Nonlinear dynamics and chaos regularization of one-dimensional pulsating detonations with small sinusoidal density perturbations

In this work, we explore the effect of initial density variation in the combustible mixture on the nonlinear dynamics of one-dimensional gaseous detonation propagation. Studies of nonlinear dynamical behavior of one-dimensional pulsating detonation are frequently based upon the reactive Euler simulations with one-step Arrhenius chemistry. In regions of the control parameters space, i.e., activation energy Ea, the 1-D detonation dynamics are shown to exhibit chaotic behavior at values of 28.5 and 30.0. Using small sinusoidal initial density perturbations, this investigation shows the emergence of various nonlinear temporal patterns as a function of the perturbation wavelength. It demonstrates that the cooperative behavior between the intrinsic instability and imposed small perturbation can lead to regularization of chaotic oscillations in one-dimensional gaseous pulsating detonation. Hence, by means of a small perturbation, an otherwise chaotic motion is rendered more stable and predictable. This result thus has implications for how intrinsically unstable detonation dynamics can be controlled.