An a posteriori data-driven method for phase-averaging optical measurements

Phase-averaging is a fundamental approach for investigating periodic and non-stationary phenomena. In fluid dynamics, these can be often encountered, and some examples are rotating blades such as those of propellers/turbines or pulsed/synthetic jets. Traditional phase-averaging approaches often rely on synchronized data acquisition systems, which might require high-speed cameras, light sources, and precise delay generators and encoders. While this is often not an issue, it can become quite challenging for smaller experimental rigs. This work proposes an a posteriori data-driven approach that reconstructs phase information from randomly acquired uncorrelated photographic frames (snapshots) using the ISOMAP algorithm. The technique enables accurate reordering of snapshots in the phase space and subsequent computation of the phase-averaged flow fields without the need for synchronization. The framework was validated through an ad hoc generated synthetic and an experimental dataset from an optical setup featuring single- and multi-propeller configurations. The results demonstrate that the proposed method effectively captures the periodic flow characteristics while addressing the challenges of synchronization and hardware limitations. Furthermore, the ability to apply this technique to archival datasets extends its applicability to a wide range of experimental fluid dynamics studies. This approach provides a scalable and cost-effective alternative to traditional methods for analysing periodic phenomena