A model for the symmetry breaking of the reverse Bénard–von Kármán vortex street produced by a flapping foil

By R. Godoy-Diana, C. Marais, Jean-Luc Aider, J. Wesfreid. Journal of Fluid Mechanics, 2008

184 citations recorded by the source corpus.

The vortex streets produced by a flapping foil of span to chord aspect ratio of 4:1 are studied in a hydrodynamic tunnel experiment. In particular, the mechanisms giving rise to the symmetry breaking of the reverse Bénard–von Kármán (BvK) vortex street that characterizes fishlike swimming and forward flapping flight are examined. Two-dimensional particle image velocimetry (PIV) measurements in the midplane perpendicular to the span axis of the foil are used to characterize the different flow regimes. The deflection angle of the mean jet flow with respect to the horizontal observed in the average velocity field is used as a measure of the asymmetry of the vortex street. Time series of the vorticity field are used to calculate the advection velocity of the vortices with respect to the free stream, defined as the phase velocity Uphase, as well as the circulation Γ of each vortex and the spacing ξ between consecutive vortices in the near wake. The observation that the symmetry-breaking results from the formation of a dipolar structure from each couple of counter-rotating vortices shed on each flapping period serves as the starting point to build a model for the symmetry-breaking threshold. A symmetry-breaking criterion based on the relation between the phase velocity of the vortex street and an idealized self-advection velocity of two consecutive counter-rotating vortices in the near wake is established. The predicted threshold for symmetry breaking accounts well for the deflected wake regimes observed in the present experiments and may be useful to explain other experimental and numerical observations of similar deflected propulsive vortex streets reported in the literature.

Subfields: Aerospace Engineering, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/7b291915ffd345c6f7775c1a09366673c8304f36

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Citations in the corpus

Recent progress in flapping wing aerodynamics and aeroelasticity (2010, background): “[130,131] investigated the vortex dynamics associated with a pitching 2-D teardrop shaped airfoil (2.”
Bifurcating flows of plunging aerofoils at high Strouhal numbers (2012, methodology): “Furthermore, deflected jets have also been observed experimentally for pitching aerofoils (Godoy-Diana et al. 2008, 2009) with onset around StA ≈ 0.33–0.44 for Re = 255.”
Unsteady propulsion near a solid boundary (2014, methodology): “Experimental methods Following Godoy-Diana et al. (2009), we use a foil with a semicircular leading edge that tapers along straight lines to its trailing edge (see figure 1).”
Force production and asymmetric deformation of a flexible flapping wing in forward flight (2013, unknown): “It should be pointed out that a small amount of asymmetry persists even for zero freestream velocity due to the intrinsic behavior of the flow, which has been discussed previously (Godoy Diana et al., 2009).”
Vortex wakes of a flapping foil (2009, methodology): “We note that we exclusively find wakes with left–right symmetry and that we do not scan the parameter region in which wakes with broken left–right symmetry are present (Godoy-Diana et al. 2008, 2009).”