Visualizing shock wave evolution in rotating detonation combustor exhaust flows with background-oriented schlieren

Employing high-speed background-oriented Schlieren (BOS) diagnostics at 10 kHz, this work investigates shock wave evolution in the exhaust plume of a liquid kerosene-fueled rotating detonation combustor (RDC) operating with oxygen-enriched air. The Farnebäck optical flow (FB-OF) algorithm is applied to process shock-laden BOS images, demonstrating superior performance over conventional cross-correlation and Horn–Schunck methods for resolving high-speed flows at moderate frame rates (10 kHz). From FB-OF processed sequences, we developed a multi-stage shock tracking algorithm that can extract and reconstruct three-dimensional shock wave evolution in RDC exhaust flows. Quantitative analysis identifies the incoming air stream's momentum flux as the primary parameter governing the detonation strength in kerosene/oxygen-enriched air RDC operation. For exhaust shock evolution analysis, the FB-OF processing applied to consecutive flow-containing BOS images—as opposed to the conventional approach using a flow/non-flow image pair—achieves comparable analytical accuracy while mitigating low-frequency constraints and enhancing image quality. The results reveal two key findings: (1) shock propagation maintains stability despite the exhaust plume turbulence, suggesting effective decoupling between the shock dynamics and the exhaust flow turbulence; and (2) while combustor detonation velocities vary significantly (1661–1316 m/s, 26% variation), exit shock expansion velocities remain consistent (540–514 m/s, <5% variation).