Numerical simulation for shock to detonation process of explosive nitromethane containing cavities

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 Harten-Lax-van Leer-contact (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.