The unsteady three-dimensional wake produced by a trapezoidal pitching panel

Abstract

Particle image velocimetry (PIV) is used to investigate the three-dimensional wakes of rigid pitching panels with a trapezoidal geometry, chosen to model idealized fish caudal fins. Experiments are performed for Strouhal numbers from 0.17 to 0.56 for two different trailing edge pitching amplitudes. A Lagrangian coherent structure (LCS) analysis is employed to investigate the formation and evolution of the panel wake. A classic reverse von Kármán vortex street pattern is observed along the mid-span of the near wake, but the vortices realign and exhibit strong interactions near the spanwise edges of the wake. At higher Strouhal numbers, the complexity of the wake increases downstream of the trailing edge as the spanwise vortices spread transversely and lose coherence as the wake splits. This wake transition is shown to correspond to a qualitative change in the LCS pattern surrounding each vortex core, and can be identified as a quantitative event that is not dependent on arbitrary threshold levels. The location of this transition is observed to depend on both the pitching amplitude and free stream velocity, but is not constant for a fixed Strouhal number. On the panel surface, the trapezoidal planform geometry is observed to create additional vortices along the swept edges that retain coherence for low Strouhal numbers or high sweep angles. These additional swept-edge structures are conjectured to add to the complex three-dimensional flow near the tips of the panel.

Generalized Lagrangian coherent structures

“…FTLE and FSLE methods have seen wide usage in both experimental [37,38,39,40] and observational [42,43,47,83,84,85,46,49,50,51] contexts.…”

“…The key point is whatever the definitions of LCSs, their formulation is typically (with a few exceptions, such as, for example, the burning manifolds of [32,33,34,35,36]) based solely on the Lagrangian trajectories associated with (1), and the goal is to identify fluid parcel groups that behave similarly, and are thus 'coherent.' This has been a rich area of study using both experimental [37,38,39,40] and observational [41,42,43,44,45,46,47,48,49,50,51,52,53] data.…”

Detection and tracking of vortex phenomena using Lagrangian coherent structures

“…8. Experimental details about the acquisition of this data can be found in Green et al (2011). In this figure, the x direction is aligned with the freestream flow from left to right, and the z direction is aligned with the span of the panel trailing edge.…”

“…These data were generated by Eldredge (2007), and have been distributed among the AIAA Low Reynolds Number Discussion Group in an effort to share insight into the different analysis methods. The current work also uses experimental two-component particle image velocimetry (PIV) data in the wake of a purely pitching trapezoidal panel (Green et al 2011). In that previous work, a loss of coherence in a reverse von Kármán street wake was shown to correspond to particular dynamics of the Lagrangian coherent structure saddle points.…”

Computational Investigation of Vortex Dynamics and Aerodynamic Performance in Flapping Propulsion

“…The wake topology and force production for the flapping circular plate is examined at Note that the "double-C"-shaped vortex structures generated around the plate trailing edge are distinct from the observations in previous studies on purely pitching [24,25,102,103], purely heaving [21], and pitching-heaving [23,26,27] panels/foils. In those previous studies, only single interconnected vortex loops were observed around the trailing edge during each half cycle, and the loops exhibited symmetry about the spanwise central plane [21,27].…”