Stability of Flame-Shock Coupling in Detonation Waves: 1D Dynamics

Abstract

In the present study, we utilize spatially high-order convergence rate methods with complex reaction kinetics in resolving the nonlinear dynamics associated with one-dimensional unstable detonations. For a spark-induced detonation, as the detonation decays towards the self-sustaining Chapman–Jouguet mode from an over-driven mode, one obtains a sequence of physical oscillations between the flame and shock front, with different frequency ranges (categorized as high frequency-low amplitude and low frequency-high amplitude), dependent on the time after initiation of the detonation. The present studies indicate that one must use sufficient spatial resolution as well as realistic, complex kinetics to accurately simulate the preferred re-explosion and instability modes. Metrics that characterize the instabilities include, in addition to peak pressure, dominant high and low frequencies and time to re-explosion. A simple model for the transmission of acoustic and entropy waves is used to interpret physical phenomena creating the different instability modes, with reasonable quantitative correspondence to simulation results.

Keywords:

• Complex kinetics
• Detonation instabilities
• High order numerical schemes
• Reactive gas dynamics

Acknowledgments

Published as part of the 23rd International Colloquium on the Dynamics of Explosions and Reactive Systems (ICDERS) Special Issue with Guest Editor Derek Dunn-Rankin.

Notes

¹The formation energy can be obtained from the standard enthalpy of formation and extrapolation to T = 0.

²This approach has been found preferable to including the formation energy in the definition of the mixture's total energy as it can in some cases yield better accuracy at composition discontinuities (Cambier, unpublished). The reason is that for flows with a high chemical energy, the equation of state requires the subtraction of this large contribution from the total energy, potentially leading to significant errors in the temperature and pressure. A similar situation is found for ideal MHD flows at very high magnetic pressure, where this is a well-known problem.

³This was verified for longer time periods than shown; for clarity purposes, the extent of the simulation results shown in the figures has been truncated.