The k-distribution method for radiation heat transfer in non-isothermal real air-gas plasmas
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The k-distribution method for treating the spectral properties of and absorbing-emitting medium represents an alternative to line-by-line calculations which reduces the number of evaluations of the radiative transport equation from the order of a million to the order of ten without any significant loss of accuracy. For problems where an appropriate reference temperature can be defined, the k-distribution method is formally exact and consists only of a change of variables in the spectral domain. However, when no appropriate reference temperature can be defined such as for strongly non-isothermal media, the method results in errors. These errors are difficult to quantify. There have been several attempts to implement corrections to the k-distribution method to extend its application to inhomogeneous media by modeling the effects of temperature, pressure, and concentration gradient. The Multi-Source Full Spectrum K-Distribution Method (MSFSK) introduced here extends the k-distribution method to non-isothermal media without variations in pressure or concentration. The MSFSK method manages to attain this goal by applying the superposition principle to the original RTE before applying the k-distribution transformation to decompose the problem into a set of sub-problems each of which is able to be solved effectively via the ordinary or modified full spectrum k-distribution method. The concept behind this new Multi-Source Full Spectrum K-Distribution Method is to break up the problem domain into isothermal or nearly isothermal emission zones. For each zone, the heat flux and flux divergence are calculated considering only emission from that zone. The RTE is solved using the full spectrum k-distribution method. The k-distribution for each gas volume is generated using the temperature of the current emission zone as the reference temperature. This process is repeated for each emission zone and the heat flux and flux divergence are summed. This method is applied to a variety of one dimensional slab geometry problems are results are presented. It is shown that the MSFSK method provides very accurate results for the radiative heat flux and flux divergence in these geometries. The effect of different quadrature schemes for performing the spectral integration on solution accuracy.