空气自由场爆炸冲击波数值建模及应用

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。

Numerical modeling and application of shock wave of free-field air explosion

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.