A rotating detonation combustor (RDC) is a novel approach to achieving pressure gain combustion. Due to the steady propagation of the detonation wave around the perimeter of the annular combustion chamber, the RDC dynamic behavior is well suited to analysis with reduced-order techniques. For flow fields with such coherent aspects, the dynamic mode decomposition (DMD) has been shown to capture well the dominant oscillatory features corresponding to stable limit-cycle or quasi-periodic behavior within its dynamic modes. Details regarding the application of the technique to RDC—such as the number of frames, the effect of subtracting the temporal mean from the processed dataset, the resulting dynamic mode shapes, and the reconstruction of the dynamics from a reduced set of dynamic modes—are analyzed and interpreted in this study. The DMD analysis is applied to two commonly observed operating conditions of rotating detonation combustion, viz., (1) a single spinning wave with weak counter-rotating waves and (2) a clapping operating mode with two counter-propagating waves at equal speed and strength. We show that care must be taken when applying DMD to RDC datasets due to the presence of standing waves (expressed as either counter-propagating azimuthal waves or longitudinal pulsations). Without accounting for these effects, the reduced-order reconstruction fails using the standard DMD approach. However, successful application of the DMD allows for the reconstruction and separation of specific wave modes, from which models of the stabilization and propagation of the primary and counter-rotating waves can be derived.

中文翻译：

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旋转爆震波的动力模态分解分析

旋转爆震燃烧器 (RDC) 是一种实现压力增益燃烧的新方法。由于爆震波围绕环形燃烧室的周边稳定传播，RDC 动态行为非常适合使用降阶技术进行分析。对于具有这种相干方面的流场，动态模式分解 (DMD) 已被证明可以很好地捕获与其动态模式内的稳定极限循环或准周期行为相对应的主要振荡特征。有关将该技术应用于 RDC 的详细信息——例如帧数、从处理过的数据集中减去时间平均值的效果、产生的动态模式形状以及从一组减少的动态模式中重建动态——是在本研究中进行了分析和解释。DMD 分析适用于两种常见的旋转爆轰燃烧工况，即：(1) 单一自旋波，具有弱反向旋转波；(2) 具有两个等速反向传播波的拍手操作模式，力量。我们表明，由于存在驻波（表示为反向传播的方位波或纵向脉动），因此在将 DMD 应用于 RDC 数据集时必须小心。如果不考虑这些影响，使用标准 DMD 方法的降阶重建将失败。然而，DMD 的成功应用允许特定波模式的重建和分离，从中可以导出主波和反向旋转波的稳定和传播模型。