Unified gas radiation model over the entire temperature range based on WSGG
Résumé
A unified gas radiation model over the entire temperature range -the Unified model based on the Weighted-Sum-of-Gray-Gases (UWSGG) is proposed, which improves the accuracy of the standard WSGG model. The pressure absorption coefficient κ p,1 and the weighting factor a 1 are approximated with quadratic polynomial functions of the temperature T . For K gray gases and 2 ≤ k ≤ K, a k are determined by translation from a 1 and κ p,k by translation and multiplicative factors from κ p,1 . An efficient inverse method and a Genetic Algorithm are used to find all the model parameters from the total radiative heat source S r computed with the Line-by-Line (LBL) method based on HITEMP2010 data. It can be noted that κ p,k depend highly on T and the a k depend weakly on T whereas in the standard WSGG model, κ p,k are usually constants and a k depend highly on T . It is shown, on 92 selected 1D cases of CO 2 -H 2 O mixtures (at atmospheric pressure with a mole fraction ratio of 2) within the temperature range [300 K; 3,000 K], that the maximum relative errors on S r for the UWSGG model with K = 6 do not exceed 7.5 %. Conversely, for the standard WSGG model by Dorigon et al. [1] on the first 72 cases (T > 2,500 K in the other cases and the model by Dorigon is limited to 2,500 K), these errors vary up to 20.4 % (seven cases have errors higher than 15.0 %, fourteen cases have errors between 10.0 % and 15.0 % and, five cases have errors between 7.5 % and 10.0 %). The accuracy of the total radiative heat flux is also improved with the UWSGG model.