Numerical investigation on formation mechanism of low-frequency detonation instability

In recent years, rotating detonation engine (RDE) has been wisely studied in the world due to its inherent advantages. In the process of the application of RDE, the stable and reliable performance of the engine is always what researchers pursue. In the process of the research on RDE, a phenomenon called Low Frequency Instability (LFI) has been widely found. But so far, the exact mechanism behind LFI hasn’t been really revealed yet. In this paper, a numerical investigation of LFI was performed. In the numerical study, Euler equation with source terms was chosen as the governing equation, ignoring viscosity, thermal conduction, and mass diffusion. The Strang’s operator splitting method, the fifth order weighted essentially non-oscillatory scheme (WENO) and the second order total variation diminishing (TVD) Runge-Kutta method were used. With the methods mentioned above, the mechanism behind LFI and the whole detailed process of shock waves causing this phenomenon were finally revealed. It is shown that near the inlet wall there exist some reverse shock waves (propagating in the opposite direction to the rotating detonation waves), which will interact with the inlet wall and therefore generate some injet blocking point (IBP) in the fresh gas layer which will make the fresh gas layer periodically irregularly distributed. The irregular fresh gas layer will cause the distribute of the pressure on the detonation front changes periodically. With the positions where the IBPs are generated moving slowly along the inlet wall, the distance between the sampling point and the last IBP will gradually changes, and this will lead to that every time the rotating detonation wave meet the sampling point, the pressure of the place where the detonation front contacts with the inlet wall (and so contacts with the sampling point) is different from the last time. Therefore, the peak pressure at the sampling point oscillates at a low frequency and in another word, a so called low frequency instability is formed.