海拔高度对长直坑道内爆炸冲击波传播的影响

李勇; 雒泓宇; 冯晓伟; 胡宇鹏; 张军; 李海涛

doi:10.11883/bzycj-2023-0230

海拔高度对长直坑道内爆炸冲击波传播的影响

doi: 10.11883/bzycj-2023-0230

李勇^{1, 2,},
雒泓宇^{1, 2},
冯晓伟^3, ,,
胡宇鹏³,
张军³,
李海涛^{1, 2}

1.
重庆大学煤矿灾害动力学与控制国家重点实验室，重庆 400044
2.
重庆大学资源与安全学院，重庆 400044
3.
中国工程物理研究院总体工程研究所，四川绵阳 621999

基金项目: 国家重点研发计划青年科学家项目（2022YFC2905700）；国家自然科学基金（12202424）

详细信息

作者简介:
李　勇（1985－　），男，博士，副教授，yong.li@cqu.edu.cn

通讯作者:
冯晓伟（1985－　），男，博士，副研究员，xiaowei_feng@126.com

中图分类号: O382.1
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- 文章访问数: 284
- HTML全文浏览量: 58
- PDF下载量: 100
- 被引次数: 0
出版历程
- 收稿日期: 2023-06-29
- 修回日期: 2023-11-20
- 网络出版日期: 2023-12-27
- 刊出日期: 2024-03-14

Influence of altitude on the propagation of explosion shock waves in a long straight tunnel

LI Yong^{1, 2
,},
LUO Hongyu^{1, 2},
FENG Xiaowei^{3
, ,},
HU Yupeng³,
ZHANG Jun³,
LI Haitao^{1, 2}

1.
State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China
2.
School of Resources and Safety Engineering, Chongqing University, Chongqing 400044, China
3.
Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang 621999, Sichuan, China

摘要

摘要: 为有效表征不同海拔坑道内爆炸冲击波的传播特征，利用非线性显式动力学有限元软件AUTODYN，研究了海拔高度对长直坑道内爆炸冲击波传播的影响规律，探讨了高海拔环境对坑道内冲击波传播的影响，基于量纲分析，建立了适用于不同海拔高度典型坑道内冲击波峰值超压的计算模型，并通过数值计算进行了验证。结果表明：随着海拔高度升高，坑道内爆炸冲击波波阵面传播速度与径向的冲击波参数偏差增大，平面波形成距离增加，冲击波峰值超压降低；在0~4000 m范围内，海拔高度每升高1000 m，冲击波冲量降低约0.91%。结合Sachs无量纲修正方法和量纲分析，推导出不同海拔高度冲击波峰值超压的理论分析模型，模型计算结果与数值计算结果的相对偏差不大于10%，能够为高海拔环境下坑道内爆炸冲击波的传播提供理论依据。
- 海拔高度 /
- 坑道 /
- 爆炸冲击波 /
- 量纲分析 /
- 传播特性
Abstract: To effectively characterize the propagation characteristics of the explosion shock waves in tunnels at different altitudes, nonlinear explicit dynamics finite element software AUTODYN and dimensional analysis were used to study the influence of altitude on the propagation of explosion shock waves in long straight tunnels, and the influence characteristics of high altitude environments on the propagation of shock waves in tunnels were explored. First of all, the accuracy of the computational method was verified by comparing the peak overpressure and the time of overpressure rise of the small-scale shock tube test and the numerical simulation at the same measurement point. Then based on the AUTODYN-2D Euler symmetric algorithm and standard atmospheric parameters, the shock wave parameters of TNT explosion with 10 kg TNT spherical charge explosion in a tunnel with a diameter of 2.5 m and a length of 40 m at altitudes from 0 to 4000 m were computed, which were arranged with gauges with an axial interval of 2 m and a radial interval of 0.25 m, such as plane wave formation distance, peak overpressure, shock wave front propagation velocity, impulse, etc. In the end, a polynomial theoretic calculation model for shock wave peak overpressure in a tunnel at different altitudes was proposed with coefficients least-squares fitted from numerical simulation data at sea level, and the variables were obtained by dimensional analysis and the extended Sachs scaling law. The results show that, with the increase of altitude, the deviations between the propagation velocity of the explosion shock wave front and the radial parameters of the shock wave in the tunnel increases, the formation distance of the plane wave increases, and the peak overpressure of the shock wave decreases. Within the altitude range of 0 to 4000 m, the average value of shock wave impulse decreases by about 0.91% for every 1000 m increase. By combining the extended Sachs scaling law with dimensional analysis, a theoretical analysis model for calculating peak overpressure of shock waves at different altitudes with no more than 10% deviation is derived, which can provide a theoretical basis for explosion shock wave propagation in tunnels at high altitudes.
- altitude /
- tunnel /
- explosion shock wave /
- dimensional analysis /
- propagation property

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图 1 激波管试验装置示意图

Figure 1. Schematic diagram of experimental shock tube

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图 2 距端口680 mm处的冲击波超压测试曲线

Figure 2. Curve of shock wave overpressure at 680 mm from the port

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图 3 激波管二维轴对称模型

Figure 3. 2D axisymmetric shock tube model

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图 4 超压时程曲线的数值计算与试验结果对比

Figure 4. Comparison between numerical simulation and experiment of overpressure-time curves

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图 5 坑道二维轴对称模型

Figure 5. 2D axisymmetric tunnel model

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图 6 不同网格尺寸下的冲击波超压时程曲线

Figure 6. Overpressure-time curves with different grid sizes

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图 7 不同网格尺寸下的计算时间

Figure 7. Computation time with different grid sizes

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图 8 h = 3000 m 时冲击波压力云图

Figure 8. Pressure nephograms of shock wave at h = 3000 m

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图 9 不同海拔高度下的峰值超压

Figure 9. Peak overpressures at different altitudes

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图 10 各测点区间段内冲击波阵面的平均速度

Figure 10. Average velocities of shock wave in different intervals

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图 11 冲击波阵面到达时间的标准偏差

Figure 11. Standard deviation of shock wave front arrival time

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图 12 冲击波峰值超压平均值

Figure 12. Average of peak overpressures

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图 13 不同监测位置的波形对比

Figure 13. Comparison of shock waves at typical points

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图 14 不同监测位置的冲击波冲量

Figure 14. Shock wave impulses of typical points

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图 15 不同海拔高度下理论与数值计算峰值超压比较

Figure 15. Comparison of peak overpressure between theory and numerical simulation at different altitudes

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表 1 TNT炸药的模型参数

Table 1. Parameters of models for TNT

ρ_TNT/(kg·m⁻³)	D/(m·s⁻¹)	p_C-J/GPa	E₀/GPa	A/GPa	B/GPa	R₁	R₂	ω
1630	6930	21	6	374	3.75	4.15	0.9	0.35

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表 2 空气模型参数

Table 2. Parameters of models for air

ρ_k/(kg·m⁻³)	γ	T_k/K	${c_V}$/(J·kg⁻¹·K⁻¹)	e_k/(J·kg⁻¹)
1.225	1.4	288.2	717.6	2.068×10⁵

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表 3 4340钢模型参数

Table 3. Parameters of models for 4340 steel

ρ_steel/(kg·m^-3)	a/MPa	b/MPa	n	c	m	$ {\dot \varepsilon _0} $/s⁻¹	θ_m/K	θ_r/K	K/GPa
7830	792	510	0.26	0.014	1.03	1	1793	288.2	159

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表 4 海拔0 ～ 4000 m处的大气参数

Table 4. Parameters of the air at altitude from 0 to 4000 m

h/m	ρ_k-h/(kg·m⁻³)	p_k-h/kPa	T_k-h/K	e_k-h/(kJ·kg⁻¹)
0	1.225	1013.25×10²	288.15	2.068×10²
1000	1.112	898.75×10²	281.65	2.021×10²
2000	1.006	794.95×10²	275.15	1.974×10²
3000	0.909	701.08×10²	268.65	1.928×10²
4000	0.819	616.40×10²	262.15	1.881×10²

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表 5 不同网格尺寸下冲击波参数计算结果

Table 5. Simulated results of shock wave parameters with different grid sizes

网格尺寸/mm	x = 18 m				x = 20 m
网格尺寸/mm	t_a/ms	$\delta_{t_{\mathrm{a}}} $/%	Δp_m/MPa	$\delta_{\Delta_{p_{\mathrm{m}}}}$/%	t_a/ms	$\delta_{t_{\mathrm{a}}} $/%	Δp_m/MPa	$\delta_{\Delta_{p_{\mathrm{m}}}} $/%
50×50	18.180	5.46	0.464	16.55	20.990	6.12	0.420	17.81
40×40	17.840	3.49	0.486	12.59	20.690	4.61	0.439	14.09
30×30	17.720	2.79	0.511	8.09	20.290	2.59	0.456	10.76
20×20	17.576	1.96	0.530	4.68	20.080	1.52	0.481	5.87
10×10	17.350	0.65	0.537	3.42	19.832	0.27	0.494	3.33
5×5	17.242	0.02	0.555	0.18	19.783	0.02	0.509	0.39
2×2	17.239		0.556		19.779		0.511

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表 6 不同海拔高度下平面波形成距离

Table 6. Plane wave formation distances at different altitudes

h/m	0	1000	2000	3000	4000
x/m	15.8	17.2	17.5	17.8	18.3

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表 7 坑道内爆炸各物理量的量纲幂次

Table 7. Dimensional power coefficients of physical quantities in the problem of explosion in tunnel

基本量纲	E	p_k-h	ρ_k-h	SΔx	Δp_m	I	t_a
M	1	1	1	0	1	1	0
L	2	−1	−3	3	−1	−1	0
T	−2	2	0	0	−2	−1	1

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表 8 坑道内爆炸各物理量的量纲幂次（初等变换）

Table 8. Dimensional power coefficients of physical quantities in the problem of explosion in tunnel (elemental transformation)

参考物理量	E	p_k-h	ρ_k-h	SΔx	Δp_m	I	t_a
E	1	0	0	1	0	1/3	1/3
p_k-h	0	1	0	−1	1	1/6	−5/6
ρ_k-h	0	0	1	0	0	1/2	1/2

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