Hydrodynamic shock wave propagation after electrical breakdown

Abstract

Laser schlieren measurements in liquid dielectrics have been used to examine the radial expansion of both the acoustic shock wave and the conductive breakdown channel during the first few microseconds after electrical breakdown under high voltage impulse conditions. It was found that the acoustic shock wave expands at a constant velocity while the expanding radius of the breakdown channel is proportional to the fourth root of the energy and the square root of time. These dependencies are predicted by modeling the breakdown channel as an expanding adiabatic ideal gas with an instantaneous input of energy. The Rankine-Hugoniot boundary conditions in the strong shock limit are used to relate discontinuities in velocity, pressure, and mass density across the cylindrical shock front using the same analysis which was used previously to describe exploding wires in air. When the expansion velocity of the gas column decreases below the acoustic wave velocity in the liquids, an acoustic wave propagates ahead of the electrohydrodynamic shock.