On deviations from ideal Chapman-Jouguet detonation velocity

Abstract

Experimental data shows that under certain conditions, measured detonation velocities exhibit deviations from theoretical values computed according to the Chapman-Jouguet (CJ) model. The purpose of this paper is to investigate why in some circumstances such deviations occur. A Zeldovitch-von Neuman-Doring model (ZND) taking into account the specific chemical kinetics of the mixture enables us to identify a critical parameter: the effective chemical reaction length. This parameter is mainly related to the chemical composition of the reactive mixture. It is shown that the ratio of this parameter to the dimension of the tube where the velocity measurements are carried out can explain deviations from ideal values. This simple model has been applied to a series of existing experimental data characterized by such deviations. Different initial conditions, namely, (1) mixtures near detonation limits, (2) low initial pressures, and (3) mixtures containing halogenated hydrocarbons, are investigated. All data show that the velocity deficit, Δ D cj , is an incrasing, but not necessarily linear, function of the ratio reaction length/dimension of the tube, d rea / d tube . To support this statement, a detailed one-dimensional numerical computation has been performed, taking into account both nonstationary hydrodynamics and detailed chemical kinetics. These computations end up with a detonation wave traveling at the ideal Chapman-Jouguet velocity. This suggests that the deviation from the CJ values ought to be explained by parameters taking into account the relative size of the surrounding of the detonation wave; d rea / d tube is such a parameter.