Formation Process of the Electric Wind Produced by a Plasma Actuator

Transcription

1 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16, No. 2; April Formation Process of the Electric Wind Produced by a Plasma Actuator N. Balcon, N. Benard and E. Moreau Laboratoire d Etudes Aérodynamiques (LEA), Université de Poitiers, ENSMA, CNRS Bld Marie et Pierre Curie Téléport FUTUROSCOPE Cede France ABSTRACT This paper is a study of a plasma actuator in the absence of external flow by means of particle image velocimetry measurements. The properties of the electric wind produced by the actuator are investigated by spatially resolved and phase-locked measurements. The use of a particle image velocimetry apparatus is of great interest to accurately examine the spatio-temporal history of the electric wind formation. The approach consists of evaluating the time required by the induced airflow to reach a stationary state and also in describing the different states of its formation. The electric wind is generated by a single dielectric barrier discharge excited by a sine waveform of 1 khz, having an amplitude of 20 kv. Turbulent kinetic energy, swirl strength, pure shear flow and mass flow rate are also used to describe the formation process of the airflow. Index Terms Plasma actuator, dielectric barrier discharge, electric wind, particle image velocimetry. 1 INTRODUCTION IN the past decade plasma actuators have demonstrated their ability to generate an electric wind in the boundary layer existing around various aerodynamic shapes. Hence they are currently receiving an increasing amount of attention from the aeronautic community due to their numerous applications in flow control. Many authors have reported on the possibility of using corona discharges and dielectric barrier discharges to modify airflows [1-2]. Their results mainly concern airflow separation around airfoils [3-8] or cylinders [9-10], airflow transitions over flat plates [11-14] and also mixing enhancement at jet nozzles exit [15-16]. Numerical models have been developed to determine the mechanisms beyond the electro-fluido-dynamic conversion operated by non-thermal plasmas. It is due to the momentum transfer occurring by collisions between neutral and charged particles (ions and electrons) accelerated by the electric field [17-18]. The dielectric barrier discharge (DBD) configuration proved its performances and effectiveness for subsonic airflow control. Moreover, recent studies demonstrated that such a control device can be operated over a wide range of pressure conditions opening new perspectives for implementation on commercial aircrafts [19-20]. In this set-up the electrodes are separated by a dielectric layer, allowing ac potentials to be applied across the capacitive discharge. The voltage is generally between 10 kv and 40 kv and the frequency ranges from 1 khz up to 10 khz. As demonstrated in [21-22] the local time response of this low cost Manuscript received on 15 July 2008, in final form 3 December actuator free of moving parts is around 10 ms. The time response is a local quantity representing the time needed by the flow to reach a local stationary state of maximum velocity. This short time response makes the DBD actuator a suitable device for closed-loop control and natural flow frequency excitation. Most of the non-stationary measurements published so far are based on Laser Doppler Velocimetry focused on the narrow region of the discharge/flow interaction. This approach is highly relevant but can not bring information concerning the transient process of the electric wind formation. Several experimental and numerical results have demonstrated the unsteady nature of the momentum transfer produced by an ac Dielectric Barrier Discharge. Indeed, the positive and negative parts of the signal lead to different force distribution and intensity on the gas. Whether the air exposed active electrode is the instantaneous cathode or anode, the momentum transfer largely differs. This phenomenon can be measured for a sine-wave excited DBD actuator within the plasma region [21-22]. However, when the flow is observed on a larger scale, the viscous effects and the resulting vortex dynamic filter these small time scale variations. In the present paper, the global formation of the electric wind produced by a single DBD actuator in quiescent air is examined with space resolved PIV measurements. Phase averaged measurements are presented to analyze the transient processes involved in the creation of a stationary electric wind. These data shed light on the formation of the wall jet and present original insights in the airflow reaction to a pulsed DBD actuation. The effects of the electrical discharge on the local Turbulent Kinetic /09/$ IEEE

2 464 N. Balcon et al.: Formation Process of the Electric Wind Produced by a Plasma Actuator Energy, on the swirl strength and pure shear flow as well as on the mass flow rate are also investigated. 2 EXPERIMENTAL SET-UP The experimental set-up consists of a typical DBD actuator enclosed in a glass box (30 cm x 40 cm x 80 cm). As illustrated on Figure 1, the DBD actuator itself is composed of two aluminum electrodes (80 micron-thick) flush mounted on a 3- mm thick dielectric layer made of PolyMethyl MethAcrylate (PMMA). Both electrodes are 80 mm span wise. The top airexposed electrode (often referred to as the active electrode) is 15 mm long. The configuration with a 5 mm gap separating the electrodes is selected to favor a maximum electric wind [23]. The grounded electrode is 20 mm long and encapsulated in epoxy resin in order to avoid any ionization beneath the flat plate and arcing between electrodes. Figure 2. Pulsed signal applied to the active electrode. Figure 3. Particle Image Velocimetry apparatus. Figure 1. Single DBD experimental set-up. The applied high voltage is generated by a TREK power supply (30 kv/40 ma) amplifying the sine signal output of a TTI function generator (TG1010A). The excitation frequency is set to 1 khz and the signal amplitude to 20 kv. To investigate the electric wind formation versus time, the DBD actuator receives pulses of increasing duration thus containing an increasing number of sine wave cycles. The potential applied to the active electrode is shown on Figure 2 with an example for a 2 ms signal and a 25 ms signal. The pulse width is adjusted to produce an integer number of sine periods (pulses of 2, 25, 50, 100, 200 and 400 periods were tested). The Particle Image Velocimetry measurement apparatus is presented on Figure 3. A Nd:Yag Laser equipped with a cylindrical lens creates a 1 mm thick green light sheet perpendicular to the flat plate at a frequency of 0.4 Hz (dual frame mode). It delivers a power of 27 mj per pulse. The glass box is seeded with incense smoke (particle average diameter of 0.3 microns) reflecting the Laser coherent light to the camera objective lens. The agreement between Pitot tube and PIV measurements has been preliminary tested to ensure the consistency of the two methods. Indeed, it has been reported that a particle precipitation could occur in the discharge [24-26]. However, the consistency of measurements can be insured by increasing the smoke particle density. With such seeding conditions the number of spurious vectors can be greatly reduced. A Lavision CCD camera captures the 30 mm x 40 mm zone situated over the DBD actuator with a 1376 x 1040 resolution. The resulting spatial resolution of the vector field is 0.73 x 0.73 mm 2 which is sufficient to partially describe the boundary layer region. The aperture of the CCD camera is operated in the dual frame mode (5 μs exposure time per frame) with the opening triggered on the falling part of the sine wave (see Figure 2, PIV opening in dual frame mode). The duration between two successive frames is adjusted for each velocity to obtain a displacement of 4 pixels for all the measured velocities which enhances the detection of correlation peaks. The recording frequency is set to 0.4 Hz (2.5 s between each acquisition) and 200 sets of dual pictures are taken for each phased acquisition (synchronized with the Laser). A statistical analysis demonstrates that 150 snapshots are sufficient to reach convergence for the first and order quantities (velocity components u and v) and also for the second order quantities (u², v² and uv). A crosscorrelation algorithm with adaptative multipass, interrogation windows of 128 x 128 to 32 x 32 pixels and a final overlap set to 50% is applied to the digital couples of images to compute the instantaneous vector fields. The accuracy of the PIV measurement is related to many parameters such as particle size, inter-frame time and detection algorithm for instance. A rough estimation of the uncertainty on the measured velocity indicates a maximum relative error level of 2.2%. The PIV system is synchronized with the pulse generator to measure the produced electric wind during the last cycle of the pulse as shown on Figure 2. This synchronization allows the phase averaged measurements necessary to analyze the formation of the wall jet.

3 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16, No. 2; April 2009 Figure 4. Velocity vector field and norm [m/s] for actuation times ranging from 2 ms to 400 ms. 465

4 466 N. Balcon et al.: Formation Process of the Electric Wind Produced by a Plasma Actuator 3 PIV ANALYSIS In this section the PIV measurements made after six different actuation times (from 2 up to 400 pulses, i.e. 2 ms to 400 ms) are presented and discussed. The Figure 4 shows the velocity vector fields and norms for each actuation duration (2, 25, 50, 100, 200 and 400 ms). The position of the origin of the x axis corresponds to the end edge of the active electrode and the origin of the y axis matches the surface of the dielectric (Figure 1). At the beginning of the excitation (after 2 ms), the interaction between the discharge and the surrounding gas results in the formation of a counter clockwise rotating vortex situated directly above the active electrode as already observed experimentally [27-29] and in simulation results [30]. The induced electric wind is directed rather downwards, ahead of the active electrode. The maximum induced velocity of 0.4 m/s is reached 1 mm above the edge of the grounded electrode (i.e. at x=5 mm). This indicates that the air acts as a low pass filter for the momentum transfer occurring in the discharge region and consequently the wall jet formation is not as fast as the electric discharge ignition. The discharge time response is in the order of nano seconds whereas the local flow time response is in the order of the milli seconds. After 25 ms of actuation the induced vortex is extended in the x direction. The maximum velocity within the boundary layer rises up to 2.2 m/s and its position is shifted to the right (approximately 8 mm beyond the edge of the active electrode). The induced flow is still not parallel to the flat plate and the growth of the recirculation flow is visible above the main stream close to the wall. As illustrated on Figure 4 the vortex moves further downstream (up to 10 mm) after 50 ms. From Figure 4, after 25 ms and after 50 ms it is possible to evaluate the convecting velocity of the vortex at approximately 0.6 m/s. For 50 ms actuation, it is also noticeable that the main flow is more parallel to the wall with a greater maximum velocity around 2.4 m/s located 10 mm beyond the edge of the active electrode. Beyond x=10 mm, the induced airflow is still detached from the wall due to pressure gradients near the wall surface and to the vortex sense of rotation. For longer actuation times (100 ms, 200 ms on Figure 4) the vortex is convected by the main stream and moved out of the field of vision. In the final case, after a 400 ms actuation, there are no more flow evolution and it can be assumed that the transient processes involved in the electric wind build up are over. It means that the steady state of the airflow generated by the single DBD actuator operated in quiescent air is reached after 400 ms corresponding to 400 periods of a 1 khz excitation. In the case of an actuator operating in the presence of an external flow, it is expected that the entrainment of the ignition vortex would be faster thereby reducing the time needed by the airflow to reach a global stationary state. Previous studies reporting response times of the tenths of ms only concerns laser doppler velocimetry measurements made in the vicinity of the dielectric surface and close to the active electrode (a few mm). The gas in this region is strongly affected by the electric discharge which is often composed of unstable short life-time streamers. The reaction of the flow in this zone may reach the short time response of the electrical discharge itself. However it does not account for the mechanisms involved in the momentum transport to more remote regions of the gas. When observed on a larger scale the flow response to the electrical discharge is not as fast. Viscous forces dissipate the momentum imparted to some neutral particles and 400 ms are needed to reach a global stationary state. From the PIV measurements exposed earlier it is possible to extract velocity profiles where the maximum velocity increase with the actuation duration is even more obvious (Figure 5). These velocity profiles are in good agreement with previously published Pitot tube measurements [31]. Let us point out that the position of the maximum velocity on Figure 4 is always located in the discharge region contrary to some results sometimes found in the literature. Indeed, a particular care is required to obtain an accurate estimation of the velocity distribution near the wall and in the discharge region. For instance, it is of major importance to generate a sufficient smoke density for the moving particles to be detected in the discharge region. The PIV correlation algorithm must also be conducted with great precaution to avoid any unrealistic shift of the maximum velocity downstream the discharge region where the electric field drops. On Figure 5a, the velocity profiles at x=5 mm of edge of the active electrode show that for a short 2 ms actuation, the induced flow along the wall is rather weak (only 0.3 m/s at its maximum situated approximately 2 mm above the dielectric surface). For longer actuation times, the vertical position of the maximum velocity is almost constant regardless of the pulse duration (between 0.5 and 1 mm above the dielectric surface). At this position, the maximum electric wind velocity clearly increases with the actuation time up to 2.7 m/s. For actuation times longer than 400 ms the shape of the velocity is unchanged and the maximum velocity remains 2.7 m/s. (a) Velocity profiles at x=5 mm for actuation times from 2 to 400 ms (b) Velocity profiles at x=20 mm for actuation times from 2 to 400 ms Figure 5. Velocity profiles extracted from PIV fields at x=5 mm and x=20 mm.

5 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16, No. 2; April Figure 5b presents the velocity profiles further downstream, 20 mm beyond the end edge of the active electrode (i.e. at the right end of the grounded electrode). At this location the discrepancy between all profiles is more important than at x=5 mm. The effects of the viscous forces experienced by the flow are notable. These forces lead to a strong dissipation of the electric wind. It is remarkable that the airflow is detached from the dielectric surface for actuation below 50 ms (the position of the maximum velocity is relatively high above the wall at around 3 mm). After a 100 ms actuation the flow is attached to the wall but the maximum induced velocity is lower that in the 50 ms case. This is probably due to the strong viscosity forces acting near the dielectric surface. The maximum velocity rises again when longer actuations (200 ms and 400 ms) are imparted to the airflow resulting in a larger momentum transfer. Figure 6. Mass flow rate versus actuation time at x=5, 10, 25 and 20 mm from the active electrode. A mass flow rate analysis is also appropriated to describe the formation of the global airflow under actuation. It is calculated in a two dimensions approximation as follows: Q = ρ L 0 u( y Where ρ is the fluid density and L is electrode length (80 mm as represented on Figure 1). On Figure 6 the mass flow rate is represented as a function of the actuation time for four positions (from x=5 mm to x=20 mm). For all positions, the flow rate increases with the actuation time in a non linear fashion. It increases rapidly at the beginning of the actuation (up to 50 ms) then it slowly decreases and reaches a plateau of low positive slope. After 50 ms the mass flow rate has reached 90% of its maximum value. Then, it takes from 50 to 400 ms to complete the remaining 10%. This sheds light on the mechanisms involved in unsteady actuation. Despite the low velocity imparted globally to the gas after 50 ms, the mass flow rate rapidly reaches a value comparable to the steady state one. This indicates that under unsteady actuation the induced airflow can be low whereas the mass flow rate is significant. The mass flow rate moderately depends on the x position. However, in the first instants of the actuation (before 100 ms) the mass flow rate dominates at the end of the electrode (at 25 ms: 0.35 g/s for x=5 mm and 0.6 g/s for x=15 mm). Then, at approximately 100 ms all the mass flow rate curves converge and after 200 ms the mass flow rate is approximately 10% greater in the plasma region (for x<10 mm) than at the end of the electrodes. This is possibly due to the dissipative effects of the parietal viscous forces. Indeed, these forces play a more important role when the airflow is attached to the wall (after 100 ms) and thus lead to a lower of mass flow rate impart away from the discharge. Additionally to the time averaged velocity fields, the experimental set-up allows the extraction of the fluctuating component of the velocity and of the corresponding kinetic energy. The Turbulent Kinetic Energy (TKE) is calculated as follows: TKE ( = 1/ [ u' v' ] (1) where u and v represent the fluctuations of the velocity in the x and y direction respectively. They are defined by: u' ( = u( u( v' ( = v( v( (2) As expected the TKE is mostly created in the discharge region and matches the strong velocities locations (Figure 7). As the actuation time increases, the region presenting a large TKE extends along the plate. Most of the TKE is located between 0 and 10 mm after 2 ms whereas it spreads along the surface forming parietal lobes between 0 and 30 mm in the following 100 ms. Moreover the TKE generated in the initial vortex dissipates and is significantly reduced after 100 ms. As illustrated on Figure 7b, the TKE is weak in the vortex region. This reveals the slow motion of the structure. The small amount of TKE corresponding to low velocity fluctuations also confirms that the vortex is well defined in space. The TKE is much stronger in the discharge region than around the vortex structure which proves that a modification of the boundary layer can be achieved by turbulence addition. Figure 7. Turbulent Kinetic Energy [m 2 /s 2 ] for actuation times of (a) 2 ms, (b) 25 ms, (c) 50 ms and (c) 100 ms. Unlike the velocity vectors representing the flow detached from the dielectric surface (see Figure 4 after 25 ms), the zone of large TKE remains mostly in contact with the wall. This is even

6 468 N. Balcon et al.: Formation Process of the Electric Wind Produced by a Plasma Actuator more visible after 50 ms (Figure 7c) where the zone of large TKE is elongated along the wall from x=0 mm to x=20 mm whereas the airflow on Figure 4 (after 50 ms) separates from the surface at x=17 mm. This can probably be attributed to a slightly moving separation point. The viscous forces inhibit the transport of TKE in the first 50 ms of actuation. After 100 ms (Figure 7c) the TKE and the velocity vectors have a relatively similar distribution concentrated near the wall due to a momentum transfer limited to the boundary layer region. The swirl and shear are also presented as a complementary measurement of the formation process of the electric wind. The swirl represents the vorticity of the flow (intensity of the eddy structures) and the shear corresponds to the stress tangential to the fluid motion. To separate the contribution of the swirl strength and the pure shear flow, the velocity gradient tensor is computed. Indeed, vorticity alone is not sufficient to identify the regions where the fluid swirls, in particular for strong shear flows found in near wall region. velocity gradients obtained from the time-averaged PIV field and the corresponding results are plotted in Figure 8 (left column for the swirl strength and right column for the pure shear flow). The swirl strength clearly highlights the formation of the large scale flow structure initiated by the plasma actuation. When the flow seaprates from the wall (at 50 ms Figure 8), the vortex is surrounded by a region of high swirl strength. However, a higher swirl strength is noticeable above the discharge and remains present from 25 up to 100 ms. This region is related to the flow entrainment induced by the plasma and directly results from the momentum transfer in the y direction. Then, the identification criterion reveals that this flow region (due to the small suction created by the pressure decrease) can not be associated with a pure shear flow. The corresponding pure shear stress is extracted from the PIV field and illustrated in Figure 8 (right column). This mechanical stress is separated in two regions. One above the active electrode and the other one following the detached flow and the vortex contours. This highlights the velocity gradients that exist in the first instants of the actuation when the wall jet separates from the wall. When the flow is reaching its stationary state, the pure shear flow is only concentrated above the end of the active electrode where the filaments initiate. Figure 8. Swirl strength and pure shear flow for 2, 25, 50 and 100 ms actuation. Different authors have demonstrated that a complete description of the flow topology can be obtained from the local velocity gradient tensor and its corresponding eigenvalues [32-33]. In the investigated two dimensional flow, this tensor has a pair of complex conjugated eigenvalues (λ cr +iλ ci ). According to the sign of λ ci, swirling strength (λ ci >0) or pure shear flow (λ ci <0) can be isolated [34-35]. Values of swirl strength and pure shear flow are computed from the 4 CONCLUSION The global formation process of an airflow experiencing a single DBD actuation has been investigated. Large scale spatially resolved measurements were performed. The results demonstrates that under short unsteady actuation (<100 ms), the airflow reacts to this impulse by forming a vortex. The formation of a steady wall jet requires more time. Turbulent Kinetic Energy, swirl and shear are also calculated and confirm the transport of an initial vortex. During the formation process, the momentum transfer occurring in the discharge region first creates a wall jet detached from the surface until 100 ms. This wall jet creates a vortex increasing in size and convected further downstream. After 400 ms of actuation the vortex is no longer visible and the Turbulent Kinetic it carries has dramatically been reduced. This duration corresponds to the time needed by the main airflow to reach a global steady state. The authors would like to emphasize that the obtained PIV vector fields are consistent with Pitot tube measurements. The maximum velocity is always located between the edges of the electrode pair where the electrical discharge occurs. The momentum transfer between charged and neutral particles taking place only in this region it is consistent that no flow acceleration is measured downstream. Since the outset of plasma actuators used in aeronautic applications, the foremost airflow control performances have been achieved using short pulses, in the order of a tenth of ms. It is worth mentioning that such a duration does not allow the maximum momentum to be transferred globally. Yet this time is sufficient to impart mass flow rate to the fluid in the boundary layer and thereby impose significant flow modifications. This

7 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16, No. 2; April indicates that the velocity limitations of the electric wind might be overcame and that the DBD actuator remains a good candidate for flow control at high velocity. Since the DBD acts in the boundary layer where instabilities initiate, significant modifications can be achieved with relatively slow electric winds by canceling or reinforcing natural flow instabilities [36]. The results also suggest that a multi-actuator configuration that would take advantage of a traveling vortex could significantly enhance the performances of plasma flow control [27]. If the momentum could be transported and reinforced by successive synchronized DBDs, large scale flow control could probably be carried out. 5 REFERENCES [1] E. Moreau, Airflow control by non-thermal plasma actuators, J. Physics D: Appl. Phys., Vol. 40, pp , [2] T.C. Corke and M.L. 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