Modelling of shock wave generation in water by electrical discharges

Over the past decade, several groups have used electrically-produce shocks in water as a means of rock fragmentation. Such experiments involve producing an electrical discharge in a water-filled cavity drilled in the rock. The authors have performed one- and two-dimensional hydrodynamic simulations for studying shock production in water, for some geometries of interest. A tabulated equation-of-state for water has been used. Two different power levels have been examined. In the first, experimentally measured current and voltage waveforms have been used to generate the electrical power vs. time waveform. In the second, the same waveform is used, but the pulse is compressed by a large factor. The power deposition profile, Q(r, t), which depends upon are dynamics, has been represented by a functional form relevant to the problem of interest. For a 1-D axisymmetric cylinder problem, the authors assume Q(r, t)=Q/sub 0/(t) (1-r/sup 2//a/sup 2/)/sup /spl alpha// where 0/spl les/r/spl les/a, a is the radius of the cavity and r is the radial distance from the axis of the cylinder. Higher a corresponds to a more peaked profile about the center. They have studied the effect of varying /spl alpha/, and the average power level, on the cavity surface pressure P/sub s/(t). With a long-duration electrical pulse, the pressure profile inside the cavity tends to be nearly uniform at the end-of-pulse, regardless of /spl alpha/. Interestingly, the general pressure level rises with the "peakedness" of Q(r). This means that for the same water mass, and the same energy input, they could generate higher pressure levels with more peaked profiles. This can be explained in terms of the equation-of-state; to achieve a given pressure, it is energetically cheaper to compress water than to heat it. Conversely, a required pressure level could be achieved with lesser electrical energy by depositing energy closer to the center. This should help in minimizing the electrical energy requirement for a given application.