水下爆炸冲击波数值仿真研究

胡亮亮; 黄瑞源; 李世超; 秦健; 王金相; 荣光

doi:10.11858/gywlxb.20190773

水下爆炸冲击波数值仿真研究

doi: 10.11858/gywlxb.20190773

胡亮亮^1,,
黄瑞源^1,*, ,,
李世超¹,
秦健²,
王金相¹,
荣光¹

1.
南京理工大学瞬态物理国家重点实验室，江苏南京　210094
2.
海军研究院，北京　100161

基金项目: 国家自然科学基金（11802001，11402266，11672138）；装备预研基金（614260404021801）；中国空气动力研究与发展中心超高速碰撞研究中心开放基金（20190303）；中央高校基本科研业务费专项资金项目（30916011348）

详细信息

作者简介:
胡亮亮（1995－），男，硕士研究生，主要从事水下爆炸数值仿真研究.E-mail: 18362906302@163.com

通讯作者:
黄瑞源（1984－），男，博士，讲师，主要从事爆炸力学与冲击动力学研究.E-mail: ryhuang@njust.edu.cn

中图分类号: O383
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出版历程
- 收稿日期: 2019-05-10
- 修回日期: 2019-05-28

Shock Wave Simulation of Underwater Explosion

1.
National Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
2.
Naval Research Academy, Beijing 100161, China

摘要

摘要: 由于在水下爆炸冲击波的数值仿真研究中，水的状态方程、人工黏性系数和网格尺寸对数值计算结果影响很大，采用常规TNT炸药的水下爆炸为例，以冲击波的峰值压力和比冲量为衡量指标，研究了这3个主要影响因素对数值仿真结果的影响。首先，通过采用常用的5种水的状态方程进行系列仿真，给出了各种状态方程的适用范围；其次，讨论了人工黏性系数对计算结果的影响，并给出了一次与二次人工黏性系数的建议取值范围；最后，通过对不同炸药当量及不同网格尺寸开展系列运算，从而得到不同炸药当量在满足工程计算精度要求下所对应的建议网格尺寸，并得到了不同炸药当量所对应的建议网格尺寸的表达式。
- 水下爆炸 /
- 数值仿真 /
- 水的状态方程 /
- 人工黏性系数 /
- 网格尺寸
Abstract: The state equation of water, artificial viscosity coefficient and mesh size have a great influence on the numerical results of underwater explosion shock wave. In order to improve the simulation accuracy of underwater explosion shock wave, the peak pressure and specific impulse of the conventional TNT explosive underwater explosion are taken as the measurement indicators, and the influence of these factors on the numerical simulation results is studied. For the five kinds commonly state equations of water, the specific values of the artificial viscosity coefficients under different working conditions and appropriate grid size for different explosive equivalents are given. These parameters can provide reference for improving simulation accuracy of underwater explosion shock wave under different working conditions. First, through a series of simulations of the commonly used five kinds of state equations of water, the calculation results of peak pressure and specific impulse are compared with the empirical formula, and the error analysis is carried out to give the applicable scope of each state equation. Secondly, the influence of the artificial viscosity coefficient on the calculation results is discussed, and a series of calculations are carried out for the primary and secondary artificial viscosity coefficients under different working conditions. The recommended range of values for the primary and secondary artificial viscosity coefficients under different working conditions is given. Finally, through a series of calculations on 0.1, 0.5, 1, 10, 50, 100, 500 and 1 000 kg equivalent explosives and different grid sizes, the recommended mesh sizes corresponding to different explosive equivalents under the requirement of engineering calculation accuracy are obtained by limiting the relative error of peak pressure less than 10%. The expressions of the recommended mesh sizes corresponding to different explosive equivalents are also given.
- underwater explosion /
- numerical simulation /
- equation of state /
- artificial viscosity /
- element density

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图 1 采用不同状态方程得到的峰值压力计算结果

Figure 1. Calculated peak pressure results using different equations of states

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图 2 采用不同状态方程得到的比冲量计算结果

Figure 2. Calculated specific impulse results obtained with different equations of states

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图 3 调整一次项黏性系数得到的计算结果

Figure 3. Calculated results obtained by adjusting the viscosity coefficient of the primary term

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图 4 调整二次项黏性系数得到的计算结果

Figure 4. Calculated results obtained by adjusting the viscosity coefficient of the quadratic term

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图 5 一次黏性系数对不同当量工况的影响

Figure 5. Effects of primary viscosity coefficient under different equivalent conditions

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图 6 采用不同网格下得到的峰值压力

Figure 6. Peak pressure obtained under different grids

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图 7 采用不同网格下得到的比冲量

Figure 7. Specific impulse obtained under different grids

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图 8 网格尺寸对不同炸药当量水下爆炸数值仿真的影响

Figure 8. Influence of grid size on different explosive equivalents numerical simulation of underwater explosion

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图 9 炸药当量与适宜网格尺寸的关系

Figure 9. Relationship between explosive equivalent and suitable grid size

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图 10 数值仿真得到的冲击波时程曲线与试验对比

Figure 10. Numerical and experimental comparison of shock wave time history curve

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表 1 TNT炸药的主要参数^[16]

Table 1. Main parameters of TNT explosives^[16]

A/GPa	B/GPa	R₁	R₂	ω	ρ₀/(kg∙m^–3)	e/(J∙kg^–1)
371.2	3.231	4.15	0.95	0.3	1630	4.19 ×10⁶

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表 2 常用Mie-Grüneisen状态方程不同形式的参数

Table 2. Commonly used parameters of the Mie-Grüneisen equation of state

Equation of state	C₀/(km·s^–1)	S₁	S₂	S₃	${\gamma _0} $	a
SNL^[20]	1.647	1.92	0	0	0	0
HULL^[21]	1.483	1.75	0	0	0.28	0
Steiberg^[22]	1.480	2.56	–1.986	0.226 8	0.50	2.67

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表 3 Autodyn程序提供的水多项式状态方程参数^{[12, 23]}

Table 3. Polynomial state equation parameters of water provided by the Autodyn program^{[12, 23]}

A₁/GPa	A₂ /GPa	A₃ /GPa	T₁ /GPa	T₂/GPa	B₀	B₁
2.2	9.54	14.57	2.2	0	0.28	0.28

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表 4 Dytran中水的多项式状态方程的参数^[24–25]

Table 4. Polynomial state equations parameters of water in Dytran^[24–25]

a₁/GPa	a₂/GPa	a₃/GPa	b₀	b₁	b₂	b₃
2.002	9.224	8.767	0.493 4	1.393 7	0	0

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表 5 1 kg炸药无限水域爆炸冲击波峰值压力

Table 5. Shock wave peak pressure of 1 kg explosive infinite water fields explosion MPa

State equation of water	R/R₀
State equation of water	7	10	15	20	25	30	35
Autodyn polynomial	165.7	95.6	56.7	40.6	31.3	24.6	20.3
Dytran polynomial	170.7	97.6	57.4	41.2	31.5	25.1	20.8
Steiberg	169.8	97.7	57.7	41.6	31.1	25.3	21.1
SNL	218.7	123.1	71.2	46.2	36.8	30.8	25.7
HULL	182.5	106.7	62.8	45.2	34.9	28.4	23.7
Empirical formula	196.7	115.2	68.3	49.4	38.4	31.2	26.2

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表 6 1 kg炸药无限水域爆炸冲击波比冲量

Table 6. Shock wave impulse of 1 kg explosives infinite water fields explosion N·s·m^–2

State equation of water	R/R₀
State equation of water	7	10	15	20	25	30	35
Autodyn polynomial	12 522.9	9 116.8	6 355.1	4 919.6	4 033.4	3 429.3	2 989.7
Dytran polynomial	12 284.8	8 943.4	6 234.2	4 826.0	3 956.7	3 364.1	2 932.8
Steiberg	12 130.7	8 831.3	6 156.0	4 765.5	3 907.1	3 321.9	2 896.0
SNL	13 237.3	9 636.9	6 717.6	5 200.2	4 263.5	3 624.9	3 160.2
HULL	11 976.6	8 719.1	6 077.9	4 704.9	3 857.5	3 279.7	2 859.2
Empirical formula	14 007.7	10 197.8	7 108.6	5 502.9	4 511.7	3 835.9	3 344.1

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表 7 5种常用水的状态方程的适用范围与特点

Table 7. Applicable scope and characteristics of common five kinds of state equations for water

State equation of water	Scope of application
Autodyn polynomial	The overall error of the peak pressure is too large, and the far field error is larger than the near field. The near field error of the specific impulse calculation is smaller than the far field.
Dytran polynomial	The near-field peak pressure error is small, the specific impulse error is large, the far-field peak pressure error is large, and the specific impulse error is small.
Steiberg	The near-field peak pressure error is small, the specific impulse error is large, the far-field peak pressure error is large, and the specific impulse error is small.
SNL	The mid-field attenuation of the pressure peak is fast, and the far-field error is small. The difference between the near-field and the far-field error is not large, which is suitable for far-field calculation.
Empirical formula	The pressure peak error is small overall, and the specific impulse error is gradually increased from near to far, suitable for near-field calculation.

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表 8 人工黏性对计算结果的影响

Table 8. Artificial viscosity effects on calculation results

Artificial viscosity coefficient	Recommended range of values	Impact on calculation results
Primary viscosity coefficient	0.005–0.040	The peak pressure of the underwater shock wave has a great influence, the contrast impulse has little effect, the primary viscosity coefficient increases, and the peak pressure decreases.
Secondary viscosity coefficient	0.8–1.0	Less influence on peak pressure and specific impulse.

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表 9 1 kg炸药采用不同网格尺寸得到的峰值压力

Table 9. Peak pressure of 1 kg explosive with different grid sizes MPa

Grid size/mm	R/R₀
Grid size/mm	7	10	15	20	25	30	35
2	188.8	110.6	65.6	47.4	36.8	30.0	25.2
5	179.0	104.8	62.1	44.9	34.9	28.4	23.9
8	161.3	94.5	56.0	40.5	31.4	25.6	21.5
12	135.7	81.5	46.1	35.7	26.5	21.5	18.1
15	112.1	65.7	38.9	27.1	21.9	17.8	14.9
20	85.6	52.4	28.7	20.7	16.1	13.1	11.0
Empirical formula	196.7	115.2	68.3	49.4	38.4	31.2	26.2

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表 10 1 kg炸药采用不同网格尺寸得到的比冲量

Table 10. Specific impulse of 1 kg explosive with different grid sizes N·s·m^–2

Grid size/mm	R/R₀
Grid size/mm	7	10	15	20	25	30	35
2	12 228.8	10 197.7	6 205.8	4 803.9	3 938.6	3 348.7	2 919.4
5	12 004.6	8 902.6	6 092.0	4 715.9	3 866.5	3 287.3	2 865.9
8	12 172.7	8 739.4	6 177.3	4 781.9	3 920.6	3 333.3	2 906.0
12	11 752.4	8 861.8	5 964.1	4 616.8	3 785.3	3 218.3	2 805.7
15	11 472.3	8 555.9	5 821.9	4 506.8	3 695.0	3 141.6	2 738.8
20	11 822.5	8 351.9	5 999.6	4 644.4	3 807.8	3 237.4	2 822.4
Empirical formula	14 007.7	10 197.8	7 108.6	5 502.9	4 511.7	3 835.9	3 344.1

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表 11 不同炸药当量下适宜网格尺寸

Table 11. Appropriate grid size for different explosive equivalents

Explosive equivalent/kg	Suitable grid size/mm
0.1	1.5
0.5	3
1	5
10	10
50	16
100	20
500	35
1 000	50

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