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The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel

Published online by Cambridge University Press:  30 April 2008

JAMES H. J. BUCHHOLZ  and
ALEXANDER J. SMITS
JAMES H. J. BUCHHOLZ
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
ALEXANDER J. SMITS
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
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Abstract

Thrust performance and wake structure were investigated for a rigid rectangular panel pitching about its leading edge in a free stream. For ReC = O(104), thrust coefficient was found to depend primarily on Strouhal number St and the aspect ratio of the panel AR. Propulsive efficiency was sensitive to aspect ratio only for AR less than 0.83; however, the magnitude of the peak efficiency of a given panel with variation in Strouhal number varied inversely with the amplitude to span ratio A/S, while the Strouhal number of optimum efficiency increased with increasing A/S. Peak efficiencies between 9% and 21% were measured. Wake structures corresponding to a subset of the thrust measurements were investigated using dye visualization and digital particle image velocimetry. In general, the wakes divided into two oblique jets; however, when operating at or near peak efficiency, the near wake in many cases represented a Kármán vortex street with the signs of the vortices reversed. The three-dimensional structure of the wakes was investigated in detail for AR = 0.54, A/S = 0.31 and ReC = 640. Three distinct wake structures were observed with variation in Strouhal number. For approximately 0.20 < St < 0.25, the main constituent of the wake was a horseshoe vortex shed by the tips and trailing edge of the panel. Streamwise variation in the circulation of the streamwise horseshoe legs was consistent with a spanwise shear layer bridging them. For St > 0.25, a reorganization of some of the spanwise vorticity yielded a bifurcating wake formed by trains of vortex rings connected to the tips of the horseshoes. For St > 0.5, an additional structure formed from a perturbation of the streamwise leg which caused a spanwise expansion. The wake model paradigm established here is robust with variation in Reynolds number and is consistent with structures observed for a wide variety of unsteady flows. Movies are available with the online version of the paper.

JFM classification

Wakes/Jets: Wakes Wakes/Jets: Vortex streets Biological Fluid Dynamics: Propulsion
Type
Papers
Information
Journal of Fluid Mechanics , Volume 603 , 25 May 2008 , pp. 331 - 365
Copyright
Copyright © Cambridge University Press 2008

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References

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Buchholz and Smits supplementary movie

Movie 1. This movie corresponds to figure 12(b) in the paper. Panel 2 (S/C=0.83) is shown, pitching in water, with St=0.21, A/S=0.31, ReC=36 000 (St=fA/U, S being the panel span, C the panel chord, A the peak-to-peak transverse amplitude of the trailing edge, f the pitching frequency, and U the free-stream velocity). This is the optimal Strouhal number for this combination of S/C and A/S with a propulsive efficiency of 21%. The temporal evolution of the structures is illustrated using rhodamine B (red) and fluorescein (green) dyes injected from spanwise arrays of dye ports on each side of a stationary fairing supporting the panel by its leading edge. From the perspective shown here, rhodamine B dye is injected from the top side of the fairing and fluorescein dye is injected from the bottom side. In the near wake, the vortices have an approximately axisymmetric shape forming a wake with the appearance of a reverse von Karman vortex street (note that the green vortices are on top whereas the red ones are below). However, as the structures convect downstream, they spread in the transverse direction, eventually losing their coherence.

Download Buchholz and Smits supplementary movie(Video)
Video 4.1 MB

Buchholz and Smits supplementary movie

Movie 2. This movie corresponds to figure 12(c) in the paper. Panel 2 is shown (S/C=0.83) with St=0.41, A/S=0.31, ReC=18 000. The dye patterns suggest the creation of two distinct vortices in each pitching cycle as at St=0.21; however, in this case, they break down within a fraction of a cycle. Portions of the vortices can be seen migrating to the opposite side, forming a bifurcating wake with two jet-like structures.

Download Buchholz and Smits supplementary movie(Video)
Video 4.2 MB

Buchholz and Smits supplementary movie

Movie 3. This movie corresponds to figure 26 in the paper. Panel 1 is shown (S/C=0.54) with St=0.64, A/S=0.31, ReC=640, illuminated with halogen light. The movie clarifies the development of the perturbations in the streamwise vortices with respect to the phase of the panel motion. Green structures are shed as the panel pitches down and red structures are shed as the panel pitches up. Growth of the hairpin is initiated one half-cycle after the creation of the structure during the generation of the opposite-signed structure.

Download Buchholz and Smits supplementary movie(Video)
Video 5.9 MB