Evolution of weakly unstable oblique detonation in disturbed inflow

Abstract

The surface instability of oblique detonation waves (ODWs) without perturbations has been extensively investigated, yet the impact of external perturbations remains under-explored. Utilizing reactive Euler equations coupled with a two-step induction-exothermic reaction model, this study conducts a numerical examination of the evolution of unstable ODW surfaces subjected to a continuous sinusoidal density/temperature perturbation inflow. The results show that, without inflow perturbations, the ODW can evolve into triple points in the downstream due to detonation instability, similar to previous work. However, a small continuous perturbation can induce a significant forward movement of the ODW unstable position. Surprisingly, as the perturbation magnitude increases, the changes in the unstable position become progressively less pronounced. By increasing the perturbation frequency, the oscillation amplitude first increases, but a decreasing period/stage occurs with a modest frequency. To investigate the response of ODW to the increase in perturbation, the frequency characteristics and numerical smoked cells of detonation surfaces are examined and analyzed using Fast Fourier Transformation. The power spectral density indicates the presence of two distinct oscillation modes within oblique detonation. Low-frequency, small-amplitude perturbations serve to amplify the instability of the detonation, and more irregular oscillations could be observed. Conversely, high-frequency, large-amplitude perturbations suppress the development of small-scale waves on the detonation wavefront and lead to a relative regular oscillation, indicating that the wavefront pressure oscillations are entirely determined by inflow perturbations and become predictable. These findings have significant implications for the control of intrinsically unstable ODWs, providing valuable insights into the regulation of ODW dynamics.