马赫数对有厚或薄来流边界层的开腔流动的影响
The effect of Mach number on open cavity flows with thick or thin incoming boundary layers
摘要：
采用整体线性分析和非线性数值模拟方法研究了开口腔的Rossiter模。长深比为2，基于空腔深度的雷诺数接近1000。研究了马赫数对这类空腔的影响。整体分析表明，在马赫数0.1至0.9范围内，对于厚的边界层，只有R1和R2模态可能变得不稳定，而对于薄的边界层，直到R4模态可能是不稳定的。在低马赫数时，压缩性是非常不稳定的。在中等马赫数下，不稳定性要么随马赫数而饱和，要么有不规则的相关性。对罗西特模式本征函数的分析表明，声反馈的尺度为Ma ^3，这解释了压缩性的强烈失稳效应。不规则的依赖关系与Rossiter模式和声腔模式之间的共振。分析解释了为什么不规则的马赫依赖性只发生在高阶Rossiter模式。在这个参数区域，三维模式是稳定的或边缘不稳定的。进行二维模拟，以评估有多少非线性政权可以捕获的线性稳定性结果。随着流动变得越来越不稳定，达到了一个越来越复杂的最后阶段。然而，光谱呈现出接近线性预测的不同音调。然而，仔细观察发现饱和状态下的主频对应于R1，而线性理论预测R2是最不稳定的模式。这与非线性区域中混合层的非线性增厚有关。此外，频率更接近Rossiter经验预测比线性不稳定性。即使在接近临界的条件下，光谱也可以由模式R1和非线性产生的谐波级联很好地描述，没有线性不稳定性的回忆。
英文摘要：
The Rossiter modes of an open cavity were studied using global linear analysis and nonlinear numerical simulations. The length over depth ratio was two and the Reynolds numbers based on cavity depth were close to 1000. The effect of Mach on such cavities was studied. The global analysis revealed that, in the Mach range 0.1 to 0.9, for thick boundary layers, only R1 and R2 modes could become unstable, whereas for thin boundary layer up to R4 could be unstable. Compressibility was very destabilizing at low Mach. At moderate Mach the instability either saturated with Mach or had an irregular dependence. Analysis of the Rossiter mode eigenfunctions indicated that the acoustic feedback scaled to Ma^3, and explained the strong destabilizing effect of compressibility. The irregular dependence was associated with resonances between Rossiter modes and acoustic cavity modes. The analysis explained why the irregular Mach dependence occurred only for higher order Rossiter modes. In this parameter region three dimensional modes are stable or marginally unstable. Two-dimensional simulations were performed to evaluate how much of the nonlinear regime could be captured by the linear stability results. As the flow became more unstable, an increasing more complex final stage was reached. Yet the spectra present distinct tones that are close to linear predictions. However, a closer look reveals the dominant frequency in the saturated state corresponds to R1 while linear theory predicts R2 as the most unstable mode. This is associated with a nonlinear thickening of the mixing layer in the nonlinear regime. Moreover, the frequencies are much closer to Rossiter empirical predictions than the linear instability ones. Even at these conditions close to critical, the spectra are well described by the mode R1 and a cascade of nonlinearly generated harmonics, with no reminiscence of the linear instability.
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