wavenumber model to modeling radiative transfer in a mixture of real gas media

In the cumulative wavenumber (CW) model, the total range of the absorption cross-section Cη is subdivided into the supplementary absorption cross-section of gray gases C_j, j=1,…,n, where n is the number of gray gases; and the wavenumber region is subdivided into intervals Δ_i=η_i−1, η_i], i=1, 2,…,p, where p is the number of intervals. The intersection of the two spectral subdivisions is used to define the modeling of the fractional gray gas D_ij. In the CW model, we solve the radiative transfer equation (RTE) in every subinterval D_ij; then it is necessary to solve n x p times the spectral form of the RTE for complete spectral integration. In this work, the CW model is used with a numerical approximation technique based on additive properties of radiative intensity to reduce the solution of RTE to n new fractional gray gas D_j for complete spectral integration. The CW model was first coupled with the discrete ordinates method and the accuracy of the simplified technique and the algorithm was first examined for one-dimensional homogeneous media; results are compared with line-by-line calculations and it is found that the CW model with the simplified technique is exact for the homogeneous media examined. Also, the fast approach is tested in the diffuse reflecting boundaries case. The CW model is implemented in a bi-dimensional enclosure containing real gases in isothermal cases. Afterwards, this approximate technique is extended to non-isothermal and non-homogeneous cases; the results are compared with line-by-line calculations taken from literature and good agreement was found. The results obtained using the acceleration technique for the CW model agree with the results of original CW model. With this acceleration technique the CPU time decreases p times. Spectral database HITRAN and HITEMP are used to obtain the molecular absorption spectrum of the gases.