The determination of arc temperatures from shock velocities

Abstract

The measurement of the high gas temperatures associated with arc discharges requires special techniques. One such method, developed by Suits (1935), depends on the measure­ment of the velocity of a sound wave passing through an arc column, although in fact Suits measured the velocity of a very weak shock wave. The new method described in the present paper is one in which temperatures are determined from the measurement of the velocity of a relatively strong shock wave propagated through an arc. The new method has the merit of consistently producing accurately measurable records and of increasing the accuracy of the temperature determination. The shock velocities are measured by means of a rotating mirror camera. Within the arc, the shock propagation is observable by virtue of the increased arc brightness produced by the shock. In the non-luminous regions surrounding the arc, the shock propagation is displayed by means of a Schlieren system. The interpretation of the measurements depends upon a one-dimensional analysis given in this paper which is similar to that of Chisnell (1955) and which describes the interaction of a plane shock with a con­tinuously varying temperature distribution. In our analysis account is taken also of the continuous variation in specific heats and molecular weight which are of importance under high gas temperature conditions. In practice plane wave theory cannot adequately describe the shock propagation, since attenuation occurs both in the free gas and in the arc column. The effects of this attenuation on the temperature determinations may be accounted for by the use of an experimentally determined attenuation relationship given in the paper. The finally developed method yields temperature values to an accuracy of ± 2%. Experiments are described for carbon and tungsten arcs in air and nitrogen for currents up to 55 amperes and pressures up to 3 atmospheres. The values obtained range from 6200 to 7700° K and are in good agreement with values determined by other techniques.