基于可压缩多相流模型的舰艇附近水下爆炸数值模拟

doi:10.12382/bgxb.2024.0956

摘要/Abstract

摘要：

研究舰艇附近水下爆炸问题对船体结构设计、爆炸冲击损害预测及人员安全保障至关重要。为此,提出改进扩散界面法中的六方程可压多相流模型以解决冲击波条件下热力学状态预测偏差,并为相关抗冲击机理研究与数值方法优化提供支撑。通过引入混合能量校正方程及更精确的气体状态方程改进模型,在非结构网格系统构建数值算法程序,采用基于最小二乘重建和 Barth-Jespersen 限制器的二阶守恒定律的单调上游中心方案(Monotonic Upstream-centered Scheme for Conservation Laws,MUSCL)-Hancock 格式、两相流带接触的Harten-Lax-van Leer(Harten-Lax-van Leer Contact,HLLC) 黎曼求解器求解齐次双曲型方程,以 Newton-Raphson 迭代法求解瞬时压力松弛方程。研究结果表明:混合能量方程校正后,模型模拟流体冲击波速度和界面的结果与欧拉方程精确解高度吻合,解决界面附近数值振荡问题;相较于实验数据,改进型模型相对误差 1.13%,准确度提升 0.33%,且通过拟合冲击 Hugoniot 曲线获得更精确的刚性气体状态方程(Stiffened Gas Equation of State,SG-EOS)参数,同时可清晰呈现水下爆炸的冲击波传播、气泡胀缩及坍塌水射流现象,但在气泡界面清晰度、射流精细度上存在缺陷,主要受数值格式极端梯度下耗散特性限制。综上,改进型六方程可压多相流模型有效提升了舰艇附近水下爆炸模拟准确性,为深入研究舰艇抗冲击机理提供重要支撑,也为后续相关数值方法的优化奠定了坚实基础。

关键词: 舰艇, 水下爆炸, 六方程模型, 可压缩多相流, 黎曼求解器

Abstract:

Studying underwater explosions near warships is crucial for hull structure design,explosion impact damage prediction,and personnel safety.To this end,an improved six-equation compressible multiphase flow model based on the diffuse interface method is proposed to resolve thermodynamic state prediction deviation under shock waves and support anti-shock mechanism research and numerical method optimization.The model is improved via a hybrid energy correction equation and a more accurate gas equation of state.A numerical algorithm on an unstructured grid system is constructed,adopting the second-order MUSCL-Hancock scheme (with least-squares reconstruction and Barth-Jespersen limiter) and two-phase HLLC Riemann solver to solve homogeneous hyperbolic equations,and Newton-Raphson iteration for instantaneous pressure relaxation equation.Results show that after total energy equation correction,the model’s simulation of shock wave velocity and interface is highly consistent with the Euler equation’s exact solution,resolving near-interface numerical oscillation.Compared with experimental data,the improved model has a 1.13% relative error and 0.33% higher accuracy; more accurate SG-EOS parameters are obtained by fitting the shock Hugoniot curve.It also clearly shows underwater explosion phenomena:shock wave propagation,bubble expansion-contraction,and bubble collapse water jet.However,it has deficiencies in bubble interface clarity and jet precision,mainly limited by numerical scheme dissipation under extreme gradients.In conclusion,the improved model effectively enhances the accuracy of simulating underwater explosions near naval vessels,supports in-depth warship anti-shock mechanism research,and lays a solid foundation for future numerical method optimization.

Key words: naval vessel, underwater explosions, six-equation model, compressible multiphase flow, Riemann solver

中图分类号:

U661.1

俞万里, 杨澳, 汤兆烈, 程晗, 张之阳, 刘葳兴. 基于可压缩多相流模型的舰艇附近水下爆炸数值模拟[J]. 兵工学报, 2025, 46(9): 240956-.

YU Wanli, YANG Ao, TANG Zhaolie, CHENG Han, ZHANG Zhiyang, LIU Weixing. Numerical Simulation of Underwater Explosions Near a Naval Vessel Based on a Compressible Multi-fluid Model[J]. Acta Armamentarii, 2025, 46(9): 240956-.

图/表 18

表1 不同研究使用的液态水SG-EOS参数

Table 1 Different SG-EOS parameters for liquid water

案例	方法	γ	p_∞/MPa
1	Liou等^[23]方法	2.80	600.00
2	Saurel等^[15]方法	4.40	850.00
3	本文方法	5.45	40.45

图1 液态水激波粒子速度比较

Fig.1 Comparison of computed shock Hugoniot curves for shock-particle velocity of liquid water

图2 四边形非结构化网格的计算单元及其边界

Fig.2 Computational unit and boundary of quadrilateral unstructured grid

表2 一维水气两相激波管问题左右初始条件

Table 2 Initial conditions on the left and right sides of 1D water-air shock tube problem

位置	α₁	ρ₁/ (kg·m^-3)	ρ₂/ (kg·m^-3)	u/ (m·s^-1)	p₁/ MPa	p₂/ MPa
左边	10^-6	1	1000	0	10³	10³
右边	1-10^-6	1	1000	0	0.1	0.1

图3 t=0.24ms时刻一维水气两相激波管问题混合密度、速度和液相体积分数分布

Fig.3 Distribution diagram of mixture density,normal velocity,and water volume fraction of a 1D water-air shock tube problem at t=0.24ms

表3 两相界面在均匀场移动问题左右初始条件

Table 3 Initial conditions on the left and right sides of advection of an interface in a uniform pressure and velocity flow problem

位置	α₁	ρ₁/ (kg·m^-3)	ρ₂/ (kg·m^-3)	u/ (m·s^-1)	p₁/ MPa	p₂/ MPa
左边	10^-8	10	10³	100	10⁵	10⁵
右边	1-10^-8	10	10³	100	10⁵	10⁵

图4 t=2.79ms时刻两相界面在均匀场移动问题混合密度、速度和气相体积分数分布

Fig.4 Distribution diagram of mixture density,normal velocity,and air volume fraction of an interface in a uniform pressure and velocity flow problem at t=2.79ms

表4 近水面水下爆炸问题的水、空气和爆炸气泡的初始条件

Table 4 Initial conditions of the water,air,and explosive gas bubble for underwater explosions

介质	α₁	ρ₁/ (kg·m^-3)	ρ₂/ (kg·m^-3)	p_m/ MPa
液态水	10^-6	1000	10³	0.1
空气	1-10^-6	1.225	10³	0.1
爆炸气泡	1-10^-6	1250	10³	10³

图5 沿爆炸中心下方距离刚性底面0cm和5.0cm的两个测量目标处冲击波压力时程曲线

Fig.5 Shockwave pressure histories of two gauge targets with standoff distances of 0 and 5.0cm along the explosive center adjacent to the rigid surface

图6 近水面水下爆炸问题的不同时刻流场气相体积分数分布

Fig.6 Distribution diagram of gas phase volume fraction in the flow field at different times for underwater explosion near the water surface

图7 近水面水下爆炸问题的不同时刻流场压力分布

Fig.7 Distribution diagram of pressure in the flow field at different times for underwater explosion near the water surface

图8 舰艇周围的计算网格分布和数学模型配置

Fig.8 Distribution diagram of computational grid and configuration diagram of mathematical model around the ship

图9 自由场中水下爆炸在不同时刻的压力分布

Fig.9 Distribution diagram of pressure of underwater explosion in a free field at 0.5ms and 1.0ms

图10 网格无关性测试

Fig.10 Grid resolution test

图11 爆炸第1阶段不同时刻舰艇附近水下爆炸流场压力分布

Fig.11 Pressure distribution diagram of flow field near the ship at different times in the first stage of underwater explosion

图12 在10ms时刻传播到空气中的透射冲击波速度矢量

Fig.12 The velocity vector plot of the weak transmitted shock wave propagating into air at t=10ms

图13 沿爆炸中心直线距离2.0m和2.5m的两个测量目标处冲击波压力时程曲线

Fig.13 Time-history curve of shock wave pressure at two measurement targets located 2.0m and 2.5m in a straight line from the center of the explosion

图14 爆炸第2阶段不同时刻舰艇附近水下爆炸流场气相体积分数分布图

Fig.14 Gas phase volume fraction distribution diagram of flow field near the ship at different times in the second stage of underwater explosion

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