Improvements of radiative transfer calculation for SF₆ thermal plasmas

Abstract

We present a comparison between an exact calculation of radiative transfer in SF6 thermal plasma based on a fine description of the spectrum with 300 000 spectral points for each temperature value, for simplified conditions (1D and 2D geometries with imposed symmetrical temperature profiles and local thermodynamic equilibrium) and two kinds of approximated calculations. The first is the classical net emission coefficient largely used in arc modelling. The second one is based on a very simplified spectral description with only seven intervals assuming a grey body condition within each interval and using the Planck and the Rosseland averaging for deducing the mean absorption coefficient (MAC). At high temperature the use of the Rosseland averaging is not satisfactory. The other two approximated methods (net emission and the Planck averaging) are acceptable but the radiative flux is in general not very accurate. The radiative transfer calculation can be improved following three ways: a better knowledge of the basic processes and in particular of the absorption coefficients for diatomic and polyatomic molecules, the use of different definitions of MACs (Planck averaging at high temperature and mean natural value at low temperature) and a careful choice of the spectral intervals.

Basic knowledge on radiative and transport properties to begin in thermal plasmas modelling

“…Concerning the classic mean, this function is adapted for the very low temperatures where the emission is really negligible in front of the absorption (no lines) and does not depend on R p . Consequently and according to the last works 25,31,32,45 on these approaches methods, the MACs can be calculated according to different mean functions: the Planck mean (with R p correction for the line's contribution) to estimate the absorption in the hot and intermediate regions, and the classic mean to treat correctly the absorption in the cold regions; -the difficulties consist in finding the fundamental data to treat all the radiative mechanisms existing in the plasma (number densities, internal partition functions, photoabsorption, photodetachment and elastic cross-sections, energy levels and their degeneracies for the atomic contributions; number densities, energy levels, transition lines and their Einstein probabilities, oscillator strengths and broadenings for the lines), to define the number of spectral interval for the calculation of the mean absorption coefficients, and to define the limit between the two regions which depends on the pressure and the plasma's size R p .…”

“…5 in the case of pure SF 6 High Voltage Circuit Breaker. 45 The results were obtained with the Net Emission Coefficient (NEC), with the P1 model using the mean absorption coefficients deduced from the Rosseland or the Planck approximations, and compared to a fine resolution of the equation (3) for a given temperature profile (see the work of Randrianandraina et al 45 ) for the definition of the mean absorption coefficients, for the discretisation and the temperature profile). From these results and from the last works published on the determination of the radiative flux and its divergence based on different approached methods, 60,61 some conclusions can be drawn concerning the radiation:…”

“…22 Nevertheless, some problems exist with this method: it cannot take into account the absorption in the intermediate and cold regions; it cannot estimate the radiative flux; it cannot be used to estimate the radiative losses for higher pressure from a simple linear law (it is not proportional to the pressure),; it depends on numerous parameters (the nature of the species, the ionisation energies of the species, the number of lines and their oscillator strengths, the broadening of the lines, the pressure, the plasma's size R p ); -P1 model requests mean absorption coefficients (MAC) calculated with a very accurate cutting of the spectra in several spectral intervals. 45 Concerning the Planck mean, the method is a good approximation to estimate the radiative flux in the hot regions only if the escape factor (i.e the R P parameter) is considered to treat the lines; the method is particularly valid for weak values of the absorption coefficients and plasma's sizes; for the tedious and cold regions the radiative flux arriving on the wall strongly depends on the R p value. For high values of absorption coefficients or plasma's sizes, the radiative flux and the divergence of the flux are overestimated and underestimated respectively.…”

Review of Thermal Plasma Simulation Technique

“…gives the comparison between Plank and Rosseland MACs with seven frequency bands. Planck averaging, whose formula is based on the assumption of an optically thin plasma, is well known to significantly overestimate the effect of line spectra with high absorption coefficient values on the value of MAC . For frequency bands including resonance lines, therefore, the value of the Planck MAC gets much larger than the spectrum absorption coefficient, as can be seen from Fig.…”

On the Selection of Integration Intervals for the Calculation of Mean Absorption Coefficients

“…The reason is that the absorption coefficient spectrum is usually very complex, containing both continuum contribution and a narrow spectral lines whereas the spectral intensity can vary several orders of magnitude in the spectral range that is usually considered [3]. To achieve a reasonable resolution of the spectrum, it is often required to use several hundred thousands of frequency steps when using line-by-line methods [4]. But even if lines are treated separately from the continuum (for example by method of escape factors described in [5]), the number of lines is usually in the order of several thousands.…”