Simulation of the hydrodynamic expansion following a nanosecond pulsed spark discharge in air at atmospheric pressure

This paper presents 2D simulations of the dynamics of formation of a nanosecond spark discharge between two point electrodes in air at atmospheric pressure at 300 and 1000 K, the induced air heating and the following hydrodynamic expansion. As a first step, we have considered that 30% of the discharge energy instantaneously heats the ambient air. At the end of the voltage pulse, it is shown that the energy density and the air temperature distributions are non-uniform in the interelectrode gap. Rapidly after the nanosecond voltage pulse, a cylindrical shock wave is formed and propagates with a velocity very close to the speed of sound of the surrounding ambient air. Furthermore, the rapid dilatation of the hot channel formed on the discharge path is observed for t 1 s, as in experiments. Then we have carried out a parametric study on the influence of the value of the fraction of discharge energy going to fast heating on the hydrodynamic expansion at 1000 K, assuming an instantaneously fast gas heating. For all values in the range of 15% to 60% studied in this work, we have observed a very similar gas dynamics. Then, we have considered that the nanosecond spark discharge heats the ambient air at 1000 K with a longer relaxation time of 1 s, and in this case we have observed the propagation of a weak pressure wave and no dilatation of the hot channel on the discharge path. Finally, the comparison with experiments seems to validate the hypothesis that the 10 ns spark discharges studied in this work at 300 and 1000 K, significantly heat the ambient air on very short time-scales.