Numerical model for electrical explosion of copper wires in water

Abstract

This paper presents a simple but quite accurate numerical model for analyzing electrical explosion of copper wires in water. The numerical model solves a circuit equation coupled with one-dimensional magneto-hydrodynamic (MHD) equations with the help of appropriate wide-range equation of state (EOS) and electrical conductivity for copper. The MHD equations are formulated in a Lagrangian form to identify the interface between the wire and surrounding water clearly. A quotidian EOS (QEOS) that is known as the simplest form of EOS is utilized to build wide-range EOS for copper. In the QEOS, we consider the liquid-vapor phase transition, which is critical in analyzing the wire explosion system. For the electrical conductivity of copper, a semi-empirical set of equations covering from solid state to partially ionized plasma state are employed. Experimental validation has been performed with copper wires of various diameters, which are exploded by a microsecond timescale pulsed capacitive discharge. The simulation results show excellent agreements with the experimental results in terms of temporal motions of a plasma channel boundary and a shock front as well as current and voltage waveforms. It is found that the wire explodes (vaporizes) along the liquid branch of a binodal curve irrespective of wire dimension and operating voltage. After the explosion, the wire becomes a plasma state right away or after the current pause (dwell), depending on the operating conditions. It is worth noting that such a peculiar characteristic of wire explosion, i.e., current pause and restrike, is well simulated with the present numerical model. In particular, it is shown that the wire cools down along the vapor branch of the binodal curve during the current dwell, due to a significant difference of thermodynamic characteristics across the binodal curve. The influence of radiation for studying nonideal plasmas with a wire explosion technique and a physical process for shock wave formation by an exploding wire is discussed as well.