Thermodynamically consistent detonation model for solid explosives

An improved reactive flow model with thermodynamic consistency is proposed to deal with the detonation hydrodynamics of solid explosives. Based on the assumption that the chemical mixture composed of solid-phase reactants and gas-phase products can arrive at mechanical equilibrium, but cannot arrive at thermal equilibrium, the solid-phase reactants and gas-phase products may possess one pressure and one velocity, but two temperatures or internal energies. With the help of the energy conservation of the mixture and pressure equivalence between the constituents, the conservation equation of internal energy and the evolution equations of the volume fraction for the solid-phase reactants and of pressure for the chemical mixture are derived. Thus, the full governing equations of the proposed detonation model include the conservation equations of mass, momentum, and total energy, and the evolution equation of pressure for the chemical mixture, and the conservation equations of mass and internal energy, and the evolution equation of the volume fraction for the solid-phase reactants. The theoretical analysis shows that there exists a distinct discrepancy between the proposed model and the Zel'dovich–Neumann–Doring detonation model for the steady structure of the detonation wave. The numerical simulation results of typical detonation problems show that the important characteristics of detonation flows can be well captured and also demonstrate that the proposed detonation model of solid explosives is reasonable.