Modeling of shock-wave generation in water by electrical discharges

Abstract

We have performed one- (1-D) and two-dimensional (2-D) hydrodynamic simulations for studying shock production in water for two geometries of interest in rock fragmentation. Two-dimensional simulations have been performed for parameters similar to those in Pronko et al.'s work (1993) and in Nantel and Kitzinger's work (1990). These simulations, using realistic equations of state for water and the electrode material, yield pressures in the same range as experimentally reported values. With some improvements, the code could be used for optimization of such experiments. One-dimensional simulations have been performed for an axisymmetric cylinder configuration similar to that in Weise and Loffler's work (1993). Two different power levels have been examined. The spatial profile of power deposition in water Q(r) is represented by a functional form relevant to the problem of interest. With a long-duration electrical pulse, the pressure profile inside the cavity is nearly uniform at the end-of-pulse, regardless of the deposition profile. The general pressure level rises with the "peakedness" of Q(r). This means that for the same water mass and for the same energy input, we could generate higher pressures with more peaked profiles. Conversely, a required pressure level could be achieved with lesser electrical energy by depositing energy closer to the cylinder axis. This should help in minimizing the electrical energy requirement for a given application.