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Schematic of the (a) experimental setup, (b) sectional view of the airfoil. All dimensions are in mm. Note the coordinate system; x, y, z are, respectively, the streamwise, transverse, spanwise directions, and u, v, w are the corresponding velocities. The mean-position, about which the airfoil oscillates symmetrically, is the zero-angle position of airfoil chord. Schematics of the optics arrangement for (c) PIV measurements, (d) visualizations. Note the narrow shadowed region during PIV measurements. Note, (a) shows side view, and (b)–(d) bottom view.
Instantaneous velocity and vorticity fields (θ max = ±15°, f = 2 Hz). Jet is (a) nearly along the center-line (TE moving down, θ = −10.2°), (b) inclined upward (TE moving up, θ = +9.2°), (c) inclined downward (TE moving down, θ = +13°). In all three situations, the flow is like a spread-out jet. Reference vector (bottom-right) shows flow velocity of 150 mm s−1. Negative is the clockwise vorticity and vice versa. Laser sheet is passed from left; grey patch is the shadow.
Dye visualization (θ max = ±15°, f = 2 Hz) when TE is near the (a) mean-position (moving down), (b) bottom-extreme, (c) mean-position (moving up), (d) top-extreme, (e) mean-position (moving down). Laser sheet is passed from bottom. Vortex structures are seen clearly only in the near-wake. Notice the smaller vortices being shed from TE in (c), visible more clearly in the close-up (bottom-right image). Note that, the small ‘blob’ of dye near leading edge in (a), (b), (e) is not a vortex, but it appears due to two reasons: first, intermittent release of dye from the dye port, and second, since the fluid motion near leading edge is small, the dye accumulates there; the movie (see the supplementary material) clearly shows that the leading edge vortices are not generated. Thus, what appears as a vortex is a ‘blob’ of dye that is convected by the flow.
Jet-inclination data (θ max = ±15°, f = 2 Hz) for (a) Exp–1, (b) Exp–2; U: up-mode, D: down-mode, S–C: jet is spread-out or along the center-line (see schematics). Numbers indicate pitching cycles. Despite the same initial conditions and pitching duration for both experiments, notice that after first few cycles, the jet inclines upward during Exp–1, and downward during Exp–2, and also, the jet meanders across the center-line once during Exp–1, but twice during Exp–2.
Conditionally averaged (defined in the text) flow data for Exp–1 (θ max = ±15°, f = 2 Hz); top row – velocity and vorticity fields, bottom row – iso-velocity contours. The flow is averaged for [see Fig. 4(a) ] (a) and (b) the first 14 cycles, (c) and (d) up-mode (24 cycles), (e) and (f) down-mode (23 cycles). Rectangular grey patch is the shadowed region; shadow-width indicates the y-amplitude of TE deflection. In (d) and (f), we show the locations of the maximum velocity (black circles), the linear fit (thick black line), and the jet-inclination angle (αjet).
Mean flow data (θ max = ±15°, f = 2 Hz): (a) vorticity field, (b) streamwise velocity profiles normalized by .
Instantaneous velocity and vorticity fields for the foil with the flexible flap for θ max = ±10°, f = 1 Hz. An undulatory reverse Bénard–Kármán vortex jet is generated. The jet moves along the center-line up to about two chords downstream of TE, and then inclines (a) upward, or (b) downward. Reference vector = 150 mm s−1.
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