Numerical investigation on formation mechanism of low-frequency detonation instability
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摘要: 对连续爆轰发动机中常见的低频爆轰不稳定性现象开展了基于含源项Euler方程的二维数值模拟研究，揭示了低频爆轰不稳定性产生的机理和详细过程。结果表明，燃烧室头部持续存在一些反传激波，这些激波与进气壁面相互作用会产生“进气阻滞点”，导致新鲜气体层不规则分布；不规则新鲜气体层会使爆轰波头上的压强分布随进气阻滞点的分布位置产生周期性变化；随着进气阻滞点产生的位置沿着进气壁面的缓慢移动，爆轰波头每次与采样点相遇时，采样点与上个进气阻滞点之间的距离会逐渐发生变化，因此采样点的压强峰值便产生了低频率的起伏振荡，即形成了所谓的低频爆轰不稳定性。Abstract: 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.
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图 1 连续爆轰发动机原理（二维圆柱流场及其展开结构）
Figure 1. Schemetic of RDE (2D cylindrical flow field and its unfolding structure)
图 3 不同网格尺寸的计算结果（温度云图和特征压力梯度对数云图）
Figure 3. Calculation results of different grid sizes (temperature nephogram and pressure gradient logarithmic nephogram)
图 4 采样点（传感器处）的压强-时间曲线
Figure 4. The pressure-time track of sampling points (or the points where the sensors are placed)
图 7 374～385 μs爆轰波头上的压强轴向分布
Figure 7. Axial distribution of the pressure on the detonation front between 374−385 μs
图 8 进气壁面上最大压强的变化（数值模拟结果）
Figure 8. Track of the peak pressure on the inlet wall (numerical result)
图 9 采样点压强振荡的形成机理
Figure 9. The schematic diagram of mechanism of the pressure oscillation at the sampling point
图 10 爆轰波每旋转两周进气阻滞点产生的位置
Figure 10. The position of IBP in every two cycles of detonation wave rotation
图 12 进气被阻滞处及左右各一点在进气阻滞点产生时的压强变化和稳定进气情况
Figure 12. Pressure track of the place where intake process is interrupted and one point on each side when IBP is being generated, and the stable intake situation
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