Dielectric-barrier-discharge vortex generators: characterisation and optimisation for flow separation control
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- Jukes, T.N. & Choi, K. Exp Fluids (2012) 52: 329. doi:10.1007/s00348-011-1213-0
We investigated the use of dielectric-barrier-discharge plasma actuators as vortex generators for flow separation control applications. Plasma actuators were placed at a yaw angle to the oncoming flow, so that they produced a spanwise wall jet. Through interaction with the oncoming boundary layer, this created a streamwise longitudinal vortex. In this experimental investigation, the effect of yaw angle, actuator length and plasma-induced velocity ratio was studied. Particular attention was given to the vortex formation mechanism and its development downstream. The DBD plasma actuators were then applied in the form of co-rotating and counter-rotating vortex arrays to control flow separation over a trailing-edge ramp. It was found that the vortex generators were successful in reducing the separation region, even at plasma-to-free-stream velocity ratios of less than 10%.
Particle image velocimetry
Flow separation control by longitudinal vortices has been a subject of study for many years. The concept and first application seems to have been by Taylor (1947) using relatively simple vane-type vortex generators, devices that have found many practical applications on commercial aircraft and in industry. Vortex generators (VGs) prevent flow separation by creating an array of streamwise vortices close to the surface of an aerodynamic body. This increases the mixing between the boundary layer and the free steam, so that high momentum fluid is brought from the outer flow into the near wall region. This re-energises the near wall fluid, allowing it to withstand more severe adverse pressure gradients. Flow separation can then be delayed, controlled or completely avoided. See Pearcey (1961), Bushnell (1992) and Lin (2002) for reviews of different types of vortex generators and flow control applications.
Vane-type VGs are the most widely used devices and consist of a row of small plates that protrude normal to the body at a small incidence to the flow, so that the pressure difference between the plate surfaces leads to a longitudinal vortex from the tip. There are a huge number of different designs of vane-type VGs (Schubauer and Spangenberg 1960; Lin 2002), which can be broadly categorised by whether they create co-rotating (CoR) or counter-rotating (CtR) vortex pairs. For CoR-VGs, flow control is effective only when the vortices have large enough spanwise spacing to prevent unfavourable interactions between adjacent vortices (i.e. the upwash from one vortex is not disturbed by the downwash from an adjacent vortex). This occurs when the initial vortex spacing is greater than about three times their height (Pearcey 1961). In addition, CoR-VGs tend to generate vortices that remain close to the wall as they travel downstream, but displace laterally under the velocity induced by the vortex images in the wall. In contrast, CtR-VGs typically have stronger initial effects since the vortices combine to give larger induced upwash and downwash motions. However, the vortices do not persist for as long downstream since the vortex pairs have more substantial interactions than for CoR systems. The effectiveness of CtR-VGs largely depends on whether the vortices are arranged to give common-flow up or common-flow down between the vortex pairs. Pearcey (1961) observed that for common-flow up configurations, the vortices initially move closer together and then lift away from the wall. This can cause the vortex pairs to lift outside of the boundary layer region, so that they are no longer effective at re-energising the boundary layer fluid, although the amount of lifting depends somewhat on the external pressure gradient (Godard and Stanislas 2006a). In common-flow down configurations, the vortices initially move laterally apart whilst remaining close to the surface until the vortices from one pair begin to interact with the vortices from adjacent pairs. This creates new common-flow up arrangements that then lift from the surface and hinder the momentum transfer process. Detailed measurements of the flow structure of streamwise vortices and vortex pairs have been taken by Shabaka et al. (1985), Mehta and Bradshaw (1988), Pauley and Eaton (1988), and Angele and Grewe (2007) and analysed numerically by You et al. (2006).
The success of vane-type VGs largely stems from the fact that streamwise vortices are characterised by remarkable organisation and longevity (Bushnell 1992), persisting for over 100 h downstream (Pearcey 1961). Plus they are cheap, simple and can be retrofitted to problem areas. Successful designs typically have vane height of the order of the boundary layer thickness, h = δ, although recent work concentrates on much smaller devices with h~0.1–0.5δ to try to minimise the device drag (so-called micro-VGs, see Lin 2002). Recently Godard and Stanislas (2006a) optimised the VG geometry over a specially designed bump to mimic an airfoil on the verge of separation. They found triangular vanes with height h ~ 0.37δ, length l = 2h, angle of incidence β = 18° and spanwise spacing λ = 6h performed best. They also found that CtR configurations were more efficient than CoR by a factor of two.
However, the main problem with vane-type VGs is that they have an inherent drag penalty. Unfortunately, this drag penalty still exists when the flow control is no longer required (unless they are mechanically retracted, which adds design complexity). For example, in applications on aircraft wings, the VGs are only usually necessary during take-off and landing, so the VGs can cause significant drag penalty over the cruise part of the flight envelope. It is therefore of interest to investigate the means of generating streamwise vortices that can be switched on and off without drag penalty when not required. One way to achieve this goal is by vortex generator jets. Small holes or slots are machined into the surface from which a jet is blown. To be efficient, such jets must be pitched to the surface and skewed to the main flow direction, so that a longitudinal vortex is generated in the boundary layer by the interaction between the jet and the cross-flow (Godard et al. 2006; Godard and Stanislas 2006b). The principle of flow control is the same as for vane-type VGs: momentum transfer between the free-stream and the near-wall region. Johnston and Nishi (1990) appear to be the first to demonstrate that VG jets do indeed generate streamwise vortices and also showed that they could reduce turbulent flow separation when the jet-to-free-stream velocity ratio was above 0.8. Compton and Johnston (1992) showed that the vortices produced were similar to vane-type VGs, but decayed faster downstream. Khan and Johnston (2000) made cross-stream velocity measurements and showed that the vortices were produced by the sweep of the cross-flow around the upper side of the jet. In addition, Zhang (1999, 2000, 2003) studied the development of CtR- and CoR-VG jets and the near-field of CoR-VG jets. A complicated flow structure was found with horseshow vortices in front of the nozzles and counter-rotating vortices immediately behind, which developed into a single streamwise vortex downstream. A review of these and other works can be found in Johnston (1999).
The DBD plasma actuator that we used in this study creates a localised region of weakly ionised plasma close to the aerodynamic surface. This produces a body force generating a wall jet that can be used to control the flow (Moreau 2007). These DBD plasma actuators are purely electrical devices, so they can be rapidly turned on and off as required. They can be flush-mounted or manufactured into the surface, so there should be no drag penalty when they are not being used. Unlike VG jets, DBD plasma actuators do not need ducting or holes. The DBD plasma actuators have, therefore, huge potential for aerospace applications and have received much attention recently (Corke et al. 2010).
These actuators have been successfully used in boundary layers (Corke et al. 2010; Moreau 2007; Grundmann and Tropea 2008), as well as around bluff bodies (Jukes and Choi 2009a, b, c, d). However, the majority of studies have used actuators that produce a body force in the streamwise direction (i.e. co-flow forcing using a DBD along the span). Whilst this can be very effective if used close to the separation point, where long-lasting global modification to the wake structure can be produced with very little energy input (Jukes and Choi 2009c), flow separation is usually three dimensional and changes the location with time. We are therefore interested in DBD actuators that cover some streamwise distance as these might be more versatile in unsteady, 3D or turbulent flows. Here, we use streamwise-oriented and yawed actuators to induce a spanwise component of body force. This concept can be traced back to 1998 (Roth et al. 1998), although the configuration was counterproductive in their study, so that the subject received little further attention. However, more recently, Jukes et al. (2006) and Choi et al. (2010) used two rows of streamwise DBD actuators in a turbulent boundary layer which alternately produced a spanwise force. Their aim was to create a spanwise oscillation of near-wall fluid to reduce skin-friction drag, similar to a mechanically oscillating wall (Choi et al. 1998). Whilst the skin friction did appear to be reduced, the DBD actuators created streamwise vortices in addition to the oscillating flow. This inspired the authors to use spanwise DBD forcing to generate streamwise vortices for flow separation control (Okita et al. 2008), where they demonstrated that a single, yawed DBD actuator could generate a large-scale streamwise vortex which could significantly delay separation over a NACA 0024 airfoil. Also of interest here are recent thrust vectoring studies by Porter et al. (2009), Bolitho and Jacob (2008) and Benard et al. (2008) who used two opposing plasma actuators, arranged so that the tangential jets from each collide to produce a wall-normal jet (see also Segawa et al. 2009). These authors demonstrated that by varying the induced force on one of the electrodes, the wall-normal jet can be vectored to produce a pitched jet, similar to a VG jet. In addition, streamwise plasma actuators have been recently used to control turbulent boundary layer separation (Schatzman and Thomas 2010), control noise on a circular cylinder (Kozlov and Thomas 2009), modify supersonic flow (Im et al. 2010) and control laminar-turbulent transition (Hanson et al. 2010). Roy and Wang (2009) also demonstrated combined spanwise, streamwise and wall-normal flows by using DBD actuators with wavy structure.
We have already demonstrated that streamwise vortices can be generated by placing yawed DBD plasma actuators in a boundary layer. In this paper, we further the investigation of Okita et al. (2008) and study the mechanisms of streamwise vortex generation. We also explore parameters such as the actuator length, yaw angle, forcing magnitude and free-stream velocity on the streamwise vortex in a boundary layer over a flat plate. In addition, we demonstrate their potential for flow separation control by using DBD actuator arrays upstream of a ramp.
2 Experimental setup and preliminary results
An adjustable flap was placed at the trailing edge of the model to create a ramp of variable angle. The flap was 300 mm long and set in the horizontal position in the first part of this paper, where we study the development of the DBD vortex generator flow. This created a 1-m-long smooth flat plate. In the latter part of this paper, we study the effect of the vortex generators on flow separation and a smaller 92-mm-long flap was installed and set at an angle of 20° to the flat section. This simulated the trailing-edge region of an airfoil at high angles of attack, as studied in a similar configuration by Thompson and Whitelaw (1985). The gap between the two sections was smoothed with thin tape to produce a radius of approximately 40 mm.
A Dantec 2D PIV system was used to measure the flow field in both the streamwise (x–y) and cross-steam (y–z) planes. The system consisted of a Litron LDY302-PIV 100 W Nd:YLF laser, a Vision Research Phantom V12.1 high-speed camera and a dedicated PC. Olive oil was used to seed the flow with nominally 1-μm droplets using a rake in the settling chamber of the wind tunnel. A high-quality micro-screw-controlled 50-mm square mirror was carefully mounted at 45° to the streamwise plane, 850 mm downstream of the flap trailing edge. This was deemed sufficiently far downstream to have no blockage effects on the upstream flow. For streamwise velocity measurement, the laser sheet was deflected upstream by the mirror, so that the light sheet illuminated the x–y plane. The camera was then focussed through the acrylic wind tunnel side wall onto the appropriate measuring volume using a Sigma 105-mm macro lens, set at f/5.6. For measurements in the cross-stream plane, the laser sheet was aimed through the wind tunnel wall to illuminate the y–z plane whilst the camera viewed the measurement volume via the mirror. To minimise optical distortion and to maintain sufficient magnification, a Sigma 420-mm telephoto lens was used at f/8. Image pairs were typically taken at a frame rate of 200 Hz, and PIV processing was performed using Dantec DynamicStudio v3.0. Velocity vectors were usually computed on a 16 (y) by 32 (x or z) pixel grid with 50% overlap using a recursive cross-correlation technique (adaptive correlation with local median filter). This corresponded to an interrogation volume of typically 0.58 × 1.16 mm for the cross-stream velocity components (or 14–40 vectors across δ). This resolution was deemed sufficient to capture the streamwise vortex structure, where between 40 and 200 vectors were used in the integration for vortex circulation. In the majority of the vector figures presented in this article, we plot every other velocity vector in both x (or z) and y directions, but contour using the entire PIV field.
3 Vortex formation mechanisms
As shown in Fig. 5, it is clear that the DBD-VG can produce a concentrated streamwise vortex. After some initiation time of around 0.1 s (corresponding to the convection time x/U ∞ ), the vortex was very stable and the core meandered by less than ±2 mm whilst the plasma was activated. The flow field presented in Fig. 5 can therefore be considered as a steady-state phenomenon. When the plasma switched off, the vortex rapidly shrunk to the wall, taking less than 0.1 s to disappear completely. Thus, a longitudinal vortex structure can be turned on and off simply by intermittently energising the DBD.
Figure 8 shows that the vortex circulation increased rapidly within the plasma region (x/l ≤ 1), where Γ is generated at a rate of about 0.5 m2/s per-metre-DBD. This shows that the plasma adds circulation in an approximately linear manner along the DBD-VG length. The circulation reached a peak at the downstream edge of the DBD-VG and thereafter decayed. Pauley and Eaton (1988) discuss that a vortex can only loose circulation to skin friction at the wall, so that in the immediate downstream of the DBD, when the vortex lies close to the wall, the circulation loss is relatively rapid (approximately 0.1 m2/s per-metre-DBD in Fig. 8). It should be noted that this initial decay rate is significantly less than the growth rate. For x/l > 5, however, the decay rate reduced indicating that the vortex is lifting from the surface. This can be seen in Fig. 7f where the core has lifted outside of the boundary layer, so that there is little interaction with the wall.
4 Parameter optimisation of plasma VGs
Using scaling with δ and U ∞ in Fig. 13b, the circulation appears to steadily increase within the plasma region at a similar same rate for all three DBD-VGs. Likewise, the circulation decays at a similar rate for each actuator. However, the peak differs with l. Thus, the plasma continually adds momentum into the vortex, which increases its circulation, but beyond the plasma region, the vortex starts to decay and loose energy to viscous interaction with the wall. Figure 13b therefore suggests that longer and stronger vortices can be formed merely by increasing the DBD length. However, one should expect that some limit will be reached for very long DBD-VGs because the energy added by the plasma should be balanced by the viscous losses at the wall. At this limit, the DBD can only act to maintain the vortex, rather than increase it. We did not reach this limit in these experiments, and our data suggest that significantly stronger vortices should be possible through simply increasing l.
5 DBD vortex generator arrays
Vortex generators for flow separation control are typically used in an array, so that a series of streamwise vortices are created along the surface span. To ensure effective flow control, the VGs must be placed sufficiently close together to ensure good spanwise coverage, yet far enough apart to avoid unfavourable interactions between adjacent vortices. This introduces a further geometrical parameter: the spanwise wavelength, λ. Furthermore, VGs can be arranged to produce either co-rotating (CoR) or counter-rotating (CtR) vortex pairs. In this section, we study two DBD vortex generator arrays designed to produce CoR and CtR vortices, and compare these structures with those from a single actuator.
We have demonstrated above that the circulation of the streamwise vortex created by a yawed DBD plasma actuator increases with U p /U ∞ and l and reaches a maximum at β = 90º. Based on these results, DBD-VGs with yaw β = 90º and length l = 40 mm were used in each array. The CoR array was a row of DBDs with similar geometry to that mentioned earlier (Fig. 3), placed at intervals of λ = 25 mm. However, the lower electrodes were modified to be only 6 mm wide. This ensured that the lower electrode from one actuator was sufficiently far from the upper electrode of the adjacent actuator, so that no plasma formed on the rear side of it. We do not expect this modification to constrain the plasma on the front side since the discharge region was normally less than 4 mm wide. The CtR array had upper electrodes placed with λ = 50 mm and a lower electrode that covered the entire span of the actuator sheet. This meant that plasma formed equally to both sides of the upper electrodes to produce bi-directional wall jets, as described by Jukes et al. (2006). It should be noted that although λ was different for each array, the same number of vortices was produced per unit width since two vortices were created by each CtR actuator. Each array spanned the test plate and there were 8 and 4 actuators in the CoR and CtR arrays, respectively. These actuators had to be used at reduced voltage compared to the earlier work (E = 8.2 kVp-p and f = 14.4 kHz), because several actuators were energised at the same time which saturated our electrical supply at higher voltages due to power limitations. The wall jet from a single DBD-VG in quiescent air had velocity U p = 1.21 m/s at this voltage and frequency.
These observations compare well with other studies on streamwise vortices created by vane-type VGs and VG jets. For example, the cross-stream velocity map presented in Fig. 19a is very similar to that presented in Godard and Stanislas (2006a) for an optimal counter-rotating array of triangular vanes. The size of the vortices differs due to different experimental facilities, notably δ, but the qualitative image of the counter-rotating vortices is nearly identical. Furthermore, the DBD-VGs also compare well to single vortex and CoR arrays produced by inclined jets by Zhang (2000, 2003). However, the primary difference between the DBD-VG and these other methods is that the DBD-VG also induces a flow towards the wall directly above the plasma region. This suction is due to continuity since the plasma is a source of momentum, not fluid, as discussed above.
6 Flow separation control
The flow separation control ability of DBD vortex generators is now demonstrated over a ramp. This was set at an angle of 20º to the flat plate to simulate the trailing-edge region of an airfoil at high angles of attack, see Fig. 1. The same CoR and CtR arrays discussed in the previous section were placed a short distance upstream of the ramp. As before, x = 0 corresponds to the leading edge of the DBD-VGs (placed 645 mm from the leading edge of the flat plate), and the actuators had length l = 40 mm. The ramp started at x = 55 mm and finished at x = 141 mm.
Figures 21 and 22 clearly show that CoR and CtR DBD-VGs were both successful in controlling the flow separation. The velocity near the ramp surface has increased significantly in both cases, and the recirculation region appears narrower and reduced. For the CoR case (Fig. 21), the array of streamwise vortices persists right to the end of the ramp. They move laterally as they travel downstream (i.e. to the right in the figure). For example, the vortex core on the left-hand side travels from approximately z = −10 mm at the start of the ramp to around z = 10 mm (∆z/λ = 0.8) towards the end of the ramp. On the left-hand side of each vortex in the plane of Fig. 21, there are large regions of induced downwash. This brings high momentum fluid towards the wall and reattaches the flow. Interestingly, and unlike the attached vortices in Fig. 16, there does not appear to be significant upwash on the right-hand side of these vortices. It should be noted that the flow does not totally reattach over the ramp, but the streamwise velocity maps are, however, reasonably uniform across the span. This is because the downwash regions are swept laterally due to the curved trajectory of the vortices, which leads to reasonably homogeneous flow control.
In contrast, the vortex pairs generated in the CtR case (Fig. 22) did not undergo lateral displacement and remain at roughly the same spanwise location along the ramp (z ≈ ±15 mm, z/λ ≈ ±0.3). The vortices grow as the travel downstream, but they do not meander like the CoR case. There is a much larger region of downwash due to the combined action of the vortex pair. This acts to completely reattach the flow for −10 < z < 10 mm (|z|/λ = 0.4). However, flow separation control was not so successful outside of this region. For example at z = 25 mm (z/λ = 0.5), there is a clear wake, but this is still significantly reduced compared to the flow without plasma. This region does not, however, have as reduced a flow separation as the CoR case at the same location. Therefore, the CtR array might be more effective at flow separation control directly downstream of the DBD, but it is less homogeneous across the span.
In this experimental investigation, we have demonstrated that yawed DBD plasma actuators can be used to create streamwise vortices. DBD-VGs have several advantages over vane-type vortex generators or vortex generator jets: they can be rapidly switched on and off, they should be without drag penalty when not in operation and they do not require ducting or machining of holes. We also expect that DBD-VGs should not need as accurate placement as DBDs oriented to produce a force with the flow (i.e. a spanwise-oriented upper electrode), which is the normal configuration for flow separation control applications. Additionally, these DBD-VGs can operate over a large streamwise distance which should be especially useful for cases where the separation point moves dynamically or is not known a priori.
The study of streamwise vortex development and its characteristics showed that the vortex circulation increased with plasma velocity ratio and actuator length and was maximised when the actuator was oriented to give force perpendicular to the flow. We believe that a circulation is set up above the DBD plasma due to mass continuity. This initiates a vortex with origin slightly above the wall and to the side of the DBD. The DBD actuator then creates a wall jet in the spanwise direction, which fuels the vortex from below. As this develops downstream, the wall jet becomes twisted by the oncoming boundary layer, lifted from the wall and then spirals around the vortex core. Co-rotating and counter-rotating vortex arrays were easily constructed, but the spanwise spacing should be carefully chosen to prevent unfavourable interactions with adjacent vortices whilst providing sufficient spanwise coverage to achieve efficient flow control.
Furthermore, the flow separation control ability of these DBD-VG arrays was demonstrated over a deflected ramp model. The flow could be completely reattached with effectiveness depending on array configuration and velocity ratio. We found that counter-rotating arrays were the most effective (directly downstream of the DBD) but were less homogenous than co-rotating arrays because CoR vortices naturally sweep across the span by their self-induced velocity. It was demonstrated that flow separation control was still possible with plasma-to-free-stream velocity ratio as low as 7% (U ∞ = 14.9 m/s).
The work has been carried out as a part of PlasmAero program with funding from the European Community’s Seventh Framework Programme FP7/2007–2013 under grant agreement no. 234201. An overview of PlasmAero can be found in Caruana (2010).