25 th ICDERS August 2 – 7, 2015 Leeds, UK Correspondence to: Richard.Saurel@univ-amu.fr 1 Modeling shocks and detonations in heterogeneous high explosives Richard Saurel 1,2 , François Fraysse 2 and Damien Furfaro 2 1 University Institute of France and Aix-Marseille University, M2P2 UMR 7340 Marseille, France 2 RS2N, 371 chemin de Gaumin, 83640 Saint-Zacharie, France 1 Introduction Shock and detonations in heterogeneous materials differ widely of similar phenomena in gas mixtures as temperatures and velocities disequilibrium are present among the phases with scales much larger than molecular ones. Chemical decomposition phenomenon is different as well, the ignition being governed by local effects (hot spots) resulting of these disequilibria. Materials equations of state are obviously also very different of those of gases. The present talk is devoted to the presentation of modern technical material in some of these areas: - Shock relations for multiphase mixtures with stiff mechanical relaxation [1]. These relations [2] enable accurate computation of the post-shock state and energy partition among the phases. - Generalized Chapman-Jouguet conditions [3]. In the detonation reaction zone, stiff mechanical relaxation holds but temperatures remain out of equilibrium. Heat exchanges result in non-negligible unreacted solid at the sonic surface and have similar (but weaker) effects as velocity divergence effects in non-ideal detonations. - A flow model valid just after the shock front where mechanical relaxation is stiff to the expansion zone, where velocity disequilibrium are present [4]. - A novel equation of state, simple and accurate for condensed energetic materials and temperature computation [5]. Chemical decomposition and hot spots modelling in this theoretical frame are in progress. The paper is organized as follows. In Section 2 the symmetric variant of the BN model [6] is presented to model non-equilibrium two-phase flow mixtures. Its mechanical equilibrium reduced version [1] is recalled in Section 3 with the associated shock relations. The CJ and ZND associated models are given in Section 4. A method to fit these shock, ZND and CJ conditions in unsteady regime, 1D and multi-D is given in Section 5. 2 Non-equilibrium flow model A symmetric variant of the two-phase flow BN model has been derived in [4]: ∂α 1 ∂t + u I ∂α 1 ∂x = µ (π 1 − π 2 )