Dynamics of detonation cellular structure in linear and nonlinear instability regimes

This study aims to classify the multi-dimensional instability of cellular detonation into different levels and explores the applicability of linear stability analysis in predicting the cellular structures in these different regimes. The development of two-dimensional cellular detonation from planar steady detonation was solved using linear stability analysis and numerical simulation along with perfect gas and one-step irreversible reaction assumptions. We firstly derived linear stability boundaries in one and two dimensions in the Mach number and reduced activation energy plane. A maximum Mach number was found for stable detonation to exist. These boundaries separate the parameter space into four regimes, i.e., stable, linear unstable, weakly nonlinear unstable and nonlinear unstable. The linear unstable regime is characterized by highly regular cellular structure in the simulation. The cell size can be predicted with linear stability analysis within a 10% error. In the weakly nonlinear unstable regime, the cellular structure grows as the detonation propagates via the expansion of large cells and merging of small cells. Accurate prediction based on linear stability analysis is limited to the initial stage of cellular detonation development. After the long-term cellular structure has been established, the prediction error remains acceptable, ranging from tens of percents to one fold, depending on the distance from the 2D stability boundary. When approaching the nonlinear unstable regime, the applicable range for linear stability analysis decreases drastically due to the emergence of longitudinal instability, the appearance and dominance of high-frequency modes of transverse instability. The transition to the nonlinear instability regime was characterized by large perturbation introduced via local explosion during the formation of the cellular structure. Qualitative descriptions of the cellular detonation dynamics could be illustrated based on linear stability analysis, including the variation of cell size and the tendency of wave front bifurcation.