﻿ 水下爆炸载荷特性数值计算方法
 舰船科学技术  2023, Vol. 45 Issue (24): 7-13    DOI: 10.3404/j.issn.1672-7649.2023.24.002 PDF

1. 武汉第二船舶设计研究所，湖北 武汉 430064;
2. 华中科技大学 船舶与海洋工程学院，湖北 武汉 430074

Numerical calculation method of underwater blast load characteristics
CAO Xiao-ming1, YU Sheng2, HE Hong-xuan2, LIU Jia-yi2
1. Wuhan Second Ship Design and Research Institute, Wuhan 430064, China;
2. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Abstract: In order to better study the impact load of underwater explosion, the blast shock wave and bubble pulsation were simulated by numerical simulation. The finite element software AUTODYN was used to establish a one-dimensional explosive-water model to simulate the explosive load generated by explosive explosion. The reliability of the finite element model was verified by comparing the empirical formula, and the error between the calculated results and empirical formula was less than 15%. At the same time, the influence of detonation distance, explosive equivalent and water depth on the shock wave and bubble pulsation of underwater explosion was studied.
Key words: underwater blast shock wave     bubble pulsation     peak shock wave     specific impulse     bubble expansion radius     bubble pulsation period
0 引　言

1 水下爆炸计算方法 1.1 水下爆炸冲击波计算方法

Geer等[9]在实验基础上总结相关数据，将水下爆炸压力分为几个阶段。其中，指数衰减阶段描绘了水下爆炸冲击波指数式衰减的主要特征。冲击波峰值Pm以及冲击波冲量I可由下述经验公式估算得出：

 ${P_m} = \left\{ \begin{gathered} 44.1{\left( {\frac{{{W^{{1 \mathord{\left/ {\vphantom {1 3}} \right. } 3}}}}}{R}} \right)^{1.5}},6 \leqslant \frac{R}{{{R_0}}} < 12 ，\\ 52.4{\left( {\frac{{{W^{{1 \mathord{\left/ {\vphantom {1 3}} \right. } 3}}}}}{R}} \right)^{1.13}},12 \leqslant \frac{R}{{{R_0}}} < 240 。\\ \end{gathered} \right.$ (1)
 $I = 5768 \times \sqrt[3]{W}{(\frac{{\sqrt[3]{W}}}{R})^{0.89}} 。$ (2)

1.2 水下爆炸气泡计算方法

1960年，Cole给出了TNT球形装药水下爆炸气泡最大膨胀半径与气泡脉动周期经验公式。1973年，Zamyshlyayev[10]在Cole研究成果基础上进一步发展，总结水下爆炸气泡最大膨胀半径与气泡脉动周期经验公式如下：

 $T = {K_T}\frac{{{W^{{1 \mathord{\left/ {\vphantom {1 3}} \right. } 3}}}}}{{{{\left( {1 + 0.1h} \right)}^{{5 \mathord{\left/ {\vphantom {5 6}} \right. } 6}}}}}，$ (3)
 ${R_{\max }} = \frac{{{K_R}}}{{{{\left( {1 + 0.1h} \right)}^{{1 \mathord{\left/ {\vphantom {1 3}} \right. } 3}}}}}{R_0} 。$ (4)

 ${P_1} = {P_0} + {\rho _0}gh 。$ (11)

3 结果分析 3.1 冲击波压力结果分析 3.1.1 有效性验证

3.1.2 不同爆距工况水下爆炸冲击波数值模拟

 图 3 不同爆距计算结果 Fig. 3 Numerical results under different detonation distance

3.1.3 不同炸药当量水下爆炸冲击波数值模拟

 图 4 不同炸药当量计算结果 Fig. 4 Numerical results under different equivalent of explosive

3.1.4 不同水深工况水下爆炸冲击波数值模拟

 图 5 不同水深计算结果 Fig. 5 Numerical results under different depth of water

3.2 气泡脉动结果分析 3.2.1 有效性验证

 图 6 验证工况气泡脉动过程中气泡半径的变化 Fig. 6 The change of bubble radius during bubble pulsation in verifying case

3.2.2 不同炸药当量水下爆炸气泡脉动数值模拟

 图 7 不同炸药当量气泡脉动过程中气泡半径的变化 Fig. 7 The change of bubble radius during the process of the bubble pulsation under different equivalent of explosive

3.2.3 不同水深水下爆炸气泡脉动数值模拟

 图 8 不同水深气泡脉动过程中气泡半径的变化 Fig. 8 The change of bubble radius during the process of the bubble pulsation under different depth of water

4 结　语

1）水下爆炸冲击波的超压峰值、二次压力峰值以及比冲量峰值均随着爆距的增加呈减小趋势，减小的速度随着爆距的增加而减缓。冲击波压力峰值、二次压力波峰值、冲击波比冲量峰值随着炸药当量的增加呈增大趋势，从冲击波压力峰值到二次压力波峰值之间相隔的时间也会随着炸药当量的增加而增加。

2）不同爆深工况下，超压曲线的压力峰值及二次压力波峰值基本相等，但爆深越大时，超压曲线负压区压力越大，两次压力峰值之间的时长越短，冲击波比冲量峰值随着水深的增加呈减小趋势。

3）水下爆炸气泡最大膨胀半径随炸药当量的增大而增大，水下爆炸气泡脉动周期随炸药当量的增大而增大，水下爆炸气泡二次脉动最大半径及二次脉动周期同样随炸药当量的增加而增大，但气泡二次脉动最大半径与第一次脉动最大半径相比较小。

4）水下爆炸气泡最大膨胀半径随爆深的增大而减小，水下爆炸气泡脉动周期随爆深的增大而减小，水下爆炸气泡最大膨胀半径和气泡脉动周期减小的速度随着爆深的增加而减缓。水下爆炸二次脉动最大半径及二次脉动周期同样随爆深的增加而减小。

 [1] TAYLOR G I. The pressure and impulse of submarine explosion waves on plates[J]. The scientific papers of GI Taylor, vol. 3. Cambridge, UK: Cambridge University Press. 1963: 287–303. [2] 库尔. 水下爆炸[M]. 罗耀杰, 韩润泽, 官信译. 北京: 国防工业出版社, 1960 [3] ZHAO Z T, RONG J L, ZHANG S X. A numerical study of underwater explosions based on the ghost fluid method[J]. Ocean Engineering, 2022, 247: 109796. [4] S TANAKA, I BATAEV, M NISHI, et al. Micropunching large-area metal sheets using underwater shock wave: experimental study and numerical simulation[J]. International Journal of Machine Tools and Manufacture, 2019, 147: 103457. [5] LI G L, SHI D Y, CHEN Y Y, et al. A study on damage characteristics of double-layer cylindrical shells subjected to underwater contact explosion[J]. International Journal of Impact Engineering. 2023, 172: 104428. [6] L J REN, H H MA, Z W SHEN, et al. Blast response of water-backed metallic sandwich panels subject to underwater explosion – Experimental and numerical investigations[J]. Composite Structures. 2019, 209: 79–92. [7] LEBLANC J, SHUKLA A. Dynamic response of curved composite panels to underwater explosive loading: Experimental and computational comparisons[J]. Composite Structures, 2011, 93: 3072–3081. [8] HONG Y J, XI Z. Dynamic response of a ring-stiffened cylindrical shell subjected to underwater explosive loading[J]. Applied Mechanics and Materials, 931(6): 105−107. [9] GEERS T L, HUNTER K S. An integrated wave-effects model for an underwater explosive bubble[J]. The Junmal of the Acoustical Society of America, 2022, 111(4): 1584–1601. [10] ZAMYSHLYAIEV B V. Dynamic loads in underwater explosion, AD-757183. [11] 张社荣, 李宏璧, 王高辉, 等. 水下爆炸冲击波数值模拟的网格尺寸确定方法[J]. 振动与冲击, 2015, 34(8): 93–100.