Empirical Model of Plane Shock Wave on the Impact Surfaceof Target Based on Dimensional Analysis
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摘要: 当飞片或靶板材料的冲击雨贡纽参数未知时,根据现有靶板撞击面冲击波压力的理论模型无法对其冲击波压力峰值和脉冲宽度进行准确预估。针对该问题,基于相似理论,对影响冲击波压力峰值和脉冲宽度的因素进行量纲分析,分别建立了冲击波压力峰值和脉冲宽度的经验模型,且模型中各项均有明确的物理意义。通过实例分析,获得了不同飞片厚度和冲击速度下,45钢冲击纯镍产生的平面冲击波的经验模型定量关系式,模型预测结果与实验测量值较为吻合。Abstract: When the equation of state (EOS) and physical parameters of the projectile and the target plate materials are unknown, it is impossible to estimate accurately the peak value and the pulse width of the shock wave pressure on the impacting surface based on the existing theoretical models.To solve this problem, using the dimensional analysis, we studied the factors influencing the peak value and the pulse width of the shock wave pressure, and established an empirical model of the peak value, and that of the pulse width of the shock wave pressure respectively, with a clear physical meaning specified for each component in the formulas.This kind of model successfully avoided the problem of unknown EOS of the projectile and target materials.The obtained formulas can be used to predict the peak value and the pulse width of the shock wave pressure.We applied this model to an actual experiment of 45 steel impacting on a Ni plate, and found that the peak values and the pulse widths of the shock wave pressure calculated by this model match well with the measured results, which proves the feasibility of our model.
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Key words:
- plane shock wave /
- peak pressure /
- pulse width /
- dimensional analysis /
- empirical model
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表 1 相应物理量的量纲
Table 1. Dimensions of the corresponding physical quantities
Physical quantities Dimension index M L T pm 1 -1 -2 τ 0 0 1 L 0 1 0 D 0 1 0 ρ01 1 -3 0 C01 0 1 -1 ρ02 1 -3 0 C02 0 1 -1 v 0 1 -1 表 2 相似比求解
Table 2. Solution of similar ratio
π term x4 x5 x6 x7 x8 x9 x1 x2 x3 π1 1 0 0 0 0 0 0 0 -1 π2 0 1 0 0 0 0 -1 -2 2 π3 0 0 1 0 0 0 0 1 -1 π4 0 0 0 1 0 0 -1 -2 2 π5 0 0 0 0 1 0 0 1 -1 π6 0 0 0 0 0 1 0 1 -1 表 3 实验数据
Table 3. Experimental data
Exp. No. L/(cm) v/(km/s) pm/(GPa) τ/(μs) 1 0.3 0.334 7.39 0.960 0 2 0.3 0.711 14.52 0.900 0 3 0.3 0.977 19.12 0.879 0 4 0.5 0.449 7.75 2.680 0 5 0.3 0.461 8.50 0.925 0 6 0.4 0.464 8.75 1.900 0 表 4 压力峰值和脉冲宽度的实测值与模型预测值的对比结果
Table 4. Comparison of the measured values of peak pressure and pulse widthwith those predicted by this model
L/(cm) v/(km/s) pm/(GPa) τ/(μs) pm, j/(GPa) τj/(μs) $\left| {\frac{{{p_{\rm{m}}} - {p_{{\rm{m, j}}}}}}{{{p_{\rm{m}}}}}} \right|/\left( \% \right)$ $\left| {\frac{{\tau - {\tau _{\rm{j}}}}}{\tau }} \right|/\left( \% \right)$ 0.3 0.461 8.50 0.925 0 9.19 0.934 2 8.12 9.95 0.4 0.464 8.75 1.900 0 9.24 1.688 2 5.60 11.15 Note:pm, j and τj are the predicted values of peak pressure (pm) and pulse width (τ), respectively. -
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