Numerical analysis of the vibration-chemistry coupling effect on one-dimensional detonation stability

Abstract

A one-dimensional numerical simulation of detonation propagation is performed with an introduction of the vibrational relaxation mechanism in a single-step chemical model for the first time. This coupling mechanism is constructed based on the energy transfer between the translational-rotational mode and the vibrational mode, together with an averaged two-temperature model in chemical kinetics. A time ratio τα between the characteristic chemical time scale and the characteristic vibrational time scale is introduced to illustrate whether this coupling effect is crucial in stabilizing the detonation. The simulation is initialized first with an extended steady-state profile and the inclusion of the vibrational energy in the equations. For the particular case considered in this study with a nondimensional heat release Q=50, a ratio of specific heat γ=1.2, and a nondimensional characteristic vibrational temperature ϑ=20, the stability boundary is indicated at an activation energy Ea=26.47 under thermal equilibrium. Two mildly unstable cases for a Chapman-Jouguet (CJ) detonation and an overdriven detonation are then studied with the variation of τα. The results reveal that the detonation is stabilized by the vibrational nonequilibrium effect with a smaller pulsation amplitude and a longer oscillation period in the shock pressure history, and the neutral stability is shifted. For the CJ detonation case, the critical τα below which the coupling effect is significant is 7.2. The stabilization of detonation can be attributed to the reduction of the overall chemical reaction rate by vibrational relaxation and thus a shift of the stability limit towards higher activation energy. For an overdriven detonation, the critical τα is approximately 21 for the studied cases. Since the changes in both overdriven factors f and τα contributed to the stabilization of detonation, a reduction of the neutral stability limit of f is foreseen when the coupling effect is significant. Lastly, the effect of different ϑ on the stability limit is demonstrated at equilibrium state with vibrational energy included and it is suggested that the shift of stability limit would reach the maximum at around ϑ=15. This inaugural work provides a reference on the importance of considering thermal nonequilibrium flow in detonation stability and the implication to the related engine design.