Characteristics analysis of the one-dimensional pulsating dynamics of chain-branching detonations

Abstract

The nonlinear pulsating mechanism of one-dimensional detonations was studied numerically using a simple two-step chain-branching model with separate induction and reaction zones. Numerical simulations were performed for a wide range of parameters, which revealed four distinct pulsating regimes classified according to the mechanism controlling the frequency of the pulsations. The dynamics of these regimes were clarified by reconstructing the characteristics, representing the trajectory of pressure waves and particle paths. The high and low frequency regimes of oscillation previously observed in one-step and realistic chemistry simulations were clarified. Under some parameter range, simultaneous low and high frequency pulsations were observed. A novel regime was also found with a pulsation period smaller than the induction time. It involves coupling between the acoustic and the reactivity disturbances propagating, respectively, along the C− and C0 characteristics. These are generated at successive lead shock pulsations and arrive at the reaction zone simultaneously. For all regimes, the dominating mechanism of the pulsating instability was found to be in good qualitative agreement with Toong’s phenomenological model based on the wave dynamics in a square wave reaction zone structure.