A Velocity-Entropy Invariance theorem for the Chapman-Jouguet detonation
Résumé
The velocity and the specific entropy of the Chapman-Jouguet (CJ) equilibrium detonation in a homogeneous explosive are shown to be invariant under the same variations of the initial pressure and temperature. The CJ state, including the adiabatic exponent, and its isentrope, can then be obtained from the CJ velocity or, conversely, the CJ velocity from one CJ variable, without equation of state of detonation products. For gaseous explosives, comparison to calculations with detailed chemical equilibrium shows agreement to within O(0.1) %. However, the CJ pressures of four carbonate liquid explosives are found about 20 % greater than measured values: the CJ-equilibrium model appears not to apply to carbonate condensed explosives. A simple criterion for assessing the representativeness of this model is thus proposed, which nevertheless cannot indicate which of its assumptions would not be satisfied, such as chemical equilibrium or single-phase fluid. This invariance might be an illustration of a general feature of hyperbolic systems and their characteristic surfaces.
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