Stabilizing a blasius boundary layer with dielectric barrier discharge plasma actuation: experimental characterization

This paper presents an experimental characterization of Dielectric Barrier Discharge (DBD) plasma actuation on a two-dimensional (2D) boundary layer around a §at plate using both Laser Doppler Anemometry (LDA) and hot wire probings. The experiments are conducted in a subsonic wind tunnel at a free-stream velocity U ∞ = 35 m/s for a single DBD actuator and several electrical parameters. Hot wire probings are used to quantify the transition delay and mean velocity pro¦les far enough from the plasma region, while mean velocity pro¦le inside the plasma extent are measured using LDA after the method has been validated from a comparison with hot wire measurements. Measurements inside the plasma extent allow to quantify the ionic wind contribution to the actuated mean velocity pro¦les in a case where the transition is delayed by the actuator. A maximal ionic wind of 7 m/s is found to be added 2 mm downstream the actuator for a consumed electrical power of 80 W/m.


INTRODUCTION
One possible way to reduce aircraft fuel consumption is to delay the boundary layer transition around wings in order to decrease skin friction drag. Stabilizing the boundary layer mean velocity pro¦les is a possible approach to achieve this aim. Among the possible techniques, plasma actuation turns out to be an interesting solution because of its easy implementation on a surface, the light weight of the actuators, and their input energy (electricity) which allows easy control and modulation. In this work, the actuation is performed using a DBD plasma actuator. This type of actuator is constituted of two electrodes stuck on each face of a dielectric material. When an alternative high voltage is applied between the electrodes, the ambient air is ionized. The charged particles drift under the e¨ect of the electric ¦eld and create a body force tangential to the wall (the ionic wind), which is used in this case for transition control. The experiments on transition delay have been successfully conducted for 2D con¦gurations on a §at plate [1,2] and on a wing pro¦le [3,4] for velocities of 20 and 35 m/s, respectively.
The ¦rst set of experiments has been made previously on an ONERA-D 2D pro¦le [5]. In this case, the transition was induced by TollmienSchlichting (T-S) waves. Mean velocity pro¦les were measured outside the plasma region and probings along the chord were performed. The maximum transition delay of 6% of chord has been observed for a free-stream velocity U ∞ = 21 m/s. The ¦rst analytic model for the tangential component of the body force ¦eld has been developed and integrated in the ONERA in-house boundary layer code 3C3D from these measurements. This model is able to represent the mean velocity pro¦les in the vicinity of the wall but could not compute the e¨ect of plasma actuation near the upper edge of the boundary layer. As a result, the computed transition delay due to plasma actuation was slightly overpredicted.
In this paper, a new set of experiments, conducted on a §at plate and for free-stream velocities higher than 30 m/s, are presented. Combined LDA and hot wire measurements are performed to assess the e¨ect of DBD plasma actuation on the boundary layer both inside and out of the plasma region. A focus is made on the mean body force e¨ect, also called steady actuation on the delay of a T-S induced transition. This new set of measurements will allow to improve the existing body force model.

EXPERIMENTAL SETUP
The experiments are conducted in the TRIN 2 subsonic open-return research wind tunnel located at ONERA Toulouse. It features a low turbulence level (1 · 10 −3 ≤ Tu ≤ 2 · 10 −3 ) and a free-stream velocity range of 25 ≤ U ∞ ≤ 50 m/s, which make it well suited to laminarity and transition studies. The experiments are performed on a §at plate set at a slightly positive angle of attack (AoA = 0.13 • ). The plate is 1.175 mm long and 40 cm wide. It is equipped with a dielectric insert made of Polymethyl methacrylate, which enables to out¦t the model with the desired number of actuators between 370 and 820 mm downstream the leading edge. In the present case of study, a single DBD actuator is set at x DBD = 470 mm from the leading edge as shown in Fig. 1. Both electrodes are 21 mm in width and their spanwise length is 150 mm. A 2-millimeter gap separates the electrodes. Below, in Figs 2, 3, and 5, the dielectric insert is represented by a lighter segment on the line parallel to the x-axis.
The air-exposed electrode is connected to a voltage ampli¦er (Trek, model 30/20A, gain 3000 V/V), while the other is grounded. The input signal has a sinusoidal waveform. The electric power consumed by a plasma actuator is computed from current and voltage Figure 1 Implementation of the DBD actuator on the §at plate measurements following the relation: A high frequency / current transformer (Magnelab, model CT-D0.5, sensibility 0.5 V/A, bandwidth 48 Hz 200 MHz) measures the instantaneous discharge current of the actuator i(t), while V (t) is the instantaneous input voltage given by the monitoring sensor of the ampli¦er. The average on a su©ciently large number of periods T of V (t)i(t), computed by a digital oscilloscope (Lecroy wavesurfer 454 bandwidth 500 MHz) gives the mean consumed power P . This value is then divided by the spanwise length of the electrodes to give the consumed power per unit of electrode length P/L in W/m. The voltage amplitude varies between 9 and 10.8 kV and the input frequency is set at 3 kHz, resulting in a consumed power range between 40 and 80 W/m. The measurements into the boundary layer are carried out using hot-wire anemometry (Dantec Streamline, 90C10 CTA module, 55P15 probes) and LDA for di¨erent con¦gurations with and without control. For the hot wire anemometry, the acquisition is performed over 80 000 samples. The signal from the anemometer is low-pass ¦ltered at 8 kHz in order to avoid aliasing and am-pli¦ed 10 times so as to bene¦t from the best available resolution of the Analog/Digital board. The sampling rate (20 kHz) is chosen to satisfy the Nyquist Shannon theorem. The raw signal is acquired simultaneously without ¦ltering so as to record the mean value. The laser used for LDA is an Oxxius Laser (wavelength 532 nm and power 300 mW). The emission optics has a 0.46-meter focal length. The DISA 55X optic reception is mounted in a forward scattered mode. Seeding is realized using DEHS (di-ethyl-hexyl-sebacat) mineral oil. The measuring volume is about 100 µm in its smaller diameter and 3 mm in its greatest diameter. The optical signal is processed by a digital burst correlator TSI IFA 655.
The measurements were conducted for a free-stream velocity U ∞ = 35 m/s.

BASELINE FLOW
As the §at plate is not equipped with pressure taps, the pressure distribution is determined from the hot wire measurements. Mean velocity pro¦les are measured along the §at plate and the boundary layer thickness is assessed for each mean velocity pro¦le. In particular, the boundary layer thickness evolution along the §at plate is given Fig. 2a. The pressure coe©cient is quanti¦ed from free-stream velocity measurements using hot wire anemometry. The resulting evolution of the pressure coe©cient is presented Fig. 2b. It features a suction peak followed by a large and weak deceleration, featuring a pressure gradient close to 0, which causes the destabilization of the T-S waves. This pressure coe©cient distribution is extrapolated in order to allow one to perform boundary layer and stability computations.
The transition location is determined by measuring the hot wire root mean square (RMS) signal along the plate length at a constant height from the wall (z = 1 mm). The tangents of the RMS signal in the laminar and the intermittent phases are then traced (black dotted line in Fig. 3). Their intersection gives the transition position. Figure 3 shows that the natural transition location for U ∞ = 35 m/s is at x tr = 670 mm. This is about 3 cm before the boundary 1 ¡ 500 Hz; 2 ¡ 600; 3 ¡ 700; 4 ¡ 800; 5 ¡ 900; 6 ¡ 1000; 7 ¡ 1100; 8 ¡ 1200; 9 ¡ 1400; 10 ¡ 1600; 11 ¡ 1800; 12 ¡ 2000; 13 ¡ 2200; 14 ¡ 2500; and 15 ¡ 3000 Hz thickens due to a turbulent regime, as seen in Fig. 2a. The actuation is performed into the laminar zone.
As the DBD actuator induces a pulsed body force at the same frequency f p as the input signal [6], it may excite the corresponding T-S waves and trigger a promoted transition if f p is not well chosen [5]. For this reason, boundary layer mean velocity pro¦les have been computed from the experimental pressure distribution using an ONERA in-house boundary layer code (3C3D) and linear stability has then been applied. This results in the N -factor chart of Fig. 4 which describes the evolution of the T-S waves ampli¦cation along the §at plate. In the present case, the turbulence level is Tu ≈ 0.13% which corresponds to a transition N -factor N tr ≈ 7.5 according to Mack relation (N tr = −8.43 − 2.4 ln(Tu)) [7].
The T-S waves frequency which triggers the transition is f tr = 600 Hz. At the actuator location (x DBD = 470 mm), T-S waves at frequencies below 700 Hz are ampli¦ed whereas the others are damped. To avoid any excitation of the T-S waves by the actuation and to focus on a steady actuation, the input signal frequency must be chosen su©ciently higher than the local T-S waves frequencies. Thus, it is set at 3 kHz.

Transition Measurements
The transition position is deter- Figure 5 Hot wire RMS signal at a constant height (z = 1 mm) along the plate for U∞ = 35 m/s (1 ¡ baseline) and two di¨erent actuation cases (2 ¡ P/L = 40 W/m and 3 ¡ P/L = 80 W/m) mined using the method described in section 3 and illustrated in Fig. 3. Figure 5 shows the evolution of a hot wire probe RMS signal along the plate for a boundary layer submitted to DBD plasma actuation at two di¨erent consumed powers: P/L = 40 and 80 W/m. The input signal frequency is set at 3 kHz for both cases. For U ∞ = 35 m/s and both consumed power, the actuation results in a transition delay of at least 30 mm. Transition delay could not be measured for a consumed power of 90 W/m. Moreover, the transition delay is greater when the consumed electrical power increases. In this study, the focus is not set on optimizing the transition delay obtained with the actuator, but to characterize experimentally the in §uence of steady DBD actuation on a boundary layer §ow. Nonetheless, knowing that the transition is delayed con¦rms that the chosen input signal frequency does not trigger any unwanted unsteady e¨ect.

Mean Velocity Pro¦les Measurements
Hot wire anemometry is a classical and reliable method to measure mean velocity pro¦les inside a boundary layer. However, it has to be used far enough from the plasma extent in order to avoid issues due to charges created by the actuator or by the generated electrical ¦eld. To ensure that the described LDA measurements are well resolved for con¦gurations with and without actuation, mean velocity pro¦les outside the plasma extent are measured using both LDA and hot wire anemometry at corresponding locations. Figure 6 compares the mean velocity pro¦le measured using LDA and hot wire anemometry without actuation at x = 650 mm from the plate leading edge. In the con¦guration without actuation, the mean velocity pro¦le measured with LDA is in good agreement with the one measured with hot wire.  Figures 7a and 8a show mean velocity pro¦les without actuation measured, respectively, 50 and 100 mm downstream the actuator using hot wire anemometry. At these locations, the boundary layer is still laminar and the mean velocity pro¦le ¦ts well to the corresponding Blasius mean velocity pro¦le. Figures 7b and 7c show the e¨ect of DBD actuation at x DBD + 50 mm for P/L = 40 and 80 W/m, respectively. At this station and for both actuation cases, the e¨ect of ionic wind is slightly visible over the entire velocity pro¦le. The ionic wind addition results in fuller pro¦les for both actuation cases. The boundary layer thickness is not a¨ected by the actuation. At this station, it was found a great accordance between the velocity pro¦les measured with LDA and with hot wire anemometry. Figures 8b and 8c show the e¨ect of DBD actuation at x DBD + 100 mm for P/L = 40 and 80 W/m, respectively. The e¨ect of DBD actuation is barely visible on the mean velocity pro¦les measured using hot wire anemometry. At this station, there is more discrepancy between the LDA and hot wire measurements, especially close to the wall. Laser Doppler anemometry seems to overestimate the contribution of ionic wind in comparison to the hot wire measurements.

Mean velocity pro¦les measured
As the boundary layer thickness δ does not change with actuation, a computation of the displacement thickness δ 1 = δ 0 (1 − U (z)/U e ) dz (Table 1) is performed to compare the mean velocity pro¦les ¤fullness.¥ This computation is made for the mean velocity pro¦les measured with hot wire anemometry because of their better accuracy.
The displacement thickness δ 1 decreases for an actuated boundary layer. This value can be seen as the distance of a mean velocity pro¦le to the (nonrealistic) mean velocity pro¦le where the velocity would be equal to U e whatever the distance from the wall. The smaller δ 1 is, the ¤fuller¥ the mean velocity pro¦le. In Table 1, the contribution of ionic wind which makes the mean velocity pro¦les   fuller, can be seen as far as 100 mm downstream the actuator through this quantity: the more the consumed energy, the ¤fuller¥ the velocity pro¦le, and the smaller the displacement thickness.

MEASUREMENTS INSIDE THE PLASMA EXTENT
Hot wire anemometry is limited to measurements outside and su©ciently far from the plasma extent due to the electrical ¦eld which could damage the probe if placed too close to the actuator. To explore the e¨ect of the body force generated by a plasma actuator on the mean velocity pro¦les inside or close to the plasma extent, LDA is performed. Figure 9 shows mean velocity pro¦les measured at several locations inside or close to the plasma extent for di¨erent cases with and without actuation. These mean velocity pro¦les are compared to the corresponding Blasius velocity pro¦le at each location. Each measurement point is shown by the sign corresponding to the particle rate measured at the same point. For all the measured velocity pro¦les, the particle rate decreases as the measurement gets closer to the wall. When comparing velocity pro¦les with and without actuation, a drop in the particle rate is noticeable when the actuator is powered. Moreover, mean velocity pro¦les measured for the highest consumed power (P/L = 80 W/m) show a lower particle rate than the mean velocity pro¦les measured for P/L = 40 W/m. Each actuated mean velocity pro¦le (see Figs. 9b and 9c) shows a noticeable deformation below z = 1 mm from the wall. As a powered DBD actuator induces an electric ¦eld, seeding particles may become charged and then drift under electrical e¨ects when moving through the plasma extent. As a consequence, the observed mean velocity pro¦le changes may be caused both by a mechanical and charged particle e¨ects. In order to know whether particles are charged through the plasma extent, velocity histograms are analyzed. The examples of such histograms are shown in Figure 9 Mean velocity pro¦les measured at xDBD + 2 mm compared to the corresponding Blasius velocity pro¦le (curve) for various cases: without actuation (a) and with actuation for P/L = 40 (b) and 80 W/m (c): 1 ¡ particle rate = 1 kHz; 2 ¡ 5; 3 ¡ 10; 4 ¡ 20; 5 ¡ 30; 6 ¡ 40; and 7 ¡ particle rate = 50 kHz Fig. 10. Figure 10a shows a velocity histogram for a measurement point without actuation. The velocity distribution has a classic gaussian shape. Figure 10b shows a velocity histogram with an actuation at P/L = 80 W/m for the same measurement point. With actuation, the velocity histogram has a nonstandard shape which appears to be a combination of two gaussian velocity distributions. Moreover, one of these is centered around the same velocity whatever the measurement point for the same set of electrical parameters (voltage amplitude and frequency). In this case, this second gaussian is centered around a velocity of 29 m/s as seen by confronting Figs. 10b and 11. This may be due to the electrical ¦eld a¨ecting the seeding particles. In order to only consider the DBD mechanical e¨ect, this second gaussian distribution is dismissed. The resulting mean velocity pro¦les are shown in Figs. 12 to 14 for various positions inside or close to the plasma extent.

Mean Velocity Pro¦les
The mean velocity pro¦les correction is more visible for the measurements at x DBD + 2 mm as featured in Fig. 13. This position corresponds to the upstream edge of the grounded electrode and is inside the plasma extent. Figure 12 shows that an e¨ect of DBD plasma actuation is visible on the mean velocity pro¦les 2 mm upstream the plasma extent beginning.

Ionic Wind Contribution in the Actuated Mean Velocity Pro¦les
In order to quantify the ionic wind contribution in the actuated mean velocity pro¦les, the added ionic wind is computed by substracting the baseline one to the actuated ones. The mean velocity pro¦les used for the calculations are those presented in Figs. 12 to 14. Figures 15 and 16 show the resulting ionic wind contribution evolution inside and close to the plasma extent for the two studied consumed electric powers.
In both actuation cases, Figs. 15a and 16a show that the ionic wind contribution is negative between Z = 0.5 and 2 mm from the wall. This may be due to a suction zone occurring downstream the exposed electrode edge as observed by Debien et al. [8]. Figure 15 shows the di¨usion of the transferred momentum from the plasma to the boundary layer. This is comparable to what can be observed in quiescent air [6]. The ionic wind is higher for a consumed power P/L = 80 W/m. The maximum found ionic wind addition corresponds to U plasma /U e = 0.2 and is around 7 m/s.

CONCLUDING REMARKS AND OUTLOOK
In this article, an experimental characterization of DBD plasma actuation on a Blasius boundary layer has been presented. A focus has been made  on steady actuation by choosing a suita ble input signal frequency: excitation of naturally ampli¦ed T-S waves has been avoided. For the presented actuation con¦gurations, a transition delay of at least 30 mm has been obtained, which con¦rmed the absence of undesired unsteady actuation e¨ects. Mean velocity pro¦les measurements have been performed outside and inside the plasma extent. Outside the plasma extent, mean velocity pro¦les measured with hot wire anemometry and LDA show a great accordance while DBD actuation is performed. Even if 50 and 100 mm downstream the actuator, the ionic wind addition is slightly visible, the boundary layer is still under in §uence of the actuation, which can be seen as the displacement thickness is greater when the actuator is powered. Inside the plasma extent, mean velocity pro¦les are measured only with LDA. As the seeding particles seem to be in §uenced by the electric ¦eld generated by the actuator, a correction has then been applied to dismiss this e¨ect. The plasma actuation e¨ect can be seen below z = 1 mm from the wall. The added ionic wind is computed by substracting mean velocity pro¦les with and without actuation. The maximal measured ionic wind is around 7 m/s for a consumed power P/L = 80 W/m. It has been noticed that the e¨ects of the ionic wind are visible some millimeters upstream the actuators.
More measurements will be done for other free-stream velocities, especially inside the plasma extent. They will allow to inquire about the dependency of the added ionic wind on the free-stream velocity. The vertical component of the velocity will also be studied. These sets of measurements will allow to improve an existing empirical body force model, which will be implemented in a boundary layer code. This model will allow a numerical study of actuation to obtain an optimized actuation con¦guration with several DBD actuators. This con¦guration will then be experimentally tested.