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, a Eulerian multi-medium calculation method based on the level set method was proposed. Using the reactive Euler equations as the control equations, the level set technique was utilized to track the multi-medium interface between the chemical reaction mixture and the cavity. Because cavity collapse and detonation propagation involve strong shock waves and strong discontinuities, the simulation becomes a computational challenge. 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 fluids on both sides of the interface, the high order weighted essential non-oscillatory finite difference method was utilized 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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