In this paper a two‐temperature model (Te >Th) is applied to a free‐burning, high‐intensity, atmospheric pressure argon arc. With appropriate boundary conditions and nonequilibrium thermodynamic and transport properties, solutions of the conservation equations are obtained for the entire arc, except for the electrode sheath regions. Significant temperature discrepancies between electrons and heavy particles are found in the arc fringes. The elevated electron temperatures in the arc fringes lead to a rearrangement of the current density distribution which, in turn, has some effect on the temperature as well as on the velocity field in the arc core. Comparisons of the results of this study with spectrometric temperature measurements show better agreement than with results based on a one‐temperature model.

Two‐temperature modeling of the free‐burning, high‐intensity arc

Chapter 5 – Electric Arcs and Arc Gas Heaters

Progress in the physics of high-power arcs has been largely due to a blend of detailed experimental and theoretical investigations aimed at explaining the electrical behaviour of the discharge in terms of fundamental physical processes. In the case of collision-dominated, high-pressure arcs the important role of radiative energy transfer, including strong self-absorption, has been established through the experimental and theoretical study of cylindrically symmetric, uncontaminated arc plasmas. As a result, an insight has been gained into the additional complications produced in naturally occurring high-pressure arcs by electrode vapour contamination and self-magnetically-propelled plasma flows. The application of similarity theory based upon the conservation equations of fluid mechanics has produced good correlation of the properties of arcs in transverse flows and magnetic fields under a number of different operating conditions. Criteria defining stable arc operation have been derived using stability theory whilst axisymmetric instabilities of arcs in accelerating flows have been related to vortex production at the arc boundary.

http://iopscience.iop.org/article/10.1088/0034-4885/43/12/002/pdf

The physics of high-power arcs

Multi-temperature thermal plasmas have often to be considered to account for the nonequilibrium effects. Recently Andre et al. have developed the calculation of concentrations in a multi-temperature plasma by artificially separating the partition functions into a product by assuming that the excitation energies are those of the lower levels (electronic, vibration, and rotation). However, at equilibrium, differences, increasing with temperature, can be observed between partition functions calculated rigorously and with their method. This paper presents a modified method where it has been assumed that the preponderant rotational energy is that of the vibrational level v=0 of the ground electronic state and the preponderant vibrational energy is that of the ground electronic state. The internal partition function can then be expressed as a product of series expressions. At equilibrium for N
2
and N

 2
 +
 
partition functions the values calculated with our method differ by less than 0.1% from those calculated rigorously. The calculation has been limited to three temperatures: heavy species Th
, electrons Te
, and vibrational T
v
temperatures. The plasma composition has been calculated by minimizing the Gibbs free enthalpy with the steepest descent numerical technique. The nonequilibrium properties have been calculated using the method of Devoto, modified by Bonnefoi and Aubreton. The ratio θ=Te/Th
was varied between 1 and 2 as well as the ratio θ
 v
 =T
 v
 /T
 h
 
for a nitrogen plasma. At equilibrium the corresponding equilibrium transport properties of Ar and N
2
are in good agreement with those of Devoto and Murphy except for T>10,000 K where we used a different interaction potential for N–N
+
. The effects of θv
and θe
on thermodynamic and transport properties of N
2
are then discussed.

New method to calculate thermodynamic and transport properties of a multi-temperature plasma : application to n2 plasma

The use of the multitemperature Saha equation (MSE) of Prigogine1 and Patapov2 for calculating particle concentrations in plasmas is shown to be an invalid procedure. Errors greater than one order of magnitude in the electron density in high‐pressure argon and nitrogen electric arc plasmas can be easily incurred by using the multitemperature Saha equation. The alternative kinetic method for calculating concentrations is shown to be based on firm concepts. Simpliying procedures and computational techniques for calculating concentrations with the kinetic method are illustrated with examples.

On the determination of particle concentrations in multitemperature plasmas

The nonequilibrium behavior of argon and helium confined‐arc plasmas at atmospheric pressure is analyzed in terms of a two‐temperature ambipolar‐diffusion model. Examination of spectroscopic data for the nonquilibrium arc shows that the free and bound electrons are mutually in equilibrium at a common electron temperature but not in equilibrium with the translational degrees of freedom of the heavy particles; the electron density in the outer portions of the arc may be as much as several orders of magnitude greater than its local thermodynamic‐equilibrium value. Integration of the electron continuity equation and the electron and heavy‐particle energy equations, with calculated transport properties and recombination coefficients, yields a satisfactory comparison with the measurements.

Nonequilibrium in Confined‐Arc Plasmas

An experimental study of subsonic Hartmann channel flow of a plasma is described. A partially ionized gas, consisting of high‐temperature atmospheric‐pressure potassium‐seeded combustion products, was passed through an insulated rectangular channel in the presence of a transverse magnetic field. The influence of the electrical‐conductivity profile within the plasma was studied by systematically varying the wall temperature with respect to the mean plasma temperature. The effect of the magnetic field was found to be sensitive to this temperature difference. Only situations where the wall temperature is less than the mean plasma temperature have been investigated. With wall temperatures several hundred degrees below the mean plasma temperature, an increase in wall‐shear stress of about 30% is observed, as compared with a factor‐of‐2 increase found in the corresponding uniform conductivity, liquid metal experiments. The experimental data for laminar flow agree well with the results of an approximate analysis. Turbulence‐damping effects, Hall‐parameter effects and fluid‐property‐variation effects are discussed. The turbulence‐damping effect is smaller in the present experiments than in the mercury‐flow experiments. No pressure gradients were observed in the u × B direction. A complete correlation of the data is proposed.

Charles H. Kruger

Papers

Nonequilibrium in Confined‐Arc Plasmas

Experiments on Hartmann Channel Flow in Plasmas