Plasma flow control of the tip vortices over a very low aspect-ratio wing

The aerodynamics of a low aspect-ratio (AR) wing is fundamentally different from a two-dimensional (2D) airfoil. It was demonstrated (Winkelman and Barlow,1980; Freymuth, 1988) that low AR wings are dominated by a leading-edge vortex (LEV) with a pair of tip vortices (TVs). Here, the formation of the TVs is attributed to the pressure difference between the pressure and suction sides of the wing (Green 1995). In other words, the flow near the wing tip is pulled outboard and moves toward the suction side of the wing, forming the streamwise vortices known as the TVs. The existence of the TVs influences the behavior of the leading-edge flow (DeVoria and Mohseni,2017; Dong et al., 2020), promoting the formation of the recirculation area near the leading edge of the wing. Moreover, the interaction of these vortices influences the flow field over the wing body, creating a three-dimensional (3D), complex wake region (Taira and Colonius, 2009a; Taira and Colonius, 2009b).

The existence of the TVs over a low AR wing leads to a significantly different lift curve as compared to that of the 2D airfoil, see Fig. 1. Although the lift slope of the low AR wing is very small at small angles of attack (AoA), it increases with an increase in the AoA. As a result, the lift coefficient C_L of a low AR wing eventually reaches to more than 1.5 times that of the 2D airfoil at α = 45°. It was shown (Torres and Mueller, 2004; Taira and Colonius, 2009a; Taira and Colonius, 2009b) that the maximum lift angle of the wing is further increased with a reduction in the AR. For low AR wings, the total lift on the wing is a combination of the spanwise circulation of the LEV through the Kutta–Joukowski theorem and the pressure force of the TVs (i.e., the vortex lift). The development of the LEV, however, is influenced by velocity induction of the TVs due to the Biot–Savart law (Harbig et al.,2013; Dong et al., 2022). The interaction between the LEV and the TVs was studied by Dong et al. (2020) and Dong et al. (2022) who demonstrated that the reattachment of the leading-edge flow and the subsequent formation of the LEV were strongly influenced by the TVs. They also observed that the size and strength of the TVs were increased with an increase in the AoA. By correlating the aerodynamic forces with the vortical structures along the span of the NACA 0015 wing, the sectional lift force exhibited considerable fluctuations close to the mid-span and maintained a relatively steady value at the wing tip, suggesting that the TVs could stabilize the unsteady LEV shedding (Zhang et al., 2020). At a very low AR (AR < 1), the leading-edge separated flow formed a large separation bubble with strong recirculated velocities in the vicinity of the leading edge due to the downwash induced by the TVs, reducing the amount of the vorticity shedding downstream, which consequently strengthened the bound vortex and generated a high lift force (DeVoria and Mohseni, 2017).

The dielectric-barrier-discharge (DBD) plasma actuators are composed of two electrodes separated by a thin dielectric sheet. When they are excited by high AC voltage at high frequencies, the air in the vicinity of the exposed electrode is weakly ionized, generating an ionic jet. This couples the momentum of the air flow, which can be used for flow control. DBD plasma flow control has unique advantages over the conventional control devices, since the DBD plasma actuators are fast response with no moving parts involved (i.e., all electric devices), which can be retrofitted to the aerodynamic bodies. Historical background on DBD plasma actuators and their applications to aerodynamics are given by Moreau (2007), Corke et al. (2010), Wang et al. (2013), Choi et al. (2015), and Kriegseis et al. (2016).

The influence of the plasma on the aerodynamic forces on a NACA 0009 airfoil was investigated by Corke et al. (2002), where both the lift and drag coefficients were increased using a DBD plasma actuator. They concluded that one of the functions of the plasma actuator was to increase the camber of the airfoil. The leading-edge flow separation was also controlled by the plasma actuator, resulting in a significant reduction in the wake area (Roth, 2003). As a result, the stall angle of the airfoil was delayed by up to 8° with an improved lift-to-drag ratio (Post and Corke, 2004). Vorobiev et al. (2008) examined the effectiveness of plasma control on an airfoil at different Reynolds numbers, showing that the lift coefficient was enhanced by up to 30% by the plasma actuator. However, this lift enhancement by the plasma actuator became weaker with an increase in the Reynolds number. It was demonstrated that the plasma actuator affected the aerodynamics of the wing in two ways—adding momentum to the flow and suppressing viscous effect in the vicinity of the trailing edge. He et al. (2009) and Feng et al. (2015) studied the impact of the plasma actuator placed at the trailing edge of the airfoil, showing that the plasma actuator could behave as a virtual Gurney flap.

Apart from the leading-edge and trailing-edge flow control, the plasma actuator was also placed close to the wing tip to modify the TVs. Hasebe et al. (2011) investigated the effect of the blowing and suction plasma actuators on the TVs of a NACA 0012 wing with an AR of 0.5, showing that the strength of the TVs was suppressed by both plasma actuators, leading to a lower lift-to-drag ratio. Boesch et al. (2010) also studied the influence of the blowing plasma actuator on the TVs of a NACA 4418 (AR = 2). They, however, concluded that the TVs became diffusive and moved outboard with plasma on, which in turn mitigated the influence of the downwash to give a high lift. Plasma control of the TVs over the delta wing was conducted by Shen and Wen (2017) who symmetrically placed the suction plasma actuator on both leading edges of a slender delta wing to modify the TVs. The separated shear layer at the wing tip was pulled toward the wing surface by the DBD plasma actuator, influencing the structure of the TVs. In particular, the TV breakdown was delayed by the symmetrical control but promoted by the asymmetrical control. The aerodynamic forces of this delta wing, however, did not exhibit any changes. Greenblatt et al. (2008) used the pulsed suction DBD plasma actuator to modify the TVs on a delta wing after the vortex breakdown. They found that the breakdown of the TVs was delayed under the influence of the plasma actuator, resulting in a significant increase in the lift. Similar results were also mentioned by Sidorenko et al. (2013), but their optimum modulation frequency of the plasma actuator was twice larger than that of Greenblatt et al. (2008).

Previously, we have studied the interaction between the TVs and the LEV over a stationary and pitching very low AR wing, where the influence of the TVs on the development of the LEV was demonstrated (Dong et al.,2020; Dong et al., 2022). Building on the understanding of the vortex interactions gained from these studies, a flow control study of a very low AR wing was carried out using DBD plasma actuators. By controlling the TVs using the plasma jet at the wing tip, we were able to influence the aerodynamic forces of the wing. The influence of the plasma actuators on the TVs was analyzed by documenting the vortex locus as well as velocity and vorticity distributions around the vortex core to understand the mechanism of plasma control of a very low AR wing.

An experimental study was conducted in a low-speed, open-return wind tunnel [Fig. 2(a)] with a test section of 1.5 $×$ 0.9 $×$ 0.8 m³ (length $×$ width $×$ height) at the University of Nottingham (Kim et al., 2022), where the port side of the TV of a very-low AR wing was controlled by the plasma actuators to modify the aerodynamic characteristics. The freestream velocity U_∞ of the wind tunnel was set at 10 m/s, which was monitored by a Pitot tube placed 0.2 m downstream of the contraction section. The wing model was manufactured from a 3-mm thick aluminum composite flat plate, which had a chord length of c = 260 mm and a half span length of s = 36 mm, corresponding to a very low aspect-ratio of 0.277 with a thickness-to-chord ratio of 1.2%, see Fig. 3. A 3D-printed elliptic leading edge (18 mm of major axis and 3 mm of minor axis) was attached. The maximum blockage of the wind tunnel due to the wing model was 1.8% at α = 90°. The wing model, whose chord Reynolds number is 2 $×$ 10⁵, was placed in the center of the wind tunnel test section where the freestream turbulence intensity was 0.3%. After installing a turbulence-generating grid 0.5 m upstream of the wing model, the turbulence intensity in the freestream was increased to 4%. This has increased the effective Reynolds number to 3 $×$ 10⁶ by promoting transition to turbulence near the leading edge of the wing. Here, the effective Reynolds number is the equivalent Reynolds number in the aerodynamic tests where the freestream turbulence level is nearly zero (Wang et al., 2014). The use of turbulence-generating grid was to remove the ambiguity in aerodynamic measurements at low to medium Reynolds numbers, where the aerodynamic forces on wings are influenced by the boundary-layer transition (Mueller, 1985). Figure 2(b) shows the laboratory-based coordinate system used in the present study, where x, y, and z denote the streamwise, cross-flow, and spanwise directions, respectively, corresponding to their mean velocity components U, V, and W and fluctuation velocities u, v, and w.

The plasma actuators were placed only one side of the wing model, see Fig. 3, where two different configurations of plasma actuators were considered. The first plasma configuration was intended to blow a synthetic plasma jet away from the wing tip, while the second plasma configuration was intended to draw the air from the wing tip. They were called the blowing and suction plasma actuators, respectively. Both plasma actuators consisted of an upper exposed electrode and a lower encapsulated electrode made of a single layer of 0.05-mm thick and 240-mm long copper tapes, separated by two layers of 0.15-mm thick Cirlex sheets. For the blowing plasma actuator, a pair of 10-mm wide upper electrodes was attached 10 mm from the wing tip as shown in Fig. 3(a). For the suction plasma actuator, on the other hand, a 3-mm wide upper electrode was attached over the tip edge of the wing, see Fig. 3(b). The Reynolds number based on the thickness of the plasma actuators and the freestream velocity was Re_p = 270, which was below the critical Reynolds number for triggering boundary-layer transition (Schlichting, 1955). Therefore, the roughness effect of the model wing due to the plasma actuators was negligible. Plasma actuators were excited with a sinusoidal waveform by a Minipuls 6 AC power supply at a peak-to-peak voltage E_PP = 18 kV and an operating frequency of 7 kHz. The plasma power cables were taken out through the bottom floor of the wind tunnel from the trailing edge of the wing model.

The wing model was mounted on a Kyowa LSM-B-SA1 three-component force transducer for aerodynamic force measurements via a 150-mm long strut to avoid the boundary layer over the wind tunnel floor, see Fig. 2. This transducer was rated at 10 N in all three components with an absolute accuracy of ±0.02 N. The measured signals from the force transducer were amplified and low-pass filtered by a Kyowa DPM-911B strain-gauge amplifier with a cutoff frequency of 100 Hz before being sent to a NI 9215 16-bit analogue-to-digital converter on a NI CompactRIO system. The AoA of the wing was controlled by a step motor driven by a NI 9512 driver, giving a minimum step angle of 0.1°. Force measurements were repeated 50 times at a sampling rate of 2000 Hz from α = 0° to α = 90° with an interval of 1.8°, each of which lasted 3 s with plasma off followed by 3 s with plasma on. The performance of plasma flow control during the “plasma on” period was evaluated against the “plasma off” condition throughout this study. The lift force F_L and drag force F_D of the wing model were calculated by $FL=FNcosα−FAsinα$ and $FD=FNsinα+ FAcosα$⁠, respectively, from the measured normal force F_N and the axial force F_A. The lift and drag coefficients were given by $CL=FL/12ρU∞2A$ and $CD=FD/12ρU∞2A$⁠, where ρ is the air density, U_∞ is the freestream velocity, and A is the plan area of the wing.

The flow field over the wing was measured using a fast-speed, two-dimensional particle image velocimetry (PIV) system by Dantec on the x–y plane and y–z plane, as shown in Fig. 2. Two seeding generators (TSI 9307-7) were placed upstream of the contraction section of the wind tunnel to create uniformly distributed tracer particles with a diameter of approximately 1 μm. A Litron LDY 302-PIV Nd:YLF dual-cavity laser with 15 mJ per pulse was used to generate a thin laser light sheet, where the particle images were captured with a CMOS high-speed camera at a resolution of 1280 $×$ 800 pixels. We used a 110 mm Canon lens in the x–y plane and a 200 mm Canon lens in the y–z plane, where the corresponding field of view was 0.55c $×$ 0.35c and 2s $×$ 1.5s, respectively. In the x-y plane measurement, the laser light sheet with a thickness of 0.5 mm was set parallel to the freestream from z = 0 to z = 2s in 0.11s increments, where the time delay between the laser pulses was set to 50 μs. To minimize the measurement error due to out-of-plane motion of seeding particles, the laser sheet thickness was increased to 2 mm and the time interval between laser pulses was reduced to 30 μs in the y–z plane measurement. To allow the camera to be set outside the wind tunnel for the y–z plane measurements, a 100 mm diametral mirror was mounted on the wind tunnel floor, 300 mm downstream the model at 45° to the freestream. Here, 14 planes were investigated from the leading edge to the mid-chord. Image pairs in both planes were taken for 4 s (1.5 s for plasma-off followed by 2.5 s of plasma-on period) at a sample rate of 320 Hz.

The raw images captured by the PIV system were processed by Dantec DynamicStudio 2015a to extract the velocity fields, where the shape and size of the individual interrogation areas (IA) were iteratively adjusted depending on the local seeding densities. The minimum and maximum IAs were limited to 8 and 32 pixels with a 50% overlap, respectively, obtaining around 16 000 vectors in each frame. The validation of velocity vectors was made using a universal outlier detection analysis (Westerweel and Scarano, 2005). Any spurious vectors were replaced by a median value calculated using 3 $×$ 3 neighborhood vectors. Uncertainty in velocity measurements using PIV was estimated by $Ue=De2T2+(−DT2)2Te2$ (Kline and McClintock, 1953), assuming that its primary sources of error were the shift distance D of seeding particles and the interval time T between image pairs. Here, D_e is the uncertainty in particle shift distance, which was about 0.15 pixel. The uncertainty in the interval time T_e between image pairs was negligible. This gave U_e = 0.54 m/s or U_e/U_∞ = 5.4%, which was similar to the PIV measurements error estimated by Westerweel (1997). Estimated errors of derived quantities, such as the vorticity and circulation, were less than 8% and 10%, respectively.

The plasma actuators were operated either at a steady mode or a pulsed mode at a 50% duty cycle. Here, the normalized pulsed frequency was given by $f+=fc/U∞$⁠, where f is the modulation frequency, c is the chord length of the wing model, and U_∞ is the freestream velocity. Preliminary tests showed that the effective pulsed-mode frequency was f⁺ = 2, which was identical to that of Sidorenko et al. (2013) who examined the flow control on a delta wing. To obtain the momentum coefficient of the plasma jet, PIV measurements of the flow velocity induced by the plasma actuator were conducted without the external flow in a transparent sealed box of 0.6 $×$ 0.3 $×$ 0.3 m³, which was pre-seeded with tracer particles via a nozzle. We waited 10 minutes before each measurement to make sure that the flow inside was in a quiescent condition. Here, the sample rate and sample duration of the PIV were set to 960 Hz and 3 s, respectively. The momentum coefficient for the plasma actuators used in this work is shown in Table I. Here, the momentum coefficient of the plasma jet was defined by $Cμ=M/12ρU∞2c$⁠, where the momentum flux is given by $M=∫ρW2dy$ (Jukes and Choi, 2009).

The results for lift and drag coefficients with blowing and suction plasma actuators are compared with those of the baseline (plasma off) as shown in Fig. 4(a). Here, it should be noted that the aerodynamic forces as well as the flow field around the two baselines, one for the blowing plasma and the other for the suction plasma, were identical within the experimental uncertainties. This clearly shows that the aerodynamic forces are modified by the plasma actuators, where C_L is significantly increased by the blowing plasma actuator but is reduced by the suction plasma actuator between α = 4° and α = 20°. Compared to the lift coefficient, the change in the drag coefficient is relatively small with the plasma actuator, which is less than 10% for all cases. The percentage changes in C_L and C_D due to the plasma actuators are shown in Fig. 4(b), where the plasma data are indicated by C_Lp and C_Dp, while the baseline data are given by C_L0 and C_D0, respectively. The most effective control is found at f⁺ = 0 (steady mode) for both types of plasma actuators. Here, the maximum reduction in C_L0 can reach 30% by the suction plasma, while the blowing plasma actuator produces an enhancement of C_L0 by 23%. With a pulsed mode of plasma actuation, the control effect is reduced, where only 16% reduction and 13% enhancement in the lift coefficient are achieved by the suction and blowing plasma at f⁺ = 2, respectively. This is due to that the plasma momentum coefficient of the steady mode of actuation is about twice that of the pulsed mode of plasma actuation, which is operating at 50% of the duty cycle. It is also observed that the most effective control of the plasma on the C_L occurs at around α = 8° for all cases. With a further increase in the AoA, the influence of the plasma actuators gradually vanishes. Figure 4(c) shows the lift-to-drag ratio of the very low AR wing, which takes the maximum value of C_L/C_D = 2 at α = 18°. The changes in C_L/C_D as shown in Fig. 4(c) indicate that the aerodynamic efficiency of the wing can be manipulated by controlling the TV using the plasma actuator. To understand the underlying mechanism of the change in the aerodynamic forces due to plasma control, the behavior of the TV with plasma at α = 10° and 15° will be demonstrated in Sec. III B.

The effect of the plasma actuators on the time-averaged, normalized streamwise vorticity (ω_xc/U_∞) is shown in Fig. 5, where ω_x is the streamwise vorticity, c is the chord length of the wing, and U_∞ is the free-stream velocity. Here, the separated flow at the wing tip wraps around from the pressure side to the suction side of the wing, forming a conical-shaped TV stretching along the wing chord. The size and strength of the TV increase downstream with an increase in the AoA. However, there is no sign of the TV breakdown in this figure at least for 0 < x/c < 0.52 at α ≤ 15°. A weak, positive vorticity distribution near the leading edge (x/c < 0.2) is resulted from the interaction of the TV with the LEV, see Yilmaz and Rockwell (2012) at Re = 1 $×$ 10⁴ and Dong et al. (2022) at Re = 2 $×$ 10⁵. Applying the plasma actuators, the streamwise vorticity within the TV core becomes weaker with the suction control and stronger with the blowing control. The diameter of the TV remains unchanged by plasma control, except for suction plasma control (f⁺= 0) at α = 10° where a reduction of the TV diameter is clearly seen.

To further examine the influence of the plasma actuators on the TV, the time-averaged vorticity field together with the turbulent intensity and the Reynolds stress distributions at the mid-chord are shown for α = 10° and 15° in Figs. 6 and 7, respectively. Here, the vortex cores, which are indicated by pink circles, are identified by the λ₂-criterion (Jeong and Hussain, 1995), where the corresponding centroids, shown in green dots, are found at the location of the minimum negative value of λ₂. Other vortex identification techniques, including Q-criterion (Chong et al., 1990) and Γ₁–criterion (Graftieaux et al., 2001), give similar results. The TV forms at the wing tip (z/s = 1) close to the wing surface, where a weak secondary vorticity is generated, see Fig. 6. The maximum turbulent intensity can be observed in the vortex core around the vortex centroid. The Reynolds stress of the TV exhibits a bi-modal two-lobed distribution.

With suction plasma control at α = 10°, see Fig. 6(a), the shear layer is forced to move around the wing wall, reducing the flow separation at the wing tip. Particularly when the suction plasma is operated at a steady mode (f⁺= 0), the shear layer is reattached to the suction side of the wing surface, creating a small separation bubble. This makes the TV weaker with low vorticity. It is interesting to observe that the turbulent intensity [Fig. 6(b)] and the Reynolds stress [Fig. 6(c)] here are increased with the suction plasma. The distribution of the Reynolds stress in the vortex core is no longer bi-modal two-lobed. The strong Reynolds stress appears at the junction of the separated shear layer and the TV, suggesting an enhanced turbulent mixing there. This is due to a large increase in the W-component turbulent intensity, since the V-component turbulent intensity is reduced by the suction plasma. For the blowing control, there is no evident movement of the shear layer but the vorticity, turbulent intensity and the Reynolds stress within the TV core are all increased. Here, the increase in the vorticity inside the TV is partly attributed to the added momentum by the blowing plasma jet, which increases the strength of the separated shear layer at the wing tip. In addition, the plasma jet velocity is in the same direction as the TV circulation, which helps to increase the vorticity as well as the turbulence intensities and the Reynolds stress.

At α = 15° (Fig. 7), the blowing control shows similar results as those at α = 10°, by increasing the vorticity, the turbulent intensity, and the Reynolds stress within and around the TV core. For the suction control, however, the turbulent intensity and the Reynolds stress are reduced, since both V- and W-component turbulence intensities are reduced at the same time. We note that the wall-ward movement of the shear layer due to suction is much weaker at α = 15° as compared to the suction control results at α = 10°. However, a small separation bubble is still observed near the wing tip with the suction plasma. The suction plasma jet is directed in an opposite direction to the TV circulation, reducing the TV vorticity as well as the turbulence intensities and the Reynolds stress.

Figure 8 shows the locus of the vortex core during the downstream development of the TV in the (y_c /c, z_c/s) plane, where y_c/c and z_c/s are the local non-dimensional coordinates for the vortex core measured from the wing surface and the mid-span, respectively. At α = 10°, the locus of the TV core with a steady suction plasma (f⁺ = 0) remains within 0 < y_c/c < 0.01 and 0.99 < z_c/s < 1 [Fig. 8(a)], as the TV is pulled toward the wing surface to form a separation bubble as shown in Fig. 6(a). The TV locus is also shifted toward the wing surface (y_c/c = 0) with a pulsed suction plasma (f⁺ = 2), although a separation bubble is not observed in this case. On the other hand, the vortex core is shifted away from the wing surface as well as from the mid-span by blowing plasma control (f ⁺ = 0 and 2). A similar plasma control behavior can be observed at α = 15°, although the vortex core does not stay near the wing surface with a suction plasma at this AoA.

The influence of the plasma actuators on the TV circulation along the wing chord is shown by an integral of the vorticity inside the TV core identified by the λ₂-criterion, see Fig. 9. Note that the result for the steady suction plasma actuator has a large uncertainty due to the difficulty in identifying the TV core near the wing surface, see Fig. 6. The circulation of the TV increases nearly linearly with x/c at α = 10°, while the linear circulation growth is limited to x/c < 0.35 at α = 15°. These results are in good agreement with Devoria and Mohseni (2017) at Re = 8 $×$ 10⁴ and Dong et al. (2022) at Re = 2 $×$ 10⁵. As demonstrated in Figs. 6 and 7, the circulation of the TV is reduced by the suction plasma and increased by the blowing plasma. Indeed, suction plasma control of the TV is very effective at α = 10°, where the TV circulation is reduced by 75% and 39% at f ⁺ = 0 and 2, respectively, see Fig. 9(a). Meanwhile, the increase in the TV circulation by blowing plasma control is 53% and 26% by f ⁺= 0 and 2, respectively. Increasing AoA to α = 15°, the effectiveness of the suction and blowing plasma becomes less but similar to each other with a 33% change (reduction or increase) at f⁺= 0 and a 14% change at f⁺= 2. A reduction in the control effectiveness of the plasma actuators at α = 15° is due to the reduced velocity ratio of the plasma jet to the W-velocity component of the separated shear layer at the wing tip. While the plasma jet velocity remains constant, the W-velocity component of the separated shear layer is increased with an increase in the AoA.

To qualify how the plasma actuator affects the vorticity transport, the time-averaged vorticity flux at the mid-chord (x/c = 0.5) is shown in Fig. 10 as a function of y/c. Here, the vorticity flux Ω is defined by $Ω=−∫ωxV2+W2dz/U∞2$⁠, where the integral of the streamwise vorticity times the local velocity magnitude is performed excluding the contribution of the secondary vorticity between z/s = 0.75 and 1.25. A steady suction plasma (f ⁺ = 0) increases the vorticity flux close to the wing surface (y/c < −0. 075) at α = 10°, see Fig. 10(a). However, there are only small changes in the vorticity flux due to a pulsed suction plasma (f ⁺ = 2) or the blowing plasma (f ⁺ = 0 and 2) in this region. Away from the wing surface (y/c > −0.075), the vorticity flux is reduced by the suction plasma, while it is increased by the blowing plasma. Here, the peak and the maximum changes in the vortex flux due to plasma control are found at the center of the vortex core (y/c ≅ −0.05). With an increase in the AoA (α = 15°), the vorticity flux is increased due to an increase in the streamwise vorticity generated in the separated shear layer as well as the increases in the V- and W-component velocities. Here, there are no appreciable changes in the vorticity flux near the wing surface (y/c < −0.09) due to plasma control. Away from the wing surface (y/c > −0.09), vortex flux is reduced by the suction plasma (f ⁺ = 0 and 2), while it is increased by the blowing plasma (f ⁺ = 0 and 2). Again, the peak and the maximum changes in the vortex flux due to plasma control are found at the center of the vortex core, which is at y/c ≅ −0.08 at α = 15°.

The W-component velocity distributions across the vortex centroid at the mid-chord (x/c = 0.5) are shown in Fig. 11. Considering that the TV core is located at y/c ≅ −0.05 and y/c ≅ −0.08 for α = 10° and α = 15°, respectively, the W-component velocity in Fig. 11 represents the circumferential velocity of the TV around the vortex core. With plasma control, the near-wall side of the W-component velocity is increased by the blowing plasma, while it is reduced by the suction plasma. As a result, the TV circulation is increased by blowing control, while it is reduced by suction control. In other words, the blowing plasma increases the TV circulation by co-flowing with the TV, while the TV circulation is reduced by the counter-flowing suction plasma. This suggests that the plasma jet-flow direction relative to the TV circulation is critical in controlling the TVs over a very low AR wing. This seems to be the mechanism of TV circulation control using plasma actuators, which in turn affects the aerodynamic forces of a very low AR wing (Fig. 4). Since the changes in the vorticity flux are only seen away from the wall (Fig. 9), the separated shear layer is not affected by the plasma actuators except for the steady suction plasma (f ⁺ = 0), where the shear layer is bent over the wing tip to form a separation bubble, see Fig. 6(a).

The V-component velocity profiles across the vortex centroid are plotted from the wing tip to the mid-span in Fig. 12, showing the circumferential velocity of the TV. Similar to the W-component velocity, which also shows the circumferential velocity of the TV (Fig. 11), the magnitude of the V-component velocity is reduced by suction plasma control, while it is increased by blowing plasma control. It should be noted that the circumferential velocity distribution extends to the mid-span (z/s = 0). Here, the effect of plasma control is seen not only around the vortex core, but also near the mid-span (z/s = 0). In other words, the plasma control can influence the entire flow domain over the wing. It is also noted that the V-component velocity reaches its maximum value closer to the wing tip with the blowing control and to the mid-span with the suction control. The shift of the peak velocity location is due to the movement of the vortex core by plasma control, as demonstrated in Fig. 8.

Figure 13 shows the influence of plasma control on the U-component velocity of the TV at α = 10° and α = 15°, where the TV centroid and core boundary are marked based on the λ₂-criterion as discussed previously. The vorticity of the TV extends to the outer vortex boundary (Skinner et al., 2020), although the majority is found within the vortex core. Here, the boundary of the outer vortex is defined by the non-dimensional vorticity at ω_xc/U_∞ = −5. The U-component velocity increases sharply from the wing surface and peaks somewhere before entering the outer vortex boundary, which probably is due to the flow acceleration around the wing tip. Thereafter, the U-component velocity reduces inside the TV, followed by a gradual increase, eventually reaching to a final value of around 1.1 U_∞ outside the outer vortex. When the TV is controlled by a steady suction plasma (f ⁺ = 0) at α = 10°, the axial velocity increases monotonically, which is due to the reattachment of the separated shear layer as shown in Fig. 6. The other plasma control cases give a similar velocity profile as the baseline, although the U-component velocity is reduced by the suction plasma and increased by the blowing plasma up to the far-side vortex core boundary at y/c = −0.05 at α = 10° and y/c = −0.056 at α = 15°. Outside the far-side vortex core boundary, the U-component velocity is increased by the suction plasma, while it is reduced by the blowing plasma. The jet-like U-component velocity profiles shown in Fig. 13 seem to suggest that vortex breakdown is not yet taking place at these AoAs. Noteworthy is that the U-component velocity inside the vortex core nearly becomes wake-like by the suction plasma. These results show a possibility that the plasma actuator can also be used to trigger or delay the TV breakdown.

Flow control of the TVs over a very low AR wing was carried out using the DBD plasma actuators at the effective Reynolds number of 3 × 10⁶, where the steady and pulsed blowing and suction plasma were examined. The results indicate a large change in the aerodynamic forces by plasma flow control, where the lift coefficient is increased by the steady blowing plasma by 23% at the AoA of 8°, while it is reduced by the steady suction plasma by 30%. With a pulsed mode of plasma actuation, the control effect is reduced, where only a 13% increase and a 16% reduction in the lift coefficient are achieved by the blowing and suction plasma, respectively. This is due to that the plasma momentum coefficient of the steady mode of actuation is about twice that of the pulsed mode of plasma actuation, which is operating at 50% of the duty cycle. Compared to the lift coefficient, the change in the drag coefficient is less than 10% for all cases with the plasma actuator. The changes in the aerodynamic forces observed in the present investigation are mainly due to the changes in the vortex lift as a result of the plasma control on the TV circulation. Effect of the plasma actuators on the interaction between LEV and TV is too small to detect since the TV stays very close to the wing tip at the angles of attack being investigated here.

With the blowing plasma, the TV moves outboard away from the wing tip, increasing the streamwise vorticity and the turbulence intensities as well as the Reynolds stress. With the suction plasma, the TV is shifted inboard closer to the wing tip. With a steady suction control at α = 10°, the separated shear layer is bent around the wing tip, reattaching to the suction side of the wing surface to create a separation bubble. Indeed, the suction plasma is very effective in controlling the TV, reducing the TV circulation by up to 75% at α = 10°. Meanwhile, the blowing plasma increases the TV circulation by up to 53%. At α = 15°, the effectiveness of the suction and blowing plasma is reduced, which is due to the reduced velocity ratio of the plasma jet to the W-velocity component of the separated shear layer at the wing tip. Co-flowing with the TV, the blowing plasma increases the TV circulation, while it is reduced by the counter-flowing suction plasma. This suggests that the plasma jet-flow direction relative to the TV circulation is critical in controlling the TVs over a very low AR wing. Observed changes in the U-component velocity by plasma control suggest an interesting possibility that the TV breakdown can be manipulated to influence the aerodynamic characteristics.

The main objective of this study is to investigate the TV behavior in the presence of the plasma actuators and to understand the associated flow control mechanism. This was achieved by dealing with the TV at only one side of the wing. The results indicate that the control effect is isolated to the close vicinity of the wind tip. Therefore, a significant interaction between the two TVs on either side of the wing is unlikely at least at the angles of attack being investigated here. We, therefore, expect that the effect of plasma actuators on the aerodynamics forces on a very low AR wing would be nearly doubled if both wing tips are simultaneously controlled. Although plasma control was carried out on the TVs over a very low AR wing, a similar plasma control strategy can be applied to the leading-edge vortices over the delta wings.

This research was supported by EPSRC (Grant No. EP/N018486/1) in the UK. This project has also received funding from the Clean Sky 2 Joint Undertaking (JU) under Grant Agreement No. 864290. The first author acknowledges the Ph.D. funding provided by the China Scholarship Council (No. 201807000111).

The authors have no conflicts to disclose.

Lei Dong: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Writing – original draft (lead). Kwing-So Choi: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (lead); Methodology (supporting); Supervision (lead); Writing – original draft (supporting); Writing – review and editing (lead). Yaxing WANG: Funding acquisition (supporting); Investigation (supporting); Methodology (supporting); Software (supporting); Supervision (supporting).

The data that support the findings of this study are available within the article.