Dynamic Response of Vehicle Surface under the Action of Underwater Middle and Far Field Explosion Shock Waves

doi:10.12382/bgxb.2023.0306

Abstract

Abstract:

The dynamic response of underwater vehicle surface after an underwater explosion in the far field is predicted by the numerical algorithm based on arbitrary Euler-Lagrange method. In this paper, the impact of free surface on shock wave reflection is taken into consideration, the model mesh is refined using the explosion similarity theory, and the finite element software is used to solve the underwater explosion model. The timing and location of peak dynamic stress on the underwater vehicle surface subjected to the shock wave are determined, and the variations in dynamic response with equivalent, blast distance and water depth are studied. A dynamic stress equation for the underwater vehicle surface is obtained by a numerical fitting method, and the equation’s reliability is assessed through the coefficient of determination. It is observed that an increase in the equivalent results in a higher decay rate of dynamic stress in a fixed blast distance interval. Conversely, an increase in the blast distance leads to a reduced growth rate of dynamic stress in the same equivalent interval, while a decrease in water depth by 100 meters is associated with an approximate 20MPa increase in dynamic stress. The research outcomes offer valuable insights and serve as a reference for future investigations in safety protection and impact resistance assessments.

Key words: underwater vehicle, middle and far field underwater explosion, arbitrary Euler-Lagrange method, explosion similarity theory, dynamic response

CLC Number:

TJ31
TJ83

ZHANG Yong, XIAO Zhengming, DUAN Hao, WU Xing, LU Min, WANG Hao. Dynamic Response of Vehicle Surface under the Action of Underwater Middle and Far Field Explosion Shock Waves[J]. Acta Armamentarii, 2024, 45(7): 2341-2350.

Figures/Tables 24

Table 1 Material model and equation of state

材料名称	材料模型	状态方程
炸药	高爆材料模型	JWL
水	空材料模型	Gruneisen
航行体	JC材料模型	Gruneisen
空气	空材料模型	多项式状态方程

Table 2 Parameters of explosive JWL equation of state

A_TNT/GPa	B_TNT/GPa	R₁	R₂	ω
371.2	3.231	4.15	0.95	0.3

Table 3 Basic material parameters of Q345 steel

参数	取值
密度/(kg·m^-3)	7.85×10³
弹性模量/Pa	2.06×10¹¹
泊松比	0.2
抗拉强度/Pa	4.9×10⁸~6.2×10⁸
屈从比	≤0.8
伸长率/%	≥22

Table 4 Johnson-Cook model parameters of Q345 steel

A/MPa	B/MPa	n	C
374	795.71	0.45	0.016

Fig.1 Schematic diagram of underwater explosion fluid-structure coupling model

Fig.2 1/4 finite element model of underwater explosion fluid-structure coupling

Table 5 Similarity between the original explosion numerical model and the scaled numerical model (taking the TNT equivalent of 800kg detonated at 10m as an example

参数	原数值模型	缩比数值模型
缩尺比	1/1	1/10
TNT当量/kg	800	0.8
爆距/m	10	1

Fig.3 Explosion pressure nephogram of 0.8kg TNT

Fig.4 Overpressure nephogram of peak shock wave

Fig.5 Shock wave overpressure peak-time curves

Fig.6 Blast distance curve for shockwave peak overpressure

Fig.7 Nephogram of dynamic stress of underwater vehicle

Fig.8 Dynamic stress-time curve of underwater vehicle (1.6kg,4m)

Fig.9 Schematic diagram of explosion on the side of underwater vehicle

Fig.10 Changing curve of surface stress of underwater vehicle withblast distance

Fig.11 Simulation and numerical fitting curves (0.8kg TNT)

Table 6 Parameters of R2 at differentblast distances (TNT,0.8kg)

爆距/m	y_i	$y ¯$	$\hat{y}$
1	510.2	119.3	510.1
2	182.1	119.3	183.1
3	98.3	119.3	97.2
4	61.3	119.3	60.1
5	40.9	119.3	40.1
6	24.2	119.3	27.8
7	19.6	199.3	19.6
8	15.3	119.3	13.8

Table 6 Parameters of R2 at differentblast distances (TNT,0.8kg)

爆距/m	y_i	$y ¯$	$\hat{y}$
1	510.2	119.3	510.1
2	182.1	119.3	183.1
3	98.3	119.3	97.2
4	61.3	119.3	60.1
5	40.9	119.3	40.1
6	24.2	119.3	27.8
7	19.6	199.3	19.6
8	15.3	119.3	13.8

Table 7 Numerical fitting functions and determination coefficients for different equivalents

当量/kg	数值拟合函数	决定系数R²
0.2	f(x)=349x^-2^.⁰³⁷+4.02	0.987
0.4	f(x)=410x^-1^.⁶²⁷-4.07	0.985
0.6	f(x)=453x^-1^.⁶⁷²-0.14	0.987
0.8	f(x)=524x^-1^.⁴¹¹-14.04	0.989
1.0	f(x)=585x^-1^.⁴³¹-14.46	0.981
1.2	f(x)=614x^-1^.⁵¹⁵-6.34	0.985
1.4	f(x)=674x^-1^.³⁶⁹-20.95	0.982
1.6	f(x)=735x^-1^.³⁰³-30.07	0.986

Table 8 Numerical fitting functions and determination coefficients for differentblast distances

爆距/m	数值拟合函数	决定系数R²
1	f(x)=251x+306.32	0.987
2	f(x)=127x+69.84	0.976
3	f(x)=66x+35.85	0.963
4	f(x)=36x+24.42	0.914
5	f(x)=30x+12.84	0.978
6	f(x)=23x+7.60	0.968
7	f(x)=14x+8.07	0.988
8	f(x)=10x+7.52	0.967

Fig.12 Changing curves of surface stress of underwater vehicle with equivalent

Fig.13 Simulation and numerical fitting curves (blast distance 2m)

Fig.14 Changing curve of surface stress of underwater vehicle with water depth

Fig.15 Surface acceleration-time curves of underwater vehicle at differentblast distances

Fig.16 Time history curves and local magnified images of surface acceleration of underwater vehicle under different equivalents

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