Numerically optimized band boundaries of Planck mean absorption coefficients in air plasma

Abstract

Radiation heat transfer plays an important role in the energy balance of plasma in an electric arc and its accurate prediction is essential for the development of new electrical devices. Unfortunately, a very complex spectrum of the absorption coefficient makes accurate radiation heat transfer calculations a very challenging task, especially with complex geometries. Numerical approximation of the absorption coefficient is therefore commonly used to reduce computing demands. This paper presents our contribution to the topic of computing requirements reduction, namely the problem of frequency band selection for mean absorption coefficients (MACs). We show that, with the proper band distribution and averaging method, even a very low number of bands can be sufficient for an accurate approximation of the real radiation heat transfer. The band selection process is based upon numerical optimization with a mean value of each band being calculated as a line limited Planck MAC. Both the line limiting factor and associated characteristic plasma absorption length are investigated in detail and an optimal value equal to the three plasma radii is proposed. Tables for three bands mean absorption coefficients in air at the pressure of 1 bar and temperature range spanning from 300 K to 30 kK are included in this paper. These tables serve as input parameters for a fast evaluation of radiation transfer using either the P1 or discrete ordinates method (DOM) approximation with satisfactory accuracy.Radiation heat transfer plays an important role in the energy balance of plasma in an electric arc and its accurate prediction is essential for the development of new electrical devices. Unfortunately, a very complex spectrum of the absorption coefficient makes accurate radiation heat transfer calculations a very challenging task, especially with complex geometries. Numerical approximation of the absorption coefficient is therefore commonly used to reduce computing demands. This paper presents our contribution to the topic of computing requirements reduction, namely the problem of frequency band selection for mean absorption coefficients (MACs). We show that, with the proper band distribution and averaging method, even a very low number of bands can be sufficient for an accurate approximation of the real radiation heat transfer. The band selection process is based upon numerical optimization with a mean value of each band being calculated as a line limited Planck MAC. Both the line limiting factor and associated characteristic plasma absorption length are investigated in detail and an optimal value equal to the three plasma radii is proposed. Tables for three bands mean absorption coefficients in air at the pressure of 1 bar and temperature range spanning from 300 K to 30 kK are included in this paper. These tables serve as input parameters for a fast evaluation of radiation transfer using either the P1 or discrete ordinates method (DOM) approximation with satisfactory accuracy.