Numerical modeling and application of shock wave of free-field air explosion
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摘要: 为建立描述任意时刻、距离下空气自由场爆炸波冲击波压力、密度、粒子速度的经验公式，支撑复杂场景下冲击波载荷的快速计算，采用一维精细数值模拟的方法计算了不同比例距离下的压力、密度、粒子速度时程，并利用曲线拟合方法得到了正相超压峰值等22个冲击波参数与比例距离关系的经验公式，采用改进修正Friedlander方程建立了冲击波压力、密度、粒子速度随时间变化的关系式；利用爆炸冲击波地面反射和建筑后绕射两个典型工况，阐释了提出模型的应用场景，并与试验、数值模拟结果对比。结果表明：压力、密度、粒子速度随比例距离、时间变化的经验关系与数值模拟结果基本吻合；爆炸冲击波地面反射和建筑后绕射两个典型工况下，理论计算与数值模拟的压力云图基本吻合，在相同硬件条件下，理论计算耗时仅为千万级网格数值模拟的5%左右，在计算速度上有明显的优越性。
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关键词:
- 自由场爆炸 /
- Friedlander 方程 /
- 冲击波反射 /
- 冲击波绕射
Abstract: In order to establish an empirical formula to describe the pressure, density and particle velocity of the blast wave at any time and distance in free field, and to support the theoretical calculation of shock wave loading in complex scenarios, the pressure, density and particle velocity histories at different scaled distances were obtained by one-dimensional numerical simulation. The empirical formula of the relationship between shock wave parameters and specific distance was obtained by using the curve fitting method, and the relationship of shock wave pressure, density and particle velocity with time were established by the improved modified Friedlander equation. Based on the two typical scenarios of ground reflection and rear diffraction of explosive shock wave, the application of the proposed model was explained. And the accuracy of the proposed model and related theoretical methods are verified by comparison with the experimental and numerical simulation results. The results show that, within the range from 0.1 to 10 m/kg1/3, the relation of scaled distance and shock wave parameters obtained by curve fitting method are highly consistent with the numerical simulation results, which R2 values are higher than 0.999. The developed basic shock wave parameters time-history curves can ensure the peak value and the maximum impulse is equal to the numerical simulation results in near-field. And in the middle and far-field, the developed time-history curves are in good agreement with the numerical simulation results. Under two typical conditions: ground reflection of explosive shock wave and rear diffraction shock wave around building, the theoretical results are in good agreement with the contour diagram of numerical simulation results. Under the same hardware condition, the time-consuming of theoretical calculation is only about 5% in the numerical simulation of 10 million-level grid, which shows that the method has obvious superiority in calculating speed.-
Key words:
- free-field explosion /
- Friedlander equation /
- shock reflection /
- shock diffraction
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图 1 不同网格数量下的压力时程数值模拟结果
Figure 1. Numerical result of pressure changing with different grid quantity
图 2 不同网格数量下的密度时程数值模拟结果
Figure 2. Numerical result of density with different grid quantity
图 3 不同网格数量下的粒子速度时程数值模拟结果
Figure 3. Numerical result of particle velocity with different grid quantity
图 8 中止密度和超密度峰值与比例距离关系
Figure 8. Relationship of cut suspend density and peak density with scaled distance
图 11 粒子速度峰值与比例距离关系
Figure 11. Relationship between peak particle velocity and scaled distance
图 12 速度积分与比例距离关系
Figure 12. Relationship between velocity integral and scaled distance
图 14 R=0.17 m/kg1/3处冲击波基本参数理论及数值模拟时程
Figure 14. Simulated and theoretical basic shock wave parameter histories at R=0.17 m/kg1/3
图 15 冲击波基本参数理论及数值模拟时程曲线
Figure 15. Simulated and theoretical basic parameter history of shock waves
图 16 空爆地面反射实验布置
Figure 16. Experimental arrangement of ground reflection of air explosion
图 20 爆炸冲击波建筑后绕射实验布置图
Figure 20. Experimental arrangement of explosion shock wave diffraction behind the building corner
图 21 冲击波绕射理论计算空间划分示意图
Figure 21. Schematic diagram of space division of shock wave diffraction theoretical calculation
图 22 z=1.35 m平面理论与数值计算结果的压力分布云图
Figure 22. Theoretical and simulated results of pressure contours on the z=1.35 m plane
密度/(kg·m−1/3) E0/GPa A/GPa B/GPa R1 R2 ω 1630 7.0 373.8 3.75 4.15 0.9 0.35 
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表 2 各测点的超压峰值（Δ
$ p $ +）和冲量极值（$i $ +）理论结果与数值模拟、试验结果对比Table 2. Comparison of peak overpressure (Δp+) and maximum impulse (i+) between theoretical values and experimental results, simulation results of each gauges
测点 δ1(Δp+)/% δ2(Δp+)/% δ3(Δp+)/% δs(Δp+)/% δ1(i+)/% δ1(i+)/% δ1(i+)/% δ1(i+)/% T1 23.5 19.5 19.3 8.6 2.4 39.6 31.7 0.8 T3 30.0 − − 8.6 21.8 − − 2.1 T4 − 23.3 − 6.9 − 23.1 − 4.8 T5 − − 0.4 7.8 − − 38.4 6.0 注：δk为理论结果相对于第k次（k=1、2、3）试验结果的误差，δs为理论结果相对于模拟结果的误差。
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