Abstract
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.
Highlights
Rotating detonation combustors (RDCs) have emerged as one of the most promising concepts to achieve the efficiency gains made possible through pressure gain combustion
We present results on the application of the dynamic mode decomposition (DMD) method described in Sect. 2 to the high-frequency images collected when operating the RDC at various conditions as discussed in Sect
We first discuss the details of the application of the DMD to the specific RDC problem, examining the influence of number of frames with and without mean subtraction, the correlation between the natural luminosity and high-speed pressure measurements, and the form of the resultant modes
Summary
Rotating detonation combustors (RDCs) have emerged as one of the most promising concepts to achieve the efficiency gains made possible through pressure gain combustion. A recent study by the authors found that, depending on the injector geometry and reactant mass flow rate, a range of different operating modes could be reliably stabilized [8,9]. These include two counter-rotating waves at equal or different speed: a dominant wave with multiple counter-rotating waves and secondary acoustic or dominant pulsed wave modes. These wave modes lead to complex pressure oscillations in the annulus. In order to interpret and identify the operating mode, these pressure signals were analyzed based on the theoretical speed of sound in the fresh and hot gas, the detonation velocity, and observations from high-speed video [5,9,10]
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