A kinetic approach to propagation and stability of detonation waves

The problem of the steady propagation and linear stability of a detonation wave is formulated in the kinetic frame for a quaternary gas mixture in which a reversible bimolecular reaction takes place. The reactive Euler equations and related Rankine‐Hugoniot conditions are deduced from the mesoscopic description of the process. The steady propagation problem is solved for a Zeldovich, von Neuman and Doering (ZND) wave, providing the detonation profiles and the wave thickness for different overdrive degrees. The one‐dimensional stability of such detonation wave is then studied in terms of an initial value problem coupled with an acoustic radiation condition at the equilibrium final state. The stability equations and their initial data are deduced from the linearized reactive Euler equations and related Rankine‐Hugoniot conditions through a normal mode analysis referred to the complex disturbances of the steady state variables. Some numerical simulations for an elementary reaction of the hydrogen‐oxygen chain are proposed in order to describe the time and space evolution of the instabilities induced by the shock front perturbation.