The role of hydrodynamic instability in detonation fronts

Abstract

Recognizing that a detonation front consists of a leading shock followed by a reaction front that separates two media with significantly different densities, and that the shock is in general stable while the reaction front is subjected to the Darrieus-Landau (DL) instability and the RayleighTaylor (RT) instability if there is an acceleration, an analysis wascarried out to elucidate the coupling between the shock dynamics and the hydrodynamic DL and RT instabilities in the commonly observed detonation instability. The study first considered compressibility effects on DL instability and showed that modification of the growth rate is of the order of the square of the Mach number. We then analyzed the instability of a shock-reaction front complex, in which the reaction front propagates at a constant velocity relative to the unburned gas, and demonstrated that this wave structure yields unstable complex roots, which are very different from that of the DL instability. A further analysis is then performed to elucidate the nature of the hydrodynamic instability of planar detonations. The results obtained show that the maximum growth rate is not very sensitive to the activation energy, indicating that the hydrodynamic instability, which was largely overlooked in previous analysis, is an important destabilizing mechanism in multidimensional detonation instability.