New gas radiation model based on the principle of weighted sum of gray gases. Application to CO₂–H₂O mixtures at high temperature

Abstract

A new gas radiation model based on the principle of weighted-sum-of-gray-gases (WSGG) is proposed. It is shown that expressing the weighting factors as linear functions of the temperature is more suitable than the fourth-order polynomial dependence to the temperature that is commonly adopted in the WSGG model. Using an efficient inverse algorithm, it was estimated a set of twelve spatially nonconstant parameters of the new model based on four gray gases, namely the coefficients of the linear functions and the pressure absorption coefficients. The inverse algorithm is based on the adjoint state of the radiative transfer equation (RTE) using as data the total radiative heat source instead of the total gas emissivity data. The parameters are fitted using data generated with line-by-line (LBL) simulations based on HITEMP2010. In the present work, the proposed gas radiation model is applied to determine the parameters of H₂O–CO₂ mixtures at atmospheric pressure with partial pressure ratio equal to 2, within the range of temperature between 400 K and 1800 K and for thicknesses of the gas layer up to 3.0 m. By applying the inverse algorithm to a given case, the present gas radiation model has the level of accuracy of the LBL method. The application of the same parameters to other test cases does not lead to the same level of accuracy, since the parameters obtained are spatially dependent. However, averaging these parameters in the inverse algorithm results in a gas radiation model with spatially constant parameters. When applied to several (1-D and 3-D) test cases in the conditions for which the parameters were obtained, this led to a significant reduction in the normalized errors on the radiative heat source and, for many of these cases, on the radiative heat flux compared to that obtained with the standard WSGG model.

Keywords:

• Adjoint method
• inverse problem
• participating gases
• radiative heat transfer
• weighted-sum-of-gray-gases model