On the Development of a Single Camera 3D Particle Tracking Algorithm to Study the Flow Field over a Rotating Wing

Abstract

Previous studies on unsteady flow fields over rotating wings have revealed distinct behaviors compared to translating wings, with rotating wings exhibiting strong three-dimensional effects and significant cycle-to-cycle variations. Existing methods have primarily been constrained to 2D measurements or to 3D/3C velocity fields in a fixed reference frame, which do not adequately account for the rotational accelerations inherent to rotating flows. To address this gap, a three-dimensional rotating reference frame diagnostic technique, rotating three-dimensional velocimetry (R3DV), was developed using a single camera setup, enabling continuous imaging of the evolving flow field directly within the rotating reference frame. A rotational calibration technique was developed to align the field of view such that images were perceived to be captured from the root of the wing, looking down the span towards the tip. Initial R3DV experiments successfully captured the leading-edge vortex over a rotating inclined flat plate. However, the traditional processing algorithm used for plenoptic flow diagnostics, based on two-frame cross-correlation, is unable to fully resolve depthwise velocities at the low magnifications that R3DV is restricted to.

A particle tracking algorithm designed uniquely to address the weaknesses of the plenoptic camera was developed. Here, the temporal history of particle motion was used to reduce spatial (predominantly out-of-plane) uncertainties. The technique leveraged the plenoptic camera's multi-perspective view generation capabilities to track particle projections across multiple 2D views, thus protecting the tracking algorithm from being compromised by ambiguities in the out-of-plane domain. Synthetic experiments demonstrated that tracking individual particles could reduce the depthwise velocity uncertainty by up to 89%. R3DV experiments revealed flow features that were previously unattainable, such as strong root-to-tip motion in the core of the leading edge vortex.

Physics-informed neural networks (PINNs) offer a solution for representing discrete spatio-temporal measurements as a continuous flow field, while integrating governing physics as a means of data regularization. Across fluid dynamics literature, PINNs have shown success in capturing complex 3D flow fields using sparse and/or noisy data. PINNs were adapted and validated for R3DV measurements after conducting an extensive set of flow field experiments at varying conditions. With results from single camera plenoptic experiments comparable to velocity fields obtained from a high-resolution multi-camera system used for benchmarking, it was established that R3DV, combined with perspective-based particle tracking and PINN can be considered a viable 3D/3C single-camera measurement technique that can capture the temporal evolution of rotating flows within the rotating frame of reference.