Investigation of the stability of transverse hydrogen injection combustion caused by plate vibration using the dynamic mode decomposition method

This article investigated the stability of transverse hydrogen injection combustion caused by the plate vibration. The finite-rate method is used to simulate the combustion. The unsteady flow field in the unstable phase of combustion is extracted. The unstable mode of the shock wave structure and the flame structure during the stage of combustion instability, the spatial and temporal characteristics of the dominant modes, as well as their stability are analyzed based on the dynamic mode decomposition (DMD) method. The results indicate that, according to the sequence of energy, the extracted first six orders modes of the shock wave structure and the flame structure have relatively low frequency with a negative growth rate and small numerical value, which presents a trend of weak convergence. The characteristics of the dominant structure of DMD modes show that the plate vibration has great effects on the reflected shock wave structure near the plate and on the upper wall surface, as well as the flame structure near the plate. According to the sequence of the mode energy and the growth rate, respectively, the extracted first six orders modes have relatively high frequency. Simultaneously, the structures of the modes extracted by the sequence of mode energy are more regular, while those extracted by the sequence of growth rate are more disorderly. The unstable shock wave structure is mainly manifested by the reflected shock wave in the vibration region and the shock wave structure reflected by the upper wall surface. The unstable flame structure is mainly concentrated near the vibration region and downstream areas.