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Abstract  A hyperbolic multiphase flow model with a single pressure and a single velocity but several temperatures is proposed to deal with the detonation dynamics of condensed energetic materials. Temperature non-equilibrium effects are mandatory in order to deal with wave propagation (shocks, detonations) in heterogeneous mixtures. The model is obtained as the asymptotic limit of a total non-equilibrium multiphase flow model in the limit of stiff mechanical relaxation only (Kapila et al. in Phys Fluids 13:3002–3024, 2001). Special attention is given to mass transfer modelling, that is obtained on the basis of entropy production analysis in each phase and in the system (Saurel et al. in J Fluid Mech 607:313–350, 2008). With the help of the shock relations given in Saurel et al. (Shock Waves 16:209–232, 2007) the model is closed and provides a generalized ZND formulation for condensed energetic materials. In particular, generalized CJ conditions are obtained. They are based on a balance between the chemical reaction energy release and internal heat exchanges among phases. Moreover, the sound speed that appears at sonic surface corresponds to the one of Wood (A textbook of sound, G. Bell and Sons LTD, London, 1930) that presents a non-monotonic behaviour versus volume fraction. Therefore, non-conventional reaction zone structure is observed. When heat exchanges are absent, the conventional ZND model with conventional CJ conditions is recovered. When heat exchanges are involved interesting features are observed. The flow behaviour presents similarities with non ideal detonations (Wood and Kirkwood in J Chem Phys 22:1920–1924, 1950) and pathological detonations (Von Neuman in Theory of detonation waves, 1942; Guenoche et al. in AIAA Prog Astron Aeronaut 75: 387–407, 1981). It also present non-conventional behaviour with detonation velocity eventually greater than the CJ one. Multidimensional resolution of the corresponding model is then addressed. This poses serious difficulties related to the presence of material interfaces and shock propagation in multiphase mixtures. The first issue is solved by an extension of the method derived in Saurel et al. (J Comput Phys 228(5):1678–1712, 2009) in the presence of heat and mass transfers. The second issue poses the difficult mathematical question of numerical approximation of non-conservative systems in the presence of shocks associated to the physical question of energy partition among phases for a multiphase shock. A novel approach is used, based on extra evolution equations used to retain the information of the material initial state. This method insures convergence in the post-shock state. Thanks to these various theoretical and numerical ingredients, one-dimensional and multidimensional unsteady detonation waves computations are done, eventually in the presence of material interfaces. Convergence of the numerical hyperbolic solver against ZND multiphase solution is reached. Material interfaces, shocks, detonations are solved with a unified formulation where the same equations are solved everywhere with the same numerical scheme. [ABSTRACT FROM AUTHOR]

A hyperbolic two-phase flow model involving five partial differential equations is constructed for liquid?gas interface modelling. The model is able to deal with interfaces of simple contact where normal velocity and pressure are continuous as well as transition fronts where heat and mass transfer occur, involving pressure and velocity jumps. These fronts correspond to extra waves in the system. The model involves two temperatures and entropies but a single pressure and a single velocity. The closure is achieved by two equations of state that reproduce the phase diagram when equilibrium is reached. Relaxation toward equilibrium is achieved by temperature and chemical potential relaxation terms whose kinetics is considered infinitely fast at specific locations only, typically at evaporation fronts. Thus, metastable states are involved for locations far from these fronts. Computational results are compared to the experimental ones. Computed and measured front speeds are of the same order of magnitude and the same tendency of increasing front speed with initial temperature is reported. Moreover, the limit case of evaporation fronts propagating in highly metastable liquids with the Chapman?Jouguet speed is recovered as an expansion wave of the present model in the limit of stiff thermal and chemical relaxation. [ABSTRACT FROM AUTHOR]