冲击波与典型材质作用后的反射压力计算

doi:10.12382/bgxb.2025.0221

摘要/Abstract

摘要：

不同入射角下爆炸冲击波与典型材质作用后的反射压力会造成严重的毁伤,目前关于冲击波与不同典型材质作用后反射压力计算尚不完善,因此研究不同入射角下冲击波与典型材质的相互作用具有重要意义。为了探究爆炸冲击波与不同典型材质作用后的反射超压,获取入射压力、不同入射角对反射压力的影响,利用冲击波波阵面上的质量和动量守恒基本关系式,以及花岗岩、空气和45^#钢的状态方程,推导出不同入射角下爆炸冲击波不同典型材质间反射压力的大小。针对上述问题开展了炸药在不同炸高下爆炸试验,测量空气自由场和冲击波遇到典型材质(45^#钢和花岗岩)反射后压力值。通过将理论计算结果与试验数据进行比对验证,对比结果表明:该理论模型预测结果与试验结果一致,能有效的预测不同入射角下,冲击波作用到不同典型材质下的反射压力值的大小,为后续爆炸冲击波与不同典型材质的反射计算提供理论支撑。

关键词: 典型材质, 反射超压, 入射角, 反射系数

Abstract:

Explosive shock waves interacting with typical materials at different angles of incidence can lead to severe reflected overpressure, posing significant threats to structures and personnel. However, the accuracy of existing reflected pressure prediction models remains limited. This study develops a theoretical model based on mass and momentum conservation equations, combined with the equations of state for air, granite, and 45# steel. A series of explosion experiments at different charge heights were conducted to measure both free-field and reflected pressures. Theoretical results were compared with experimental data, showing strong agreement. The proposed model effectively predicts reflected overpressure across a range of incidence angles and material types, offering valuable support for shock wave damage assessment and protection design.

Key words: typical materials, reflected overpressure, angle of incidence, reflection coefficient

李玉琪, 宁建国, 许香照. 冲击波与典型材质作用后的反射压力计算[J]. 兵工学报, 2025, 46(10): 250221-.

LI Yuqi, NING Jianguo, XU Xiangzhao. Calculation of Reflected Pressure from Shock Wave Interaction with Typical Materials[J]. Acta Armamentarii, 2025, 46(10): 250221-.

图/表 23

图1 爆炸冲击波在空气与固体介质交界面上的反射与透射

Fig.1 Reflection and transmission of blast shock waves at the air-solid interface

图2 反射压力计算流程图

Fig.2 Flowchart of reflected pressure calculation

图3 爆炸冲击波前后的物理量

Fig.3 Physical quantities before and after the blast shock wave

表1 空气状态方程参数

Table 1 Parameters of the equation of state for air

参数	数值	参数	数值
ρ/(kg·m^-3)	1.29	γ	1.4
c/(m·s^-1)	340	P₀/MPa	0.1

表2 花岗岩状态方程参数

Table 2 Parameters of the equation of state for marble

参数	数值
ρ/(kg·m^-3)	2670
c/(ms^-1)	3030
S	1.66

表3 45#钢状态方程参数

Table 3 Parameters of the equation of state for 45# steel

参数	数值
ρ/(kg·m^-3)	7580
c/(m·s^-1)	4200
S	2.02

图4 45#钢板和空气及其反射的u-p曲线

Fig.4 u-p curves of 45# steel, air, and their reflected waves

图5 0.5m炸高下试验布局示意图

Fig.5 Experimental layout diagram with a charge height of 0.5m

图6 地面传感器及其布置示意图

Fig.6 Schematic diagram of ground sensors and their arrangement

图7 试验场地布置图

Fig.7 Test site layout for blast experiment

图8 0.5m炸高试验场地高射拍摄图

Fig.8 Aerial photograph of the experimental site at a blast height of 0.5m

图9 4个自由场超压数据图

Fig.9 Free-field overpressure data from four trials

表4 自由场超压数据

Table 4 Free-field overpressure data

传感器距离炸心距离/m	超压值/MPa	压力值/MPa
1.0	0.242	0.342
1.4	0.120	0.220
1.8	0.084	0.184
2.0	0.066	0.166

图10 3次试验反射场超压数据图

Fig.10 Reflected overpressure data from three trials

表5 反射场超压数据

Table 5 Reflected overpressure data

传感器编号	炸高/ m	传感器距离炸心水平距离/m	地面介质	超压值/ MPa	压力值/ MPa
1	0.5	0.87	花岗岩	0.370	0.470
2		1.31		0.191	0.291
1		0.71	花岗岩	0.517	0.617
3	0.7	0.71	45^#钢板	0.545	0.645
4		1.21		0.350	0.450
2	0.9	1.07	花岗岩	0.256	0.356
4		1.07	45^#钢板	0.340	0.440

图11 2.0m处自由场超压数据图

Fig.11 Free-field overpressure data at 2.0m

图12 花岗岩材质反射后竖直方向上的粒子速度ug,y

Fig.12 Vertical particle velocity ug,y of reflected airflow at the surface of granite

图13 45#钢材质反射后竖直方向上的粒子速度us,y

Fig.13 Vertical particle velocity us,y of reflected airflow at the surface of 45# steel

表6 理论计算结果与试验结果对比

Table 6 Comparison of theoretical calculations and experimental results

传感器编号	地面介质	距离/ m	炸高/ m	反射压力值/MPa	计算结果/ MPa	误差/ %
1	花岗岩	0.87	0.5	0.470	0.420	10.0
2	花岗岩	1.31		0.291	0.243	16.4
1	花岗岩	0.71		0.617	0.595	3.6
3	45^#钢板	0.71	0.7	0.645	0.614	4.8
4	45^#钢板	1.21		0.450	0.366	18.6
2	花岗岩	1.07	0.9	0.356	0.314	11.7
4	45^#钢板	1.07		0.440	0.361	17.9

图14 0.7m炸高工况入射角与压力的关系

Fig.14 Relationship between incidence angle and pressure at a blast height of 0.7m

图15 0.7m炸高工况入射角与反射系数的关系

Fig.15 Relationship between incident angle and reflection coefficient under explosion condition with burst height of 0.7m

图16 200g炸药不同炸高工况入射角与反射系数的关系

Fig.16 Relationship between incident angle and reflection coefficient under different detonation heights with 200g explosive

图17 不同炸药量在0.7m炸高下入射角与反射系数的关系

Fig.17 Relationship between incident angle and reflection coefficient at a detonation height of 0.7m for different explosive quantities

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