Effect of Shock Wave Load in Underwater Explosion of Cased Charge near Seabed

doi:10.12382/bgxb.2024.0643

Abstract

Abstract:

Bottom mines are typically deployed on the seabed and are designed to damage the surface ships and submarines during underwater explosion.The casing of bottom mine is the key factor influencing the energy output structure of charge underwater explosion (UNDEX).Based on the theory of UNDEX,the coupled Euler-Lagrange (CEL) method is used to establish a numerical model of the UNDEX of cased charge near the seabed.The characteristics of shock wave loads generated by the underwater explosion of cased charge are studied and the effects of various factors,such as charge shape,detonation mode,casing configuration,casing thickness ratio,and casing-to-charge mass ratio,on the characteristics of shock wave loads generated by underwater detonation of charges are analyzed.Furthermore,a casing with a variable wall thickness suitable for near seabed conditions is proposed,which significantly enhances the shock wave load.The results show that the constraint characteristics of the casing can cause the slower attenuation in the shock wave due to the underwater explosion of charge with distance.The casing with variable wall thickness has an enhancing effect on the shock wave load due to the underwater explosion of charges.The peak pressure of shock wave at 800 mm significantly increases with the increase of δ,and the growth rate can reach 9.74%.It can provide reference for the design of underwater weapons.

Key words: casing with a variable wall thickness, cased charge, underwater explosion, shock wave load, enhancement effect

CLC Number:

TJ301

LIU Gangwei, ZHANG Jingyuan, SHI Zhangsong, TAN Bo, SONG Pu, HU Hongwei, LU Yongjin. Effect of Shock Wave Load in Underwater Explosion of Cased Charge near Seabed[J]. Acta Armamentarii, 2025, 46(8): 240643-.

Figures/Tables 32

Table 1 Parameters of the water polynomial equation

ρ₀/ (kg·m^-3)	A₁/ MPa	A₂/ MPa	A₃/ MPa	B₀	B₁	T₁/ MPa	T₂/ MPa
1000	2200	9540	14600	0.28	0.28	2200	0

Table 2 HMX material parameters

ρ/ (kg·m^-3)	A/ GPa	B/ GPa	R₁	R₂	ω	E_q/ (GJ·m^-3)	$p C - J$ / GPa
1890	778.28	7.07	4.20	1.00	0.30	10.50	42.00

Table 2 HMX material parameters

ρ/ (kg·m^-3)	A/ GPa	B/ GPa	R₁	R₂	ω	E_q/ (GJ·m^-3)	$p C - J$ / GPa
1890	778.28	7.07	4.20	1.00	0.30	10.50	42.00

Table 3 Shock equation parameters

ρ/ (kg·m^-3)	Gruneisen 系数	C₀/ (m·s^-1)	S₁	S₂
4419	1.23	5130	1.028	0

Table 4 Parameters of the steinberg Guinan constitutive model

G₀/ GPa	Y₀/ GPa	Y_max/ GPa	β	n	G'_P	G'_T/ (MPa·K^-1)	Y'_P
41.9	1.33	2.12	12	0.1	0.4819	-26.98	-0.0153

Table 5 Sand material parameters

序号	ρ/(kg·m^-3)	p/MPa	c/(m·s^-1)
1	1.674	0	265
2	1.739	4.577	852
3	1.874	14.98	1721
4	1.997	29.15	1875
5	2.143	59.17	2265
6	2.250	98.10	2956
7	2.380	179.4	3112
8	2.485	289.4	4600
9	2.585	450.2	4634
10	2.631	650.7	4634

Fig.1 Numerical modelling of spherical charge

Fig.2 Grid convergence analysis

Fig.3 Comparison of numerically calculated peak shock wave pressures calculated value with theoretical values

Table 6 Simulation calculation and theoretical results of peak pressure of shock wave

距离/ mm	数值计算/ MPa	Zhang 方程/MPa	Cole 经验公式 /MPa	数值计算与 Zhang方程误差/%	数值计算与 Cole经验公式误差/%
400	189.35	202.25	174.32	-6.42	8.62
600	106.44	112.41	97.53	-5.31	9.13
800	71.58	75.84	69.74	-5.61	2.64
1000	53.04	57.40	54.20	-7.59	-2.14

Fig.4 Shock wave experiment with cased charge

Table 7 Comparison between the experimental data of shock wave pressure and the calculated data[23]

测点	实验数据/MPa	计算数据/MPa	误差/%
P1	14.94	15.52	3.88
P2	12.20	12.63	3.52
P3	9.60	9.81	2.19
P4	7.36	7.4	0.54
P5	5.52	5.49	-0.54
P6	8.83	8.01	-9.29
P7	4.39	4.25	-3.19
P8	3.23	3.28	1.55
P9	3.57	3.24	-9.24
P10	28.82	29.98	4.02

Fig.5 Shock wave experiment with sinking charge on the bottom wall[24]

Table 8 Comparison between the experimental results of shock wave pressure and the calculated results [24]

测点	实验结果/MPa	计算结果/MPa	误差/%
P1	10.45	10.24	-2.00
P2	13.03	13.23	-1.53
P3	6.96	7.13	-2.44
P4	10.39	10.47	-0.77

Table 9 Numerical model case setting for underwater explosion shock wave of cased charge

工况	装药形状	长径比	起爆方式	壳体设置
Case1	球形装药		中心起爆	无壳
Case2	柱形装药	0.5	中心起爆	无壳
Case3	柱形装药	1.0	中心起爆	无壳
Case4	柱形装药	2.0	中心起爆	无壳
Case5	球形装药		底部起爆	无壳
Case6	球形装药		顶部起爆	无壳
Case7	球形装药		中心起爆	底半球壳
Case8	球形装药		中心起爆	完整球壳

Fig.6 Numerical model of charges with different a

Fig.7 Numerical model of charges for different detonation modes

Fig.8 Numerical model of different cased charges

Fig.9 Changes in peak pressures of shock waves of charges with four shapes with burst range

Fig.10 Change in peak pressure of shock wave with burst range at different detonation modes

Fig.11 Peak shock wave pressures at different test points

Table 10 Numerical model case setting for shock wave caused by variable wall thickness sinking bottom explosion

工况	壳体材料	厚度比	质量比
Case 9	Al 6061-T6	2	8.95
Case 10	Al 6061-T6	4	8.95
Case 11	Al 6061-T6	6	8.95
Case 12	Al 6061-T6	8	8.95
Case 13 (对照组)	Al 6061-T6	10	8.95
Case 14	Steel 4340	10	25.86
Case 15	Ti6%Al4%V	10	14.56

Fig.12 Numerical model of charge with thickness-variable casing

Fig.13 Numerical model of charge for different casing materials

Fig.14 Pressure cloud map of cased charge with uniform wall thickness

Fig.15 Pressure cloud map of thickness-variable cased charge for δ=10

Table 11 Calculated results of peak shock wave pressure

爆距/mm	冲击波峰值压力/MPa
爆距/mm	Case 9	Case 10	Case 11	Case 12	Case 13
400	476.27	472.43	469.93	470.93	469.95
600	219.13	223.02	233.78	236.88	238.55
800	152.92	150.78	159.39	163.38	167.82
1000	113.81	108.12	109.11	108.62	111.70

Fig.16 Peak shock wave pressure of thickness-variable cased charge

Fig.17 Variation curves of peak shock wave pressure with δ

Fig.18 Shock wave spatial distribution test points setting

Fig.19 Spatial distribution of peak shock wave pressure

Fig.20 Peak shock wave pressures for different mass ratios

Table 12 Peak shock wave pressures for different mass ratios

爆距/mm	冲击波峰值压力/MPa
爆距/mm	Case 13	Case 14	Case 15
400	469.95	511.15	541.31
600	238.55	300.43	252.62
800	167.82	182.86	179.17
1000	111.70	121.99	125.85

References 24

[1]	KAN R Z, NIE J X, LIU Z, et al. Non-ideal explosive underwater explosion shockwave model[J]. Physics of Fluids, 2023, 35(8):087121.
[2]	WANG J T, HANG G Y, SHEN H M, et al. Numerical simulation of shock wave damage to medium-range and long-range targets[J]. Journal of Physics: Conference Series, 2023, 2478(2):22002.
[3]	WANG Q S, LIU S C, LOU H R. Calibration of numerical simulation methods for underwater explosion with centrifugal tests[J]. Shock and Vibration, 2019:1-19.DOI:10.1155/2019/2670836.
[4]	MACBETH C D, BURTON P W. Surface waves generated by underwater explosions offshore Scotland[J]. Geophysical Journal International, 1988, 94:285-294.
[5]	XU L Y, WANG S P, LIU Y L, et al. Numerical simulation on the whole process of an underwater explosion between a deformable seabed and a free surface[J]. Ocean Engineering, 2021, 219:108311.
[6]	MENG L, HUANG R Y, QIN J, et al. Study on the influence of rigid wall surface on the bubble characteristics of underwater explosion[J]. Journal of Physics: Conference Series, 2020, 1507(3):32020.
[7]	WANG G H, ZHANG S R, YU M, et al. Investigation of the shock wave propagation characteristics and cavitation effects of underwater explosion near boundaries[J]. Applied Ocean Research, 2014, 46:40-53.
[8]	RAJASEKAR J, KIM T H, KIM H D. Visualization of shock wave propagation due to underwater explosion[J]. Journal of Visualization, 2020, 23(5):825-837.
[9]	CHEN L K, HUANG S H, CHEN H J, et al. New correlations for evaluating the equivalent bare charge mass for a cased charge[J]. Defence Technology, 2023, 28:251-266.
[10]	ZHANG S, WANG Z Q, LI S T, et al. Study of the coupling characteristics of damage elements with cased charge[J]. Chaos,Solitons & Fractals, 2023, 176:114086.
[11]	梁斌, 卢永刚, 陈忠富, 等. 不同材料壳体装药在空气中爆炸威力试验研究[J]. 现代防御技术, 2008, 36(5):26-31.
	LIANG B, LU Y G, CHEN Z F, et al. Experimentation investigation of blast effect of explosive charge with different shell material in air[J]. Modern Defense Technology, 2008, 36(5):26-31. (in Chinese)
[12]	王长利, 周刚, 蔡宗义, 等. 带壳装药热爆炸冲击波超压测量及分析[J]. 兵工学报, 2012, 33(5):574-578.
	WANG C L, ZHOU G, CAI Z Y, et al. Measurement and analysis of shock wave overpressure of thermal explosion of charge with shell[J]. Acta Armamentarii, 2012, 33(5):574-578. (in Chinese)
[13]	裴善报, 刘荣忠, 郭锐, 等. 带壳装药水下爆炸的冲击波和气泡脉动特性[J]. 火工品, 2013(2):21-24.
	PEI S B, LIU R Z, GUO Y, et al. Shock wave and bubble pulse features of underwater explosion of explosive with metal shell[J]. Initiators & Pyrotechnics, 2013(2):21-24. (in Chinese)
[14]	COLE R H. Underwater explosions[M]. Princeton,NJ,US: Princeton University Press, 1948.
[15]	ZAMYSHLYAEV B V, YAKOVLEV Y S. Dynamic loads in underwater explosion[R]. Suitland,ML,US: Naval Intelligence Support Center, 1973.
[16]	ZHANG A M, LI S M, CUI P, et al. A unified theory for bubble dynamics[J]. Physics of Fluids, 2023, 35(3):033323.
[17]	HEUZÉ O. General form of the Mie-Grüneisen equation of state[J]. Comptes Rendus Mécanique, 2012, 340(10):679-687.
[18]	LEE E L, HORNIG H C, KURY J W. Adiabatic expansion of high explosive detonation products[R]. Livermore,CA,US: University of California Radiation Laboratory, 1968.
[19]	LEE E L, FINGER M, COLLINS W. JWL equations of state coeffs for high explosives[R]. Livermore,CA,US: Lawrence Livermore National Laboratory, 1973.
[20]	ANSYS. Autodyn explicit software for nonlinear dynamics[M]. Theory Manual Reversion 4.3. Canonsburg,PA,US: Century Dynamics Inc., 2005.
[21]	LAINE L. S A Derivation of mechanical properties for sand[C]// Proceedings of the 4th Asia-Pacific Conference on Shock and Impact Loads on Structures. Singapore: Nanyang Technological University, 2001:361-368.
[22]	ZHANG Z F, LI H L, ZHANG J Y, et al. Bubble motion and jet load near elastic-plastic structure under deep-water explosion[J]. Ocean Engineering, 2024, 294:116750.
[23]	JONES D A, NORTHEAST E D. Effects of case thickness on the performance of underwater mines[M]. Melbourne,Australia: DSTO Aeronautical and Maritime Research Laboratory, 1995.
[24]	杨莉, 汪玉, 汪斌, 等. 沉底装药水中爆炸现象的实验研究[J]. 爆炸与冲击, 2013, 33(2):175-180.
	YANG L, WANG Y, WANG B, et al. Experimental investigation on loading characteristics of underwater explosion from a bottom charge[J]. Explosion and Shock waves, 2013, 33(2):175-180. (in Chinese)