Weakly Nonlinear Dynamics of Near-CJ Detonation Waves

Abstract

The renewed interest in safety issues for both large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations, as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature are running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem.A proper treatment of perturbations in the back of a ChapmanJouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interaction of highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-waveresonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderately state sensitive chemical reactions (no large activation energy). Then, the acoustic perturbations do not influence the chemistry at the order considered, and we may concentrate on the second effect: the three-wave resonance.KeywordsAcoustic ModeAcoustic ResonanceAcoustic PerturbationReaction Progress VariableDetonation StructureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.