Line by line based band identification for non-gray gas modeling with a banded approach

The banded approach or box model is a method to include the non-grayness of combustion gases in radiation heat transfer calculations. However, the determination of the correct limits for the bands and the effective band absorption coefficients is still something of a black art. In this study, the line by line (LBL) spectral absorption coefficient profile has been implemented to obtain the effective number of bands, and bands’ limits for pure H₂O, pure CO₂ and a H₂O-CO₂ gas mixture. A mathematical technique has been used to smooth the LBL profiles of pure gases in atmospheric pressure in order to be used for identifying the gray bands. The optimization for selecting the bands is done by analyzing the radiative heat transfer in several one-dimensional benchmarks. After obtaining the optimal band dividing scheme, a set of correlations for the pressure based gray band absorption coefficient of pure gases is found by integrating the line by line spectral absorption coefficient weighted by the corresponding black body intensity along the bands. In contrary to the previous similar works, by using the LBL data for pressure based gray absorption coefficient of the bands, the current correlations are independent of gas concentration and path length. The present approach could successfully support the non-gray walls. The method has been validated using several benchmarks and exhibited comparable accuracy with other available models.