Steady detonation waves for gases undergoing dissociation/recombination and bimolecular reactions

The one-dimensional steady propagation problem of a shock wave that models detonation as a combustion process in a mixture of reacting gases is studied. For this purpose, suitable reactive Euler equations deduced from appropriate closures of the Boltzmann-like equations holding at the mesoscopic level are used. The considered chemical reactions driving detonation are of either the dissociation/recombination or bimolecular type. After a jump discontinuity governed by the Rankine-Hugoniot conditions, the reactions proceed until chemical equilibrium is reached. The physical consistency of the solutions is discussed in terms of the relevant Hugoniot diagrams, which show different features for exothermic and endothermic processes and determine the allowed range of detonation velocities.