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Three-Dimensional Transitory Control of Flow Separation

The flow dynamics of 3-D flow attachment induced by a single [O(1 ms)] pulse effected by spanwise-compact actuation within a 2-D separated flow domain over the static airfoil (a = 19°) are assessed from phase-averaged PIV images that are taken at successive time increments relative to the onset of the actuation.  Figure 1 shows color raster plots of spanwise vorticity concentrations superposed with velocity vectors in the cross stream plane z = 0 in the near wake of the airfoil (-0.05 < x/c < 0.45, -0.2 < y/c < 0.6) for 2-D (Figures 1a-e) and 3-D (Figures 1f‑j) actuation.  Figures 1a and f (t = 0) show the stalled flow immediately following the actuation trigger but before the onset of the pulsed jets.  It is noteworthy that the CW vorticity concentrations within the separated shear layer are somewhat higher and perhaps less diffused in the cross stream direction when the flow is unbounded, which is in agreement with the slightly lower static CL(a) and earlier onset of static stall for the extended span.

The effects of the actuation are evident at t/Tconv = 1.3 and are characterized by the advection of a strong CW vortex (Figures 1b and g) that results from the disruption and “severing” of the separating shear layer by the actuation jets.  While the severed CW vortex is evident for both actuator configurations, the vortex induced by the 3-D actuation is clearly more coherent and has higher vorticity concentrations.  By t/Tconv 2.1 (Figures 1c, and h), the vortex has advected out of the field of view and the flow fields induced by the two actuation configurations are remarkably different.  The 2-D actuation leads to flow attachment over the airfoil, and the vorticity layer that is associated with the attached flow follows closely the motion of the severed CW vortex as shown in Figure 1c.  However, the effects of the 3-D actuation on the vorticity layer in the center plane over the airfoil results in slower advection and, as a result, there is almost complete absence of CW vorticity within this domain of the wake indicating accumulation of CW vorticity over the airfoil (Figure 1h).  These data indicate a significant disparity in time scales of the interaction of the 2-D and 3-D actuation configurations with the cross flows.  The longer accumulation of vorticity on the airfoil by the 3-D actuation corresponds to stronger increase in center plane circulation as discussed in connection with Figure 2.  The attached surface boundary layer following 3-D actuation appears in Figure 1i while its 2-D counterpart (Figure 1d) continues its advection.  It is also noteworthy that the CCW vorticity in Figure 1i exhibits a stronger concentration near the trailing edge indicating that the momentary flow attachment affects the flow over the entire airfoil and probably leads to some accumulation of CCW vorticity (there is no evidence of a similar effect with the 2-D actuation).  Finally, at t/Tconv = 4.5 the flow response to the 2-D actuation begins to slowly relax to the baseline stalled state as the cross-stream extent of the wake increases (Figure 1e), while it appears that the relaxation of the response to the 3-D actuation is somewhat slower (Figure 1j).

These flow transients are also observed in off-center planes beyond the edges of actuation. To illustrate the spanwise variations in the flow for the spanwise-limited actuation pulse, the corresponding phase-averaged PIV flow field measurements taken in an off-center plane beyond the extent of the actuator array at z » 0.63Sa (note that the spanwise edges of the actuators are at z = ±0.5Sa) are shown in Figures 1k‑o. It is important to note that the flow response to the single pulse at this off-center plane beyond the extent of the actuators is very similar to z = 0. In particular, the shedding of the large CW vertical structure (Figure 1l) following the severing of the upstream separating shear layer by the pulse jet actuators confirms the extension of control to the unactuated airfoil domain. The subsequent narrowing of the wake explains the fractional increase in measured lift that is above the fractional span of the actuators. However, following the actuation pulse, the flow in the off-center plane at t/Tconv = 2.6 and 4.5 (Figures 1n and o) is slightly different from the center plane (Figures 1i and j).

The differences in the transient flow response are quantified by computing the phase averaged change in circulation about the airfoil (Figure 2).  The sectional circulation in the centerline plane (Woo et al., 2008) for the 2-D actuation exhibits the nominal reduction in circulation that is associated with the severing and shedding of the 2-D vortex (t/Tconv = 1.5), followed by a local peak (|DG/Go|max » 20%, at t/Tconv = 2.5) associated with the attachment and accumulation of vorticity with the boundary layer on the suction side of the airfoil, and followed by a slow relaxation.  The variation of the sectional circulation in the center plane following 3-D actuation is remarkably different.  To begin with, the loss in circulation due to the shedding of the severed CW vortex (t/Tconv = 1.5) is larger (in agreement with the stronger vortex in Figure 1g).  Perhaps more important is the stronger circulation peak (t/Tconv = 2.5) which is nearly 200% larger than peak associated with the 2-D actuation indicating that the control authority of pulsed actuation is enhanced with stronger concentrations of vorticity shed and accumulated.  Furthermore, 3-D actuation results in a second circulation peak that is even more pronounced off centerline (z = 0.63Sa).  This second peak is associated with delayed 3-D relaxation off centerline following the shedding of the CW vortex (note that the off-center plane circulations are nearly identical up to t/Tconv » 2.5 when the flow begins to relax).  Figures 1 and 6 indicate that during relaxation, there are spanwise variations in the flow response.  Finally, the phase averaged circulation traces show that while the duration of the relaxation of the circulation on the centerline is similar to the relaxation associated with 2-D actuation, the corresponding duration of the relaxation off centerline is significantly longer.  Furthermore, these data indicate that the effects of the 3-D actuation extend well beyond the spanwise extent of the actuator.

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