Influence of the Reaction Heat on the Linear Stability Spectra of Steady Detonation in the Kinetic Frame

The structure and linear stability of the one-dimensional steady overdriven detonation wave supported by a chemical reaction of type A + A ⇋ B + B are examined in the frame of the Boltzmann equation extended to chemically reacting gases. The structure of the steady wave solution is determined solving the system of the Rankine-Hugoniot conditions supplemented with the rate law, in a chemical regime which corresponds to the early stage of the reaction process. The response of such steady wave solution to one-dimensional disturbances is investigated using a normal mode linear analysis which leads to an initial value problem for the state variable disturbances in the reaction zone. Some results are obtained numerically in order to describe the stability spectra of the steady solution. The emphasis of the present study is on the influence of the reaction heat on the linear stability spectra.