Experimental characteristics of a two-electrode plasma synthetic jet actuator array in serial

Yan ZHOU,Zhixun XIA,Zhenbing LUO,Lin WANG,Xiong DENG

Science and Technology on Scramjet Laboratory,National University of Defense Technology,Changsha 410073,China

KEYWORDS Capacitive power supply;Flow control;Plasma synthetic jet;Pulse arc discharge;Serial actuator array;Two-electrode

AbstractPlasma Synthetic Jet(PSJ)actuators have shown wide and promising application prospects in high-speed fiow control,due to their advantages including high exhaust speed,wide frequency band,rapid response,and non-moving components.Although previous studies on PSJ actuators are abundant,most of them have focused on the performance of a single actuator.However,in practice,an actuator array is very necessary for large-scale aerodynamic actuation on account of the small affected area of a single PSJ.In this paper,the characteristics of a twoelectrode plasma synthetic jet actuator array in serial are investigated experimentally.Compared to a parallel actuator array,the serial actuator array requires simpler power supply design and is much easier to realize.High-speed photography of the discharge evolution,voltage-current measurement,and shadowgraphy visualization are used in the investigation.Experimental results show that,for the serial actuator array,weak discharges happen firstly between energized and suspending electrodes,and then a strong pulse arc discharge is triggered.The breakdown voltage in serial is irrelevant to such factors as the number of actuators,the maximum or minimum gap in serial,the connection sequence,etc.It is mainly determined by the sum of gaps.For serial actuators with the same anode-to-cathode spacing,the energy deposition is the same,and the jet is synchronous and similar.Because of the entrainment and merging of adjacent jet vortices,the jet front speed of an aligned synchronous jet array increases as the orifice distance decreases.To achieve the highest jet front velocity,the orifice of the actuator has an optimal diameter.

1.Introduction

Due to considerable potential uses in a number of areas,such as fiow separation control,boundary layer transition,mixing enhancement,drag and noise reduction,etc.1–5,Active Flow Control(AFC)methods have been one of the hotspots in fiuid mechanics.Plasma actuators are an attractive type of activeflow control technique6–9.They have advantages including fast response,wide bandwidth,and absence of moving components.According to the configuration,plasma actuators may be divided into several typical categories,such as Dielectric Barrier Discharge(DBD)actuators,DC glow discharge actuators,localized arc filament plasma actuators,plasma synthetic jet actuators,etc.

As one of the enabling AFC methods which show a promise of manipulating high-speed fiows10–14,a Plasma Synthetic Jet(PSJ,also called SparkJet or pulsed plasma jet)actuator wasfirstly developed in 2003 by Grossman et al.15It is a kind of synthetic or Zero Net Mass Flux(ZNMF)devices because the actuator is refilled from the freestream after each pulse rather than from an external supply of gas.A jet is created by fast joule heating of a pulse arc discharge in a small cavity with an orifice15–17.The operation cycle of a PSJ actuator consists of three distinct stages:energy deposition,air expulsion,and air recovery15,18.A PSJ actuator has favorable features of both a plasma actuator and a ZNMF jet.Its unique properties,such as requiring no moving parts and fiow supplies19,20,responding fast21,22,wide frequency band(from zero to several kHz)10,11,23,high efflux speed(several hundred m/s)22,24,25,etc.make the PSJ most suitable for high-speed fiow control.

To characterize this type of actuator,numerous experimental and numerical methods have been applied.For experimentalinvestigations,the mostly used techniques include voltage-current measurement13,26,high-speed schlieren14,25or shadowgraphy13,22,quantitative schlieren27,optical emission spectroscopy28,Particle Image Velocimetry(PIV)29–31,thrust measurement32,short-exposure-time Intensified Charge-Coupled Device(ICCD)photograph28,pressure measurement in the cavity32,total pressure measurement of the jet20,Digital Speckle Tomography(DST)32,infrared camera20,33,and so on.Fornumericalinvestigations,usefulnumericalmethods include analytical model34,35,instantaneous energy deposition model15,source term model21,non-confined arc simulation36,plasma kinetic models37,and so on.

To date,research achievements on the characteristics of PSJ actuators are abundant.The influences of some electrical parameters(such as types of power supply,energies,frequencies,and positive slopes),geometrical parameters(such as cavity volumes,orifice diameters,throat lengths,and electrodes locations),and environment parameters(such as ambient pressures)are investigated.A comparison between an Inductive Power Supply(IPS)and a Capacitive Power Supply(CPS)shows that the CPS produces a more powerful jet(higher velocity and shorter expulsion time),and probably heats the gas and the cavity less significantly than the IPS33.Compared with a two-electrode actuator,a novel three-electrode actuator increases the cavity volume as well as the input energy and keeps a relatively low disruptive voltage22.For three different positive slopes(0.90,0.36,and 0.26 kV/ns),as the positive slope(i.e.,the rising rate of the applied voltage from zero to the maximum)decreases,the heating energy of the spark discharge and the jet velocity increases37.Nanosecond discharge has a higher heating efficiency,but can only be used for very small actuators due to its low discharge energy37.For a CPS,as the discharge frequency rises,the breakdown voltage,peak discharge current,and discharge energy decrease34.With the same energy deposition,there exists a saturated frequency,above which the total mechanical energy of the pulsed jet drops sharply34.The discharge energy,cavity volume,and ambient pressure determine the dimensionless energy deposition of the actuator(i.e.,the ratio of the discharge energy to the internal energy of gas in the cavity)which influences the performance of the PSJ.As the dimensionless energy deposition rises,three typical fiow field evolution patterns(shock wave,weak jet with vortex rings,and strong jet without vortex rings)appear successively38.As the orifice diameter enlarges,the peak jet front velocity increases while the jet duration time and the jet delay time drop39.As the ambient pressure drops,the breakdown voltage and peak discharge current decrease while the transfer efficiency from capacitor energy to discharge energy is almost constant.The strength of the precursor shock increases at first and then decreases.The strength reaches maximum at 0.6 atm(1 atm=101325 Pa)40.

However,most of the previous studies on PSJ actuators have focused on the performance of a single actuator.For practical applications,a group of actuators may be needed to expand the controlled fiowfield or improve the control authority.An actuator array can be connected in two basic ways:parallel or serial,as shown in Fig.1.For a parallel actuator array,the on–off switch and the working phase and frequency of each actuator can be controlled separately,which makes the work of the actuator array more fiexible.However,parallel actuators cannot be connected directly to one capacity,because in that case,the breakdown and pulse arc discharge can only happen in one actuator which has the narrowest gas gap41,42.Consequently,several highvoltage power supplies or a very complex electric circuit are required.For a serial actuator array,actuators can be connected to one capacity,which makes the power supply much simpler.However,the working states of the actuators cannot be controlled separately,and all the actuators will work synchronously.In a specific application,a serialparallel hybrid connection actuator array can be adopted to achieve the most desired control effect.Besides,Zhang et al.43,44also proposed an innovative multichannel discharge PSJ actuator array which achieves a voltage relay by using a group of parallel resistances and capacitors in the discharge circuit.

In this paper,the characteristics of a PSJ actuator array working in the serial mode are investigated experimentally.Voltage–current measurement,high-speed photography of the discharge,and shadowgraphy visualization of the PSJflowfield are adopted in experiments.Firstly,the discharge process,breakdown voltage,discharge waveform,and electrical circuit efficiency are investigated.Then,the fiow characteristics of the actuator array are presented.

Fig.1Actuator arrays connected in two basic ways.

2.Experimental setup

2.1.Power supply

The power supply used in this paper is a high-voltage pulse capacitive power supply.The circuit diagram of the power supply is shown in Fig.2.According to Ref.33,a CPS creates quicker energy dissipation,so it can produce a more powerful jet which is profitable for high-speed fiow control.The CPS consists of a DC power supply(500 V,1000 W),an Insulated Gate Bipolar Transistor(IGBT),a high-voltage Pulse Transformer(PT,1:20),and an energy-storage capacitor Cd(0.4 lF).The IGBT controls the working frequency of the actuators.In this paper,the working frequency is set to 5 Hz.During the on-state of the IGBT,the PT is powered by the low-voltage DC power supply and then charges the capacitor.When the voltage across the capacitor reaches the breakdown voltage,the pulse arc discharge starts,and the energy in the capacitor Cdis transferred to the arc quickly.During the pulse discharge,the actuator array,the wire,and the capacitor Cdconstitute a serial RLC overdamped circuit.In this study,the serial actuators are aligned,and the distance between the centers of two adjacent orifices is identical(defined as the orifice distance Loin Fig.2).

2.2.Serial actuator array configuration

The serial actuator array shown in Fig.3 is used in this study.Fig.3(a)shows the configuration of the actuator array.A consistent coordinate system is used throughout this paper:x axis is along the line link of the aligned actuator orifice centers,y axis(which is the injection orientation of the PSJ)is parallel to the actuator orifice throat,and z axis is parallel to the anode and cathode.The serial actuator array is composed of n single two-electrode PSJ actuators.The sectional view of a single actuator is shown in Fig.3(b),and the photo of a single actuator is shown in Fig.3(c).A single actuator consists of three components:a shell,a top cap,and electrodes.A cylindrical chamber of diameter D and height H was made from the boron nitride shell.Tungsten electrodes of 1 mm diameter,an anode and a cathode,were positioned in the same plane in the chamber through two small holes.The anode-to-cathode spacing is Le.The distance between the electrodes and the chamber’s bottom is H/2.A cylindrical orifice of diameter d was drilled in the boron nitride top cap.The length of the throat(i.e.,the thickness of the cap)is 3 mm.The electrodes and the wire are welded together.The electrodes,the shell,and the cap are fixed using silicone sealant.

Fig.2Power supply.

2.3.Measurement system

2.3.1.Discharge waveforms

The voltage was measured using a high-voltage probe(Tektronics P6015A,75 MHz,0–20 kV).The discharge current through the anode wire was acquired using a current probe(Pearson 4997,20 MHz,0–20 kA).Voltage and current signals were recorded by an oscilloscope(Tektronix DPO3014,100 MHz,2.5?109samples per second).

2.3.2.High-speed photography and shadowgraphy

Flow characteristics of the PSJ were acquired using high-speed shadowgraph imaging.A standard Z-type shadowgraph setup was used in this study.The light source is a continuous YAG:Nd laser(wavelength k=532 nm,100 mW).Two 200-mm-indiameter f/10 concave mirrors were used to collimate the light through the test section and then imaged on a high-speed framing camera.A Photron FASTCAM SA-X2 with an AF NIKKOR 80–200 mm f/2.8D ED lens was used to capture shadowgraph images.The exposure time was set to 0.368 ls to providean instantaneoussnapshotoftheflow.A synchro-controller(MicroPulse 725)was used to synchronize the pulse discharge with the camera acquisitions.The spatial resolution of the camera was 0.2 mm/pixel,the minimal resolution of the image was 0.5 pixel,and the interval between two successive images was 10 ls.Therefore,the precursor shock and jet velocities measured from the shadowgraph images had an uncertainty of±10 m/s.

The picture of the discharge was captured using a PCO Dimax HD high-speed camera with an AF NIKKOR 60 mm f/2.8D lens.The frame rate of the camera was set to 33.3 kHz.The exposure time was set to 1.4 ls.

3.Experimental results

3.1.Discharge characteristics

3.1.1.Discharge process in serial

In order to visualize the discharge process by a high-speed camera,part of the shell and the cap has to be removed to expose the gap between the anode and the cathode.An experiment has been conducted to determine the influence of the absence of the shell and the cap.Results show very similar breakdown voltages and voltage-current trajectories for the discharges in the open space and the small chamber at a low discharge frequency(5 Hz)in this paper.It is believed that,although there may be some differences(such as the shape of the pulse arc),the discharge characteristics in the two circumstances have certain similarities.The study of the discharge in the open space is helpful for understanding the discharge process of the actuator array in some extent.In the discharge process visualization,a typical experiment of three actuators in serial is conducted,and the electrodes(hereafter referred to as E1–E6)are connected as shown in Fig.4.For clear imaging,the electrodes are fixed in the same plane(the focal plane of the high-speed camera)perpendicular to the ground using an insulating base.The anode-to-cathode gaps are all set to 1.5 mm.The electric potential time histories of the electrodes compared to that of the ground electrode are shown in Fig.5.Since E2 and E3(as well as E4 and E5)are connected by the wire,the difference of the electric potential between them is negligible.Therefore,only the time histories of E1,E2,E5,and E6 are presented.

Fig.3Serial PSJ actuator array and single two-electrode actuators used.

Fig.4Connection and setup of electrodes.

Before the pulse arc discharge is triggered,capacitor Cdis being charged,and the potential of E1 goes up continuously.Because capacitor Cdhasn’t been connected to the ground electrode,the potential of E6 is negative and goes down continuously.E2 and E5 are disconnected to capacitor Cd,so their potentials are close to zero.

At the moment near the trigger,due to a preliminary weak discharge between E1 and E2,a positive pulse of the potential of E2 is induced.The peak potential of the pulse is close to the maximum potential of E1.Similarly,the potential of E5 has a negative pulse,and the peak potential is close to the minimum potential of E6.The pulses of the potentials of E2 and E5 lead to an air breakdown in the middle gap,and then a pulse arc discharge is triggered in all three gaps of the actuators.

After the discharge is triggered,the absolute values of the potentials of four electrodes drop very quickly,and then begin to oscillate,as happening in the single-actuator mode.In the oscillation,the potentials of E1,E2,and E5 have the same phase as the positive of the power supply,and the potential of E6 has the same phase as the negative of the power supply.

Fig.5Electric potential time histories of E1,E2,E5,and E6 compared to that of ground electrode.

Fig.6 shows pictures of the pulse arc discharge captured by the high-speed camera(in Fig.6,t is the time).The pulse arc evolution in one discharge is presented in Fig.6(a).It is seen that,before a pulse arc discharge is triggered(Fig.6(a),t=?30 ls),there are preliminary weak discharges between the two energized electrodes(E1 and E6)directly connected to capacitor Cdand the two suspending electrodes(E2 and E5).At this moment,capacitor Cdis being charged,so electrode E1 has a rising positive electric potential.In the air gap between electrodes E1 and E2,due to the high potential of electrode E1,an inhomogeneous electric field and a weak discharge are created.Near electrode E1,the electric field is stronger,which leads to a higher ionization rate,so the light is brighter in this area.Because capacitor Cdhasn’t been connected to the ground electrode,the electric potential of electrode E6 is not zero but negative.Therefore,a similar inhomogeneous electric field and weak discharge are also created in the air gap between electrodes E5 and E6.

When the voltage between electrodes E1 and E6 reaches about 7.5 kV,a pulse arc discharge is triggered(Fig.6(a),t=0 ls).For the three gaps in serial with the same distance Le,the discharge is similar.At the beginning,the discharge is very strong.The discharge area is difficult to distinguish,and only a bright ‘‘cloud”is observed.To get a clearer image,an optical filter of 10%transmissivity is used,and the unsaturated image at t=0 ls is shown in Fig.6(b).It is seen that the discharge area consists of two basic parts:the plasma core zone in the center and the corona around.

As the energy in the oscillating circuit dissipates gradually,the discharge becomes weak.A filamentary arc surrounded by the corona is observed in the gap(Fig.6(a),t=60 ls).Due to the impact of the inflating and rising hot air created by the adjacent discharge,the shape of the arc is distorted.As the discharge continues,the arc and the surrounding corona become weak gradually and disappear after about 540 and 930 ls,respectively.

3.1.2.Breakdown voltage of pulse arc discharges in serial

The breakdown voltage in serial Ubrefers to the maximum voltage across the actuator array when a pulse arc discharge is triggered.It is an important parameter that determines the performances of the actuators and power supply.A higher breakdown voltage leads to more input energy(i.e.,CdUb2/2)into the actuators,but has more strict requirements for the components,circuit,and capacity of the power supply.In order to investigate the relationship between the breakdown voltage and the number,air gap,and sequence of actuators in serial,different experimental cases were conducted,as list in Table 1,where n represents the number of actuators in serial,and Lsumrepresents the sum of gap distances in serial.The environment pressure is about 99 kPa,and the working frequency is set to 5 Hz.

Typical voltage time histories across capacitor Cdfor different cases are shown in Fig.7.The results show that the breakdown voltage is irrelevant to such factors as the number of actuators n,the maximum or minimum gap in serial,the connection sequence,etc.It is mainly determined by the sum of gaps Lsum.As Lsumincreases,the breakdown voltage becomes higher.When Lsumequals to 1.5,3.0,and 4.5 mm,the breakdown voltage is about 4.1,5.9,and 7.5 kV,respectively.However,the oscillating curves of the voltage after the breakdown are significantly affected by the number of actuators n.This is mainly caused by the difference between the serial resistance and inductance in the circuit.When Lsumis constant,as n increases,the oscillating amplitude of the voltage becomes higher notably,and the period of the oscillation decreases slightly.Moreover,when n reaches to a certain number,the oscillation becomes abnormal at the later period of the discharge,as shown in Cases 8 and 9 of Fig.7.

Fig.6Pictures of pulse arc discharge captured by high-speed camera.

Table 1Experimental cases.

3.1.3.Electrical circuit efficiency in serial

For a constant Lsum,the breakdown voltage and input energy are not affected by the number of actuators in serial.However,owing to the difference between the serial resistance and inductance in the circuit,the voltage-current curves are significantly affected,which leads to an alteration of the electrical circuit efficiency.Typical current time histories in serial circuit for three different cases are shown in Fig.8.In the three cases,Lsumis set to 3 mm,but n is 1,3,and 6,respectively.It’s shown that,as n increases,the period of the oscillation decreases,and an abnormal oscillation occurs,like the voltage curves.Moreover,the peak current also decreases.For an ideal serial RLC overdamped circuit,the peak current is described as follows:

where C is the overall capacitance of the serial circuit,L is the overall inductance,and R is the overall resistance.Because the capacitance of the wire and arc is very small compared to that of capacitor Cd,the capacitance of the serial circuit C is mainly determined by that of capacitor Cd.On the other side,the inductance and resistance are mainly determined by those of the wire and arc.As n increases,the length of the wire increases.The inductance Lwand resistance Rwof the wire(which are basically proportional to the length of the wire)increase.However,the capacitance C is almost constant.As a result,the peak current decreases.

Fig.7Typical voltage time histories across actuator array.

The electrical circuit efficiency of the actuators in serial is defined as follows16:where Eais the energy of the arc,Ecis the energy in the energystorage capacitor Cd,ujis the anode-to-cathode voltage of the jth actuator,and i is the discharge current of the serial circuit.It should be noted that tjis the duration of the discharge of the jth actuator,which is determinate for a discharge,andis the integration of the discharge powerfrom the time of the breakdown to the time of the end of the discharge,which is not time-dependent.Therefore,although there is tjin the expression of gd,the efficiency gdis not time-dependent.

Fig.8Typical current time histories in serial circuit.

According to this definition,for n actuators in serial,if we want to calculate the discharge power and then take the integral,we will have to measure i,u1,u2,...,unat the same time during one discharge.However,the high-voltage probes that we have are not enough.Therefore,to calculate the efficiency,we use the following equations:where Ewis the energy dissipated in the wire.In this way,we only need to measure one current signal and one voltage signal during the discharge.The discharge efficiencies of different cases are calculated,as shown in Table 2.It is seen that,as n rises,an increase of the parasite resistance in the wire leads to a decrease of the arc energy.As a result,the electrical circuit efficiency is reduced slightly.

3.2.Flow characteristics

3.2.1.Flow characteristics in serial

A typical fiow evolution of PSJs in serial is shown in Fig.9.Three identical actuators are used.The diameter D and height H of the chamber are 5.4 and 8.6 mm,respectively,so the volume V is about 207 mm3.The orifice diameter d is 2 mm,and the anode-to-cathode spacing Leis set to 1.5 mm.The actuators are parallel,and the distance between the centers of two adjacent orifices Lois 15 mm.

As seen in Fig.9,three mushroom-shaped jets(Jets A,B,and C)as well as spherically symmetric precursor shocks(Shocks A,B,and C)are generated.The generations of PSJs and precursor shocks are synchronous,and the shapes of the jets are similar.Time histories of the heights and velocities of the jet fronts and the precursor shocks are plotted in Fig.10.It is seen that the time histories of the jet fronts(which indicate the speeds of the jets)are nearly coincident(Fig.10(a)).Due to the entrainment and friction of the jets developing downstream,the jet fronts slow down with an increasing distance from the jet exit,which indicates that the jet velocities are decreasing with time(Fig.10(b)).Because the distance between adjacent orifices is relatively far,the interaction between PSJs is insignificant.Before 400 ls,three jets seem to be separate.After 400 ls,the jets begin to contact.However,at this time,the strength of the vortexes in the jets has become weak,sothe entrainment effect is not significant.The three jets seem to move downstream in parallel.At the beginning,three separate spherically symmetric precursor shocks are generated(Fig.9(a)).The precursor shocks firstly expand at a supersonic speed,but soon afterward,the precursor shock speed decelerates to the local sound speed(?350 m/s)and then keeps nearly constant over time.With expansion,the three shocks begin to intersect with each other(Fig.9(b)).In the interaction,the three shocks begin to merge together gradually(Fig.9(c))and transform into a new shock(labeled as ‘‘merged shock”in Fig.9(d))which continues to migrate downstream at the former constant speed(Figs.9(e)–(f))and 10(b)).

Table 2Electrical circuit efficiency of actuators in serial.

3.2.2.Influence of orifice distance

For fiow control application,the arrangement of the actuator array is one of the important parameters that determine the control effect.In this study,aligned actuator arrays with a wide range of orifice distances have been investigated.Due to the very weak interaction between adjacent jets,the jet shape and velocity will be very similar when the orifice distance exceeds 12 mm,so here only the results of four different orifice distances(Lo=2.75,6,9,and 12 mm)are presented.The volume of the actuator chamber is about 220 mm3,the orifice diameter is 3 mm,and the anode-to-cathode spacing is set to 1 mm.It should be noted that,when Lois 9 mm and 12 mm,the actuator array consists of three separate actuators as shown in Fig.3(a),so it has three separate chambers.The chambers,orifices,and three pairs of anode and cathode are all aligned in the x axis direction.However,when Lois 2.75 mm and 6 mm,the three actuators are too close,so they are integrated rather than separate.The two-electrode PSJ actuator array shares one chamber which has a larger size in the x axis direction,and the six electrodes are all in the same chamber.In this case,to make heating of the air in the chamber uniform,the three pairs of anode and cathode should still keep aligned in the x axis direction.

Fig.11 shows the shadowgraph images of PSJs for different orifice distances.When Loequals to 2.75 mm,the three orifices are intersected.The precursor shocks merge into one ellipsoid shock at the beginning.The three jets merge together into a wider rectangular jet which is similar to a ‘‘slot plasma synthetic jet”25.When Loequals to 6 and 9 mm,the three jets are separate at the beginning.As migrating downstream,the jet fronts begin to expand and approach.Due to the strong entrainment,they merge together gradually and transform into a single large vortex,but the jets close to the exit are still separate.The longer the orifice distance is,the later the merge happens,and the weaker the merging effect is.When Loincreases to 12 mm,no merging is observed,and the three jets keep separate in the whole process.

Fig.9Flow evolution of three PSJs in serial.

Fig.10Time histories of heights and velocities of jet fronts and precursor shock.

Fig.11Shadowgraph images of PSJs for different orifice distances.

Fig.12Time histories of heights of jet fronts for different orifice distances.

Time histories of the height of the jet front for different orifi cedistances are shown inFig.12.Itis observedthat,as the orifi ce distance decreases,the average speed of the jet front increases.The variety of the speed is caused by merging of the jet front vortexes.At the beginning,the heights of the jet front for 6,9,and 12 mm orifice distances are basically the same.However,for 6 and 9 mm orifice distances,as the jet front vortexes merge,the jet front speeds increase,so the heights successively(at about60 lsfora6 mmdistance and120 lsfora 9 mm distance)exceed the three separate jets of a 12 mm distance.Meanwhile,due to the greater merging effect,the jet front of a 6 mm orifice distance is significantly higher than that of a 9 mm orifice distance.For a 2.75 mm orifice distance,merging occurs at the beginning,so the jet front height is the highest in the whole process.Because the actuator array is made up of singleactuators,when the interaction between the jets isnegligible,the performance of the actuators is like the performance of a singleactuatoroperating alonewiththesamepowerdeposition.Therefore,it is believed that,in this case,the performance of actuators with a 12 mm orifice distance can be a representative of a single actuator’s performance which has the same power deposition.It is seen that,due to the entrainment of an adjacent turbulent jet,a combination of actuators actually performs better than one actuator alone.The jet front velocity will increase monotonously as the orifice distance becomes smaller.

3.2.3.Influence of orifice diameter

With the chamber volume,the anode-to-cathode spacing,and the orifice distance kept at 440 mm3,1 mm,and 15 mm,respectively,PSJ actuator arrays of 5 different orifice diameters(d=1,2,3,4,and 5 mm)are investigated.Shadowgraph images are shown in Fig.13,and time histories of the heights of the jet fronts are shown in Fig.14.

It is shown that,when d equals to 1 mm and 2 mm,the precursor shock is very weak and almost invisible.As d increases,the precursor shock becomes stronger.The jet is a vortex ring at the beginning(Fig.13(a1)–(a5)),and the width of the vortex ring equals to the orifice diameter d.The vortex ring transforms into a continuous turbulent jet gradually.The width of the turbulence increases as d becomes larger(Fig.13(b1)–(b5)).

The influence of the orifice diameter on the jet speed is significant.The previous study conducted by Zong et al.39showed that,as the orifice diameter enlarges,the jet front velocity increases.However,this relationship is not always valid.When d is very small,the blocking effect of the boundary layer in the throat is significant.As d becomes larger,the jetflow rate increases sharply,and the jet velocity will also increase.However,when d reaches a critical value,due to the limitation of the actuator,the jet fiow rate is near saturation.As d increases further,the jet velocity will decrease.To achieve the highest jet front velocity,there is an optimal orifice diameter(which is mainly determined by the input energy and the chamber volume).As shown in Figs.13 and 14,for the actuators used in this experiment,the optimal orifice diameter is around 3 mm.

Fig.13Shadowgraph images of PSJs for different orifice diameters.

Fig.14Time histories of heights of jet fronts for different orifice diameters.

Fig.15Time histories of velocities of jet fronts for different orifice diameters.

Fig.15 shows time histories of the velocities of the jet fronts for different orifice diameters.It is seen that,when the orifice diameter is smaller than 3 mm,the jet front speed increases to a peak at first and then decreases gradually.The jet front speed is relatively low at the beginning of the ejection,and the air seems to be choked.The smaller the orifice is,the longer the choke lasts,and the later the jet front reaches the peak speed.When the orifice diameter is larger than 3 mm,the choke is not significant,and the jet front reaches the peak speed immediately after the ejection.

4.Discussion

For a DBD or DC glow discharge actuator,a large-area discharge can be generated to have a wide control area in theflowfield.However,the characteristic of a PSJ actuator is very different.The energy deposition is more concentrated for the pulse arc discharge of a PSJ actuator.Moreover,to generate a high-speed jet which can penetrate the supersonic boundary layer,a large orifice(such as a large-aspect ratio exit slot)is not suitable.Therefore,a single-PSJ actuator usually has a very small affected area,which is one of the most critical limitations for its application.In this paper,we achieve the direct serial working mode of multi-two-electrode PSJ actuators.Compared to a parallel array and an actuator array based on a voltage relay by a group of parallel resistances and capacitors,the best advantage of a serial array is its simpler construction and less weight.Moreover,experiments show that a serial actuator array doesn’t lead to a significant decrease of the electrical circuit efficiency.

However,a serial array also has its disadvantage.Unlike a parallel array and an actuator array based on a voltage relay,the breakdown voltage of a serial array increases with the sum of gap distances,which will limit the total number of actuators in serial.One solution is a serial-parallel hybrid connection actuator array.Otherwise,like a three-electrode PSJ actuator,a trigger electrode may be used to generate a low-power spark discharge which can trigger the main discharge between the anode and the cathode at a lower voltage.In the preliminary experiments,we find that when a trigger electrode is added in actuator 1 as shown in Fig.2,the main discharge can be triggered at a lower voltage sometimes,but a strong discharge is also easy to occur between the anode of actuator 1 and the trigger electrode,which will damage the power supply system.An innovative circuit design needs to be studied in the future.

The investigation on the discharge process is a focal point in this paper.The breakdown is considered as a result of weak preliminary weak discharges between energized and suspending electrodes.This will lead to a potential difference and breakdown between the suspending electrodes.However,due to a limited view field of the camera at such a high frame rate,we only investigate the case of three actuators in serial.It is still an open question whether a serial array with more actuators has a different breakdown mechanism.

5.Conclusions

In this paper,the discharge and fiow characteristics of a serial two-electrode PSJ actuator array using a high-voltage pulse capacitive power supply are investigated experimentally.

The serial discharge evolution is captured using a highspeed camera for the first time.For a typical serial array of threeactuators,preliminaryweak dischargesarefound between energized and suspending electrodes before the pulse arc discharge.The breakdown mechanism is referred as the pulse of the potential of the suspending electrodes induced by these preliminary weak discharges.The breakdown voltage in serial Ubis irrelevant to such factors as the number of actuators n,the maximum or minimum gap in serial,the connection sequence,etc.It is mainly determined by the sum of gaps Lsum.When Lsumis identical,the electrical circuit ef ficiency and peak current decrease slightly as the serial actuator number increases.

For serial actuators with the same Le,due to similar energy deposition,the generations of three PSJs are synchronous,and the shapes of the jets and precursor shocks are similar.The precursor shocks firstly expand at a supersonic speed,but soon afterward,their speeds decelerate to the local sound speed and then keep nearly constant over time.With expansion,they begin to interact and transform into a new ‘‘merged shock”.When the orifice distance is large,the jets of the actuator array have little interaction and develop separately and independently.As the actuators become closer,entrainment and merging will happen and speed up the jet front.The closer the orifice distance is,the earlier the merging happens,and the larger the average velocity of the jet front is.When the orifice distance is close enough to become interested,the jets will merge at the beginning and become a wider rectangular jet similar to a ‘‘slot plasma synthetic jet”.The orifice diameter has a more complicated influence on the jet front speed,and there is an optimal orifice diameter to achieve the highest jet front velocity.This is because when the orifice diameter is small,the blocking effect of the boundary layer in the throat is significant so the increase of the jet mass fiow rate is dominant.After the orifice diameter reaches the critical value,the increase of the orifice sectional area becomes dominant,so the jet front velocity decreases with the orifice sectional area.

Acknowledgements

The present research was supported by the National Natural Science Foundation of China(Nos.11372349,11502295,and 11572349).