水下中远场爆炸冲击波作用下航行体表面动态响应分析

doi:10.12382/bgxb.2023.0306

摘要/Abstract

摘要：

针对水下中远场爆炸作用下航行体表面动态响应复杂、预测困难的问题,基于任意欧拉-拉格朗日数值算法,考虑自由面对冲击波反射的影响,利用爆炸相似理论细化模型网格,运用有限元软件对水下爆炸模型进行求解。分析冲击波作用下航行体表面动态应力峰值出现的时间和区域,并对其动态响应随当量、爆距及水深的变化规律进行研究。利用数值拟合方法得到航行体表面动态应力方程,并通过决定系数验证其可靠性,在定当量、爆距情况下可直接求解其动态应力。研究结果表明:当量增加,动态应力在相同爆距区间内衰减速率增大;爆距增大,动态应力在相同当量区间内增长速率降低;深度每下降100m,动态应力增长20MPa左右。所得研究结果可为中远场水下爆炸作用下航行体安全防护和抗冲击研究提供一定参考。

关键词: 水下航行体, 中远场水下爆炸, 任意欧拉-拉格朗日方法, 爆炸相似理论, 动态响应

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

中图分类号:

TJ31
TJ83

张勇, 肖正明, 段浩, 伍星, 卢敏, 王浩. 水下中远场爆炸冲击波作用下航行体表面动态响应分析[J]. 兵工学报, 2024, 45(7): 2341-2350.

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.

图/表 24

表1 材料模型和状态方程

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

表2 炸药JWL状态方程参数

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

表3 Q345钢的基本材料参数

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

表4 Q345钢的Johnson-Cook模型参数

Table 4 Johnson-Cook model parameters of Q345 steel

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

图1 水下爆炸流固耦合模型示意图

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

图2 水下爆炸1/4有限元缩比模型

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

表5 原爆炸数值模型与缩比数值模型相似关系(以TNT当量800kg在10m处引爆为例)

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

图3 0.8kg TNT炸药爆炸压力云图

Fig.3 Explosion pressure nephogram of 0.8kg TNT

图4 冲击波超压峰值云图

Fig.4 Overpressure nephogram of peak shock wave

图5 冲击波超压峰值时程曲线

Fig.5 Shock wave overpressure peak-time curves

图6 冲击波超压峰值随爆距变化曲线

Fig.6 Blast distance curve for shockwave peak overpressure

图7 航行体动态应力云图

Fig.7 Nephogram of dynamic stress of underwater vehicle

图8 航行体动态应力时程曲线(1.6kg,4m)

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

图9 航行体侧面起爆示意图

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

图10 航行体表面应力随爆距变化曲线

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

图11 仿真模拟曲线和数值拟合曲线(0.8kg TNT)

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

表6 不同爆距下R2中各参数值(TNT,0.8kg)

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

表6 不同爆距下R2中各参数值(TNT,0.8kg)

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

表7 不同当量的数值拟合函数及决定系数

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

表8 不同爆距的数值拟合函数及决定系数

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

图12 航行体表面应力随当量变化曲线

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

图13 仿真模拟曲线和数值拟合曲线(爆距2m)

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

图14 航行体表面应力随水深变化曲线

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

图15 航行体表面加速度在不同爆距下的时程曲线

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

图16 航行体表面加速度在不同当量下的时程曲线和局部放大图

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

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