基于LS-DYNA的液电效应冲击波数值模拟

液电效应机理复杂，鲜有成熟的商用数值模拟软件能够描述等离子体通道内部特性，为了将液电效应产生的冲击波运用于已有的数值模拟软件中，以满足工程需要，介绍了两种基于显式动力学软件LS-DYNA间接模拟液电效应产生冲击波的方法:水下爆炸等效（分为爆炸能量等效与冲击波能量等效）和理想气体等效，并进行了比较与改进，分析了不同沉积能量下采用不同等效方法得到的峰压计算结果的差异。结果显示，在沉积能量相同的条件下，基于爆炸能量等效方法得到的冲击波峰值压力最高，基于冲击波能量等效方法得到的冲击波峰值压力次之，基于理想气体等效方法得到的冲击波峰值压力最低，理想气体等效模拟的峰压相较于前两种等效方法小1～2个数量级；爆炸能量等效与冲击波能量等效的冲击波波速相等，且高于理想气体等效的冲击波波速；沉积能量减小会使得3种等效方法模拟的峰压均有不同程度的减小，但大小顺序不发生变化；改进后的等效爆炸方法能够适应沉积能量的变化，与Touya经验公式拟合较好；基于LS-DYNA对液电效应冲击波峰值压力进行准确模拟，除了选取适合的等效方法，还应结合具体的放电条件，建立适当的数值模型，在满足计算要求的条件下实现冲击波峰值压力的快速计算。

Numerical simulation of the shock wave generated by electro-hydraulic effect based on LS-DYNA

Due to the complexity of the mechanism of the electro-hydraulic effect, few commercial numerical simulation software can describe the internal characteristics of the plasma channel. In order to apply shock waves generated by hydro-electric effects to the existing numerical simulation software to meet the needs of engineering applications, in this paper, two methods based on LS-DYNA were introduced to simulate indirectly the shock wave generated by the electro-hydraulic effect, i.e. Underwater explosion equivalence (including explosion energy equivalence and shock wave energy equivalence) and ideal gas equivalence. Explosion energy equivalence is mainly based on the principle that the deposited energy injected into the plasma channel is equal to the combustion energy of the explosive. Shock wave energy equivalence is mainly based on the principle that the shock wave energy generated by an explosion is equal to that generated by the hydro-electric effect. However, ideal gas equivalence method is different from underwater explosion equivalence. Adopting ideal gas equivalence method, the plasma channel is regarded as an adiabatic expansion ideal gas, and the pressure in the plasma channel is characterized by the relevant keywords in LS-DYNA. In addition, the peak pressure of the shock wave generated by various methods was compared, and underwater explosion equivalence was improved based on the empirical formula of an underwater explosion and the empirical formula of the hydro-electric effect. Moreover, the difference in peak pressure based on different equivalence methods under different deposition energies was analyzed. The results show that the peak pressure of shock wave calculated by three different equivalent methods is different. The peak pressure based on the explosion energy equivalence method is the highest, The peak pressure based on the explosion energy equivalence method is medium, and the peak pressure based on the explosion energy equivalence method is the lowest. The peak pressure based on the ideal gas equivalence method is one to two orders of magnitude less than that based on the former two methods. The shock wave velocity based on the explosion energy equivalence method is equal to that based on the shock wave energy equivalence method, and higher than that based on ideal gas equivalence method.With the decrease of the deposited energy, the peak pressures based on the three equivalence methods all decrease in varying degrees, however, the order of the peak pressure does not change. The improved method for underwater explosion equivalence can simulate the peak pressure of the shock wave more accurately at different deposited energies, and the peak pressure fits well with the Touya empirical formula. In order to simulate accurately the peak pressure of the shock wave based on LS-DYNA, in addition to selecting the appropriate equivalence method, we should also combine the specific discharge conditions and establish an appropriate numerical model to realize the rapid calculation of the peak pressure under the conditions satisfying the calculation requirements.