Double shock solutions for non-ideal detonations with endothermic reaction step

We analyzed the problem of one-dimensional steady detonation wave with momentum losses caused by the presence of solid inert objects on the path of the wave. The process is modeled by reactive Euler equations with two-step kinetics with exothermic first step and endothermic second step. We showed that the steady-state solutions exist for the whole range of detonation wave velocities D from the ideal detonation velocity down to the speed of sound in the fresh mixture, and that these solutions could be divided in three categories. The solutions with high detonation wave velocities retain the typical structure of self-sustained detonation wave with embedded Chapman–Jouguet point. The solutions with very low detonation wave velocities remain fully subsonic relative to the detonation front, which make them not self-sustained. Finally, the solutions with detonation velocity values between two aforementioned cases contain the second shock wave behind the detonation front. While first two types of steady-state solutions also exist in the problems with one-step chemistry, the last type emerges only at the presence of the endothermic reaction step.