水下爆炸冲击波壁压理论及数值计算方法改进研究

刘晓波; 李帅; 张阿漫

doi:10.11883/bzycj-2021-0106

水下爆炸冲击波壁压理论及数值计算方法改进研究

doi: 10.11883/bzycj-2021-0106

哈尔滨工程大学船舶工程学院，黑龙江哈尔滨 150001

基金项目: 国家自然科学基金（51709056）；中央高校基本科研业务费（3072020CFJ0105）；黑龙江省博士后科研启动金（LBH-Q20016）

详细信息

作者简介:
刘晓波（1997－　），男，硕士，liuxiaobo_2020@163.com

通讯作者:
李　帅（1990－　），男，博士，副教授，hgcls@163.com

中图分类号: O382
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- 被引次数: 0
出版历程
- 收稿日期: 2021-03-24
- 修回日期: 2021-07-01
- 网络出版日期: 2021-12-03
- 刊出日期: 2022-01-20

An improvement of the wall-pressure theory and numerical method for shock waves in underwater explosion

College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China

摘要

摘要: 水下爆炸冲击波是舰船抗冲击评估中重要的载荷成分，也是水中结构物毁伤程度快速预报的关键和依据。通过小当量实验发现，由于传统 Taylor 平板理论公式忽略了冲击波波速的非线性变化，导致其在预报近距离水下爆炸冲击波壁压脉宽时出现偏差。为此，给出了比例爆距R/W^1/3为0.11～5.30 m/kg^1/3 (R为爆距，W为炸药质量)下的冲击波速度拟合公式，对传统Taylor理论公式进行修正。修正后，在R/W^1/3=0.11 m/kg^1/3下，壁压脉宽及冲量偏差大幅减小；在R/W^1/3≥0.21 m/kg^1/3下，两者偏差均小于12%。此外，在处理水下近场和中远场爆炸问题时，发现数值耗散会导致壁压峰值被明显削弱，于是提出了一种可行的数值策略消除计算中数值耗散导致的削弱效应，结果与修正的Taylor平板理论公式吻合良好，峰值偏差均小于9%。改进后的冲击波壁压理论公式及数值计算方法可为舰船抗爆抗冲击领域提供理论和技术支撑。
- 水下爆炸 /
- 壁压 /
- 冲击波 /
- Taylor平板理论
Abstract: Underwater blast shock wave is an important load in the evaluation of the impact resistance of ships, and it is also the key and basis for the fast prediction of the structure damage in underwater explosions. In the present study, a series of small equivalent underwater explosion experiments were carried out in the explosion tank. By comparing the theoretical predicted and experimental measured wall pressure characteristics, the applicability of the traditional Taylor formula in predicting the wall pressure of the underwater explosion shock wave was explored. It is found that the deviation of the Taylor plate theory in predicting the pulse width of the wall-pressure is mainly because the nonlinear variation of the shock wave velocity is not considered. Given this, a fitting formula of the shock wave velocity for 0.11 m/kg^1/3≤R/W^1/3≤5.30 m/kg^1/3, where R is the detonation distance and W is the charge weight, is given to improve the traditional Taylor theoretical formula. The corrected theoretical values are in good agreement with the experimental values. For R/W^1/3=0.11 m/kg^1/3, the pulse-width deviation of the wall-pressure of the shock wave between the improved Taylor formula and the experimental result is reduced from 79.6% to 26.6%, and the deviation of the impulse is reduced from 119.3% to 58.4%. For R/W^1/3≥0.21 m/kg^1/3, the deviations of the pulse-width and the impulse of wall-pressure are both less than 12%. Moreover, in the simulation of the wall-pressure change at different distances by numerical method (e.g., finite element method), it is found that the numerical dissipation causes the plate to move in advance (before the arrival of the shock wave front), leading to a significant decrease in the peak of the wall-pressure when dealing with the near-field and far-field underwater explosion problems. Therefore, a feasible numerical strategy was proposed to eliminate the weakening effect caused by numerical dissipation. The improved numerical results are in great agreement with the improved Taylor plate theory, and the deviation of the wall-pressure peak is less than 9%. The improved theoretical formula and numerical method for the shock wave wall pressure can provide theoretical and technical supports for the field of explosion protection of ships.
- underwater explosion /
- wall pressure /
- shock wave /
- Taylor plate theory

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图 1 冲击波与平板的相互作用示意图

Figure 1. Schematic diagram of the interaction between the shock wave and the plate

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图 2 实验模型设置示意图

Figure 2. Schematic diagram of the experimental model setting

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图 3 接触爆炸下平板中心壁压时历曲线对比

Figure 3. Comparison of the wall pressure history curves in the contact explosion

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图 4 近场爆炸和远场爆炸工况下壁压曲线对比

Figure 4. Comparison of wall pressure curves in the near-field explosion and far-field explosion

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图 5 水下爆炸冲击波速度随比例爆距的变化

Figure 5. Variation of the shock wave velocity in the underwater explosion with scaled explosion distance

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图 6 冲击波速度修正前后壁压曲线对比

Figure 6. Comparison of the wall pressure curves before and after the shock wave velocity correction

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图 7 冲击波波头耗散对靶板作用示意图

Figure 7. Schematic diagram of the effect of shock wave head dissipation on the target plate

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图 8 有限元模型

Figure 8. The finite element model

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图 9 R/W^1/3=0.42 m/kg^1/3时，冲击波波头耗散对壁压曲线的影响

Figure 9. Influence of shock wave head dissipation on the wall pressure curve at R/W^1/3=0.42 m/kg^1/3

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图 10 R/W^1/3 =1. 06 m/kg^1/3时，冲击波波头耗散对壁压曲线的影响

Figure 10. Influence of shock wave head dissipation on the wall pressure curve at R/W^1/3 = 1.06 m/kg^1/3

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图 11 R/W^1/3=1.59 m/kg^1/3时, 冲击波波头耗散对壁压曲线的影响

Figure 11. Influence of shock wave head dissipation on the wall pressure curve at R/W^1/3=1.59 m/kg^1/3

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表 1 冲击波壁压峰值实验值与传统Taylor理论公式结果对比

Table 1. Comparison of the experimental and theoretical Taylor formula results of wall pressure

工况	钢板材料	D/mm	W/g	(R·W^−1/3)/(m·kg^−1/3)	R/R₀	壁压峰值
工况	钢板材料	D/mm	W/g	(R·W^−1/3)/(m·kg^−1/3)	R/R₀	p_b,th/MPa	p_b,exp/MPa	δ_p/%
1	Q235	3	9.9	0.11	2.0	3340.0	3460.0	3.6
2	Q235	3	9.9	0.21	4.0	960.0	1020.0	6.3
3		1	5.0	0.88	16.6	107.0	81.2	−24.1
4	A3	16	1.0	1.63	30.7	61.0	58.0	−4.9
5	Q235	20	13.0	1.86	35.1	57.4	48.1	−16.2
6	Q235	20	13.0	2.62	49.5	38.8	33.8	−12.9
7	Q235	20	13.0	2.79	52.6	36.4	32.3	−11.3
8	Q235	20	13.0	3.34	63.1	29.6	27.7	−6.4
9	Q235	20	13.0	3.72	70.2	26.3	26.2	−0.4
10	Q235	20	13.0	4.16	78.4	23.2	22.9	−1.3
11	Q235	20	13.0	4.65	87.7	20.4	19.2	−5.9

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表 2 冲击波壁压脉宽、冲量实验值与传统Taylor理论公式结果对比

Table 2. Comparison of the experimental and theoretical Taylor formula results of wall pressure pulse width and impulse

工况	(R·W^−1/3)/(m·kg^−1/3)	R/R₀	脉宽			冲量
工况	(R·W^−1/3)/(m·kg^−1/3)	R/R₀	t_b,exp/µs	t_b,th/µs	δ_t/%	I_exp/(Pa·s)	I_th/(Pa·s)	δ_I/%
1	0.11	2.0	5.7	10.3	79.6	5585.9	12253.0	119.3
2	0.21	4.0	11.5	12.6	10.2	3402.4	4255.4	25.1
3	0.88	16.6	7.7	8.4	9.1	262.4	304.7	16.1
4	1.63	30.7	24.6	25.6	4.1	449.2	492.7	9.7
5	1.86	35.1	55.7	58.5	5.0	880.7	946.2	7.4
6	2.62	49.5	63.6	66.4	4.4	665.3	708.6	6.5
7	2.79	52.6	64.9	68.2	5.1	644.1	673.9	4.6
8	3.34	63.1	70.5	72.3	2.6	550.9	578.4	5.0
9	3.72	70.2	72.2	75.1	4.0	524.7	528.7	0.8
10	4.16	78.4	75.7	78.5	3.7	470.0	480.1	2.1
11	4.65	87.7	80.5	82.1	2.0	411.1	435.2	5.9

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表 3 不同比例爆距处的冲击波速度

Table 3. The shock wave velocities at different values of $R/W^{1/3} $

(R·W^−1/3)/(m·kg^−1/3)	R/R₀	c/(m·s⁻¹)	(R·W^−1/3)/(m·kg^−1/3)	R/R₀	c/(m·s⁻¹)	(R·W^−1/3)/(m·kg^−1/3)	R/R₀	c/(m·s⁻¹)
0.11	2.00	2835	0.32	6.00	1773	0.90	17.00	1563
0.12	2.25	2612	0.34	6.50	1745	0.95	18.00	1558
0.13	2.50	2471	0.37	7.00	1721	1.01	19.00	1553
0.15	2.75	2338	0.40	7.50	1700	1.06	20.00	1550
0.16	3.00	2244	0.42	8.00	1683	1.33	25.00	1536
0.17	3.25	2154	0.45	8.50	1667	1.59	30.00	1526
0.19	3.50	2098	0.48	9.00	1653	1.86	35.00	1520
0.20	3.75	2034	0.50	9.50	1641	2.12	40.00	1515
0.21	4.00	1984	0.53	10.00	1631	2.39	45.00	1511
0.23	4.25	1949	0.58	11.00	1612	2.65	50.00	1508
0.24	4.50	1913	0.64	12.00	1598	3.18	60.00	1503
0.25	4.75	1882	0.69	13.00	1586	3.71	70.00	1500
0.27	5.00	1856	0.74	14.00	1581	4.24	80.00	1498
0.28	5.25	1830	0.80	15.00	1574	4.77	90.00	1496
0.29	5.50	1810	0.85	16.00	1568	5.30	100.00	1494

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表 4 冲击波速度修正前后脉宽和壁压冲量及偏差对比

Table 4. Comparisons of the pulse width and impulse of the wall pressure and their deviations before and after the shock wave velocity correction

(R·W^−1/3)/(m·kg^−1/3)	脉宽					冲量
(R·W^−1/3)/(m·kg^−1/3)	t_b,exp/µs	t_b,th/µs	δ_t/%	t_b,th1/µs	δ_t1/%	I_exp/(Pa·s)	I_th/(Pa·s)	δ_I/%	I_th1/(Pa·s)	δ_I1/%
0.11	5.7	10.3	79.6	7.2	26.6	5585.9	12253.0	119.3	8850.4	58.4
0.21	11.5	12.6	10.2	10.9	2.7	3402.4	4255.4	25.1	3678.3	8.1
0.88	7.7	8.4	9.1	8.1	4.9	262.4	304.7	16.1	293.1	11.7

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表 5 冲击波波头耗散对壁压峰值的影响

Table 5. Influence of shock wave head dissipation on wall pressure peak

R/R₀	(R·W^−1/3)/(m·kg^−1/3)	v/(m·s⁻¹)	壁压峰值
R/R₀	(R·W^−1/3)/(m·kg^−1/3)	v/(m·s⁻¹)	p_b,th/MPa	p_b,sim1/MPa	δ_p,s1/%	p_b,sim2/MPa	δ_p,s2/%
6	0.32	49.8	491.8	407.3	−17.1	533.2	8.4
7	0.37	43.2	390.2	312.0	−18.6	412.2	5.6
8	0.42	37.6	319.4	247.6	−23.1	324.7	1.7
9	0.48	33.7	267.7	202.2	−22.4	270.8	1.2
10	0.53	30.4	228.6	168.8	−24.0	229.6	0.4
11	0.58	27.4	198.1	143.5	−25.4	197.4	−0.4
12	0.64	25.0	174.8	130.5	−23.1	179.6	2.8
14	0.74	22.6	146.8	100.5	−25.9	142.4	−3.0
16	0.85	18.5	126.2	95.1	−24.6	128.3	1.7
18	0.95	15.5	110.5	82.7	−25.2	104.5	−5.4
20	1.06	14.2	98.1	69.7	−29.0	99.1	1.0
25	1.33	12.7	76.2	54.0	−29.1	76.0	−0.3
30	1.59	10.1	62.0	40.7	−34.4	58.6	−5.5
40	2.12	7.3	44.8	28.5	−36.4	41.4	−7.6

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表 6 冲击波波头耗散对壁压冲量的影响

Table 6. Influence of shock wave head dissipation on wall pressure impulse

R/R₀	(R·W^−1/3)/(m·kg^−1/3)	v/(m·s⁻¹)	冲量
R/R₀	(R·W^−1/3)/(m·kg^−1/3)	v/(m·s⁻¹)	I_th /(kPa·s)	I_sim1 /(kPa·s)	δ_Is1/%	I_sim2 /(kPa·s)	δ_Is2/%
6	0.32	49.8	24.2	18.7	−22.7	22.7	−6.2
7	0.37	43.2	20.0	15.2	−24.0	19.2	−4.0
8	0.42	37.6	16.9	12.8	−24.3	16.2	−4.1
9	0.48	33.7	14.6	10.1	−30.8	13.7	−6.2
10	0.53	30.4	12.7	9.3	−26.8	12.1	−4.7
11	0.58	27.4	11.3	8.3	−26.5	11.0	−2.7
12	0.64	25.0	10.1	7.2	−28.7	9.7	−3.4
14	0.74	22.6	8.7	5.7	−34.5	8.0	−8.1
16	0.85	18.5	7.7	4.8	−37.7	6.9	−10.4
18	0.95	15.5	6.8	4.1	−39.7	6.0	−11.8
20	1.06	14.2	6.1	3.6	−41.0	5.4	−11.5
25	1.33	12.7	4.9	2.7	−44.9	4.0	−18.4
30	1.59	10.1	4.1	2.0	−51.2	3.1	−24.4
40	2.12	7.3	3.1	1.4	−54.8	2.3	−25.8

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