Reynolds-number scaling of vortex pinch-off on low-aspect-ratio propulsors

Abstract

Impulsively started, low-aspect-ratio elliptical flat plates have been investigated experimentally to understand the vortex pinch-off dynamics at transitional and fully turbulent Reynolds numbers. The range of Reynolds numbers investigated is representative of those observed in animals that employ rowing and paddling modes of drag-based propulsion and manoeuvring. Elliptical flat plates with five aspect ratios ranging from one to two have been considered, as abstractions of propulsor planforms found in nature. It has been shown that Reynolds-number scaling is primarily determined by plate aspect ratio in terms of both drag forces and vortex pinch-off. Due to vortex-ring growth time scales that are longer than those associated with the development of flow instabilities, the scaling of drag is Reynolds-number-dependent for the aspect-ratio-one flat plate. With increasing aspect ratio, the Reynolds-number dependency decreases as a result of the shorter growth time scales associated with high-aspect-ratio elliptical vortex rings. Large drag peaks are observed during early-stage vortex growth for the higher-aspect-ratio flat plates. The collapse of these peaks with Reynolds number provides insight into the evolutionary convergence process of propulsor planforms used in drag-based swimming modes over diverse scales towards aspect ratios greater than one.

On the separation mechanics of accelerating spheres

“…The first motion consisted of an impulsive start from rest to the final towing velocity over a distance of half the characteristic length scale (0.5D). 17 The model was towed at the final velocity for 40D to maintain sufficient averaging periods for steady-state drag calculations. This motion was undertaken at Reynolds numbers based on the existing data for a circular flat plate 17 (discussed in Section IV) and is shown in Figure 4 by the red curve for the first 25D of the motion.…”

“…17 The model was towed at the final velocity for 40D to maintain sufficient averaging periods for steady-state drag calculations. This motion was undertaken at Reynolds numbers based on the existing data for a circular flat plate 17 (discussed in Section IV) and is shown in Figure 4 by the red curve for the first 25D of the motion. Figure 4 shows normalized velocity plotted against the dimensionless distance.…”

“…The circular flat-plate data reported by Fernando and Rival 17 are shown in Figure 7(a) as the drag coefficient plotted against dimensionless distance. A detailed analysis of these data can be found in their study, which is therefore only briefly summarized here for brevity.…”

Load-estimation techniques for unsteady incompressible flows

“…6 and 7. Here, a circular plate is accelerated from rest and experiences a rapid spike and relaxation in drag through a complex process of vortex-ring formation and pinch off; see Fernando and Rival (2016) for details about the experimental setup. In Fig.…”

“…Note for this test case, the plate is accelerating; see Fernando and Rival (2016) for details on the experiment in instantaneous load estimation, either using classical approaches or ones with drift-volume estimates, and further will also allow for complimentary understanding of topological features (Huang and Green 2015) by connecting sources of vorticity production on a body to its wake. Undoubtedly there remains much work in the development and validation of these Lagrangian-based analyses, and in turn, it is hoped that with access to new high-density Lagrangian tracking, we will further uncover the salient mechanisms of this broad class of unsteady flows.…”