三介质Mie-Grüneisen混合模型在水下爆炸防护层问题中的应用

doi:10.19596/j.cnki.1001-246x.8658

摘要/Abstract

摘要：

研究水下爆炸中的防护层问题, 将爆炸气体、水、防护层或其他材料看成一个混合流场后, 它们的物理状态可以直接用统一形式的Mie-Grüneisen状态方程来表示, 再用Mie-Grüneisen混合模型模拟爆炸气体、水、固态防护层之间的复杂相互作用。计算时, 通过状态方程中的特定参数来区分流体成分的物理特性, 并通过体积分数来区分界面, 同时添加自由进出口边界条件; 计算过程中, 对防护层的效果进行细致研究。研究发现, 防护层的效果取决于材料的冲击阻抗。当冲击波从一种介质进入新介质时, 在新介质冲击阻抗较小的情况下其压力会降低。同时, 进入防护层的冲击波被结构物反射又会形成第二个冲击波。在这个过程中, 对防护层的厚度和距离进行关注, 但是这两个因素并未产生重要影响。

关键词: 防护层, 冲击波, Mie-Grüneisen混合模型, 状态方程, 界面

Abstract:

In this paper, our main concern is the effects of the mitigation layer in the underwater explosion problem. As the explosive gaseous products, water, mitigation layer, and so on constitute a fluid mixture, the physical states of these components are covered by a uniform Mie-Grüneisen equation of states(EOS). Then the Mie-Grüneisen mixture model is applied to simulate the complicated interaction among gaseous product, water and solid layer. In the calculation, the particular parameters of EOS are used to make a distinction among the physical properties of fluid components and the volume fractions are used to identify the interfaces. In addition, the inlet and outlet boundary conditions are implemented here. During the calculation process, the effect of the mitigation layer is investigated here. According to the investigation, it is found that the effect of the layer is decided by the shock impedance of layer material. The pressure of the shock wave will decrease when it penetrates a new medium with lower impedance. On the other side, the penetrated shock wave in the layer is reflected by the structure and produces a second shock wave. During this process, the affection of layer thickness and distance is also studied here. But both two factors are unimportant under the mitigation mechanism.

Key words: mitigation layer, shock wave, Mie-Grüneisen mixture model, equation of States, interface

吴宗铎, 满庆洋, 严谨, 庞建华, 孙一方. 三介质Mie-Grüneisen混合模型在水下爆炸防护层问题中的应用[J]. 计算物理, 2023, 40(5): 556-569.

Zongduo WU, Qingyang MAN, Jin YAN, Jianhua PANG, Yifang SUN. Applications of Three-component Mie-GrüNeisen Mixture Model in Underwater Explosion Mitigation Problem[J]. Chinese Journal of Computational Physics, 2023, 40(5): 556-569.

图/表 17

表1 部分材料的Mie-Grüneisen状态参数

Table 1 Mie-Grüneisen state parameters for some materials

	ρ₀/(kg·m^-3)	c₀/(m·s^-1)	s	γ₀	α	适用范围/GPa
水	1 000	1 480	2.560, -1.986, 0.227(s₁, s₂, s₃)	0.5	1.0	0~120
铁(Fe-1018)、钢	7 850	3 574	1.920	1.69	1.0	0~270
聚乙烯塑料	915	2 900	1.481	1.644	1.0	0~50
砂石	1 950	2 450	1.86	1.28	1.0

表2 不同数值模型需要方程数的比较

Table 2 Comparison of equations required in different numerical models

介质数量	多相模型^[33]	五方程模型^[34]	Mie-Grüneisen混合模型
2	7个方程，1个逼近关系式	5个方程，1个逼近关系式	6个方程
3	11个方程，2~3个逼近关系式	7个方程，2~3个逼近关系式	7个方程
4	15个方程，3~6个逼近关系式	9个方程，3~6个逼近关系式	8个方程

图1 TNT-水冲击问题的p、u计算结果

Fig.1 The p、u results of TNT-water impact problem

图2 近壁面气泡问题的压力云图(a) Ref.[36]计算结果；(b) 本文计算结果

Fig.2 Pressure contours of near-wall bubbles problem (a) Ref.[36]'s results; (b) our results

图3 近壁面气泡问题的网格无关性(a) dx=dy=0.007 5；(b) dx=dy=0.003 75

Fig.3 Grid sizes independence in near-wall bubbles problem (a) dx=dy=0.007 5; (b) dx=dy=0.003 75

图4 近壁面气泡问题的时间步无关性(a) CFL=0.6; (b) CFL=0.2

Fig.4 Time step independence in near-wall bubbles problem (a) CFL=0.6; (b) CFL=0.2

图5 正上方固壁处的压力时程曲线

Fig.5 Time evolution of pressure at the rigid body right

图6 砂石中冲击波反射后的压力分布(a) 0.2 ms时刻Ref.[28]计算结果；(b) 0.2 ms时刻本文计算结果；(c) 0.4 ms时刻Ref.[28]计算结果；(d) 0.4 ms时刻本文计算结果

Fig.6 Pressure distribution of shock wave in sand after reflection (a) Ref.[28]'s results at 0.2 ms; (b) our results at 0.2 ms; (c) Ref.[28]'s results at 0.4 ms; (d) our results at 0.4 ms

图7 冲击波作用于砂石上不同时刻的密度分布(a) 0.2 ms时刻本文计算结果; (b) 0.4 ms时刻本文计算结果

Fig.7 Density distribution at different time instants with the impact of the shock wave on sand (a) our results at 0.2 ms; (b) our results at 0.4 ms

图8 4种防护情况下压力沿中线x=0的分布

Fig.8 Pressure distribution along the center line x=0.0 for four mitigation cases

图9 4种防护情况下压力时程曲线

Fig.9 Pressure history curves for four mitigation cases

表3 4种介质受冲击阻抗对比

Table 3 The shock impedance contrast of the four mediums under impact

	ρ₀/(kg·m^-3)	冲击波运动时间/ms	冲击波运动距离/m	冲击阻抗SI/(MPa·m·s^-1)
钢铁	7 800	0.138	0.5	28.26
砂石	1 950	0.227	0.5	4.30
聚乙烯塑料(实心)	915	0.139	0.5	3.29
聚乙烯塑料(空心)	750	0.172	0.5	2.33
水	1 000	0.172	0.6~0.075 × 2	2.62

图10 炸药与防护层布置示意图

Fig.10 Schematic diagram of explosive charge and mitigation layer

图11 有无防护层情况下，压力的时程曲线

Fig.11 Pressure history curves whether the mitigation layer exists or not

图12 不同时刻下压力沿中线x=0的分布

Fig.12 Pressure distribution along the center line x=0.0 at different time instants

图13 不同防护层厚度下的压力时程曲线

Fig.13 Pressure history curves for different layer thickness

图14 防护层位置不同时的压力时程曲线

Fig.14 Pressure history curves for different layer positions

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