Evaluation of the two-γ model and the energy balance process of a Chapman-Jouguet detonation

Two issues related to the application of Chapman-Jouguet (C-J) theory have been investigated in this study. Firstly, the solution of the two-γ analytical model cannot agree with the exact solution calculated from the Chemical Equilibrium Compositions and Applications (CEA) code even all the required parameters are substituted with the exact ones. To root the source, the original derivation has been reviewed. It is believed that the perfect gas approximation induces the discrepancy, which will result in a huge discrepancy in the heat release at C-J state. Hence, a four-γ model for ideal gases has been derived, whose results are consistent with those from the CEA code though it requires more input parameters. Sensitive analysis implies that the accuracy of the four-γ model is greatly impacted by γ₂‾ and q_CJ. Besides, a parabola function that can describe the heat release and the lower heating value correlation has been proposed. Using this function, about ±5% relative error of estimated M_S can be achieved when γ₂‾ is equal to 9/7 for most selected stoichiometric gas mixtures. Secondly, the energy distribution in a C-J detonation process is found quite different when attaching the reference frame to the ground or the detonation wave front. Hence, regarding the C-J state as the equivalent burned state at the exit of a detonation combustor is questionable. Accordingly, a four-step thermodynamic process for a closed system has been developed, which can quantitatively analyze the energy balance process of a C-J detonation. Discussion is made by comparing the process with a traditional steady thermodynamic process as well as constant-volume combustion.