Numerical optimization of Mean Absorption Coefficient in Air using Planck Modified Mean Function

Abstract

The Divergence of Radiative Flux (DRF) is the term present in the energy balance of the plasma that describes the radiative behavior of the arc. This property is obtained by the resolution of the Radiative Transfer Equation (RTE). Because of its complexity, many approximate methods are developed to reduce the computational time. This paper will describe the approximate methods already used in numerical simulation: Net Emission Coefficient (NEC) and Mean Absorption Coefficient (MAC). This last property requires having a good definition of spectral ranges and mean functions to have a physical representation of radiative losses. In this paper, the spectral ranges will be defined from the continuum of the absorption coefficient and Planck Modified Mean Function (PMMF) will be used to calculate MACs. This mean function requires a good definition of the characteristic absorption length R.In this paper, we will develop an optimization methodology that allows finding the best R in order to have an accurate DRF using MACs. To quantify the accuracy of these approximate methods, a 1D resolution of RTE will be performed in the case of Air plasma at P=1bar in Local Thermodynamic Equilibrium (LTE). The exact DRF solution will be considered as a reference when compared with the DRF of approximate methods.