Minimizing airfoil drag at low angles of attack with DBD-based turbulent drag reduction methods

Zhi SU, Hohu ZONG, Hu LIANG, Jun LI, Like XIE, Xueheng LIU,Weiling KONG, Borui ZHENG

aScience and Technology on Plasma Dynamics Laboratory, Air Force Engineering University, Xi’an 710038, China

bInstitute of Aero-engine, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China

cThe Green Aerotechnics Research Institute of Chongqing Jiaotong University, Chongqing 404100, China

KEYWORDSDielectric barrier discharge;Dimensionless scaling;Plasma actuator;Turbulent friction drag;Wake

AbstractDielectric Barrier Discharge(DBD)based turbulent drag reduction methods are used to reduce the total drag on a NACA 0012 airfoil at low angels of attack.The interaction of DBD with turbulent boundary layer was investigated, based on which the drag reduction experiments were conducted.The results show that unidirectional steady discharge is more effective than oscillating discharge in terms of drag reduction,while steady impinging discharge fails to finish the mission(i.e.drag increase).In the best scenario,a maximum relative drag reduction as high as 64%is achieved at the freestream velocity of 5 m/s,and a drag reduction of 13.7%keeps existing at the freestream velocity of 20 m/s.For unidirectional discharge,the jet velocity ratio and the dimensionless actuator spacing are the two key parameters affecting the effectiveness.The drag reduction magnitude varies inversely with the dimensionless spacing,and a threshold value of the dimensionless actuator spacing of 540 (approximately five times of the low-speed streak spacing) exists, above which the drag increases.When the jet velocity ratio smaller than 0.05,marginal drag variation is observed.In contrast,when the jet velocity ratio larger than 0.05,the experimental data bifurcates,one into the drag increase zone and the other into the drag reduction zone, depending on the value of dimensionless actuator spacing.In both zones, the drag variation magnitude increases with the jet velocity ratio.The total drag reduction can be divided into the reduction in pressure drag and turbulent friction drag,as well as the increase in friction drag brought by transition promotion.The reduction in turbulent friction drag plays an important role in the total drag reduction.

1.Introduction

Skin friction drag constitutes more than half of the total flight drag at low angles of attack under cruise condition.In order to reduce the flight drag, in the last several decades, large amounts of researches have been conducted to reduce skin friction drag, particularly in turbulent boundary layers, to improve aircraft range and payload and reduce fuel consumption.In this process, various turbulent drag reduction methods, including passive ones such as riblets and active ones such as suction, blowing and spanwise wall oscillation, have been developed,1–2which are reviewed briefly in the following content.

Riblets are small streamwise ridges carved on the surface,whose height is typically 8–12 times of the viscous length scales(δν) and the spacing is around 15–20 δν.Through stabilizing the streamwise vortices in the inner layer and reducing turbulent burst events,3–5a drag reduction of up to 8 % can be achieved by riblets.Suction and blowing work similarly by inhibiting the ejection of low-speed fluids away from the wall and the sweep of high-speed fluid toward the wall,which altogether serves to reduce the occurrence of burst events6–7and can produce a drag reduction of 20%–30%with feedback control.8In the work of Antonia et al.,9a local drag reduction of as high as 50% was demonstrated at a freestream velocity(U∞) of 3.5 m/s with a porous suction strip arranged in the spanwise direction.Spanwise wall oscillation has been proposed for turbulent drag reduction, with the aim of modulating the low-speed streaks through the Stokes layer of the oscillating wall.A drag reduction of up to 40%–45% can be achieved with this method10–11.

However, owing to the complex mechanical systems required and the relatively high power consumption of the driving motor, the prices for the drag reduction produced by active drag reduction methods like suction, blowing and wall oscillation are quite high,making them infeasible for aeronautical applications.This has motivated a number of investigations into the use of Dielectric Barrier Discharge (DBD)actuators in turbulent drag reduction.DBD plasma actuator consists of two groups of electrodes separated by a dielectric layer.By the directional movement of ionized air in the electric field, a near-wall jet is induced by the electrostatic body force in near-wall region.Characterized by a simple structure, fast response and low power consumption, DBD actuators frequently used in boundary layer separation control12–17are becoming a popular device in turbulent drag reduction researches.

Morphologically, methods using DBD in turbulent drag reduction can be divided into two main categories, namely,oscillating/travelling discharge methods and steady discharge methods, both of which actuate the boundary layer flow in the spanwise direction.Evidences supporting that oscillating/-travelling discharge methods might be able to reduce the turbulent friction drag can be traced back to early 2000 in the Direct Numerical Simulation (DNS) of Du et al.18–19Subsequently, in 2003, the oscillating body force hypothesized by Du et al.was experimentally achieved by Wilkinson who employed a symmetry DBD actuator driven by two groups of high-voltage sine waves operating at beat frequency, but no drag reduction was demonstrated.20The effectiveness of this method in producing oscillating body force using DBD was also proved by Hehner et al.21–22.

In 2006, the response of a Zero-Pressure-Gradient (ZPG)turbulent boundary layer to the DBD-induced oscillating body force was investigated experimentally by Jukes et al.23using hot-wire measurements at U∞=1.8 m/s.A local skin friction drag reduction of up to 45 % was demonstrated, physically ascribed to the break of the link between the outer and inner boundary layer using plasma-induced streamwise vortices.In 2011, a travelling body force actuation was achieved by Choi et al.in experiments using an asymmetric DBD actuator array fed by 12 power supplies.Similar drag reduction results as those by Jukes et al.were achieved24and the mechanism was analyzed.25More recently, in 2017, the DNS by Mahfoze and Laizet demonstrated that the near-wall oscillating jets generated by DBD can reduce turbulent friction drag by 33.5%in a channel flow at U∞= 4.5 m/s26.

In contrast with oscillating Alternating-Current(AC)DBD plasma actuators which for now are only effective for drag reduction in less than 5 m/s, a novel pulsed DC discharge was proposed by McGowan et al.27Using the pulsed DC waveform to drive a typical asymmetric DBD actuator array,turbulent drag reduction experiments of a ZPG turbulent boundary layer were carried out.28–29Although disputes exist in their body force data30–31and drag reduction data,32a remarkable drag reduction of more than 70%and an effective freestream velocity of up to 52 m/s were achieved, accompanied by a net power saving of more than 300 %.28This remarkable drag reduction result was supposed to result from the disruption of the autonomous cycle for the production of streamwise vortices and low-speed streaks.28–29Following this,Yates et al.33investigated the drag reduction performance of the pulsed DC discharge in an adverse pressure gradient boundary layer at U∞= 27.1 m/s, and a reduction in nearwall shear stress of 42 % was speculated based on the reduction in VITA events.In addition to the pulsed DC discharge,Cheng et al.34compared the effects of the DBD-induced unidirectional discharge and impinging discharge in the case of a ZPG turbulent boundary layer at U∞=2.4 m/s.A peak drag reduction value of 26 % is produced by the impinging discharge with large spacing.For the application on airfoil, Li et al.35investigated the variation of near-wall shear stress on the airfoil surface downstream of an impinging discharge DBD actuator,but the local shear stress was found to increase by 6 % at Ma = 0.3–0.6.Besides, there are also researches investigating the drag reduction performance of the streamwise DBD plasma actuator.By comparing the slope of velocity profiles in log law region, a local drag reduction of 8.78 % was demonstrated in a ZPG turbulent boundary layer36.

Up to now, turbulent drag reduction with various DBD plasma actuator layouts and discharge scenarios has been investigated and significant achievements were made.However,there are still three problems to be solved.First,in previous studies, different discharge scenarios are conducted under various discharge parameters and flow conditions, which should be compared in the same condition.Second, the overwhelming majority of studies dealt with the ZPG flat plate.This is much idealized because the zero pressure gradient and turbulent condition are not always satisfied in practical applications.There is always strong pressure gradient on airfoils during operation and the total drag of an airfoil has various sources,including turbulent friction drag,laminar friction drag, pressure drag, etc., which is much more complex than that on a ZPG flat plate.It is unknown whether the DBDbased turbulent drag reduction methods still work under the complex pressure gradient on airfoils (combining both the adverse and favorable pressure gradient) and what the influence of these methods on other parts of drag besides the turbulent friction drag is.Thus, the overall influence of the DBDbased methods on the drag of an airfoil should be investigated.Third, in the existing studies, alternating-current plasma actuator is only able to reduce turbulent drag at a freestream velocity of no more than 5 m/s.This velocity ceiling should at least be elevated to dozens of meters per second,in order to be truly meaningful to the aeronautical community.

The current research takes a step forward to solve these problems.The flow structure induced by different DBDbased discharge scenarios in the turbulent boundary layer of a flat plate is first compared using the Particle Image Velocimetry (PIV) method.Then, these scenarios are conducted experimentally in the drag reduction application on a NACA-0012 airfoil at low angles of attack in a freestream velocity range of 5–30 m/s, and the influence of different working modes on the total drag is assessed and compared directly by a wake rake.Hot-wire measurements are also deployed to assist the characterization of wake behaviors in the frequency domain.The key parameters of drag reduction are extracted and the dimensionless scaling is analyzed in detail.The experimental setup, including the wind tunnel, airfoil model, plasma discharge system and measuring system,is described in Section 2.Then, in Section 3, the induced flow structure of different discharge scenarios is compared.In Section 4, the drag measurement results of airfoil at various parameters are presented.Based on these data, a drag reduction map spanned by jet velocity ratio and nondimensional actuator spacing is established, and a discussion is made in Section 5.Finally, a short summary is provided in Section 6.

2.Experimental setup

2.1.Wind tunnel and models

The experiments were carried out in a closed-return wind tunnel with a square test section of 1.2 m in width, 1 m in height and 3 m in length.The freestream velocity in current investigation ranges from 5 m/s to 30 m/s, with a typical turbulence level of less than 0.5 %.As shown in Fig.1, a plexiglass flat plate(1.7 m in length,1.2 m in width and 0.02 m in thickness)was mounted horizontally in the middle of the test section.The flat plate has an elliptic leading edge and a sharp trailing edge.The leading edge is located at approximately 0.65 m downstream from the exit of the wind tunnel convergent section.During the PIV test, the boundary layer is tripped by a sandpaper strip(#30,width:20 mm)at 100 mm downstream of the leading edge of the flat plate, which then interacts with the plasma discharge and is measured by the PIV system.Due to the development of the boundary layer, a favorable pressure gradient can be produced in the turbulent boundary layer.

Fig.1 Experimental setup of PIV test.

During the drag measurement, a NACA 0015 airfoil was 3D-printed by photosensitive resin and fixed vertically on the flat plate by virtue of a threaded hole from its bottom, as shown in Fig.2.The chord length(c)and span(l)of the airfoil are 0.15 m and 0.4 m, respectively, resulting in an aspect ratio of 2.67.For majority of the tests in present study,the angle of attack (α) of the airfoil was kept at 0°, to make sure that the friction drag dominates the total drag and simulate the cruising condition.The Reynolds number based on the chord length (Rec) ranges from 49700 to 298000.To better simulate the airfoil flow field in practical applications, no force transition is used in the drag measurements.

2.2.Plasma actuator and power supply

As shown in Fig.3, two configurations of DBD plasma actuator were used in the experiments, both consisting of highvoltage electrodes and ground electrodes(copper foil,of thickness 0.05 mm), separated by a dielectric layer (Kapton, of thickness 0.12 mm).In the asymmetrical configuration as shown in Fig.3(a), only one high-voltage electrode was used to generate a unidirectional steady plasma jet(Mode A),while in Figs.3 (b) and 3(c), two high-voltage electrodes were arranged at the opposing sides of the ground electrode in the symmetrical configuration to produce either a steady impinging plasma jet (Mode B) or an alternating oscillatory plasma jet (Mode C).In all these configurations, the inner edges of the high-voltage electrodes were aligned with the outer edges of the ground electrode, resulting in zero overlapping.The width of the high-voltage electrodes (wh) was fixed at 2 mm,while that of the ground electrodes (wg) varied between 2 mm and 10 mm.

In PIV tests, only one DBD unit is placed in streamwise direction on the flat plate,which is 1235 mm downstream from the leading edge of flat plate.The total length of discharge is 70 mm and the measurement is conducted at 40 mm downstream from the upstream end of the actuator.In wake measurements, an array of DBD actuator units aligned in the streamwise direction were fabricated and wrapped around the middle part of the airfoil to cover a spanwise extent of approximately 100 mm, as shown in Fig.3(d).The length of each DBD actuator is 340 mm.The spanwise spacing of two neighboring DBD units (L) ranges from 7 mm to 18 mm, to check its impact on the drag reduction effectiveness.A coordinate system is established at the center of the actuator array,with x-, y-and z-axis along the streamwise, vertical and spanwise direction of the airfoil, respectively.

Fig.2 Wake measuring setup.

Fig.3 DBD actuator array.

Two high-voltage generators (Electrofluidsystems Minipulse 2.0) producing steady or modulated sinusoidal voltage waveforms were used to drive the DBD actuator array.Representative discharge waveforms in three different working modes of the plasma actuator, as measured by two highvoltage probes (Tektronix P6015A) and a current probe (Tektronix P6022),are shown in Fig.4,where U1and U2denote the voltages applied to the left and right high-voltage electrodes,respectively, and I is the total current flowing towards the ground electrode.Note that in oscillating and steady impinging modes, the peak-to-peak amplitude (Up-p) and carrier frequency (fc) of the two high-voltage waveforms were kept strictly the same.

As shown in Fig.4(a), when the high-voltage generators were operating at unidirectional steady working mode(i.e.Mode A), the right high-voltage electrode was disabled and a continuous sinusoidal high-voltage waveform was fed to the left high-voltage electrode.For steady impinging mode(i.e.Mode B), two steady high-voltage waveforms were fed to the two high-voltage electrodes respectively, as shown in Fig.4(b).The waveform of oscillating mode (i.e.Mode C) is shown in Fig.4(c).Two square-wave Transistor-Transistor Logic(TTL)signals with a duty cycle of 50%were transmitted to the‘‘Enable”port of the two high-voltage generators respectively,and the phase delay between these two signals was set as 180°.In such a way,the two high-voltage electrodes will be activated alternately.By adjusting the modulation frequency of the square wave (fm), the jet oscillation frequency can be easily changed, as shown in Fig.4(c).In the current research, the phase, φ, is defined based on the high-voltage waveform on the right electrode, with φ = 0 indicating the ignition of discharge and φ=π indicating the high-voltage waveform getting back to zero.

2.3.PIV system

A planar PIV system consisting of a camera(LaVision Imager Pro X, with the resolution of 1600 pixel × 1400 pixel), a Nd:YAG double-pulse laser(with pulse energy 200 mJ),and a programmable timing unit (LaVision v9) is deployed to evaluate the spanwise velocity field induced by the DBD in the turbulent boundary layer, as shown in Fig.1.The tracer particles are sprayed in the settling chamber by injecting high-pressure air through a Laskin nozzle submerged in liquid olive oil,and a 200 mm lens (Nikon AF Micro-Nikkor 1:4D) is mounted in front of the camera to image a Field of View(FOV) of 23.6 mm × 20.7 mm.The size of the tracer particles is around 1–3 μm.The laser thickness in the measurement domain is adjusted to be approximately 2 mm.The illuminated particle images are recorded at a repetition rate of 10 Hz.

The PIV system and the discharge system are synchronized by a DG535 digital delay generator, working in phase-locked mode.By adjusting the time delay between camera acquisition and discharge ignition (i.e.the phase, φ), velocity fields at different instances can be acquired.In each case,500 image pairs are acquired and the interrogation window size and overlapping ratio in the final pass of cross-correlation are set as 24×24 and 75%,respectively,resulting in a spatial resolution of 9 velocity vectors per millimeter.

2.4.Wake measuring system

As a classical method to assess the airfoil drag,wake rake measurement is more suitable for the present study than direct force measurement.Specifically, a high-resolved force balance mounted beneath the airfoil is sensitive to EMI (Electromagnetic Interference) produced by high-voltage discharge,whereas the pressure transducers connected to wake rake can be well shielded by copper mesh and placed far away from the model.

Based on the momentum equation, the total drag (denoted as D)and drag coefficient(CD)of the airfoil can be determined as37

where q is the air density (taken as 1.226 kg/m3); y1and y2define the lower and upper bounds of the airfoil wake respectively;U(y)is the wake velocity;U∞is the freestream velocity.

To obtain the wake velocity distribution, 16 total pressure probes were configured in the wake rake, with a spacing of 4 mm, as shown in Fig.2.To make sure that the wake was fully developed, the distance between the trailing edge of the airfoil model and the probe tip was set as 450 mm,and the vertical location of the probe tip was adjusted to be at the height of half airfoil span, i.e.aligned to the middle of the plasma zone.Each of the pressure probes in the wake rake was connected to a differential pressure sensor (model: HSTLFYDX01;range:0–1 kPa;accuracy:0.1%F.S.),with a typical measurement uncertainty of less than 1 Pa.The analogue signals (0–5 V) outputted by the pressure sensors were converted into digital signals by a NI DAQ device (model number: NI USB 6210),and further read by a desktop.During each acquisition,the wake pressures were sampled for 10 s at a sampling frequency of 250 Hz, resulting in 2500 data points.The mean value of these data points was used to derive the time-averaged wake velocity.The standard deviation of the drag measurement is around 4.29 % of the total drag.

Apart from wake rake measurements, a constanttemperature hot-wire anemometry was deployed to obtain the frequency spectrum of wake velocity.The wire is of 5 μm in diameter and 1.25 mm in length, and the overheat ratio was set as 1.6.A planform of the airfoil, wake rake and hotwire probe is provided in Fig.2(b).As indicated, the probe was fixed on a two-dimensional motorized traversing stage,which is interchangeable with the pressure rake system and enables automatic scanning of the wake profile along y- and z-direction.The y- and z-range of the traversing system are 550 mm and 100 mm, respectively.Prior to wake measurements, an in-situ calibration of the hot-wire was performed by removing the airfoil model and correlating the freestream velocity indicated by a Pitot tube with the voltage outputted by the wire.The streamwise distance from the trailing edge of the airfoil model to the hot-wire is 315 mm.For the purpose of this study,41 measurement stations were arranged along the y-direction at middle-span height (i.e.z = 0 mm), with a uniform spacing of 2 mm.At each station, the instantaneous velocity trace was sampled for 5 s at a rate of 2.5 kHz,resulting in 125000 data points for statistical and frequency spectrum analysis.

A representative wake velocity profile obtained by the rake at α=0°and z=0 mm is shown in Fig.5(a).The blue circles are the dimensionless velocity calculated by dividing velocity data measured in the current research (U) by the maximum velocity in the wake(Umax).Note that,to obtain a fine resolution of the wake profile,two repetitive measurements were performed by the wake rake for every case tested presented in this paper: one at its original location and the other translated by half of the probe spacing along the y-direction, resulting in a total of 32 velocity points.While calculating the drag,the wake velocity profile was first fitted by a Gaussian curve (see Fig.5(a)) and then integrated numerically according to Eq.(1).Fig.5(b)compares the drag data measured by wake rake with that predicted by the XFoil program38or presented in Refs.39–41The critical N-factor used in the XFoil program to determine transition was set as 5, in view of the turbulence level in our wind tunnel.Overall, the experimental and XFoil data are consistent reasonably well.There is a relatively large deviation at Rec≤50000 due to the uncertainty in transition location prediction in XFoil, but the experimental data agree well with the data by Ohtake et al.40in this range of Rec.These results justify the accuracy of wake rake measurements.

Further, several sets of wake profiles were measured in a spanwise range covering two consecutive plasma actuator units to examine the spanwise homogeneity of the baseline and controlled flow field, as shown in Fig.6.The inflow velocity and angle of attack are U∞= 5 m/s and α = 0° respectively.Actuation parameters including the voltage amplitude,frequency, ground electrode width and actuator spacing are Up-p= 9.4 kV, fc= 10 kHz, wg= 10 mm and L = 18 mm respectively.These values are the default flow and actuator parameter values in the following content unless otherwise noticed.A rather uniform distribution of the drag coefficient along spanwise direction is demonstrated, even in actuated case.This is not surprising, in the sense that even though different levels of drag reduction might be expected at different locations in between the actuators, this difference in nearwake velocity profile quickly smears out during downstream propagation.At the wake rake location, the drag coefficient measured at a single place of z = 0 mm is sufficient to reflect the mean drag covered by the plasma zone.

Fig.5 Wake profile and drag coefficient of airfoil at α = 0°.

3.PIV results

Up to now, various actuator layouts and working modes of DBD have been tested in literature for turbulent drag reduction.These are summarized in Table 1.18–20,23–26,28,33–35Among these methods, four different working modes are involved, i.e.Mode A: The unidirectional steady plasma jet mode, Mode B: Steady impinging plasma jets mode, Mode C: Oscillating plasma jet mode, and Mode D: Travelingwave plasma jet mode.In this paper, the first three modes are investigated.The traveling-wave plasma jet is not involved due to the limited number of high-voltage power supplies,with more than 10 power supplies required to produce the travelingwave plasma jet.

Fig.6 Spanwise homogeneity of measured drag coefficient.

The flow structure induced by different discharge scenarios at a freestream velocity of U∞=5 m/s and 60 mm downstream of the discharge beginning is shown in Fig.7 and Fig.8,where the width of the ground electrode is 10 mm and the junctions of the two high-voltage electrodes and ground electrode are at z = ±5 mm, respectively.It can be seen that, for Mode A, a large-scale streamwise vortex is produced by the DBD-induced wall-bounded jet.The flow field is dominated by the spanwise motion, with the high velocity region at the bottom of the streamwise vortex.For Mode B,two opposite streamwise vortices are induced,whose upwash sides merge together,forming a vertical jet in the middle.Both spanwise and vertical motion are significant in the flow field.

For Mode C,the flow field is highly unsteady,which cannot be simply analyzed in the time-averaged sense.So, the phaseaveraged measurement is conducted at eight different phases with a step of 0.25π and three different oscillating frequency of fm=20,100,500 Hz.The results are shown in Fig.8.Both spanwise and vertical jets exist in Mode C.At low modulation frequency of 20 Hz, the spanwise jet produced at the first half cycle extends over the opposing high-voltage electrode and thus can decelerate rapidly by the reversed body force produced in the next half cycle, resulting in an alternation of two seemingly independent spanwise jets and streamwise vortices.This flow pattern is very much alike to that in Mode A if only half an oscillation period is taken into account.As a comparison, when the modulation frequency in Mode C goes up to 500 Hz, the spanwise jet formed in one half cycle is so short that it cannot even pass the symmetry plane of the actuator,due to a severe shrinkage of the jet growth time.Eventually, the near-wall jets produced in the first and second half cycle coexist and collide with each other in the middle and no oscillation exists, forming a quasi-steady vertical jet structure similar to that in Mode B.The flow structure induced by Mode C is in an intermediate state between that of Mode A and Mode B, which can be adjusted readily by changing the modulating frequency of the oscillating high-voltage waveform.

4.Wake measurement results

Actuator layout (e.g.symmetry and spacing), working mode,discharge strength (e.g.voltage and frequency), freestream velocity and angle of attack are identified as the five main fac-tors that could potentially influence the drag reduction level.The former three of these factors fall into the category of control parameters,while the latter two determine base-flow properties.Following this outline, a detailed parametric study is conducted in Sections 4.1–4.4 to obtain the basic variation trends of the total drag.And the key dimensionless parameters are extracted in this process,which are analyzed in Section 4.5 to derive a general rule for drag reduction.

Table 1 Different working modes used for drag reduction.

Fig.7 Time-averaged velocity (Uyz) and vorticity (ωx) field induced by DBD working in Mode A and Mode B in spanwise plane of turbulent boundary layer.

4.1.Influence of actuator working mode

For purpose of working mode comparison, eight groups were tested:one in baseline,one in Mode A,one in Mode B and the rest five in Mode C at increasing modulation frequencies of fm= 20, 50, 100, 200, 500 Hz.Other factors, including the sinusoidal waveform parameters(Up-p=9.4 kV,fc=10 kHz)and the geometrical parameters of the actuator (wg= 10 mm and L = 18 mm) are kept the same.The wake rake measurement results in these eight groups are shown in Fig.9(a).For all the actuated cases,the peak velocity defect in the wake profile is reduced noticeably, and the highest and lowest drag reductions are achieved in Mode A, (unidirectional steady jet) and Mode B (impinging steady jet), respectively.Since near-wall impinging jets usually produce a steady vertical jet,the above results, to some extent, support the conclusion reached in Ref.9that w-control (spanwise perturbation) is superior than v-control(vertical perturbation)in terms of drag reduction.

The wake profiles obtained in oscillating working mode fall ubiquitously in between that of Mode A and Mode B,and differ slightly with increasing oscillating frequency.This is largely expected because the flow patterns at Mode C transit gradually from that of Mode A to Mode B with the oscillating frequency increasing,as shown in Fig.8.Therefore,it is not surprising to achieve an intermediate wake velocity profile with oscillating plasma actuation.

Fig.9(b) shows the relative drag variation to baseline, as defined by the following expression:

where CD,plasmaand CD,baselinerepresent the drag coefficient with and without plasma actuation,respectively.The modulating frequency in Fig.9(b)is nondimensionalized and produces the Strouhal number St = fmc/U∞.Significant drag variation is demonstrated.The maximum drag reduction percentage reaches 31.7%in case of unidirectional steady jet mode(Mode A), consistent with the peak wake velocity deficit variation in Fig.9(a).This result validates the efficacy of DBD-based turbulent drag reduction methods to reduce the total drag of airfoils.Impinging plasma jet (Mode B) ends up with a 3.6 % increase in the total drag, as a result of the competing effects of decreasing peak velocity deficit and increasing wake width (see Fig.9(a)).For oscillating plasma jet (Mode C), the relative drag reduction decreases from 20.4%to 14.3%,as the modulation frequency increases from 20 Hz to 500 Hz, which agrees well with the transition of flow pattern from alternating independent spanwise jets to quasi-steady impinging jets in previous analysis.

Fig.8 Phase-averaged velocity field induced by DBD working in Mode C in spanwise plane of turbulent boundary layer.

4.2.Influence of voltage amplitude and freestream velocity

Since unidirectional steady plasma jet delivers the most drag reduction among the three working modes, it is set as the default working mode in all the following parametric investigations.Fig.10 shows the drag reduction percentage at increasing voltage amplitude for a fixed freestream velocity of 5 m/s.

At Up-p< 2 kV, no drag reduction is observed due to the weak plasma discharge which induces indiscernible perturbations to the boundary layer flow.With increasing voltage amplitude, the relative drag reduction continues increasing and reaches a peak value of 42.8 % at Up-p= 6.2 kV, after which a mild decrease is exhibited.This trend indicates that,at a fixed freestream velocity, there exists an optimal range of plasma jet intensity in order to achieve the most drag reduction,and the brutal rule of‘‘the stronger the plasma actuation,the better the control effect”does not hold here.42–43Similar phenomenon is also demonstrated in the work by Thomas et al.in a ZPG turbulent boundary layer28.

Besides the voltage amplitude which decides the power consumption of plasma discharge, another vital parameter is the effective velocity range.As shown in Fig.11, with constant voltage amplitude and increasing freestream velocity,a monotonous decrease of the drag coefficient exists in both baseline and actuated cases.For the present actuator layout and working mode, prominent drag reduction only exists at U∞<10 m/s, below which the drag reduction magnitude varies inversely with the freestream velocity.At U∞≥10 m/s,a small drag increase is observed (<10 %), and this drag increase seems to saturate at high freestream velocity.This trend of drag reduction is inverse to the trend exhibited in Fig.10,which indicates that the ratio of plasma jet velocity to freestream velocity does serve as a key factor influencing the overall drag reduction magnitude.The drag increase at high freestream velocity and the decrease of drag reduction at large voltage amplitude can be attributed to the enhancement of the Streak Transient Growth (STG) in turbulent boundary layer by the upwash and downwash of the large-scale streamwise vortices produced by plasma actuation44.

Fig.9 Wake profile and percentage change in drag coefficient at different working modes.

Fig.10 Variation of total drag with increasing voltage amplitude at U∞=5 m/s.

Fig.11 Variation of drag coefficient and drag reduction percentage with increasing freestream velocity at a fixed voltage amplitude of Up-p= 9.4 kV.

Besides the drag coefficient,frequency characteristics of the wake are presented based on hot-wire measurements.During data processing, the instantaneous wake velocity was first low-pass filtered at a cutoff frequency of 2500 Hz to eliminate the high-frequency electrical noise and then translated to the frequency domain using Fast Fourier Transformation (FFT).Fig.12 compares the frequency spectrums measured in baseline and actuated conditions at a fixed location of y = 0 mm.Other parameters are set as Up-p= 9.4 kV and L = 18 mm.As a result, the whole spectrum at U∞= 5 m/s is suppressed by plasma actuation, indicating significantly less velocity fluctuations in drag-reduced wake flows.This phenomenon is to some extent expected,since the turbulence production rate in wake flows is proportional to the maximum wake velocity deficit.45With plasma actuation, the friction drag is decreased and the friction velocity of turbulent boundary layer is reduced, leading to a drop in the maximum wake velocity deficit and eventually a reduction of wake velocity fluctuation.

Fig.12 Frequency characteristics of wake.

With increasing freestream velocity, the two frequency spectrums begin to overlap with each other, and a marginal increase of the velocity fluctuation can be picked in highfrequency band, which is consistent with the small drag increase at high freestream velocity.In reference with the analysis in previous paragraph, the decaying variation of velocity fluctuation is supposed to be caused by the insignificant change of peak velocity deficit at high freestream velocity due to the limited discharge strength.This also demonstrates the influence of the ratio of plasma jet velocity to freestream velocity on drag reduction.However, it can be inferred that this ratio is not the only factor, because if it is the only one, the lowvoltage region in Fig.10 should be equivalent to the highvelocity region in Fig.11, exhibiting roughly the same drag variation.So, more factors should be investigated.

4.3.Influence of spanwise actuator spacing

Previous studies on ZPG turbulent boundary layers demonstrate that,the spanwise spacing between neighboring actuator units strongly influences the drag reduction performance.24,28,34As a follow-up,influence of the spanwise spacing between adjacent actuator units on the drag reduction of airfoil is investigated.Three levels of L = 7, 10, 18 mm are realized by setting the ground electrode width as wg=2,5,10 mm respectively.In each case, a matrix spanned by voltage amplitude and freestream velocity is examined, and the results are compared in Fig.13, where the red line indicates ΔCD= 0,and the black dashed lines are the isolines with the spacing of 10 %.The data with |ΔCD| < 5 % are deleted to reduce the influence of random error.

For all the three cases,favorable drag reduction can only be achieved at low freestream velocity, while at high velocity, the total drag increases.The global maximum of relative drag reduction is observed at L = 7 mm, Up-p= 6 kV and U∞= 5 m/s, reaching as high as 64%.At L = 7 mm and Up-p= 8 kV, a drag reduction of 13.7% is achieved at a freestream velocity of up to 20 m/s.This drag-reduction velocity limit is four times higher than those reported in similar studies(2–5 m/s, Refs.23–26,34).

The threshold velocity dividing the drag reduction and drag increase region remains roughly unchanged among the three cases,being around 20 m/s.Nevertheless,with decreasing actuator spacing, the overall drag reduction value tends to increase, signifying that the relative comparison of actuation length scale (i.e.spacing) and boundary layer length scale might play a role.Compared to the freestream velocity, the influence of voltage amplitude is relatively weak, in the sense that as long as a minimum amplitude to effectively perturb the flow (～4 kV) is exceeded, the total drag drops quickly to a specific value, and further noticeable increase of the discharge voltage does not give prominent drop of the total drag.Besides, with increasing L, the centroid of the drag reducing region moves upwards monotonically, demonstrating that the influence of L, Up-pand U∞is closely related with each other.

4.4.Influence of angle of attack

The flow condition on airfoil changes sharply with angle of attack because of the significant change in pressure gradient.This section is intended to check the impact of angle of attack on total drag reduction, in the range of α = 0–16°.The freestream velocity was set as U∞= 10 m/s and different voltage amplitudes of Up-p=2–8 kV were used.Corresponding results are shown in Fig.14.Overall, plasma actuators in unidirectional steady working mode are able to reduce the drag at all angles of attack.The largest drag reduction of 50.8 % is achieved at α = 0°, Up-p= 8 kV and L = 7 mm, which decreases gradually with increasing angle of attack.As the angle of attack further increases (α > 10°), significant flow separation appears on the airfoil surface and pressure drag gets dominant,as indicated by the sharp drag increase in Fig.14(a).For this specific scenario,the relative drag reduction is mainly contributed by the elimination of pressure drag, thus increasing with the angle of attack.The plasma actuator functions as a vortex generator to suppress flow separation and reduce pressure drag, as reported by Jukes42and Kelley43et al.Since the prime concern of this paper is drag reduction at low angles of attack under cruise condition, further analysis will not be made on the results at large angles of attack.

The cruise angle of attack of transportation aircraft is usually selected to have the maximum lift-to-drag ratio.In the present case of NACA-0012 airfoil,this favorable angle is around 6°, and its corresponding drag reduction map is shown in Fig.15(a).Compared with that at α = 0°, the overall value of drag reduction decreases obviously due to the intensification of pressure gradient, with the peak drag reduction of 44.8 %achieved at U∞= 5 m/s and Up-p= 8 kV.Since the suction and pressure surfaces of the airfoil are dominated by adverse and favorable pressure gradient respectively, the influence of the sign of pressure gradient can be realized by switching on the plasma actuator at each side of the airfoil independently.The corresponding results are shown in Figs.15(b) and 15(c).Similar to the case with discharge on both sides, drag reduction can only be found at low freestream velocity,regardless of the sign of pressure gradient.For the same inflow and discharge parameters, drag reduction achieved by suctionside actuation is in general higher than that obtained from pressure-side actuation, indicating that an adverse streamwise pressure gradient is beneficial to the drag reduction.This may account for the suppression of potential flow separation at the trailing edge of the suction side.

Fig.14 Drag coefficient and drag reduction percentage at increasing angles of attack.

4.5.Dimensionless scaling and design map

In previous analysis, modulation frequency (fm), voltage amplitude (equivalent to plasma jet velocity), and spanwise actuator spacing (L) are identified as the main actuation parameters influencing the drag reduction effectiveness.They can be combined with the characteristic velocity and length scales,to form three dimensionless parameters:Strouhal number (St), jet velocity ratio (r), and dimensionless spacing (L+)as follows:

where ν is the kinematic viscosity of air; Ujdenotes the peak plasma jet velocity estimated by the analytical expression presented in the work of Zhu and Wu46and Soloviev and Krivtsov47; uτand δvdenote the friction velocity and viscous length scale of the boundary layer,respectively.Since uτis spatially dependent, the friction velocity of a turbulent boundary layer developing on a flat plate with equal freestream velocity and Reynolds number is used as a reference, as follows48:

where Rexrepresents the Reynolds number based on the length of development of the turbulent boundary layer.With the above efforts, we are able to derive the three dimensionless parameters for every case tested.Since the impact of Strouhal number has already been treated in Fig.9(b), the following content focuses on the scaling of r and L+.

Physically,the jet velocity ratio r signifies the relative intensity of plasma jet to the incoming flow (i.e.the ability to perturb the flow field), while the dimensionless spacing L+determines how many streaks exist in between two adjacent plasma actuators.For effective drag reduction with pulsed-DC plasma actuator, Thomas et al.suggested an interelectrode spacing of 800δν–1000δν, namely, 8–10 low-speed streaks.28As a comparison, Jukes et al.demonstrated that a much narrower spanwise electrode spacing (<25δν) is needed for oscillating DBD to deliver satisfying drag reduction performance.24Recently,Cheng et al.tested two impinging spanwise jets, and concluded that the one with large spacing (400δν) is superior to that with small spacing (100δv).34These observations differ noticeably from each other, as a direct result of the diverse working modes of the spanwise actuator array.

Fig.15 Drag reduction map at α = 6°.

In the most favorable working mode (Mode A: unidirectional steady jet),scaling between the total drag reduction with the jet velocity ratio and dimensionless spacing is shown in Fig.16.As a result,in semi-logarithmic coordinate,the relative drag reduction varies almost linearly with dimensionless spacing,and thus can be fitted by a line.The slope of the fitting line in Fig.16(a) is 32.73.The x-intercept of the fitting line (540)can be interpreted as the threshold actuator spacing, below which turbulent friction drag is reduced (ΔCD< 0).This threshold spacing equals roughly-five times of spanwise spacing between low-speed streaks, close to the optimal spacing of 400δνreported by Cheng et al.34Once the critical spacing is exceeded, the total drag increases.

As for the scaling shown in Fig.16(b), the experimental data bifurcate at a threshold jet velocity ratio of 0.05.Specifically,when r<0.05,the strength of plasma jet is too weak to perturb the incoming boundary layer, resulting in negligible variation in drag coefficient.Once the jet velocity ratio exceeds 0.05, both drag increase and drag reduction may occur,depending on how the actuator spacing compares with the threshold spacing of 540δν.Two dash lines are used to fit the experimental data lying in drag-reduction and drag-increase zones, and both of their slopes are close to k = 17.65, nearly half the value of the slope concerning the dimensionless spacing.Based on the above analysis, a relation between the total drag reduction and the dimensionless parameters can be derived:

where Lth=540 and rth=0.05 are the threshold values of L+and r, respectively.Different from the effects of the dimensional parameters that are closely related to each other, these two dimensionless parameters (i.e.r and L+) are relatively independent.We can say that different flow and discharge parameters, like freestream velocity, voltage amplitude and actuator spacing, work by changing these two dimensionless parameters, to influence the drag reduction.

Fig.16 Scaling between drag reduction magnitude and dimensionless spacing,jet velocity ratio(symbols represent experimental data; dash lines denote fitting results).

In Fig.17, all the experimental data obtained in Mode A are plotted in a dimensionless map spanned by r and L+.The diameter of the circle is proportional to the magnitude of drag variation, while the color of the circle indicates either drag increase (red) or drag reduction (blue).Overall, three zones exist in this dimensionless map:the no-effect zone at left side(r<0.05),the drag-increase zone at top right(r ≥0.05&L+≥540), and the drag-reduction zone at bottom right(r ≥0.05&L+<540).Division of these three zones is a direct consequence of the scaling shown in Fig.16,and thus will not be interpreted further.From an engineering perspective, the map can be treated as a first-hand reference for subsequent designs of DBD actuators in drag reduction research concerning airfoil at low angles of attack.

A possible mechanism for the above-mentioned dimensionless rules is the interplay of two different effects brought by the Large-Scale Streamwise Vortices (LSSVs) induced by the plasma actuation.On the one hand, the LSSVs confine and stabilize the near-wall streaks like small streamwise riblets(termed as‘‘virtual riblets”for simplicity),and on the other hand,they also enhance the STG and promote local turbulence generation.When L+is small, ‘‘virtual riblets”effect dominates and the drag is reduced effectively,while at large L+,the confinement effect gets weaker and the drag reduction effect attenuates.The enhancement of STG effect dominates in this condition, which promotes local turbulence generation and increases the turbulent friction drag.Further detailed flow visualization of the near-wall coherent structures is needed to verify this mechanism in future study.

5.Discussion

5.1.Sources of total drag reduction

A discussion is made to illustrate the sources of total drag reduction.Theoretically, the total drag measured by the wake rake consists of pressure drag (CD,p) and friction drag (CD,f).Depending on the flow status,friction drag can be further split into laminar friction drag (CD,LF) and turbulent friction drag(CD,TF), as follows:

Since laminar friction drag is in general much lower than turbulent friction drag, the total drag reduction observed in this study (about 40 %–60 %) might be attributed to three aspects: transition delay, pressure drag reduction and turbulent friction drag reduction.

Fig.17 Dimensionless map for airfoil drag reduction at low angles of attack by DBD actuator.

First, for transition delay with plasma actuators, the basic idea is to cancel the Tollmien–Schlichting (T-S) waves.Since both the propagation and development of T-S waves are in streamwise direction, streamwise body forces are required to effectively interact with the T-S waves, as demonstrated in Ref.49In the current study, plasma actuators are configured in the spanwise direction, largely unlikely to be able to cancel the T-S waves and delay the transition.In fact, the periodical spanwise body force induced by plasma array might disrupt the two-dimensional nature of T-S waves, resulting in early transition.Therefore, the reduction of pressure drag and turbulent friction drag are the only two sources of the total drag reduction.

For pressure drag reduction (denoted by ΔCD,p) with plasma actuation, the main mechanism is supposed to be suppressing flow separation by transition promotion.50Specifically, at low Reynolds number, the laminar flow region on the airfoil is large and a small laminar separation zone exists near the trailing edge, which has been validated by the XFoil prediction.Once the laminar boundary layer is tripped to turbulent by plasma actuation, its velocity profile becomes fuller and less prone to separate at adverse pressure gradient,leading to a reduction in separation area and thus the pressure drag.However,it should be noted that flow transition directly leads to an increase in the total friction drag(denoted as ΔCD,f)due to an upstream extension of the turbulent flow area.So, the reduction in total drag brought by pressure drag reduction will be partly offset by the increase in friction drag caused by transition promotion.

Besides the drag variation due to the transition brought by plasma actuation, i.e.ΔCD,pand ΔCD,fmentioned above, the plasma actuation can also reduce the friction drag in the turbulent region (denoted as ΔCD,TF).So, the sources of total drag variation include the pressure drag reduction,the drag increase caused by transition promotion and the reduction in turbulent friction drag.As a result, the following relation can be acquired:

where the sum of the underlined terms bears the meaning of transition-caused total drag variation,which is denoted further by ΔCD,xtrfor simplicity.

5.2.Proportion of turbulent friction drag in total drag reduction

To derive the turbulent drag reduction term ΔCD,TFin the right side of Eq.(8)and demonstrate the significance of viscous friction drag in total drag reduction of the airfoil at low angles of attack,ΔCD,xtrhas to be estimated reasonably.So,a budget estimation is made in this section using the XFoil program.The transition-caused total drag variation is determined by manually setting the transition location(denoted as xtr)at different chord locations in the program.Fig.18 demonstrates the variation of the total drag coefficients of the NACA-0012 airfoil with forced transition locations at different freestream velocities derived from the XFoil program.The natural transition location in each condition is denoted by the filled markers in Fig.18.On this basis, a conservative estimation of the minimum turbulent drag reduction can be made by the following relation:

where ΔCDis the total drag reduction acquired in the experiments and max(ΔCD,xtr) is the maximum transition-caused drag reduction picked from Fig.18.

Taking the condition at L=7 mm and Up-p=8 kV as an example, the turbulent drag reduction is estimated and shown in Fig.19 based on the conservative estimation above.Overall,there exists a significant value of the turbulent drag reduction,which decreases with increasing freestream velocity.The proportion of the turbulent drag reduction in the total drag reduction keeps increasing with the freestream velocity.At U∞≥20 m/s, turbulent drag reduction becomes the only source of total drag reduction due to the absence of laminar separation at large Reynolds number.This demonstrates the significance of turbulent friction drag reduction in the drag reduction application on airfoils at low angles of attack.

5.3.Analysis on net power saving

The power saved by plasma actuator working in the unidirectional steady jet mode per unit span(Psave)can be computed as follows:

where Pais the power consumed by the plasma actuator per unit span; Lspanis the spanwise range of the actuator;Dbaselineand Dplasmadenote the airfoil drag in baseline and actuated conditions, respectively; Tmis the time period of current and voltage measurements.A positive Psavemeans energy saving.The results of all the cases tested in the experiments are shown in Fig.20.Although no positive power saving is achieved in the current condition, the minimum absolute value of Psaveis only 13.6 W/m, while the typical value of power consumption in airflow control applications by AC-DBD is around 100 W/m.51Because the influence of plasma actuation on the flow field can persist to some extent in both the time and space domain even when the actuator is turned off,28it is quite promising to achieve net power saving by using duty cycled high-voltage waveform and applying the plasma actuator only on the leading edge of airfoil, so that the power consumption will be reduced and the perturbation by DBD can flow downstream and reduce the drag of the whole airfoil.

Fig.18 Variation of total drag coefficient with forced transition location (filled marker in each curve indicates the case of natural transition).

Fig.19 Components of drag reduction by plasma actuation and ratio of turbulent friction drag reduction to total drag reduction.

Fig.20 Net power saving by plasma actuation.

6.Conclusions

In this study, the flow structures induced by DBD working in different discharge scenarios in a turbulent boundary layer are first compared using PIV method.And then a spanwise plasma actuator array is deployed to reduce the drag of a NACA-0012 airfoil at low angles of attack.Influence of various factors including the discharge scenario, voltage, freestream velocity,angle of attack and actuator spacing on drag reduction effectiveness are analyzed,based on which key parameters for drag reduction are extracted and a dimensionless drag variation map spanned by jet velocity ratio and dimensionless spacing is drawn.Moreover, a discussion concerning the sources of drag reduction is presented.Main conclusions are listed as follows:

In turbulent boundary layer, a large-scale streamwise vortex is induced by the unidirectional steady discharge, while two opposite streamwise vortices combined with a vertical jet in the middle are produced by the steady impinging discharge.The oscillating discharge is in an intermediate state between that of the previous two working modes.The flow structure by oscillating discharge transits gradually from alternating streamwise vortices to a quasi-steady flow field similar to that of steady impinging discharge.

A maximum drag reduction as high as 64%is achieved by unidirectional steady plasma jet at U∞= 5 m/s.Steady impinging plasma jets fail to achieve any drag reduction,while oscillating plasma jet delivers less amount of drag reduction than unidirectional steady plasma jet.As freestream velocity increases, the magnitude of drag reduction decreases, being 13.7 % at U∞=20 m/s.The drag reduction percentage first decreases and then increases with increasing angles of attack.

There are three zones of drag reduction in the dimensionless drag variation map spanned by the two key dimensionless parameters,i.e.jet velocity ratio(r)and dimensionless spacing(L+): the no-effect zone at left side (r < 0.05), the dragincrease zone at top right (r ≥0.05 & L+≥540), and the drag-reduction zone at bottom right (r ≥0.05 & L+< 540).Little effect can be produced by the plasma actuation in the no-effect zone.The drag variation magnitude increases logarithmically with increasing r in both the drag-increase and drag-reduction zone, with the slope in the semi-logarithmic coordinate around 17.65.With increasing L+, the percentage of drag reduction also decreases logarithmically,with the slope in the semi-logarithmic coordinate around 32.73.The total drag reduction of airfoil at low angles of attack can be divided into pressure drag reduction,turbulent friction drag reduction and the increase in friction drag brought by transition promotion.The reduction in turbulent friction drag plays an important role in the total drag reduction.

These results provide a first-hand reference for the design of DBD plasma actuators in drag reduction applications of airfoil at low angles of attack.In future studies, detailed measurements of the turbulent boundary layer on airfoil are needed to be conducted to illustrate the sources of drag reduction in detail.And the net power saving can be potentially achieved by using duty cycled high-voltage waveform and applying the plasma actuator only on the leading edge of airfoil.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was co-supported by the National Natural Science Foundation of China (Nos.12002384 and 11802341), the National Key Laboratory Foundation of China (No.614220210200112), the National Science and Technology Major Project, China (No.J2019-II-0014-0035), and the Academician Workstation Foundation of the Green Aerotechnics Research Institute of Chongqing Jiaotong University, China(No.GATRI2020C06003).