Thermodynamically consistent diffuse interface model for the numerical simulation of interaction between solid explosive detonation and inert materials

An improved diffuse interface model is proposed to numerically simulate the interaction dynamics between solid explosive detonation and compressible inert materials. The chemical reaction of solid explosive detonation is simplified as the solid-phase reactant is converted into a gas-phase product. Thus, the mixture within a control volume is regarded to be composed of three kinds of components: solid-phase reactant, gas-phase product, and inert materials. Due to their differences in thermodynamic properties, three kinds of components can be thought to be in mechanical equilibrium and thermal nonequilibrium. The evolution equation for the volume fractions of all components is derived on the basis of the entropy production and pressure equality among the components. The evolution equation for the pressure of the mixture is also obtained and added to the diffuse interface model. Thus, the governing equations of the proposed diffuse interface model include the conservation equations for the mass of each component, the conservation equations for the momentum and total energy of the mixture, the evolution equation for the volume fraction of each component, and the evolution equation for the pressure of the mixture. The important characteristics of the proposed model are simultaneous consideration of mass transfer from the chemical reaction and heat exchange from thermal nonequilibrium and also direct calculation of the pressure from the governing equations. The proposed model owns thermodynamic consistency to effectively eliminate nonphysical oscillations near the material interface. Meanwhile, it can apply to arbitrary expressions of the equation of state, allow for any number of inert materials, and also treat large density ratios across the material interface.