水中金属丝电爆炸动力学过程的零维模型

金属丝电爆炸包含丰富的物理内容，近年来国内的实验和理论研究取得了重要进展，理解该过程有助于完善Z箍缩及磁加载等离子体动力学过程的物理建模，校验物性参数。在自相似运动假设条件下，发展了冷启动计算的水中电爆炸丝零维动力学模型。从一维磁流体模型出发，推导了描述丝等离子体膨胀的零维动能方程和内能方程，采用实际气体状态方程和修正的李-莫尔电导率参数作为封闭条件，根据质量守恒及水中激波雨贡纽关系式获得了丝等离子体的边界条件。应用于水中铜丝电爆炸动力学过程和能量转化分析，结果表明：该零维模型的物理假设合理，在一定范围内改变丝直径等参数可产生不同的放电模式，与一维模型及实验结果符合较好，能够为同类实验的优化设计和数据分析提供参考。

Zero-dimensional modeling of the underwater electrical explosion of wires

The physical mechanism of electrically exploding wires has caused much attention recently; fruitful experimental results have been reported by domestic researchers. Modeling and studying of the electrical metal wire explosion problems can help to understand the basic physics of Z pinches and other related magnetically driven plasma problems, and to evaluate the parameters of the state equation and electrical conductivity. A zero-dimensional (0D) dynamical model of the underwater electrical wire explosion is developed, in which the single wire is modeled as a plasma cylinder undergoing self-similar radial motion with uniform density, temperature and pressure, while its velocity varies linearly with radius. The kinetic equation and internal energy equation are derived from the hydrodynamic equations and used as the basic governing equations. To close the 0D model, other parameters are supplemented, with the real gas quotidian equation of state (QEOS) model for pressure and internal energy, the modified Lee-More electrical conductivity model for resistivity, and an external circuit model for the current density. The boundary conditions are constructed from the shock Hugoniot relations in water, the pressure at the wire boundary is assumed to be equal to the water pressure behind the shock. The calculations are carried out from a cold start of wires with density and temperature in laboratory status. Results of the 0D model are validated by comparing with the results from simulations of one-dimensional (1D) magneto-hydrodynamic (MHD) model and experiments. Examples of electrical explosion of copper wires in water are taken in the applications, the rise time of the short-circuit current pulse is 5 μs and the wires vary from 50 μm to 200 μm in diameter. Results from the 0D-dynamical model agree well with the MHD simulation results and experimental data, typical discharging modes are achieved by varying the parameters of the wires. The 0D model can be used for parameters optimizing and data analysis in similar experiments.