不同状态方程对固体介质中斜激波反射的影响

相比气体,固体介质在高压下的状态方程更为复杂,形式也多种多样.现有关于固体介质中激波反射的理论研究,一般直接采用某种状态方程,缺乏对采用不同状态方程得到的结果的对比.本项工作采用激波极曲线的理论分析方法,选择4种不同组合形式的状态方程(一次冲击激波采用线性的冲击波速度与粒子速度关系式,二次冲击激波采用Gr(u|¨)neisen状态方程;一次冲击和二次冲击激波均采用冲击波速度与粒子速度关系式:一次冲击激波采用线性冲击波速度与粒子速度关系式,二次冲击激波采用刚性气体状态方程;以及一次冲击激波和二次冲击激波均采用刚性气体状态方程),研究固体介质中的斜激波反射,比较了采用不同组合形式的状态方程对反射激波波后压力的影响.利用量纲分析方法讨论了简化状态方程达到较高精度的条件.此外,用ANSYS/LS-DYNA软件,对激波极曲线理论给出的结果进行了验证.本项工作可为固体介质中激波反射问题状态方程的选取提供一定的指导.

EFFECTS OF DIFFERENT EQUATIONS OF STATE ON THE OBLIQUE SHOCK WAVE REFLECTION IN SOLIDS

The equations of state of solids under high pressure are more complicated than that of gases in a variety of forms. While the existing investigations on the oblique shock wave reflection usually take one of the equations of state, lacking of the comparisons among them. Therefore, this paper aims at the oblique shock wave reflection in solids through shock polar methodology under four different forms of equations of state (principal shock taking with linear shock–particle velocity relationship and second shock taking with Gr ¨uneisen equation of state, principal and second shock both taking with shock–particle velocity relationship, principal shock taking with linear shock–particle velocity relationship and second shock taking with stiffened gas equation of state, and principal and second shock both taking with stiffened gas equation of state). The effects of different equations of state on the pressure behind the reflected shock wave are discussed. By conducting the dimensional analysis, we provide an applicable condition for employing a simplified equation of state to achieve high accuracy. Moreover, numerical simulations performed by ANSYS/LS-DYNA software are conducted to validate the results through shock polar methodology. The results of this paper could be helpful for the decision of the equation of state on the oblique shock wave reflection in solids.