Linear and nonlinear stabilities analysis of gaseous detonation waves in complex reactive systems

Abstract

The stability of gaseous detonation waves is crucial for the operation of detonation-based propulsion systems and the assessment of industrial explosion hazards. However, research on the stability of detonation waves in complex reactive systems that are composed of actual fuels and oxidants and can be described by numerous elementary chemical reactions, has not been fully carried out. To investigate the relationship between linear and nonlinear stabilities in gaseous detonation wave propagation for complex reactive systems, the linear stability analysis and the one-dimensionally nonlinear numerical simulations of H₂/O₂/Ar (argon) detonations based on the reactive Euler equations and detailed reaction mechanisms are carried out. The results show that in complex reactive systems characterized by elementary chemical reactions, the results of linear stability computation of detonation are consistent with those from one-dimensionally nonlinear oscillations of detonation wave. Utilizing these linear stability results, a neutral stability curve and a perturbation frequency transition curve in the phase plane of initial pressure versus inert gas (Ar) dilution ratio are derived, especially the new frequency transition curve clearly describes the transition of perturbations from low-frequency to high-frequency mode. One-dimensional nonlinear simulations show that near the perturbation frequency transition curve, the oscillations of the detonation wave can also transform between the low-frequency, high-amplitude oscillation mode and the high-frequency, low-amplitude oscillation mode, with the oscillation frequency corresponding to the mode that exhibits the maximum growth rate identified in the linear stability analysis. This investigation into detonation stability in complex reactive gases offers guidance for selecting appropriate initial conditions and gas compositions in practical applications of detonation.