Electric-discharge excited blast waves in a flat subsonic nozzle

Abstract

The persistence of pressure waves generated by an electric discharge in the throat of a subsonic nozzle is studied analytically and numerically with particular reference to the operation of the high-power EUREKA excimer laser under construction at the national Italian ENEA Frascati laboratories. The attention is focused on transverse waves traveling parallel to the discharge electrodes. After some analytical estimates, a quasi-twodimensional numerical simulation is presented of the propagation of these waves in the anticipated geometry of the discharge chamber of the EUREKA laser. The possibility of reflection of pressure waves on the thermal slug left behind by the previous discharge is also considered. N a high-power, high-repetition-rate excimer laser, gas flows at a subsonic speed through a nozzle of elongated cross section in the throat of which an electric discharge is periodically fired with a repetition rate of the order of 1 kHz. Only about 1% of the energy released by the discharge is usefully converted into electromagnetic waves in the laser cavity positioned at the throat of the nozzle. All of the remaining energy instantaneously heats up the gas, with respect to the propagation time of sound, and produces blast waves that, if still present in the discharge chamber when the next pulse fires, may cause instability of the following discharges. A one-dimensional picture of the phenomenon is shown in Fig. 1. The initial instantaneous temperature and pressure increase subsequently divides up into three waves: an entropy wave (the thermal slug), which travels with the main flow velocity and forward and backward pressure waves with velocity V + a and V — a, respectively (a being the speed of sound). In the simplified one-dimensional situation depicted in Fig. 1, these waves propagate out and do not interfere with following discharges if only enough time is allowed for all three waves to abandon the discharge volume. Provided that V<a/2, the slowest wave is the entropy wave; therefore, this criterion may be expressed figuratively by saying that the gas where one discharge has occurred must be washed out of the discharge volume before another discharge may be fired. However, various circumstances may disrupt such an ideal behavior: 1) If the pressure waves are strong enough to behave as shock waves, the entropy change through the backward wave may change the thermodynamical state of the gas arriving at the discharge section. 2) Obstacles or bends in the feed and exhaust ducts may reflect the waves back onto the discharge section. 3) Transverse waves, propagating at an angle with respect to the flow direction, may be excited by disuniformities in the discharge and come back on reflection by the lateral walls. Problem 1 is not a major concern for the typical energy release during a discharge of the order of 50 -s-100 J/l under a gas pressure of the order of some atmospheres. The shock strength can be calculated from the equation of state of an ideal gas to be given by