Numerical simulation for shock to detonation process of explosive nitromethane containing cavities
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摘要: 为研究冲击波加载下含空穴液体炸药硝基甲烷的起爆过程，提出了一种基于水平集方法的欧拉多介质计算方法。采用反应欧拉方程组作为控制方程，通过水平集方法追踪化学反应混合物与空穴之间的界面。为提高计算方法的鲁棒性，在界面附近的计算单元内应用修正的虚拟流体方法，将多介质问题转化成单介质问题。对于这两种流体，均采用高阶加权本质无振荡（weighted essentially non-oscillatory, WENO）有限差分方法计算单元边界的数值通量，使得模拟结果具有高可靠性。由于Jones-Wilkins-Lee（JWL）状态方程与理想气体状态方程形式差别很大，爆轰产物的质量分数又直接影响了化学反应区内守恒变量和原始变量的相互转化过程，难以给出爆炸混合物状态方程的显式表达形式，因此发展了一种能够解决以上难题的虚拟流体状态预测方法。通过求解涉及化学反应的复杂多介质黎曼问题，获得界面两侧虚拟流体的变量状态。对不同强度冲击波加载下硝基甲烷与空穴的相互作用问题开展了数值模拟，数值结果可以说明：提出的计算方法能够捕捉到空穴压缩、塌陷、闭合以及消失后的流体动力学全过程。Abstract: In order to study the initiation process of liquid explosive nitromethane containing cavities under shock wave loading, an Eulerian multi-material computational approach based on the level set method was developed. The reactive Euler equations were adopted as the governing equations, the level set method was utilized to track the multi-medium interface between the chemical reaction mixture and the cavity. To improve the robustness of calculation method, the modified ghost fluid method was applied in computational cells near the interface. Based on the modified ghost fluid method, a multi-medium problem was transformed into a single media problem. For these two fluid phases on both sides of the interface, the high order weighted essential non-oscillatory finite difference method was implemented to calculate the numerical fluxes on cell boundary, making the simulation results reliable. However, the Jones Wilkins Lee equation of state differs greatly from the ideal gas equation of state. In addition, the mass fraction of detonation product directly affects the transformation process between the conserved variables and the primitive variables in reaction zone, making it difficult to provide an explicit expression for the equation of state of explosive mixture. In order to solve the above problems, a ghost fluid state prediction method based on the HLLC approximate Riemann solver was developed. By dealing with a complex multi-medium Riemann problem considering chemical reaction, the variable states of ghost fluid on both sides of the interface can be obtained. The multi-medium calculation method was used to simulate the interaction problems between liquid nitromethane and the cavity under the loading condition with different impact strengths. The numerical results illustrate that the method proposed in the paper can capture the entire fluid dynamics process of cavity compression, cavity collapse, cavity closure and cavity disappearance.
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Key words:
- liquid nitromethane /
- cavity collapse /
- multi-medium interface /
- level set method /
- ghost fluid
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图 2 4 GPa压力下不同时刻的密度分布
Figure 2. Density distributions under 4 GPa pressure at different times
图 3 4 GPa压力下不同时刻的压力分布
Figure 3. Pressure distributions under 4 GPa pressure at different times
图 4 4 GPa压力下不同时刻的密度分布
Figure 4. Density distributions under 4 GPa pressure at different times
图 5 4 GPa压力下不同时刻的压力分布
Figure 5. Pressure distributions under 4 GPa pressure at different times
图 6 4 GPa压力下不同时刻的爆轰产物质量分数分布
Figure 6. Detonation product mass fraction distributions under 4 GPa pressure at different times
图 7 4 Gpa压力下0 μs、0.17 μs、0.37 μs时的中轴线密度、压力和速度分布
Figure 7. Density, pressure and velocity distributions on the central axis under 4 GPa pressure at 0 μs, 0.17 μs, 0.37 μs
图 8 4 Gpa压力下0.74 μs、1.35 μs、2.2 μs时的中轴线密度、压力和速度分布
Figure 8. Density, pressure and velocity distributions on the central axis under 4 GPa pressure at 0.74 μs, 1.35 μs, 2.2 μs
图 9 不同网格尺寸下0.37 μs时的密度分布
Figure 9. Density distributions with different mesh sizes at 0.37 μs
图 10 0.37 μs时的中轴线密度和压力分布
Figure 10. Density and pressure distributions on the central axis at 0.37 μs
图 11 6 GPa压力下不同时刻的密度分布
Figure 11. Density distributions under 6 GPa pressure at different times
图 12 6 GPa压力下不同时刻的压力分布
Figure 12. Pressure distributions under 6 GPa pressure at different times
图 13 6 GPa压力下不同时刻的密度分布
Figure 13. Density distributions under 6 GPa pressure at different times
图 14 6 GPa压力下不同时刻的压力分布
Figure 14. Pressure distributions under 6 GPa pressure at different times
图 15 6 GPa压力下不同时刻的爆轰产物质量分数分布
Figure 15. Product mass fraction distributions under 6 GPa pressure at different times
图 16 6 GPa压力下0 μs、0.15 μs、0.3 μs时的中轴线密度、压力和速度分布
Figure 16. Density, pressure and velocity distributions on the central axis under 6 GPa pressure at 0 μs, 0.15 μs, 0.3 μs
图 17 6 GPa压力下0.7 μs、1.11 μs、1.94 μs、2.49 μs时的中轴线密度、压力和速度分布
Figure 17. Density, pressure and velocity distributions on the central axis under 6 GPa pressure at 0.7 μs, 1.11 μs, 1.94 μs, 2.49 μs
图 18 8 GPa压力下不同时刻的密度分布
Figure 18. Density distributions under 8 GPa pressure at different times
图 19 8 GPa压力下不同时刻的压力分布
Figure 19. Pressure distributions under 8 GPa pressure at different times
图 20 8 GPa压力下不同时刻的密度分布
Figure 20. Density distributions under 8 GPa pressure at different times
图 21 8 GPa压力下不同时刻的压力分布
Figure 21. Pressure distributions under 8 GPa pressure at different times
图 22 8 GPa压力下不同时刻的爆轰产物质量分数分布
Figure 22. Detonation product mass fraction distributions under 8 GPa pressure at different times
图 23 8 GPa压力下0 μs、0.14 μs、0.27 μs时的中轴线密度、压力和速度分布
Figure 23. Density, pressure and velocity distributions on the central axis under 8 GPa pressure at 0 μs, 0.14 μs, 0.27 μs
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