Energy transfer processes in a partially ionized gas
The following paper is divided into three more or less separate sections. The first section (Chapters II - VI) deals with an analysis of the transport properties of a partially ionized gas subject to the constraint that the average random energy of all constituent particles is exactly equal (equipar...
| Summary: | The following paper is divided into three more or less separate sections. The first section (Chapters II - VI) deals with an analysis of the transport properties of a partially ionized gas subject to the constraint that the average random energy of all constituent particles is exactly equal (equipartition of energy). This constraint is necessary so that the formal Chapman-Enskog solution of Boltzman's equation can be used to evaluate the various transport coefficients. Subject to this constraint, a set of tractable equations describing the mass and energy diffusion in a partially ionized gas is obtained that includes all terms correct to the order of the square root of the ratio of the electron to atom mass compared to one. The transport coefficients are evaluated for helium and argon over the complete range of partial ionization assuming that the species particle densities are quite close to their equilibrium values.
The analysis indicates that the electron and ion diffusion velocities are more closely coupled than the equations of Chapman and Cowling show. The added coupling implicitly applies the constraint of zero mass velocity to the gas locally. Because of this constraint a current in the direction of (E x B) x B occurs in addition to the direct and Hall currents.
It is shown that the only part of the thermal conductivity that can be influenced by a magnetic field is that part of the energy carried by the diffusion of the charged particles. For this reason, magnetic fields, in general, cannot be nearly as effective in reducing heat transfer rates as was previously thought, e. g., a magnetic field will have no influence on the thermal conductivity in a fully ionized gas, except through its influence on the current density and the thermal diffusion.
Chapters VII - IX comprise the second section of this paper and deal with the development of a similarity solution for axially symmetric electric discharges. A number of parameters are obtained and discussed. The solution is evaluated for a discharge in argon gas at one atmosphere pressure in which the temperature on the axis of the discharge varies from 6,000°K to 19,000°K. The current-voltage characteristic obtained from this solution is compared with an experimentally determined curve of H. Maecker.
The third section of this paper (Chapters X - XIII) is concerned with the mechanisms of energy transfer in arc jet devices. Use is made of the previous sections of the paper to determine the relative magnitude of the amount of energy that is transferred to the gas in the various parts of the electric discharge. The various possible electrode configurations are discussed in detail and compared. The design and performance of an annular electrode arc heater with a rotating arc is next described and discussed. Because of a number of undesirable performance characteristics of this type of electrode configuration, a modified heater was constructed with the cathode emission occurring along the axis of the applied magnetic field. Details of the unexpectedly good performance of this configuration are given. It is shown that the arc potential drop depends primarily on the strength of the applied magnetic field and the gas enthalpy downstream of the arc. The dependence of the arc potential drop on the arc current and the ambient pressure is shown to be weak over the ranges tested, e. g., 50 to 300 amperes for the current and 1 to 4 atmospheres for the pressure. Some heat transfer measurements taken with this equipment are presented.
Appendix I is concerned with the evaluation of the transport coefficients in a partially ionized gas. Formulae are developed for determining the viscosity, thermal conductivity, and electric conductivity of the plasma. These coefficients are computed for argon and helium at one atmosphere pressure and over the temperature range of partial ionization.
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