Quantitative Correlation between One-Dimensional Periodically Oscillating Detonation Waves and Two-Dimensional Regular Cellular Detonation Waves

The objective of this study is to establish a quantitative relationship between one-dimensional (1D) periodically oscillating detonation waves and two-dimensional (2D) regular cellular detonation waves. Numerical simulations were conducted for stoichiometric hydrogen-air detonation waves using the conservative Euler equations coupled with a single-step overall chemical reaction model. The evolution of both 1D periodically oscillating detonation waves and 2D regular cellular detonation waves was analyzed through flux-vector analysis. The results reveal that the period of forming a 2D detonation cell is equivalent to the period of the 1D periodically oscillating detonation wave. Furthermore, 2D regular cellular detonation waves exhibit two distinct time scales:(1) the collision period of triple-points, and (2) the ignition delay time of the heated gas behind the incident shock wave. These two time scales reach a balance for regular cellular detonation waves. The findings demonstrate that the ignition delay time is the key physical parameter for establishing a direct quantitative correlation between the two systems.