Stability of imploding shocks generated by underwater electrical explosion of cylindrical wire array

Abstract

The results of two-dimensional hydrodynamic simulations of the dynamics and stability of azimuthal non-uniformities in converging shock waves generated by an underwater explosion of a cylindrical wire array and their effect on the cumulation of energy in the vicinity of the converging axis are presented. It has been shown that in spite of the fact that such non-uniformities are always weakly unstable, for a broad range of experimentally relevant regimes these non-uniformities remain small and do not significantly affect the cumulation of energy. Only the non-uniformities with wavelengths comparable to the distance from the axis of convergence exhibit substantial growth that considerably attenuates the energy cumulation. V

Spectroscopy of a plasma formed in the vicinity of implosion of the shock wave generated by underwater electrical explosion of spherical wire array

“…Nevertheless, in experiments with the explosion of a 5 mm in radius cylindrical wire array, azimuthal symmetry of converging SW down to a radius r % 100 lm was obtained by shadow imaging. In addition, the results of spectroscopy of the plasma formed inside a copper capillary placed coaxially inside the array indicate the axial and azimuthal symmetry of the cylindrical converging SW. 19 Recently, the results of two-dimensional HD simulations 23 showed that artificially introduced non-uniformity of the cylindrical converging SW should be self-repaired, which agrees with the Whitham model. 24 Self-similar analysis of the converging SW implosion 17 showed that the pressure p behind the SW front located at the radius r can be calculated at instant t as p ¼ p o ðr=r o Þ 2À2=a , where p 0 and r 0 are the pressure and radius, respectively, at some previous instant t 0 < t, and a is the self-similarity parameter that equals 0.75 and 0.6 for cylindrical and spherical SWs, respectively.…”

Shock wave convergence in water with parabolic wall boundaries

“…16 was used. The simulation is based on the finite volume method and uses conservation laws of mass, energy, and momentum coupled with the equations of state (EOS) of water and copper.…”

Uniformity of cylindrical imploding underwater shockwaves at very small radii

“…The pressure of water at that location was calculated using a 2D HD simulation coupled with EOSs of water and copper. These simulations, based on the cell-centered finite volume method and three conservation laws (mass, momentum, and energy), are described in detail by Kozlov et al 16 The results of these simulations are shown in Fig. 6.…”

“…[13][14][15] Also, the SSW's time-of-flight to the axis (cylindrical wire array) or origin (spherical wire array) of implosion leading to intense light emission from compressed and heated water at those locations was used for comparison with the results of one dimensional (1D) and two dimensional (2D) Hydrodynamic (HD) simulations, coupled with the EOS of water and copper. 16 In these simulations, which considered symmetrical SSW convergence, only the energy deposition rate into the wires, calculated using the experimentally obtained resistive voltage and discharge current waveforms, was an input parameter.…”