基于能量密度因子法的复杂环境下爆炸冲击波超压峰值解析计算

为了快速计算复杂环境条件下的爆炸冲击波超压峰值,利用量纲分析(dimensional analysis, DA)方法推导得到了空中爆炸自由场冲击波超压峰值定性关系式,借助Taylor展开得到了多项式形式的函数表达式。对上述函数关系式的物理意义进行分析,通过能量密度因子(energy concentration factor, ECF)的概念,将空中爆炸自由场冲击波超压峰值计算公式推广到工程上常见的复杂几何环境。利用函数关系式证明了工程中广泛使用的多种估算自由场冲击波超压峰值的经验公式在物理和数学上的合理性,由能量密度因子法得到了包括地面爆炸、两端无限长坑道内爆炸、一端封闭一端开放长坑道内爆炸、十字坑道内爆炸、四周开放的双层建筑间爆炸和长直街道中爆炸等的超压计算解析公式。最后,将解析公式计算结果与实验和数值模拟结果进行了比较分析。结果表明:解析公式与实验和数值结果符合得非常好。

Analytical Calculation of the Blast Wave Peak Overpressures under Complex Environments Based on the Energy Concentration Factor Method

In order to fast calculate the blast wave peak overpressure under complex environments, by utilizing the dimensional analysis (DA) method, a qualitative function relationship of the blast wave peak overpressure of the explosion in free air has been derived, and then, based on the Taylor expansion, a polynomial form function was obtained. By analyzing the physical meaning of the polynomial function, the concept of energy concentration factor (ECF) has been introduced, and by employing the ECF, the polynomial function of the blast wave peak overpressure of the explosion in free field was extended to complex environments in engineering applications. The physical and mathematical rationality of the widely used empirical formulas for the peak overpressure in free field explosions were verified by the polynomial function derived in this paper. Analytical calculation formulas of blast wave peak overpressure for some complex configuration cases, such as the free hemispherical rigid ground explosion, the two open-end tunnel explosion, the one closed-end tunnel explosion, the crossed tunnel explosion, the open-sided multi-storey buildings explosion and the long straight street explosion, et al, have been got by the ECF method. The comparison of the analytical calculation results in this paper with the experimental and numerical results indicates that the analytical results agree very well with the experiments and numerical simulations.