The behavior of the propagating velocity of rotating detonation waves and counter-rotating shock waves in a hollow combustor

The propagating velocity behavior, mathematical model and influencing factors of rotating detonation waves and counter-rotating shock waves in a hollow combustor with Laval nozzle are investigated. We use our in-house solver BYRFoam developed on OpenFOAM platform. The existence of the shock wave propagating in the opposite direction of the detonation wave in the combustor, called the counter-rotating shock wave, is observed for a wide range. The regular pattern of the propagation of the counter-rotating shock wave is studied and verified by experimental data. The propagating velocity behavior of rotating detonation waves and counter-rotating shock waves is discussed, and the mathematical model of the counter-rotating shock wave is proposed and verified. The results show that there is a clear quantitative relationship between the counter-rotating shock wave and the peak periodic undulation phenomenon of the pressure time curve, that is, the wave packet. This mathematical model connects the counter-rotating shock wave phenomenon in the experiment with the wave packet phenomenon in the experiment. The influencing factors of the counter-rotating shock wave are studied. The results show that increasing inlet total pressure and decreasing nozzle shrinkage ratio can significantly weaken the counter-rotating shock wave in a combustor. Based on this, the relevant parameters of rotating detonation engine (RDE) can be optimized to make the rotating detonation propagate more stable and therefore make the RDE operate more stable, which is of great significance to the practical application of RDE.