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In recent years, there is an increasing interest in using detonative combustion for developing next-generation aerospace propulsion system. The detonation phenomenon remains an active field of research, particularly in understanding its dynamics and being able to control it. Gaseous detonation waves are inherently unstable. Evidence from both experimental and numerical simulations shows that the unsteady dynamics of detonation propagation is described by an ensemble of interacting transverse waves and small-scale instabilities embedded within the frontal wave structure. It is becoming clear with recent advance in detonation physics that propagation mechanism as well as critical phenomena of gaseous detonation strongly depend on the unstable nature of the frontal wave structure. In this work, we examine the possibility of using a small perturbation to control the unstable dynamics of detonation propagation.

In its simplest form we investigate the one-dimensional pulsating gaseous detonation where instabilities could be manifested only in longitudinal direction. The flow dynamics is simulated using the reactive Euler equations coupled with a one-step Arrhenius kinetic model. Two types of ideal combustible mixtures are considered, namely for an initially stable, steady detonation with a low activation energy and an unstable, pulsating detonation with the activation energy value above the neutral stability boundary. The initial density is perturbed by a weak sinusoidal non-uniformity with different wavelengths. Using small sinusoidal initial density perturbations, this investigation shows the emergence of various nonlinear temporal patterns as a function of the perturbation wavelength. For the stable detonation, the shock front oscillation is found to be in-phase and modulated solely by the imposed initial density variation. For the pulsating detonation, the oscillatory behavior is not affected by short wavelength initial density disturbance. However, additional unstable modes are excited as the wavelength of the sinusoidal density perturbation increases. Increasing further the wavelength again stabilizes the pulsating detonation from chaotic oscillation back to single mode via an inverse bifurcation route. The phenomenon of frequency locking is observed. In all cases studied, the average propagation speed of the detonation wave remains close to the Chapman-Jouguet value. This study thus demonstrates that by means of a small perturbation, the unstable detonation front could be controlled so its dynamics be rendered more predictable.