Effect of Friction and Heat Losses on the Mean Structure of One-Dimensional Detonations

Detonations are supersonic combustion fronts, which are prone to be unstable and chaotic, all the more since losses are invoked. It is thus mandatory to get their proper mean structure in order to quantify the relative importance of the different mechanisms of losses. Indeed, in this case, the detonation velocity differs from that given by the ideal Chapman-Jouguet (CJ) model. It will also be shown that the energy related to the mechanical fluctuations constitutes another source of energy withdrawal. This physical analysis relies on numerical simulation of the longitudinal unstable modes of detonation, including losses. It is based on the integration of the hyberbolic equations with source terms, using high-order numerical schemes: third-order Runge-Kutta scheme for temporal advancement, fifth-order Weighted Essentially Non-Oscillatory for the convection discretization, Strang splitting for the coupling with stiff source terms, together with adaptive mesh resolution. It is indeed necessary to refine the mean subsonic reaction zone, which has been defined along the Master Equation, deduced from the Favre-averaged equations.