Mechanism of Vorticity Generation in Plasma Streamwise Vortex Generators

Abstract

An experimental investigation into the mechanism of streamwise vorticity generation in an array of plasma streamwise vortex generators is presented. The array is flush mounted to a flat plate on which a nominally zero pressure gradient turbulent boundary layer develops upstream. The investigation is focused on characterization of the influence of freestream velocity, applied peak-to-peak voltage, length of the active electrode, and spanwise interelectrode spacing on streamwise vorticity generation. It is shown that the actuator creates wall-normal vorticity and reorients it into the streamwise direction. In addition, spanwise boundary-layer vorticity is reoriented into the streamwise direction. Scaling relations based on the vorticity transport equation are obtained and experimentally validated. These provide guidance for optimizing the actuators for particular flow control applications. NomenclatureA v = vortex cross-sectional area in the y-z plane E = electric field E pp = peak-to-peak excitation voltage F B = body force vector L = active surface electrode length M ∞ = freestream Mach number Re x = Reynolds number S xj = mean strain rate s xj = fluctuating strain rate U = streamwise mean velocity component h Ui = spanwise cycle-average mean velocity U ∞ = freestream velocity u j = j component velocity fluctuation u τ = wall friction velocity V = wall-normal mean velocity component V p = plasma-induced wall-normal velocity W = spanwise mean velocity component W P = plasma-induced spanwise mean velocity x, y, z = streamwise, wall-normal, and spanwise spatial coordinates, respectively δ = 99% boundary-layer thickness δ = boundary-layer displacement thickness λ = spanwise interelectrode spacing Γx = circulation ω x = streamwise component mean vorticity ω 0 x = streamwise vorticity fluctuation

Flat plate drag reduction using plasma-generated streamwise vortices

“…For configuration B, the spatially averaged streamwise vorticity ω x v over the vortex enclosed by the contour of 10 % of the maximum vorticity is calculated from the PIV-measured time-averaged vorticity data in the y-z plane at the trailing edge (x + = 0) of the middle plasma-actuator pair. For E < 4.25 kV p−p , ω x v scales linearly with E 3.5 (figure 12) -similar to Wicks, Thomas & Corke's (2015) finding. However, when E > 4.25 kV p-p , the rise in ω x v with E is slowed down and ω x v ∝ E 1.6 .…”

“…Thomas et al (2009) found that the plasma-generated body force was proportional to E 3.5 at low voltages but to E 2.3 at high voltages. With ω x v scaled with this body force (Wicks, Thomas & Corke 2015), ω x v is expected to increase with E faster at low voltages but slower at high voltages. The difference between our and Thomas et al's (2009) results may be due to a difference in the dielectric material or its thickness between the two studies.…”

Unsteady Flow Separation Control over a NACA 0015 using NS-DBD Plasma Actuators

“…stall applications [27]. Successful implementation of these plasma actuators in high speed flows requires the use of thicker dielectrics and higher voltages [28,29,30,31] to increase the supplied body force [32]. Even when these changes are implemented there is a limit to the effectiveness of DBD actuators driven by an AC waveform [30].…”

Stall Control by Plasma Actuators: Characterization along the Airfoil Span

“…The above considerations and the outcome of some bench tests led to set a sharpness r = 5. This tip effect , also known for corona actuators [27,28], enhances the stall control but is known to scale with U −2 ∞ , progressively losing intensity as the freestream velocity is increased [20]; however, to keep a better authority on the flow at higher velocities, the sharp tips can be separated by a suitable inter-tip spacing d. Thanks to the orthogonality of the induced velocity to the electrode perimeter, in the gaps between adjacent tips, opposite transverse motions are created, giving rise to pairs of counterrotating vortex structures. This improves the boundary layer mixing, so that, with this geometry, the actuator behaves also as a vortex generator (VG), as described in Reference [17,29] and as sketched in Figure 4 in plane form.…”