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Energies 2020, 13, 1374 5 of 20 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. ∞ @ D M N Figure 4. Sketch of the effects of triangular tips on the exposed electrode: momentum injection (blue) and vortices generation (red). If the tip spacing is suitably chosen, this effect significantly enhances the actuator authority. In literature, the optimal spanwise spacing for a plasma vortex generator has been found to depend only on the discharge length, independently of the incoming boundary layer thickness [26]. The optimal spacing turned out to be twice the discharge length, in such a way as to permit the right development of a double plasma sheet between adjacent elements (between adjacent tips in the present shape). To check this property and to determine a suitable spacing d for the present application, some bench tests were conducted following the method described in Reference [30]. The available power supply of 40 kVpp gives a discharge length of 18 mm, and this led to setting a tip spacing of d = 36 mm. In this DBD geometry, the last important parameter is the tip length h, that required a further analysis, strictly linked to the airspeed U∞. This relation is based on the study of the formation and evolution of the streamwise vorticity ωx, crucial for the correct working of a VG. The generation of ωx vorticity was at first investigated for low freestream values in Reference [31]; then, its characterization was extended at higher velocities in Reference [26]. To design the present actuator, the x-component of the vorticity transport equation was dimensionally analyzed [20], confirming that the VG effect is due to a reorientation of the large spanwise vorticity ωz carried by the approaching boundary layer. This process gives rise to the ωx component but requires a minimum residence time of the fluid particles over the electrode to effectively occur. The main time scale is the convective time, defined as TC = h/U∞ along the tip length h; instead, the viscous scale Tν = δ2/ν, based on the thickness δ of the approaching boundary layer, turns out to be much longer, namely Tν ≫ TC, so that an inviscid analysis is satisfying. To quantify the reorientation time, it can be considered that the vortex structures lay within the boundary layer (their size is enlarged for clarity in Figure 4). Then, the VG effect implies that a fluid particle of the external flow that travels along the actuator is pushed toward the wall while it rotates around the streamwise direction. The velocity of the transverse (spanwise) motion can be assumed in the order of the ionic wind Vi (less than 5 m/s), and the particle can be considered to sweep transversally almost half the inter-tip spacing d. Thus, the recirculation time scale can be defined as TR = d/(2Vi), and to allow a complete vorticity reorientation, the primary time constraint becomes TC ≥ TR or, at least, of the same order of magnitude. This means that a fast fluid particle traveling along the DBD has enough time to be dragged toward the wall before leaving the electrode zone. For this application, the value of h was initially estimated considering a freestream velocity of U∞ = 20 m/s so that, accounting for the time scales described above, the tips length was set toPDF Image | Stall Control by Plasma Actuators: Characterization along the Airfoil Span
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