Analysis of a liquid kerosene–fueled air-breathing rotating detonation engine using the cross-correlation method

In a recent experimental investigation, the operational behavior of a liquid-kerosene-fueled air-breathing/ramjet rotating detonation engine was characterized using high-speed visual diagnostics. Although high-speed photography has been widely used for quantitative analysis of rotating detonation waves, resolving flow-field structures from pressure signals remains challenging in liquid-fueled air-breathing configurations. This study applies cross-correlation analysis of high-frequency dynamic pressure data to evaluate key operational and flow-field features—including wave velocity, propagation direction, and shock angle. Compared with Fourier analysis, the cross-correlation method provides improved temporal resolution and enables higher measurement precision. This level of accuracy can be achieved with only a few wave laps, whereas FFT-based techniques may require up to 100 laps under ideal operating conditions. Consequently, cross-correlation is particularly suitable for capturing unsteady or transient operating states where high temporal resolution is essential. The directional persistence of the rotating detonation wave was quantified, and a unidirectionality metric was introduced to describe its temporal stability. This metric exhibits a non-monotonic dependence on equivalence ratio, increasing initially and then decreasing, with a maximum at an equivalence ratio of 1.14. This trend correlates with the relative standard deviation of the detonation frequency, suggesting that both parameters may serve as indicators of wave stability. Furthermore, cross-correlation analysis of axially aligned high-frequency pressure transducers was considered to evaluate the shock angle. The upstream oblique shock wave was found to exhibit a considerably larger angle (60°–65°) than the rotating detonation wave (17.9°–22.4°), enhancing understanding of flow-field organization in air-breathing rotating detonation and expanding methodologies for detonation dynamics assessment.