Numerical investigation of dynamic behavior of metal Pb driven by oblique shock waves
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摘要: 高强度冲击加载作用下金属材料的动态物理行为是当前冲击波领域基础研究和工程应用最为关注的焦点。采用光滑粒子法(SPH)开展不同位置起爆诱发的斜冲击波对碰加载金属铅的二维数值模拟研究，得到了金属铅内入射斜冲击波的角度和强度，并利用极曲线方法理论上导出发生马赫反射时的临界入射角和入射马赫数关系。根据计算结果可知，金属铅内入射斜波对碰后将发生马赫反射。随着起爆位置与金属铅表面距离的增加，不仅金属铅内入射冲击波强度和入射角增加，而且形成的马赫杆宽度也在增加。由自由面速度剖面给出了马赫杆宽度及张角，结果与理论预测的结果吻合较好。Abstract: Dynamic behaviors of metal materials subjected to intense shock loading is presently a focus in basic research and engineering application in the field of shock wave study. This work investigated dynamic behaviors within the metal Pb loaded by two oblique shock waves via Smooth Particle Hydro dynamic (SPH) method, with an emphasis on the influence of different initiation points on the dynamic behaviors in the collision zone. Utilizing the shock polar theory, we obtained the critical angle for an incident oblique shock wave varying with the Mach number, which indicated a transition from regular to Mach reflection. The comparison of the numerical data with the theoretical plot confirmed the interaction of two oblique shock waves, thus essentially revealing the Mach reflection and the formation of the Mach stem. As the distance of the initiation point from the Pb surface increases, so do both the incident pressure and the angle for an oblique shock wave, including also the generated Mach stem. Based on the free surface velocity profiles, we calculated the width of the Mach stem and the Mach angle, the results being in good agreement with the theoretical prediction.
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Key words:
- Pb /
- collide /
- Mach reflection /
- oblique shock wave
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图 4 入射斜冲击波在铅内的相互作用
Figure 4. Interaction of incident oblique shock wave within the metal Pb
图 5 理论计算的入射斜波临界角αC与马赫数Ma0关系与数值模拟对比
Figure 5. Comparison of theoretical relationship of incident angle αC varying with Mach number Ma0 and numerical simulations
图 6 金属铅内呈现的入射波、反射波和马赫波示意图
Figure 6. Schematic illustration of incident, reflected and Mach shock waves within the metal
图 7 金属铅内具有相同纵坐标值标定点压力历史剖面
Figure 7. Pressure histories for the gauge points with the same longitudinal coordinates
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