Non-dimensional wavenumber in full-spectrum k-distribution computations with or without a reference state

- A full-spectrum k-distribution formulation without a reference temperature is proposed.
- Instead of a reference cumulative k-distribution, a non-dimensional wavenumber is used.
- The formulation can be employed without a reference state.
- The use of the non-dimensional wavenumber simplifies the approach of nonhomogenous media.

In the full spectrum k-distribution method, the k-distributions are Planck function weighted. These k-distributions depend on temperature, which varies with location in nonisothermal media. Consequently, in order to apply the method to nonuniform media, k-distributions evaluated at different local temperatures are correlated by a k-distribution evaluated at an arbitrarily chosen reference blackbody temperature. On the other hand, in the original band method, the k-distributions are directly related to spectral locations. Such k-distributions can replace Planck function weighted k-distributions computed at a reference temperature. This approach was employed by Maurente et al. [1] in order to deal with gas mixtures in non-equilibrium media. In this paper the formulation is presented for the equilibrium case. The proposed formulation simplifies the application of the FSK method to nonuniform media, and brings new directions to k-distribution issues. It can be employed with a reference state, but not a reference temperature, with reference state and temperature, as in the traditional FSK, and without any reference state, being in this case the continuous limit of the recently developed Rank Correlated SLW [2]. Results were obtained for test cases considering one-dimensional, nonuniform media, constituted by CO2 and inert gases, and compared to line-by-line solutions.