Calculations of radiative intensity in one-dimensional gaseous media with black boundaries using the statistical narrow band model

Abstract

Directional radiative intensity over specific spectral region provides fruitful information inside gas fired systems, and is very useful for inverse analysis, such as temperature and species concentration reconstruction. The statistical narrow band (SNB) model has acceptable time efficiency for practical applications and has been shown to have good accuracy to calculate integral radiative quantities, such as radiative heat flux and radiative source term. No previous work provides its accuracy information for solving spectral radiative intensity in combustion systems, which is to be investigated in this work. The SNB model is applied to solve radiative transfer in one-dimensional gaseous media with black boundaries. Gaseous media of CO2 and H2O with uniform and non-uniform distributions of temperature and mole fraction are considered. The line-by-line (LBL) method is considered as the benchmark solution. Results show that the accuracy of spectral radiative intensity for CO2 media is very good (with errors less than 2%) in most bands. The errors of spectral radiative intensity for H2O media are larger than 5% in many spectral bands and the maximum error is larger than 10%. Accordingly, a strategy to improve the accuracy of the SNB model by generating a new set of narrow band parameters is proposed in this work. Results show that errors in most bands reduce to less than 2% using the new set of parameters. While spectral radiative intensity shows different magnitudes of errors for different gaseous media and different sets of narrow band parameters, radiative heat flux always has good accuracy with largest error less than 3.5%. This work provides comprehensive accuracy information of the SNB model to calculate radiative intensity and radiative heat flux in gaseous media, and the proposed strategy to generate narrow band parameters improves the accuracy of the SNB model significantly.