Trapped vorticity for controlled modification of an airfoil's aerodynamic loads

The aerodynamic loads on a static airfoil are modified below its stall margin by deliberate formation and regulation of trapped vorticity on the suction and pressure surfaces near the trailing edge. Vorticity accumulation and shedding are effected using a hybrid actuator comprising a miniature two-dimensional passive protuberance having a cross-stream scale that is nominally commensurate with the local boundary layer thickness, and the vorticity flux is regulated using integrated spanwise arrays of equally spaced high aspect ratio synthetic jet actuators. The aerodynamic loads are varied by independent differential control of flux of opposite sense vorticity from both sides of the airfoil that are characterized using measurements of the force/torque, surface pressure, and particle image velocimetry over the suction surface and in the airfoil's near wake. The induced changes in circulation and lift and in the pitching moment are traced to complex transitory changes in vorticity flux associated with the onset and termination of the actuation. These changes are characterized by transitory variations in the balance of flux and shedding of clockwise and counterclockwise vorticities that are triggered, respectively, by actuation on the pressure or suction surfaces. These investigations indicate that hybrid flow control by trapped vorticity, which has the potential to manipulate prestall aerodynamic loads without mechanical control surfaces, may enable novel wing designs.

Figure 1

Conceptual bidirectional control of a pitching moment by hybrid formation and control of trapped vorticity at suction (a) and pressure (c) sides of an airfoil tail. Passive formation of trapped vorticity is shown in panel (b).

Figure 2

NACA4415 airfoil with modified profile geometry near the trailing edge (a) and a close-up of the trailing edge region (b).

Figure 3

Synthetic jet calibration: variation of the rms jet velocity (a) and momentum coefficient (b) at the center of the jet orifice with the jet power fraction ${\varepsilon }^{\prime }$.

Figure 4

Distributions of static pressure $C_p$ when the actuators are mounted at [$x_{\mathrm{SS}}=0.86c$, $x_{\mathrm{PS}}=0.95c$] for $\alpha =3^{\circ }$ (a), $9^{\circ }$ (b), and ${15}^{\circ }$ (c) and actuation level $u_f=0$ ($▴$), 1 ($▴$), and $-1$ ($▴$). Corresponding $C_p$ for the smooth airfoil (-) is shown for reference.

Figure 5

Variation of $C_L$ (a), $C_M$ (b), and $C_D$ (c) with $\alpha$ for the smooth airfoil (•) and modified [$x_{\mathrm{SS}}=0.86c$, $x_{\mathrm{PS}}=0.95c$] airfoil with $u_f=0$ ($•$), 1 ($•$), and $-1$ ($•$). Variation of $\mathrm{\Delta }{C}_L$ (d), $\mathrm{\Delta }{C}_M$ (e), and $\mathrm{\Delta }{C}_D$ (f) with $u_f$ for $\alpha =0^{\circ }$ ($•$), $3^{\circ }$ ($•$), and ${15}^{\circ }$ ($•$).

Figure 6

Variation of $\mathrm{\Delta }{C}_M$ with $\mathrm{\Delta }{C}_L$, [relative to the base (smooth) airfoil] in the presence of the inactive (a)–(c) and active ($-1<u_f<1$), (d)–(i) actuation. (a), (d), (g) The SS and PS actuators are flush with the airfoil's trailing edge. (b), (e), (f) The SS actuator is fixed at $x_{\mathrm{SS}}=0.88c$ and the PS actuator is moved within $0.96c<x_{\mathrm{PS}}<c$. (c), (f), (i) The PS actuator is fixed at $x_{\mathrm{SS}}=0.98c$ and the SS actuator is moved within $0.83c<x_{\mathrm{SS}}<c$. The data in panels (b), (c), (e), (f) are colored by the position of the moving actuators, and the data in panels (e), (f), (h), (i) are colored by the magnitude of the actuation.

Figure 7

Variation of $\mathrm{\Delta }\widehat{C_M}$ with $\mathrm{\Delta }\widehat{C_L}$ for all the test cases: $0.83<x_{SS}<1$, $0.96<x_{\mathrm{PS}}<1$, $-5^{\circ }<\alpha <{15}^{\circ }$, and $-1<u_f<1$.

Figure 8

Raster plots of the time-averaged spanwise vorticity ${\omega }_{z}c/U_0$ at $\alpha =-3^{\circ }$ (a), (e), (i), $3^{\circ }$ (b), (f), (j), $9^{\circ }$ (c), (g), (k), and ${15}^{\circ }$ (d), (h), (l) with $u_f=0$ (a)–(d), 1 (e)–(h), and $-1$ (i)–(l).

Figure 9

Time-averaged cross-stream distributions of vorticity flux in the wake ($x/c=1.05$) for $-1<u_f<1$ for the static model at $\alpha =-5^{\circ }$ (a), $3^{\circ }$ (b), and ${15}^{\circ }$ (c). The traces are colored such that black corresponds to the unactuated flow and increasing levels of red (blue) correspond to increasing levels of SS (PS) actuation.

Figure 10

Raster plots of phase-averaged spanwise vorticity during the cycle of the synthetic jet at $\varphi =0^{\circ }$ (a), ${80}^{\circ }$ (b), ${160}^{\circ }$ (c), ${240}^{\circ }$ (d), and ${320}^{\circ }$ (e), and the corresponding time history of circulation within the domain. Dashed lines indicate time-averaged circulation when $u_f=0$ (black) and $u_f=1$ (red).

Figure 11

Time histories of ${\mathrm{\Delta }C}_M$ (a), ${\mathrm{\Delta }C}_L$ (b), and $\alpha$ (c) during step changes in actuation between SS and PS actuators. Black traces indicate corresponding steady-state values based on a look up table using $\alpha$ and $u_f$.

Figure 12

Time histories of $\mathrm{\Delta }{C}_p$ at the leading edge (a), on the suction surface at $x/c=0.39$ (b), on the pressure surface at $x/c=0.4c$ (c), and at the trailing edge (d), with corresponding static values.

Figure 13

Raster plots of phase-averaged spanwise vorticity following actuation transitions at $t/T_{\mathrm{conv}}=0.3$, 0.33, and 0.36 for PS-SS (a)–(c) and SS-PS (d)–(f) and at $t/T_{\mathrm{conv}}=0$, 0.07, and 0.46 for 0-SS (g)–(i) and SS-0 (j)–(l).

Figure 14

Color raster plots of time variation of the cross-stream vorticity flux at $x/c=1.04$ following transitions 0-SS (a), SS-0 (b), PS-SS (c), and SS-PS (d).

Figure 15

Respective time histories of vorticity flux of the four actuation transitions in Fig. 14. Vorticity flux from suction and pressure sides of the airfoil is computed separately (red and blue traces, respectively). The total flux is shown in green.

Figure 16

Time histories of the changes in circulation about the airfoil corresponding to the four actuation transitions in Fig. 14.