柱形装药条件下锥形水中爆炸激波管内的冲击波特性

郑监; 卢芳云; 陈荣

doi:10.11883/bzycj-2020-0316

柱形装药条件下锥形水中爆炸激波管内的冲击波特性

doi: 10.11883/bzycj-2020-0316

国防科技大学文理学院，湖南长沙 410073

基金项目: 国家自然科学基金（11872376）

详细信息

作者简介:
郑　监（1993－　），男，博士研究生，zhengjian14@nudt.edu.cn

通讯作者:
卢芳云（1963－　），女，博士，教授，博士生导师，fylu@nudt.edu.cn

中图分类号: O382
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- 被引次数: 0
出版历程
- 收稿日期: 2020-09-04
- 修回日期: 2021-03-03
- 网络出版日期: 2021-09-16
- 刊出日期: 2021-10-13

Shock wave characteristics in a conical water explosion shock tube under cylindrical charge condition

College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, Hunan, China

摘要

摘要: 锥形水中爆炸激波管是进行水中爆炸实验的一种装置，该装置能够通过较小装药量在相同距离处实现自由场水中较大装药量爆炸的冲击波峰值。为了获得柱形装药条件下锥形水中爆炸激波管内的冲击波特性，本文通过数值计算的方式，对不同圆锥角和不同柱形装药质量下锥形激波管内的冲击波传播过程进行了模拟，通过对不同工况下激波管内冲击波特性进行分析，发现其初始冲击波的衰减规律符合自由场水中的指数衰减形式，并拟合得到了与自由场水中爆炸相容的冲击波峰值、比冲量和能流密度经验公式；发现其二次脉动压力周期与炸药质量呈反常规的变化规律，并引入等效静水压深度解释了这一现象；发现其二次脉动压力幅值与初始冲击波幅值之比比自由场水中更大，而二次脉动压力的比冲量与初始冲击波冲量之比与自由场水中相当。
- 水中爆炸 /
- 锥形激波管 /
- 冲击波 /
- 二次脉动
Abstract: A conical shock tube is a kind of underwater explosive devices which uses small conical explosive charge to form high intensity shock pressure. Theoretically, the shock wave pressure in the conical shock tube is the same as that generated by a virtual spherical explosive charge in free field water. However, considering the effect of practical factors, the characteristics of shock wave in the actual device and the theoretical device are different to some extent. In order to investigate the shock wave characteristics in the conical water explosion shock tube under a cylindrical charge condition, and to obtain the variation rules of the peak pressure value, the specific impulse and the energy flux density, a series of numerical calculations with different cone angles and different quality of cylindrical charges were conducted. The reliability of the simulation methods was verified by comparing with the published experimental data. Through the analysis of the pressure data obtained by the validated simulation method, it is found that the shock wave in the tube follows the same scaling law as it is in the free field underwater explosion. The constants k and n of the empirical expressions for peak pressure, the impulse and the energy flux density for the shock wave in shock tube are obtained by data fitting. Furthermore, the relationships among the coefficient k, index n and cone angle α were deduced, and the result shows that the coefficients k have well linear relationship with constructed angle coefficient β, and the indexes n can be quantitatively expressed by cone angle α. Regarding the free field as a special case with a cone angle of 360°, it’s constants k and n also conform to the obtained relationships. It is also found that the secondary pulsation pressure period shows an anomalous change rule with explosive mass, which can be well explained by the significant increasement of the equivalent hydrostatic pressure depth. The ratio between the secondary impulse pressure peak and initial pressure peak is bigger than that in free field while the ratio between the secondary impulse pressure’s impulse to the initial pressure impulse is almost the same. These results can provide support for the application of conical shock tubes.
- underwater explosion /
- conical shock tube /
- shock wave /
- secondary impulse

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图 1 锥形管内冲击波与自由场冲击波^[14]

Figure 1. Shock wave in conical shock tube and free field^[14]

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图 2 锥形激波管示意图^[14]

Figure 2. Schematic of conical shock tube^[14]

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图 3 不同的尖端装药类型示意图

Figure 3. Different charge type in the top end of the tube

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图 4 锥形激波管的计算模型示意图

Figure 4. The calculation model of the conical shock tube

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图 5 锥形激波管的压力时程曲线对比

Figure 5. Compare of the pressure profile from references [8-10] and the simulation results

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图 6 锥形激波管中冲击波的传播过程(α=4°, m=1.28 g)

Figure 6. Shock wave propagation process in the conical shock tube (α=4°, m=1.28 g)

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图 7 爆轰产物界面的发展(α=4°, m=1.28 g)

Figure 7. Evolution of the interface between water and detonation products (α=4°, m=1.28 g)

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图 8 典型的压力历史曲线(m=1.28 g, R/m^1/3=1.84)

Figure 8. Typical pressure profile in the shock tube (m=1.28 g, R/m^1/3=1.84)

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图 9 冲击波压力幅值在管内的衰减（Z=R/m^1/3）

Figure 9. Decay of the pressure peak in the shock tube (Z=R/m^1/3)

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图 10 冲击波峰值压力系数k_p与角度系数β_p之间的关系

Figure 10. Relationship between maximum pressure coefficient k_p and angular coefficient β_p

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图 11 冲击波比冲量在管内的衰减

Figure 11. Decay of the specific impulse of shock wave in the shock tube

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图 12 冲击波能流密度在管内的衰减

Figure 12. Decay of the energy flow density of shock wave in the shock tube

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图 13 冲击波冲量系数k_i与角度系数β_i之间的关系

Figure 13. Relationship between k_i, the coefficient of the specific impluse and β_i, the angular coefficient

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图 14 冲击波能流密度系数k_e与角度系数β_e之间的关系

Figure 14. Relationship between k_e, the coefficient of the energy flow density and β_e, the angular coefficient

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图 15 冲击波比冲量指数n_i与质量放大系数η之间的关系

Figure 15. Relationship between specific impulse exponent n_i and amplification factor η

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图 16 冲击波能量密度指数n_e与质量放大系数η之间的关系

Figure 16. Relationship between energy density exponent n_e and amplification factor η

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图 17 二次脉动压力周期T与炸药质量m之间的关系

Figure 17. Relationship between T, the period of the second pulse, and m, the mass of the explosive

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图 18 不同质量m下的等效静水压深度D

Figure 18. Equivalent hydrostatic depth (D) due to different mass of the explosive (m)

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表 1 TNT的JWL状态方程参数

Table 1. The JWL EOS parameters for TNT

参数	A/GPa	B/Pa	R₁	R₁	ω
取值	373.8	374.7	4.15	0.9	0.35

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表 2 水的状态方程参数

Table 2. The EOS parameters for water

ρ₀/（kg·m⁻³）	A₁/GPa	A₂/GPa	A₃/GPa	B₀	B₁	T₁/GPa	T₂/Pa
1×10³	2.2	9.54	14.57	0.28	0.28	2.2	0

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表 3 4340钢的基本参数

Table 3. Basic parameters for 4340 steel

参数	ρ/（kg·m⁻³）	E/Pa	ν	A_s/Pa	B_s/Pa	n_s	C	m_s
取值	7.83×10³	2.0×10¹¹	0.29	7.92×10⁸	5.10×10⁸	0.26	0.014	1.03
注：ν为泊松比，E为弹性模量.

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表 4 基于数值模拟结果拟合得到的初始冲击波压力峰值、比冲量和能流密度曲线方程的参数及决定系数

Table 4. Parameters and determination coefficient of fitting curve Eq. for simulational results of maximum pressure, specific impulse and energy flow density

α	k_p	n_p	R²(p_m)	k_i/10⁵	n_i	R²(i)	k_e/10⁵	n_e	R²(e)
4°	864.04	1.13	0.9793	2.99	0.464	0.9567	581	1.62	0.9978
6°	647.76	1.13	0.9847	2.22	0.476	0.9183	349	1.69	0.9980
8°	517.21	1.13	0.9807	1.73	0.490	0.9380	242	1.79	0.9988
10°	430.14	1.13	0.9741	1.59	0.583	0.9474	181	1.86	0.9992
360°^[16]	52.16	1.13		0.0058	0.891		0.98	2.10

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表 5 二次脉动压力幅值与初始冲击波幅值之比

Table 5. The secondary impulse pressure peak to the initial shock pressure peak ratio

(R·m^−1/3)/(m·kg^−1/3)	p_2m/p_m
(R·m^−1/3)/(m·kg^−1/3)	α=4°	α=6°	α=8°	α=10°
1.84	0.14	0.18	0.22	0.19
1.46	0.21	0.24	0.29	0.24
1.28	0.26	0.33	0.21	0.19
平均	0.20	0.25	0.24	0.21

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表 6 二次脉动压力的正冲量与初始冲击波冲量之比

Table 6. The secondary impulse pressure’s impulse to the initial shock pressure impulse ratio

(R·m^−1/3)/(m·kg^−1/3)	i₂/i₁
(R·m^−1/3)/(m·kg^−1/3)	α=4°	α=6°	α=8°	α=10°
1.84	3.57	3.75	3.45	3.29
1.46	3.80	3.74	4.05	3.38
1.28	3.57	4.03	4.00	3.69
平均	3.65	3.84	3.83	3.45

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表 7 冲击波峰值、比冲量和能流密度经验公式及其系数

Table 7. Constants of empirical expressions for peak pressure, the impulse and the energy flux density

目标物理量	表达式	系数表达式	指数表达式	角度系数
p_m (MPa)	p_m=k_p$(m^{1/3}/R)^{n_{ {p} }} $	k_p =38.35β_p+13.81	n_p=1.13	β_p=$\eta^{n_{ {p} }/3}$
I (Pa·s)	I/m^1/3=k_i$(m^{1/3}/R)^{n_{ {i} }} $	k_i =5923.5β_i−163.5	n_i=0.46−0.432×0.9974^η	β_i=$\eta ^{(1+n_{ {i} })/3}$
E (Pa·m)	E/m^1/3=k_e$(m^{1/3}/R)^{n_{ {e} }} $	k_e =49279β_e+48721	n_e=1.61−0.491×0.9988^η	β_e=$\eta^{ (1+n_{ {e} })/3}$

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