Unified gas radiation model over the entire temperature range based on WSGG

Abstract

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 ${\kappa }_{p,1}$ and the weighting factor $a_1$ are approximated with quadratic polynomial functions of the temperature $T$. For $K$ gray gases and $2\le k\le K$, $a_k$ are determined by translation from $a_1$ and ${\kappa }_{p,k}$ by translation and multiplicative factors from ${\kappa }_{p,1}$. 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 ${\kappa }_{p,k}$ depend highly on $T$ and the $a_k$ depend weakly on $T$ whereas in the standard WSGG model, ${\kappa }_{p,k}$ 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. (2013) on the first 72 cases ($T>$ 2500 K in the other cases and the model by Dorigon is limited to 2500 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.