Three-dimensionality of leading-edge vortices on high aspect ratio plunging wings

To investigate the effect of sweep on the leading-edge vortex of high aspect ratio plunging wings, this article presents force, bending moment, and volumetric velocity measurements for high aspect ratio $\mathrm{AR}=10$ wings with sweep angles of 0° and 40°. The effect of the sweep angle on the bending moment is the largest at the minimum effective angle of attack. This is because as the leading-edge vortex sheds it moves inboard on the unswept wing while moving outboard on the swept wing. Where the leg of the leading-edge vortex connects with the wing there is significant three-dimensional flow. The axial velocity along the vortex filament, which may be towards to the wing tip or the wing root (reversed flow), exhibits increasing magnitude as the effective angle of attack decreases and the vortex filament deforms. Reversed axial flow along the vortex filament has the largest magnitudes for the unswept wing. In the vortex core, jetlike, wakelike, and uniform axial velocity profiles were observed. Unlike the classical vortex breakdown, the transition from the jetlike to the wakelike axial flow does not appear to be abrupt. The measurements also revealed evidence of spanwise instabilities in the leading-edge vortex filament.

Figure 1

Schematic of leading-edge vortices for aspect ratio $\mathrm{AR}=4$ oscillating wings: (a),(b) Ω vortex for pitching wings at $k=0.05$ [13, 15, 16]; (c) arch-type vortex at $k=0.20$ for a pitching wing [17]; (d) for a plunging wing at $k=1.88$ [19]; (e) for a plunging wing at $k=3.14$ [19]; (f) for a pitching swept wing [27].

Figure 2

(a) Plunging motion and plunge velocity; (b) top and side views of the wing and the coordinate system.

Figure 3

Test rig: (a) isometric view, (b) front view.

Figure 4

(a) Lift coefficient, (b) bending moment coefficient of the stationary wings.

Figure 5

Variations of the time-averaged (a) lift coefficient, (b) bending moment coefficient with reduced frequency, $\alpha ={15}^{\circ }$.

Figure 6

Variation of the (a) lift coefficient, and (b) bending moment coefficient for $\alpha ={15}^{\circ }$, $k=1.1$, $A/c=0.5$.

Figure 7

Isosurfaces of $Qc/U_{\infty }=100$ and near-surface streamlines, $\alpha ={15}^{\circ }$, $k=1.1$, $A/c=0.5$. Top views of the unswept wing (left column), swept wing with airfoil cross section (middle column), swept wing with flat-plate cross section (right column); $t/T=0$ (top row), $t/T=0.125$ (middle row), $t/T=0.250$ (bottom row).

Figure 8

Isosurfaces of $Qc/U_{\infty }=100$ and near-surface streamlines, $\alpha ={15}^{\circ }$, $k=1.1$, $A/c=0.5$. Top and side views of the unswept wing (left column), swept wing with airfoil cross section (middle column), swept wing with flat-plate cross section (right column); $t/T=0.375$ (top), $t/T=0.500$ (bottom).

Figure 9

Isosurfaces of $Qc/U_{\infty }=100$ and near-surface streamlines, $\alpha ={15}^{\circ }$, $k=1.1$, $A/c=0.5$. Top and side views of the unswept wing (left column), swept wing with airfoil cross section (middle column), swept wing with flat-plate cross section (right column); $t/T=0.625$ (top), $t/T=0.750$ (bottom).

Figure 10

Isosurfaces of $Qc/U_{\infty }=100$ and near-surface streamlines, $\alpha ={15}^{\circ }$, $k=1.1$, $A/c=0.5$. Rear view of the unswept wing (left column), swept wing with airfoil cross section (middle column), swept wing with flat-plate cross section (right column); $t/T=0.750$.

Figure 11

Variation of the phase-averaged axial velocity at the vortex center, $\alpha ={15}^{\circ }$, $k=1.1$, $A/c=0.5$.

Figure 12

(a) Axial velocity at the vortex center; (b) example of the measurement line at $z/c=0.5$ station; (c) axial velocity profiles along the chordwise coordinate at three stations, $\mathrm{\Lambda }=0^{\circ }$, $\alpha ={15}^{\circ }$, $k=1.1$, $A/c=0.5$.

Figure 13

(a) Axial velocity at the vortex center; (b) axial velocity profiles (solid lines) and with spanwise component of freestream removed (dashed lines) along the chordwise coordinate at five stations, $\mathrm{\Lambda }={40}^{\circ }$, $\alpha ={15}^{\circ }$, $k=1.1$, $A/c=0.5$.

Figure 14

Contour plots of axial velocity and spanwise velocity in the plane shown, $\mathrm{\Lambda }={40}^{\circ }$, $\alpha ={15}^{\circ }$, $k=1.1$, $A/c=0.5$.

Figure 15

Isosurfaces of normalized vorticity magnitude $\omega c/U_{\infty }=13.4$ for $\alpha ={15}^{\circ }$, $k=1.1$, $A/c=0.5$. Top view of the swept wing with flat-plate cross section; $t/T=0.875$.