Net Emission Coefficient Research Articles

Calculation of the interruption capability of SF/sub 6/-CF/sub 4/ and SF/sub 6/-C/sub 2/F/sub 6/ mixtures. I. Plasma properties

For a gas used in circuit breakers, the extinction capability corresponds roughly to the rate of evolution of the electrical resistance during the arc decay. This property is very prominent for SF/sub 6/ which explains its wide use in high-voltage circuit breakers. But in severe winter conditions, this gas may partially liquefy, and some mixtures of SF/sub 6/ with other gases are considered. The present work deals with a calculation of the extinction capability of SF/sub 6/-CF/sub 4/ and SF/sub 6/-C/sub 2/F/sub 6/ mixtures. This first paper consists of the study of the material functions of the plasma assumed to be in local thermal equilibrium (LTE). The equilibrium composition and the thermodynamic properties have been calculated from the partition functions. The transport coefficients have been computed by the method of Chapman-Enskog and the net emission coefficient obtained assuming isothermal and homogeneous plasma. CF/sub 4/ and C/sub 2/F/sub 6/ present dissociation phenomena analogous to those of SF/sub 6/ which leads to similar variations of mass density, specific heat, and thermal conductivity. The electrical conductivities are practically identical for all the mixtures. The net emission coefficient is enhanced by the presence of carbon in spite of a strong absorption of the resonance lines.

Theoretical radiative emission results for argon/copper thermal plasmas

Theoretically determined radiative properties for argon and argon/copper plasmas at one atmosphere, in the temperature range from 3000 to 25000 K, are presented. The spectrum from 0.03 to 25 μm is covered. The spectral emission coefficient, integrated emission coefficient, and net emission coefficient are the properties considered. To determine the limits of the optically thin regime, the intensity for a line-of-sight in an isothermal, homogeneous plasma versus pathlength is compared to the intensity calculated with the optically thin assumption. To obtain information on the dominating emission mechanisms, the fractional contributions of the bound bound (line), free-bound, and free-free emission are shown. To obtain information on the dominating species, plots of the fractional contributions of each of the atom and ion types is presented. Because it is of interest to know how much of the total radiation is in the vacuum ultraviolet wavelength region, fractional plots of this are presented too.

Radiative transfer calculation in SF6 arc plasmas using partial characteristics

The partial characteristics of the radiation which correspond to partial sources and partial sinks of radiation along a given direction, were calculated for a SF6 arc plasma between 3000 and 30000 K. These partial characteristics allow rapid calculation of the 3D radiative transfer in this type of plasma. The method was applied to several simple cases and showed the validity limits of the use of a net emission coefficient in the modelling of the arcs. It was shown that, to calculate the radiative transfer and the temperature in the hot regions, the use of a net emission coefficient is valid when the plasma is approximately isothermal. In the case of strong temperature gradients in the hot regions, the net emission coefficient depends strongly on the chosen plasma thickness whose value is difficult to estimate.

Volumetric emission of argon plasmas in the presence of vapors of Fe, Si, and Al

The net volumetric emission was calculated for argon plasmas at atmospheric pressure in the presence of metal vapors for different elements, over the temperature range from 3000 to 30,000 K. The computations are based on the escape factor model, using a semi-empirical method for the determination of line profiles and line broadening effects. Results for iron, .silicon, and aluminum show an important influence of the presence of even the smallest concentrations of the metal vapors on the net emission coefficient of the plasma. The effect is strongest for iron, followed by aluminum and .silicon. Special attention is given to self-absorption effects which are most important in the first millimeter o% the optical path of the emitted radiation. The effect is incorporated into the calculation procedure of the net emission coefficient and can be used as a volumetric energy sink as long as the absorption length is shorter than the radius of the control volume used in the computation scheme.

Effect of the presence of iron vapors on the volumetric emission of Ar/Fe and Ar/Fe/HZ plasmas

The net volumetric emission coefficient was calculated using the escape factor method for Ar/Fe and Ar/H2/Fe plasmas, at atmospheric pressure, over the temperature range from 3000 K to 30,000 K. The calculation involved 712 lines for Ar I, Ar II, and Ar III, 3481 lines for Fe I, Fe II, and Fe III, and 230 lines for H in the Ar/H2/Fe case. A semiempirical method was used for the determination of line profiles and line broadening. The results show a strong influence of the presence of even traces of iron vapors at low temperatures where the volumetric emission increases by several orders of magnitude. Special attention is given to self-absorption of the argon resonance lines which prevents the radiation from escaping within a few millimeters from the emission source.

Net emission coefficient of radiation in SF6 arc plasmas

Calculations have been made of spectral absorptivities of SF6 plasmas as a function of wavelength from 10 nm to 30 mu m, temperature from 300 to 30000 K and pressure from 1 to 10 atm. Net emission coefficients of radiation have been derived from these absorptivities for cylindrical isothermal plasmas of radii from 0.1 to 2 cm. In addition calculations have been performed as a function of pressure, temperature and radius of the fraction of the emitted radiation that is below the photo-ionization threshold of 130 nm.

Calculation of net emission coefficient of thermal plasmas in mixtures of gas with metallic vapour

The net emission coefficient of Ar-Cu, N2-Cu, SF6-Cu and Ar-Fe mixtures was calculated for homogeneous and isothermal plasmas at atmospheric pressure in the temperature range between 3000 and 25000 K. The increase in power radiated due to the presence of metal vapours depends on the vapour itself (the net emission is higher with iron than with copper) and on the type of gas. The influence of pressure was calculated for the SF6-Cu mixture. In the last part of the paper the values of the net emission coefficient were used to calculate the temperature profile in stationary arc in Ar-Cu and N2-Cu mixtures. The influence of copper on radiation is preponderant on the temperature field at higher currents whereas the effect on electrical conductivity is important at lower currents.

Influence of radiation on temperature field calculation in SF6 arcs

Comparison between measured and calculated temperatures in SF6 arcs shows that the values of the net emission coefficients calculated by various authors are, in all cases, too low. This underestimation of the emission coefficient is of the order of two to three.

Calculation of net emission coefficient in N2, SF6 and SF6-N2 arc plasmas

The net emission coefficient of SF6-N2 mixtures was calculated for temperatures between 8000 and 24000 K and pressures between 1 and 8 bar. The calculation of the radiative transfer of the lines required a study of line broadening and was performed assuming that line overlapping had a negligible influence. The results show that the resonance lines, although they are strongly absorbed, make up a large part of the net radiation-about as much as the continuum. Also, the nitrogen lines are more strongly absorbed than the lines of sulphur or fluorine. At low temperatures the radiation of SF6 is stronger than that of nitrogen. When T>12000 K the net radiation of the mixture is not proportional to the net radiations of the gases owing to variations in emissivity and line broadening with temperature and composition of the mixture.

A Comparison of Experiment, CEPXS/ONETRAN, Tigerp, and Tiger Net Electron Emission Coefficients for Various Bremsstrahlung Spectra

This work compares a carefully designed experiment to measure photoemission with the predictions of three different codes (CEPXS/ONETRAN, TIGERP, and TIGER) for the complex bremsstrahlung spectra typical of very intense pulsed power x-ray generators. The Monte Carlo codes TIGER and TIGERP can calculate the net photon-induced electron emission but accurate results may require that statistical error be minimized. CEPXS/ONETRAN is a new deterministic coupled electron/photon transport code that is faster than Monte Carlo and is not subject to statistical error. The comparison of net yields is a sensitive test of the relative accuracy and efficiency of these various codes. We find that all of the codes substantially agree with the experiments for the forward net yields. However, for reverse net yields from high-Z materials, the codes overpredict relative to measurements.

A method for computing the radial temperature profiles in high-pressure, high-current arcs

A method is described for calculating the radial temperature profiles of wall-stabilised arcs in which the energy loss due to radiation is dominant. The radiative energy loss is evaluated using equations derived from the first two moments of the radiative transfer equation (i.e. the diffusion approximation). These equations are solved by the orthogonal collocation method to yield the radial distribution of the net emission coefficient. The nonlinear energy balance equation is then solved using a least-squares minimisation technique.

Theoretical predictions of ablation-stabilised arcs confined in cylindrical tubes

The properties of ablation-stabilised arcs confined in uniform cylinders, open at both ends, are calculated. It is assumed that the arc temperature is uniform with radius. The axial variations of the arc temperature, pressure, radius and plasma velocity are calculated as functions of current by solving the coupled equations of conservation of mass, momentum and energy. It is assumed that a specified fraction of the arc radiation is absorbed at the ablating cylinder wall and that the remainder is absorbed in the ablated vapour from the wall. Radiation losses from the arc are treated by assuming either (i) that the effective emission coefficients of the arc are proportional to pressure and that the arc radiation losses can be characterised by a net emission coefficient, or (ii) that the arc emits black-body radiation appropriate to the central temperature of the arc. For both approximations, detailed numerical solutions show that the arc temperature and radius are almost uniform with axial position. By assuming that the arc temperature and radius are indeed uniform, simple analytic formulae for arc temperature, pressure and Mach number are obtained. Comparisons between theoretical and experimental voltage-current characteristics show good agreement.

5043. A semi-empirical formula to describe the net emission coefficient of self-absorbed spectral lines for use in modelling high-pressure discharge lamps: B F Jones and D A J Mottram,J Phys D: Appl Phys,14 (7), 1981, 1183–1194

5043. A semi-empirical formula to describe the net emission coefficient of self-absorbed spectral lines for use in modelling high-pressure discharge lamps: B F Jones and D A J Mottram,J Phys D: Appl Phys,14 (7), 1981, 1183–1194

A semi-empirical formula to describe the net emission coefficient of self-absorbed spectral lines for use in modelling high-pressure discharge lamps

The net emission coefficient of a self-absorbed spectral line can be described by a semi-empirical formula which contains terms representing the generation and absorption of radiation. Four empirical constants are determined by applying least-squares fitting to the results of an exact radiation flux density calculation in a cylindrical arc tube. Calculations on the D-lines under conditions which are typical of high-pressure sodium lamps are described. In this case, the empirical formula predicts radiation flux densities which agree to better than 10% with the exact calculation even when the arc tube bore and arc temperature are changed by 15% from their original values. This method allows economical and accurate calculation of energy balances in arcs containing several self-absorbed spectral lines.

A radiation and convection model of the vertical mercury arc containing sodium and scandium iodides

A model has been developed for a multicomponent gas discharge containing several radiative species, Hg, I, Na, Sc, Sc+, and ScI, subject to radial and axial segregation. Net emission coefficients for self-absorbed radiation from these species are deduced individually and collectively from experiment and imprisonment theory. The vertical arc convection model has been modified to take into account the axial variation of material parameters with segregation and to calculate quartz wall temperatures. Calculated lamp parameters are found to be in reasonable agreement with experimental data.

Theoretical description of ac arcs in mercury and argon

The energy balance and circuit equations, together with Ohm’s law, are solved numerically to obtain temperature profiles, current, and voltage as functions of time for wall−stabilized ac arcs. Experimental measurements of current and voltage oscillograms and also temperature profiles have been made for 1.5− and 7.5−A rms arcs in mercury vapor. Derived net emission coefficients of radiation as a function of temperature for the 1.5− and 7.5−A arcs are consistent with one another; furthermore, the experimental temperature profiles for both arcs are in good agreement with our theoretical predictions. Theoretical current and voltage waveforms and central temperatures for a 20−A rms arc in argon are in good agreement with the experimental results of Detloff and Uhlenbusch. Radial convection has little influence on these results. An approximate criterion for arc extinction or reignition at current zero is given in terms of the steady−state V−I characteristic and the arc time constant. By relating the present analysis to methods using the Cassie−Francis and the Mayr equations, expressions are derived for the undetermined constants used in these equations for arcs dominated by thermal conduction losses.

Characteristics of Radiation-Dominated Electric Arcs

Temperature profiles of arcs when radiation is the principal energy transfer process have been derived from material functions. Arcs which are optically thin are approximately isothermal or constricted depending on whether εN/σ is an increasing or decreasing function of temperature; εN is the net emission coefficient and σ the electrical conductivity. Arcs which are optically thick have a temperature profile similar to conduction dominated arcs. Theoretically predicted examples of these three types of arcs are a 2000-A arc at 30 atm in air, a low current arc in the vapor of a rare-earth metal at 20 Torr, and a 4000-A arc at 1000 atm in air. For arcs which are nearly isothermal, it is possible at any value of current and radius to make approximate calculations of (1) the temperature of the arc core, (2) the electric field strength, (3) the thickness of the outer arc sheath, and (4) the fraction of the input energy carried to the wall by conduction. Such calculations are made for arcs in air and are compared with the results of exact calculations which take into account the details of the self-absorption of radiation. Approximate calculations show that when εN/σ has a maximum as a function of temperature, multiple solutions for the temperature profile are possible for some values of arc current and radius.