IntroductionRadiative heat transfer through molecular gases is a very important mode of energy transfer when dealing with combustion systems or modelling atmospheric processes. The most accurate radiative transfer results are obtained through line-by-line (LBL) calculations, which require, however, a prohibitively large computational effort. Consequently a number of global and band models have been proposed. Presently, the most accurate global models are the Full-Spectrum k-distributions (FSK) by Modest and coworkers [1, 2]. Earlier, somewhat less refined, related methods include the Spectral-Line-Based WeightedSum-of-Gray-Gases [3][4][5] or SLW and Absorption-Distribution-Function(ADF) [6,7] models. All of these methods are orders-of-magnitude more efficient than LBL calculations, and they all use full-spectrum kdistributions, which, in general, need to be calculated from high-resolution databases, such as HITRAN [8], HITEMP [9] or -for CO 2 -the new CDSD-1000 [10,11]. Both the SLW and ADF methods use simplified k-distributions reducing them to step-functions (gray gases), whereas the full-spectrum k-distribution method uses Gaussian quadrature to integrate over g-space resulting in better accuracy. Assembling such k-distributions is a rather tedious task and, therefore, to make simple engineering calculations feasible, Denison and Webb [12,13] have proposed several simple full-spectrum k-distribution correlations for CO 2 and H 2 O, based on the outdated HITRAN92 [8] database, combined with some extrapolations of their own for high temperatures. Recently, Zhang and Modest [14] provided an updated correlation for CO 2 based on the newer HITEMP database which is purported to be accurate to at least 1000K. Unfortunately, it appears that the HITEMP database shows some erroneous behavior for temperatures beyond 1200K, as seen by comparison with experimental data [10,15]. The new CDSD-1000 databank [10,11], on the other hand, follows experimental data much more closely. Thus, it is the purpose of this note to provide a simple engineering correlation for full-spectrum k-distributions evaluated from the CDSD-1000 databank. * To whom all correspondence should be addressed. Fax: (814)863-8682; Email: mfm6@psu.edu 1
Mathematical FormulationThe k-distributions are obtained by reordering the spectrally varying absorption coefficient into a monotonically increasing function with, in the case of full-spectrum k-distributions, the blackbody intensity (Planck function) as a weight factor. This has been described in detail in the original paper by Modest and Zhang [16].The full-spectrum k-distribution is defined aswhich is a function of temperature T p through the black body intensity and of the state of the gas through p, x; η) where T g is the gas temperature, p is the absolute pressure, x is the concentration and η is the wave number.For RTE solution methods, the cumulative full-spectrum k-distribution is used, defined bywhereis the Heaviside unit step-function. Physically, g is the Planck-function-weighted fraction of the...
