Assessment of radiative property models in non-gray sooting media

Abstract

The radiative transfer equation (RTE) is solved by the Finite Volume Method (FVM) in 1D and 2D axisymmetric configurations containing mixtures of water vapor, carbon dioxide and soot. Several radiative property models, namely simple gray models, the Statistical Narrow Band Correlated- k (SNBCK) model, the Weighted-Sum-of-Gray-Gases (WSGG) model, the Full-Spectrum Correlated- k (FSCK) model, the Spectral-Line-Based Weighted-Sum-of-Gray-Gases (SLW) model, a Gray-Narrow-Band (GNB) model and a Gray-Wide-Band (GWB) model, are assessed by comparison with reference calculations based on the Ray Tracing (RT) method coupled with the Statistical Narrow Band (SNB) model. Different treatments of overlapping bands are implemented with the SNBCK model, namely the correlated approach, the uncorrelated approach, and the mixing schemes of Modest and Riazzi (J. Quant. Spectros. Rad. Trans. 90 (2005) 169–189) and of Solovjov and Webb (J. Quant. Spectros. Rad. Trans. 65 (2000) 655–672) (Superposition and Multiplication). The Full Spectrum (FS) k-distributions required to run both FSCK and SLW are assembled from the same narrow band (NB) database as for the SNB and the SNBCK models using either the mixing model of Modest and Riazzi or the Multiplication scheme. The correlated SNBCK is the most accurate model but is too time consuming for engineering applications. The computational efficiency of the SNBCK can be considerably improved without altering the quality of the solutions by using the gas mixing scheme of Modest and Riazzi. Numerical results show that, in this case, good accuracy for spectrally-integrated quantities is obtained by considering only a 2-point Gauss–Legendre quadrature scheme. The FSCK and the SLW, using FS k-distributions assembled with the Modest and Riazzi scheme, are found to be the best compromise in terms of accuracy and computational requirements. It is found that FSCK predictions remain satisfactory by reducing the number of quadrature points of the Gauss–Legendre scheme up to seven.