A weighted-sum-of-gray soot-fractal-aggregates model for nongray heat radiation in the high temperature gas-soot mixture

Abstract

Soot, a product of insufficient combustion, is usually in the form of aggregate. The multi-scattering of soot fractal aggregates has been proved to play an important role in studying the soot radiative properties, which is rarely considered in predicting the radiative heat transfer in combustion flame. In the present study, based on the Rayleigh-Debey-Gans-Fractal-Aggregate (RDG-FA) theory, a model, named Weighted Sum of Gray Soot fractal Aggregates (WSGSA), used to calculate the radiative properties of nongray soot fractal aggregates in gas-soot mixture is developed by combining the features of full-spectrum k-distribution (FSK) model and Weighted-Sum-of-Gray-Gases (WSGG) model. Four gray soot fractal aggregates obtained from reordering in the form of the k-distribution at Gauss-Legendre integral points are selected to represent the nongray soot fractal aggregate, while corresponding weighting factors are obtained by fitting the radiation data obtained by the line-by-line (LBL) model with soot radiation data. Then, the WSGSA model is systematically validated by studying the radiative heat transfer properties in a one-dimensional plane-parallel slab system only with soot aggregates. The maximum relative discrepancies of emittance under different temperatures and different path lengths are less than 12%, while the maximum relative discrepancies of radiative heat source term and radiative heat flux are both less than 11% with path length less than 3 m. Moreover, combined with the WSGG model, the performance of the WSGSA model is further validated by predicting the radiative heat transfer properties in the mixture consisted of gases and soot aggregates, and acceptable results are also obtained. All the results reveal that the developed model can be applied to predict the radiative heat transfer in the mixture containing gases and soot aggregates, even in the case of significant changes in temperature and species concentration.