爆炸冲击波反射流场的理论计算方法

贾雷明; 王澍霏; 田宙

doi:10.11883/bzycj-2018-0167

爆炸冲击波反射流场的理论计算方法

doi: 10.11883/bzycj-2018-0167

贾雷明^{1, 2,},
王澍霏^{1, 2},
田宙²

1.
清华大学工程物理系，北京 100084
2.
西北核技术研究，陕西西安 710024

详细信息

作者简介:
贾雷明（1989－　），男，博士研究生，jialeiming@nint.ac.cn

中图分类号: O382
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- 被引次数: 0
出版历程
- 收稿日期: 2018-05-06
- 修回日期: 2018-07-19
- 网络出版日期: 2019-07-25
- 刊出日期: 2019-06-01

A theoretical method for the calculation of flow field behind blast reflected waves

JIA Leiming^{1, 2
,},
WANG Shufei^{1, 2},
TIAN Zhou²

1.
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
2.
Northwest Institute of Nuclear Technology, Xi’an 710024, Shaanxi, China

摘要

摘要: 爆炸冲击波遇到固壁，依次发生正规和非正规反射。本文中基于镜像方法，将爆炸冲击波在固壁反射等效为真实和虚拟爆炸流场的相互作用，建立了波后流场的理论计算方法。首先，假定反射波是以虚拟爆源为中心的圆弧，马赫杆是以爆心在固壁投影点为中心的圆弧。然后，根据爆炸自由场传播规律，利用基于几何近似的方法，建立流场中冲击波结构随时间演化的计算方法，确定任意时刻波后流场区域。最后，利用新发展的叠加模型LAMBR (LAMB revisied)，将真实和虚拟爆炸流场进行叠加，给出波后流场中的压力、密度和速度等物理量。通过与数值模拟结果和已有数据进行对比，发现该方法得到的流场物理量分布、峰值等能够反映流场发展的主要规律，从而验证了该理论方法的合理性。而且，该理论方法所需的时间相较于数值模拟大大缩短。
- 爆炸冲击波 /
- 非正规反射 /
- 镜像方法 /
- 理论计算
Abstract: Upon impinging on a rigid surface, the blast wave would go through regular and irregular reflection successively. A theoretical model is developed for the determination of the flow field behind the reflected wave, which is based on the method of image and identifies the field around blast wave reflection with that resulting from the interaction of real and imaginary bursts. Firstly, approximations of both reflected wave and Mach stems to circular arcs, centered on the imaginary burst point and ground zero respectively, are made. Then, given the blast free field, the method based on geometrical similarity is applied to calculate the temporal evolution of shock wave structures and differentiate different flow zones. Lastly, a newly developed addition model LAMBR (LAMB revisied) is employed to obtain the field parameters behind the reflected wave. The field parameter contours and peak values are in good agreement with the numerical results and the data from UFC 3-340-02, so the theoretical model is valid. And, the time needed for the theoretical calculation is much shorter than that for numerical simulation.
- blast wave /
- irregular reflection /
- method of image /
- theoretical calculation

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图 1 爆炸冲击波反射示意图

Figure 1. Schematic diagram of blast wave reflection

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图 2 镜像法示意图

Figure 2. Diagram of the method of image for blast wave reflection

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图 3 1 kg TNT 爆炸自由场冲击波参数

Figure 3. Free field blast wave parameters for 1 kg TNT explosion

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图 4 不同爆高情况下三波点轨迹

Figure 4. Triple point trajectories at different heights of explosion

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图 5 H=0.793 4 m时，不同时刻流场压力云图(黑线为物质界面)

Figure 5. Pressure contours at various time instants (black line stands for material interface) for H=0.793 4 m

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图 6 H=0.793 4 m时，不同时刻流场物理量沿y=0.03 m的分布

Figure 6. Parameters along y=0.03 m at various time instants for H=0.793 4 m

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表 1 不同比例爆高条件下g 的取值

Table 1. The value of g at different scaled heights of explosion

$\bar H$/(m·kg^−1/3)	${\bar x_{{{T,1}}}}$/(m·kg^−1/3)	${\bar x_{{{T,2}}}}$/(m·kg^−1/3)	g_UFC	g_Yi
0.396 7	0.793 4	1.895 8	0.837 7	0.361 1
0.595 1	0.793 4	2.444 0	0.774 2	0.299 5
0.793 4	0.793 4	3.424 8	0.638 8	0.254 0
0.991 7	1.586 8	4.020 8	0.537 2	0.218 9
注: UFC 中数据采用英制单位，本文使用时换算为国际单位制。

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表 2 非正规反射起始点坐标${x_{{T_0}}}$

Table 2. The ${x_{{T_0}}}$ value of the starting point of IR

H /m	${x_{{T_0}}}$/m
H /m	数值计算	理论分析
0.396 7	0.333 2	0.328 4
0.595 1	0.473 4	0.488 4
0.793 4	0.620 2	0.646 4
0.991 7	0.796 0	0.805 9

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表 3 沿直线y=0.03 m的物理量峰值

Table 3. Peak values of parameters along the line y=0.03 m

t/s	p_s/(10⁵Pa)			ρ_s/(kg·m⁻³)					u_s/(m·s⁻¹)
t/s	NS	TA	ε/%	NS	TA₁	ε₁/%	TA₂	ε₂/%	NS	TA₁	ε₁/%	TA₂	ε₂/%
4.76×10⁻⁴	40.82	36.56	−10.44	7.81	7.86	0.64	6.54	−16.26	728.93	688.84	−5.50	513.35	−25.45
9.96×10⁻⁴	9.73	10.70	9.97	4.42	5.70	28.96	5.71	29.19	732.33	766.03	4.60	482.88	−34.06
1.92×10⁻³	4.46	4.41	−1.12	3.19	3.37	5.64	3.76	17.87	418.37	413.92	−1.06	342.21	−18.20
3.60×10⁻³	2.51	2.57	2.39	2.29	2.36	3.06	2.59	13.10	239.09	245.65	2.74	229.38	−4.07
注：NS 为数值结果，TA 为理论结果，ε=(TA-NS)/NS 为偏差。下标 1、2 分别表示基于 LAMBR 和 LAMB 模型的理论结果。

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