The rank correlated FSK model for prediction of gas radiation in non-uniform media, and its relationship to the rank correlated SLW model

Abstract

Following previous theoretical development based on the assumption of a rank correlated spectrum, the Rank Correlated Full Spectrum k-distribution (RC-FSK) method is proposed. The method proves advantageous in modeling radiation transfer in high temperature gases in non-uniform media in two important ways. First, and perhaps most importantly, the method requires no specification of a reference gas thermodynamic state. Second, the spectral construction of the RC-FSK model is simpler, requiring only two cumulative k-distributions. Further, although not exhaustive, example problems presented here suggest that the method may also yield improved accuracy relative to prior methods, and may exhibit less sensitivity to the blackbody source temperature used in the model predictions. This paper outlines the theoretical development of the RC-FSK method, comparing the spectral construction with prior correlated spectrum FSK method formulations. The work presents predictions using the new Rank Correlated FSK method and previous FSK methods in three different example problems. Lineby-line benchmark predictions are used to assess the accuracy.

An exploration of the influence of spectral model parameters on the accuracy of the rank correlated SLW model

“…Finally, it may be mentioned that a recent work has shown that the rank correlated spectrum assumption may be applied to the Full Spectrum correlated-k (FSK) model [19]. That work revealed that the two formulations (RC-FSK and RC-SLW models) are virtually identical, and when Figure 7.…”

The impact of radiative heat transfer in combustion processes and its modeling – with a focus on turbulent flames

“…The main advantage of this method is thus to allow the approximation of any function of the absorption coefficient, that would require many thousands of spectral components at high spectral resolution, by a sum over a few components (~10 and equal to the order of the quadrature used for the calculation). A large gain in terms of computational time can thus be achieved by application of the Full Spectrum k-distribution method [91], [92].…”

“…The Rank Correlated FSK (RC-FSK) [92] method (developed from its predecessor, the RC-SLW model [97]) does not require the arbitrary definition of the reference state of the gas. It has been shown that the RC-FSK and RC-SLW methods are theoretically identical, and produce identical predictions if the same numerical implementation is employed [92]. This method is also founded on a relationship between gas spectra of the form of Eq.…”

Assessment of engineering gas radiative property models in high pressure turbulent jet diffusion flames

“…The concept of Rank-Correlated spectrum was first developed for SLW methods [13] before being applied to the FSK methods [14]. The two approaches (Rank Correlated SLW and Rank Correlated FSK) were found to be theoretically identical, and produce identical predictions when implemented using the same strategy to evaluate the gray gases weights [14]. The main advantage of the RC-FSK/SLW model is that no reference state is needed to make calculations in non-uniform media.…”

“…These schemes require, in general, the definition of a reference thermodynamic state. Recently, the assumption of Rank Correlated (RC) / comonotonic [12] spectrum was introduced, leading to either the RC-SLW model [13] or the RC-FSK model [14], which were found to be identical when the same strategy is applied to evaluate the gray gases weights [14]. The Rank Correlated method requires no specification of a reference gas thermodynamic state.…”