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

Abstract

In radiation modeling of thermal plasmas non-grey models are applied where the radiative transport is described in several frequency bands (spectral intervals). Hereby mean absorption coefficients have to be calculated by a spectral integration procedure, providing a constant mean absorption coefficient for each band. Depending on the number of bands, one or more integration boundaries have to be selected in order to do the integration. In this paper we evaluate the influence of the selection of these integration boundaries on the mean absorption coefficient and the also radiation transfer by applying the mean absorption coefficients in a radiation transport model. Using a simplified twoband model we demonstrate that the selection of the integration boundary has a large impact on the total model accuracy. We show that in some cases selecting a band boundary right at the frequency where the continuum absorption shows a jump can introduce a significant error into the radiation calculation. The process of the integration interval selection thus demands a global optimization procedure to properly evaluate the boundaries of each frequency band.

Review of Thermal Plasma Simulation Technique

“…A suitable n is dependent on various plasma conditions, and therefore a careful check regarding the dependence of calculation accuracy on n is required to predict the radiative transfer of the thermal plasma by the P‐1 approximation with MAC, as has been discussed in Ref. . In addition, the users of computational software using the P‐1 approximation (or the DOM) with MAC, which cannot handle multiple frequency bands, must be well aware that the calculation could derive a very unrealistic radiation field.…”

Optimal Band Selection for the Calculation of Planck Mean Absorption Coefficients

“…A baseline calculation of the radiation transfer resolving the whole spectrum is the first step in the optimization procedure (spectral solution [5]). This is a computationally expensive step because the radiation transfer needs to be solved for each of the approximately 500 000 points in the spectrum.…”

“…1 is used with a spatial resolution of 100×100 points. A relative error norm ∆F ν is used to quantify the difference between the two approaches [5], where the error is evaluated along the radius only:…”

“…To address these questions, numerical optimization procedures have been developed to find an optimal number and distribution of the bands [5,6]. In this paper, we apply the optimization procedure as introduced in [5,7] to a specific mixture of SF 6 and copper vapor.…”

“…To address these questions, numerical optimization procedures have been developed to find an optimal number and distribution of the bands [5,6]. In this paper, we apply the optimization procedure as introduced in [5,7] to a specific mixture of SF 6 and copper vapor. Since the amount of metal vapor in the arc chamber or switchgear can vary from 0 to 100% in the real application, it is necessary to quantify the error that is introduced when using the same band limits for various mixture ratios.…”