Applications of Three-component Mie-GrüNeisen Mixture Model in Underwater Explosion Mitigation Problem

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

Abstract

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

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.

Figures/Tables 17

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

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

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

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

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

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

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

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

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

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

Fig.9 Pressure history curves for four mitigation cases

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

Fig.10 Schematic diagram of explosive charge and mitigation layer

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

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

Fig.13 Pressure history curves for different layer thickness

Fig.14 Pressure history curves for different layer positions

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