Exp Fluids (2007) 43:603–616 DOI 10.1007/s00348-007-0344-9

RESEARCH ARTICLE

Control of an axisymmetric subsonic air jet by plasma actuator N. Benard Æ J. Jolibois Æ M. Forte Æ G. Touchard Æ E. Moreau

Received: 2 March 2007 / Revised: 6 June 2007 / Accepted: 7 June 2007 / Published online: 10 July 2007
Springer-Verlag 2007

Abstract It is known that surface non-thermal plasma actuators have proved their efficiency for aerodynamics flow control. In this study, a dielectric barrier discharge (DBD) is mounted on the diffuser of an axisymmetric turbulent air jet in order to control the flow separation along a 12-degree diffuser bevel. The momentum created by the actuator is applied to separate an air flow naturally attached to the diffuser for air flow velocity up to 40 m s–1. Laser sheet visualizations and LDV measurements are achieved to characterize the unforced and forced air jet. The flow separation, the induced velocity fluctuations, the jet mixing improvement and vectoring are investigated. The main results of this study demonstrate that DBD actuators are suitable to fully detach the air flow along the bevel for a velocity of 20 m s–1 and that a jet vectoring between 13.5 and 5.5 could be achieved for velocity ranging between 20 and 40 m s–1. Considerations about a potential improvement of the jet mixing are also introduced and the laser sheet visualization attests that induced flow perturbations are highly 3D.

1 Introduction The aeronautic industry has keen interest in the improvement of both military and civil aircrafts. While the civil

N. Benard (&)
J. Jolibois
M. Forte
G. Touchard
E. Moreau Laboratoire d’Etudes Ae´rodynamiques, Bld Marie et Pierre Curie, 86962 Chasseneuil, France e-mail: [email protected]

sector is waiting for economic and environmental progress (exploitation cost, pollution and noise reductions), the military sector looks for enhanced performance directed towards the furtivity and the manoeuvrability of aircrafts. This performance increase generally requires the control of the shear layer around profiles, of air jets or at the reactor exhaust. This study in particular deals with the free shear layer developed downstream of an axisymmetric air jet with a diffuser exit. Round free jets are characterized by two flow regions: the free shear layer and the surrounding region. The radial increase of the free shear layer is promoted by the viscous diffusion and the convection of the large coherent structures. These large eddies interact with the mixing layer at the macroscopic level, while small scale turbulence induces microscopic disturbances (at a molecular scale). The control of the free shear layer often requires generating local 3D flow perturbations acting on the coherent structures and their ruptures for small scales turbulence creation. The control of a round air jet thus requires an intensification of the energy transmission through various flow scale structures. The manipulation of the air jet at the motor exhaust concerns both spreading of the mixing layer and jet vectoring. The spreading of the mixing layer has effects on the pollution, noise level and infra-red signature. Jet vectorization allows an increase of the flight manoeuvrability but it also allows to decrease the pollution by accelerating the take-off and landing phase by control of the motor engine thrust. Two flow control strategies coexist, one being ‘passive’ while the second is generally qualified as ‘active’. The passive methods consist in modifying the jet exit geometry (by vortex generator or tabs) in a permanent way which confers a new jet structure including large longitudinal

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vorticity and 3D flow deformations but passive control is only optimized for a specific flight phase. The permanent character of these devices could be compatible with the reduction of noise (Bridges et al. 2003; Papamoschou 2004) or the spreading of the mixing layer (Bohl and Foss 1996) but are generally limited by a thrust loss (Zaman et al. 1994). These methods are moreover unsuited with the vectorization of jet because they imply complex mechanical systems, increasing the aircraft weight and the global maintenance costs. The second actuator category is defined as active with a non-permanent control by addition of mass flux (or zero mass-flux) and energy to the flow structure for instance. This category includes various efficient actuators concept as acoustic exciters, mechanical devices and fluidic jets. Acoustic waves were used to directly modify the coherent flow structures and indirectly interact with the dissipative scales. These devices are particularly used for spreading enhancement via high frequency excitation or via jet forcing at the fundamental or sub harmonic flow frequency (Ng and Bradley 1988). The use of piezo-electric actuators generates synthetic jets (zero mass flux), which excite the flow at high frequencies (1,200 Hz) and thus force the dissipative structures directly (Davis and Glezer 2000). Another active mixing enhancer system consists in injecting flow parallel to the primary air jet (via a specific nozzle) in order to destabilize the jet (Papamoschou 2000). The coherent structures could also be manipulated using small jets, which create an increase of the longitudinal vorticity in particular if the jet is forced at the proper frequency identified at the end of the potential core (Denis et al. 1999). Concerning the vectorization of air round jets, most of the flow control devices are based on the Coanda effect, which is the tendency of a moving fluid to attach itself to a surface and flow along it. According to Strykowski et al. (1996), a secondary flow in opposite direction to the main air jet allows to separate the primary flow along a collar and creates a jet vectorization of 16 at supersonic regime (M = 1.2). Pack and Seifert (2001) also design a vectorization device, based on periodic excitations (300–700 Hz) on a part of the circumference of the turbulent jet, which improves the expansion rate of the jet and its capacity to be reattached on the manipulated region. Ben Chiekh et al. (2003) coupled a passive device (an exit equipped with a large angle diffuser) and an active system (synthetic jet), the flow being naturally separated of the walls of the large angle diffuser. The synthetic jets placed in the direction of the primary flow (at the bevel angle between the jet exit and the beginning of the diffuser) permit to attach the flow along one lip of the diffuser. A local singular action or two simultaneous actions in opposite positions result, respectively, in a mixing increase or a jet vectoring.

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According to these considerations, an optimal control device must limit the thrust loss, allow a large frequency excitation range, avoid weight addition and provide secured mechanisms without generation of noise or vibration. These conditions could be achieved by control devices based on non-thermal surface plasma technology. The actuation by surface plasma, although bringing a momentum largely lower than the main flow, however allows flow control over various bluff bodies. Corona discharge (CD) and surface dielectric barrier discharge (DBD) are two electrofluidodynamic actuators suitable for the control of flow separation and reattachment. These actuators are generally composed of at least two electrodes between which, a high voltage is applied. Charged particles (ions) appear in the inter electrode space and the momentum transfer from the ionized particles to the neutral atmospheric air component produces a local flow of a few m s–1 called ‘ionic wind’ (Roth et al. 2000; Leger et al. 2001 for instance). This local velocity usually flows tangentially to the dielectric wall which supports the two electrodes and allows to manipulate the boundary layer. Plasma actuators transform electrical power to flow velocity and add momentum in the shear layer without moving parts. According to Forte et al., the momentum addition begins in a few milliseconds (10 ms) following the beginning of the actuation (Forte et al. 2006b). Simultaneous manipulation of the coherent structures and the small scale turbulence could be achieved using a modulation of the input signal. The electrical signal waveform and frequency are transmitted to the ionic wind (Forte et al. 2006b), highfrequencies (up to 500 kHz according to Fridman et al. 2005) acting on the small scale structures (at the Kolmogorov scale) can consequently be produced. All of these advantages have expanded control by plasma actuators for various subsonic aerodynamic academical and industrial flows. Different authors in America and Europe have demonstrated that the separation and the reattachment processes over an airfoil at high incidence could be controlled by DC and AC actuators, both leading to better flight performances (lift increase and drag decrease) (Corke et al. 2006; Sosa et al. 2007; Jolibois et al. 2006). The boundary layer separation at the edge of a cylinder can also be manipulated via CD (Artana et al. 2003) or DBD (McLaughlin et al. 2006), with vortex shedding frequency directly triggered with the imposed signal. Flow manipulation of the boundary layer surrounding a flat plate in incidence (Leger et al. 2001) or not (Hultgren and Ashpis 2003; Moreau et al. 2006; Grundmann et al. 2006) were experimentally investigated for external velocity up to 25 m s–1 with promising results concerning momentum addition, flow separation, flow reattachment, drag reduction and delay of the turbulent transition. A wide review concerning

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non-thermal plasmas and their use for flow control has been recently published by Moreau (2007). However, only two main publications dealing with the control of an air jet by surface plasma actuators are available to date. The first one, published by Corke and Matlis (2000), investigates phased plasma actuators to generate unsteady vortical disturbances in order to prevent and delay the boundary layer separation along the jet diffuser. They conclude that their actuators have few effects on the timeaveraged velocity but the velocity fluctuations are strongly increased. A rectangular subsonic jet with a small angle diffuser was investigated by Labergue et al. (2007). The flow naturally attached to the diffuser bevel is separated using a DBD actuator placed on the bevel in counter-flow blowing. This paper highlighted by Particle Image Velocimetry (PIV) the ability of the DBD actuator to separate the flow (the airflow is partially detached for a maximal velocity of 30 m s–1) using the produced tangential ionic wind (up to 5 m s–1). New data about the induced 3D flow perturbations are also introduced with the detection of vortex formation over the entire width of the active electrode. In this study, we focus on the flow separation along the bevel of an axisymmetric air jet equipped with a small angle diffuser (a = 12). The flow naturally attached is detached using a surface DBD actuator placed on the bevel in counter-flow mode. Velocity range between 20 and 40 m s–1 is investigated using smoke visualizations and quantitative data are obtained by bi-component LDV. The separation process, velocity fluctuations, deviation angles and the width of the jet under DBD excitation are studied.

the second, which constitutes the air jet exit. This second part is removable and it modifies the jet exit configuration. In this study, the jet diameter upstream of the diffuser is 50 mm. The diffuser has a small angle (12 relative to the jet direction), the bevel is 30 mm long and the resulting exit diameter is 62.5 mm. All the pieces are made of a dielectric material (vinyl polychloride). In this configuration, the air flow is naturally attached to the bevel for jet centreline velocity ranging between 10 and 40 m s–1. The Reynolds number (at 20C and at atmospheric pressure conditions) based on the diameter upstream of the diffuser (D = 50 mm) varies between 64,100 and 128,200 for airflow velocity ranging between 20 and 40 m s–1. A circular rough band made of aluminium oxide (h = 350 lm) is stuck 200 mm upstream the diffuser exit in order to impose the laminar to turbulent transition. The effects obtained by the DBD actuator are consequently not due to the transition and results should be applicable for higher Reynolds numbers.

2 Experimental set-up

2.3 Pitot measurements

2.1 Jet and nozzle configurations

The easiest way to quantify the produced ionic wind consists in using a time-averaged glass dielectric Pitot tube measurement (dpitot = 0.5 mm). The mean pressure and the resulted velocity are obtained using a Furness FC014 manometer which allows 0–98 Pa measurements. The

The axisymmetric jet nozzle is composed of two independent parts (Fig. 1). One is called the injector and support

Fig. 1 Jet and diffuser geometry

2.2 The wind tunnel facility The low speed wind tunnel facility is a circular open-air type with a 0.132 m2 cross-section. It has a 1.45 m long chamber (five honeycombs are located 0.5 m downstream the exit of the fan) (Fig. 2b). The circular jet exit of 50 mm (Fig. 2c) is obtained by means of a contraction outlet (contraction ratio of 1:17), which improves the flow uniformity. The air flow is driven by a centrifugal fan (FEVI F18G-1R-500, France) with eight radial blades rotating at a maximum rpm of 3,000 delivering 0.3 m3 s–1 (Fig. 2a). A maximum velocity ejection of 45 m s–1 can be reached with this open wind tunnel.

Fig. 2 Schematic view of the wind tunnel

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analogue output is numerically transformed by an A/D converter (Keithley KUSB-310B, Cleveland, OH, USA) at a frequency of 200 Hz integrated for 4 s (800 samples), permitting the statistical convergence of the computed velocity. 2.4 High speed digital visualizations Flow visualizations are performed using a short-pulsed laser in order to enhance the image quality by illuminating the flow structures with ultra-short pulses of light. Laser sheet take a 2D slice through the 3D flow. The experimental system is composed of a pulsed Nd: YLF laser that generates a visible green light (k = 527 nm) at 50 mJ per pulse. A combination of concave and cylindrical lens converts the laser beam of about 4 mm diameter into a 0.8-mm-thick sheet near the centre. Five hundred frames at a recording rate of 923 frames per seconds (resolution of 1,024 · 512 pixels) are taken with a high speed CCD camera (VDS, HCC-1000, 35 mm Nikkor lens, La Jolla, CA, USA). A fog generator (Deltalab, EI511) atomizes pharmaceutical oil (Deltalab, Ondina 15) into fine droplets (ddroplets = 0.5–2 lm) dedicated to the laser light scattering and the produced smoke is injected into the centrifugal fan. The smoke quantity is adjusted with a manual pressure reducer. Images with exposure duration between about 0.5 and 3 ls are obtained by synchronizing the laser with the camera shutter. The flow structures of the air jet are observed and recorded by utilizing the laser illumination, either along a stream-wise plane (O, X, Y) or on cross-stream planes (at x = 50 mm) forming a 90 angle with the jet axis (O, Y, Z) (Fig. 3). Snapshots, time-averaged and rms images are processed by the help of the commercial software Davis v7. 2.5 Bi-components Laser Doppler Velocimeter Time-averaged velocity and turbulent components are measured with a bi-component laser Doppler velocimeter (LDV). The light source is a 5 W Argon–ion laser. Blue

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and green beams (wavelengths of 514 and 488 nm, respectively) composed the two measurement volumes (the diameters of the probe volume in the radial and the streamwise direction are 3 and 0.2 mm, respectively). The optical system is fixed on a micrometric displacement system (±0.01 mm) and measurements are performed over a spatial range of four nozzle diameters in the Ox direction. The sampling frequency varies between 10 and 20 kHz and 40,000 bursts are stored for each acquisition point. The acquisition duration is fixed to 20 s. Data are computed with a flow velocity analyser provided by Dantec Dynamics, Skovlunde, Denmark. Sources of error include optical, statistical and positional, the uncertainty in the measurement of the beam half angle coupled with the error on the burst counter corresponds to an uncertainty of 0.8% of the velocity fluctuations. For all the LDV measurements, the origin is located at the diffuser exit, at the intersection of the vertical and horizontal symmetry planes (see Fig. 3).

3 The DBD actuators Corona discharges and DBD are commonly used as plasma actuators for air flow control. In both cases, the velocity profiles induced by both discharges are nearly similar (Moreau 2007). However, in this study a surface DBD is preferentially chosen for different reasons. Contrary to the CD which may present filamentary discharges and sparks, the DBD is characterized by a more stable and homogeneous discharge over the whole surface. The arc transition is prevented by the dielectric barrier and the micro discharges are uniformly distributed in time and space between the sheet electrodes. It is also less sensitive to environmental parameters (Moreau 2007). According to the recent research of Boeuf et al. (2007), and as previously observed experimentally by Pons et al. (2005), the electrohydrodymanic time averaged force per unit volume for a DBD actuator is concentrated in a thin layer of ~2 mm. These actuators seem to be particularly efficient for a targeted control of the shear layer over bluff bodies because the force created by the control device generally needs to be located near the reattachment or the separation point occurring close to the wall. 3.1 The DBD configuration

Fig. 3 Coordinate system

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In this study, the surface DBD is generated between two thin aluminium electrodes (e = 0.1 mm) separated by a 3-mm-thick dielectric (vinyl polychloride with a relative permittivity value of 5) (Fig. 4). The active and grounded electrodes are designed to reach a maximal ionic wind for a moderate dielectric thickness. The electrode configuration takes into account recent research concerning the

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generated by a HV power amplifier TREK 30/20A (20 mA, 20 kHz).

4 Results and discussions 4.1 Electric characteristics of the dielectric barrier discharge Fig. 4 Schematic view of the DBD actuator

optimization of ionic wind production established by Forte et al. (2006b) in our lab. They recommended the use of large electrodes (~20 mm) and small gap (0–5 mm). The grounded electrode is encapsulated with silicon gel avoiding the production of secondary ionic wind below the dielectric barrier. Details of the retained DBD configuration are summarized in Table 1. 3.2 Location of the DBD electrodes The active electrode is placed tangentially at the lip of the diffuser and its span-wise length is 40 mm (Fig. 5). The DBD action takes place in ~1/4 of the exit circumference (90) because manipulation of flow on a half diameter has proved to be not more efficient in term of jet vectoring for control with fluidic jet (Collin et al. 2005). The active electrode is placed in contact with the primary air jet when the grounded electrode is on the outer nozzle surface. Fifty per cent of the grounding electrode width is stuck on the external edge of the diffuser. The discharge only occurs on the upstream side of the inner electrode and presents a 6 cm2 surface. In this configuration, the produced ionic wind occurs in a counter-flow mode allowing a pressure gradient increase (in the azimuthal direction) and a flow separation along the bevel of the diffuser. 3.3 The electrical devices The outer electrode is grounded and the non-thermal plasma is generated by exciting the active electrode with an AC sine wave high-voltage (HV) at a frequency of 1.5 kHz and peak-to-peak amplitude of 40 kV. The signal is Table 1 Electrode configuration Dielectric thickness

3 mm

Electrodes thickness

0.1 mm

Active electrode width

15 mm

Ground electrode width

20 mm

Inter-electrodes space

5 mm

Electrodes length

40 mm

The experimental behaviour of voltage and current versus time is presented in Fig. 6. The primary remark concerns the tension wave form, which is slightly deformed at the peak HV due to the low value of the slew rate of the HV amplifier (slew rate of 500 V ls–1). The current signal alternates high peak pulses during positive half-cycle and many pulses with smaller amplitudes during the negative one. In fact, on one hand, it seems that the discharge acting during the positive half-cycle behaves nearly like a typical positive corona, with streamers and then current peaks. Moreover, it seems that it is more filamentary than the discharge acting during the negative half-cycle. On the other hand, the discharge acting during the negative halfcycle seems to be more diffuse, and produces a higher velocity than the one produced by the positive corona (Forte et al. 2006a). Figure 7 presents electrical result concerning the electrical power consumption for various applied voltages. As previously reported by different authors (Enloe et al. 2004; Pons et al. 2005; Roth and Dai 2006), the electric power consumption versus HV relation exhibits a power-law behaviour. The data introduced in Fig. 7 demonstrate that non-thermal plasma actuators require a moderate supplied power (4.8 W at ±20 kV and 1.5 kHz). 4.2 Characterization of the produced ionic wind The wall tangential velocity induced by the electric wind is measured using the method introduced in Sect. 1.3. Data are acquired without external air stream. The HV is fixed at ±20 kV and frequency is 1.5 kHz. Acquisitions are performed for various x¢ positions in the ox¢y¢ system, the reference point being located at the diffuser beginning in the median plane of the electrodes (Fig. 8). These positions cover the whole bevel length of the diffuser. For x¢ < 14 mm, all the velocity profiles have a similar behaviour with a maximal velocity located close to the wall at y¢  0.5 mm. An induced air flow exists until a wall distance y¢ equal to 5 mm (5 mm far from the wall). The maximal velocity occurs 8 mm upstream of the end of the active electrode and presents an absolute peak value of 6.2 m s–1 at y¢ = 0.5 mm (Fig. 9). A velocity increase could be achieved by applying higher voltage or frequency but glow to arc transition could then damage the dielectric. It is important to keep in mind that these Pitot

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Fig. 5 Schematic view of the electrode placement for a counter-flow ionic wind

Fig. 6 Measure of the voltage and current temporal evolution at the electrode edges Fig. 8 Velocity profiles along the diffuser wall for ±20 kV at 1.5 kHz

also above the active electrode. For our DBD configuration, this characteristic could be responsible of a small mass transfer from the potential core of the free jet toward the shear layer at the bevel. 4.3 Visualizations by high speed camera

Fig. 7 Time-averaged electrical power consumption for various high-voltage for f = 1.5 kHz

measurements only indicate and quantify the velocity component (parallel to the wall) of the ionic wind. Bicomponents LDV measurements have demonstrated that the secondary velocity component (perpendicular to the wall) induced by the actuator is not null (Moreau 2007). The discharge induces a low pressure region at the wall but

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The image processing consists in computing the timeaveraged and the fluctuations of the digitalized images, both based on a grey-scale analysis. Figure 10 presents the laser sheet visualizations along the stream-wise direction for air jet velocity of 20, 30 and 40 m s–1. Snapshots, timeaveraged and rms images are simultaneous plotted for a free jet exit and a manipulated jet. The DBD actuator is systematically located at the upper 1/4 of the diffuser circumference (±45 from the top). According to the structural characteristic of an axisymmetric air jet in a static external environment, the potential core of the jet is surrounded by a turbulent mixing layer. These regions are merged in laser sheet visualizations and the analysis of the snapshot and the time-average is somewhat subjective. The main relevant data concern the

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Fig. 9 Velocity profiles for the maximal velocity induced by ionic wind (at x = 8 mm)

grey-scale fluctuations around the mean value. A qualitative overview of a potential mixing enhancement could be visualized. The snapshot demonstrates that the flow is naturally attached at the bevel for each investigated velocity. When the high voltage is supplied between the DBD electrodes,

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flow is deflected downstream for velocity of 20 and 30 m s–1 in particular at one diameter distance. Air flow is also deflected at the lower part of the diffuser and contrary to the upper region, the flow structure seems more organized with larger eddies now. For a velocity of 40 m s–1 an analysis based on the snapshot is hazardous but the DBD action appears to be limited. The jet deflection is also apparent on the time-averaged images for the two lowest velocities. The deviation angle appears to be constant for a distance equal to two diameters. A jet vectorization for the highest air flow speed is not present. The velocity fluctuations based on grey-scale analysis are more suitable for the analysis of the plasma actuator effects on the free shear layer. The upper shear layer is larger for each flow velocity when ionic wind is produced. The small addition of momentum induced by the discharge appears sufficient to enhance the mixing process even at the maximal air jet velocity. The lower shear layer presents an opposite behaviour with a noticeable width reduction. Visualizations in a plane perpendicular to the direction of the primary flow were also performed at a distance of 50 mm of the jet exit (Fig. 11). The snapshots present the characteristic structures of a turbulent shear layer in the

Fig. 10 Snapshot, timeaveraged and rms images based on grey-scale analysis. The DBD actuator (E = ±20 kV, f = 1.5 kHz) is placed in the upper part of the diffuser

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span-wise direction with a mix of coherent structure and small scale eddies without an apparent azimuthal mode. For these results, the qualitative data about the flow separation are most visible on the time-averaged visualization. First, a slight dissymmetry exists, the airflow is attached to the edges of the diffuser except for the diffuser perimeter where is located the active electrode. This electrode locally perturbs the air flow and creates a flow detachment 1–2 mm upstream the end of the diffuser. Under plasma excitation the flow is detached from the bevel for a perimeter equal to twice the electrode length. The discharge expands and increases the flow detachment

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at 20 and 30 m s–1, but no effect is identifiable at 40 m s–1. The rms images systematically present an annular region of fluctuation. The actuation by DBD results in an enlargement of the upper mixing layer and a width reduction of the lower mixing region. We also notice a slight deviation of the lower mixing layer. The jet could be vectored due to the separation occurring at the upper part of the diffuser wall, combined with the effects of the enhanced mixing at the upper side. Contrary to the longitudinal views, the variation in the shear layer structure due to the plasma is not clear for the highest velocity. 4.4 Characterization of the baseline profiles by LDV measurements

Fig. 11 Snapshot, time-averaged and rms images based on grey-scale analysis for span-wise visualizations. The DBD actuator (E = ±20 kV, f = 1.5 kHz) is placed in the upper part of the diffuser

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The distribution of the normalized time-averaged velocity using LDV at the exit plane of the primary air jet (x/D = 0.1) for three Reynolds numbers are plotted in Fig. 12. The flow is symmetric and the shapes of the timeaveraged velocity profiles are similar over the velocity range tested. The analysis of the rms velocity fluctuations indicates that the peak turbulence level in the shear layer remains constant over the Reynolds numbers investigated (turbulence intensity of 15%) except at the lower part of the diffuser for an air jet velocity at 40 m s–1. In this region, a turbulence peak appears with local turbulence intensity up to 100% greater than the mean turbulence level. This fluctuation increase is related to instabilities at the lower part of the diffuser at which successive flow separations and reattachments occur. This phenomenon is certainly due to the circular roughness which could induce imperfections in this region. The potential core turbulence level is around 3–4%. The velocity profiles of the potential core are uniforms within ±0.007 Uj. The shape factor of the boundary layer is ranging between 1.15 and 1.27 if one assumes that the jet is virtually free, without diffuser (displacement and momentum thickness are computed on the distance between the potential core and a jet diameter of 50 mm). These values demonstrate that the flow is fully turbulent. The real shape factor is larger with a mean value of 5. In this condition, the boundary layer is large, approaching the separation regime and the manipulation of the separation process would be easier as a thinner boundary layer remain attached longer than a thicker boundary layer (Schlichting 1987). The turbulent layer thickness (d) is around 13 mm, this distance corresponds to the half-diameter of the diffuser reduced from the half-diameter of the 50 mm jet exit. The momentum thickness (h) of the unforced jet shear layer is D/35. This value is significantly higher than established values for a turbulent boundary layer (D/190) but is rather close to the momentum thickness obtained by Pack and Seifert (2001). These authors obtained a

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Fig. 12 Mean and rms distribution of the primary velocity component, baseline profiles at x/D = 0.1

momentum thickness of D/25 for a flow exit equipped with a 30 diffuser and a 1.85D bevel length. Their study and this one used trips upstream the exit to activate the laminar to turbulence transition. These trips induced different flow characteristics compared to the literature data but it is essential to assure that the forced flow perturbations are only due to the DBD actuators rather than an activation of the transition. The secondary components (along Y) of the velocity in the cross-stream direction present self-similar profiles like the distribution of the primary velocity components (Fig. 13). The upper positive and lower negative values confirm that air jet is following the inclination of the diffuser. However, a slight asymmetry exists with a vertical maximal velocity equal to about 0.045 at the upper part of the diffuser when it is equal to 0.04 at the lower one. The secondary turbulence intensity is of a same scale order than the turbulent intensity of the primary velocity component. The fluctuations are symmetrical but some larger rms values appear in the potential core for velocity of 40 m s–1. These fluctuations could be responsible for the jet instabilities and oscillations observed for this flow regime. 4.5 The DBD effects on the flow separation by LDV measurements The time-averaged velocities of the primary component for unforced and forced air jet at x/D = 0.1 are plotted in Fig. 14. The DBD actuation leads to a velocity decrease in the upper part of the diffuser and a slight velocity increase at the lower cross-stream position. We observe a maximal velocity reduction of 50, 45 and 32%, respectively, for centreline velocities of 20, 30 and 40 m s–1, respectively.

This maximal velocity reduction occurs approximately at the free diffuser air jet level (y/D ~ 0.5) but the flow is not fully detached from the diffuser bevel. Under the discharge excitation, the boundary layer thickness (d) is increased of 4 and 2.5 mm for jet velocities of 20 and 30–40 m s–1, respectively (20 and 30% increase in layer thickness for 20 and 30–40 m s–1). The maximal jet deviation is 4.5, 3 and 2 mm for Uj equal to 20, 30 and 40 m s–1, respectively. The upper mass flux loss is partially reported to the lower part of the diffuser but no velocity increase in the potential core is observable. According to the continuity equation, a part of the mass flux needs to be transposed to tangential slices of the investigated plan; the flow perturbations induced by the DBD actuator are consequently strongly 3D as reported by Labergue et al. (2007). We also notice that the momentum thickness (h) slightly increases when the DBD actuator is on (15 and 8%, respectively for air velocity of 20 and 40 m s–1) which produces a slight improvement of the mixing and fluid entrainment. The gain in mixing properties could be primarily imputed to the turbulent layer thickness enhancement higher than the momentum thickness increase. Concerning the rms velocity fluctuations, the modified airflow presents an augmentation in the maximum rms values at the upper part of the diffuser (40% increase in u¢). This turbulence intensity increase is partially balanced by a small decrease in the lower part of the diffuser (–10% in u¢). We also notice an enlargement of the upper shear layer with a maximal width for Uj = 20 m s–1. The lower part of the flow presents an opposite behaviour with a width reduction of the shear layer. These results confirm the dissymmetry in a possible mixing enhancement observed with the flow visualizations. One can remark that for the maximal Reynolds number the shape of the turbulence

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Fig. 13 Mean and rms distribution of the secondary velocity component, baseline profiles at x/D = 0.1

Fig. 14 Cross-stream distribution of the timeaveraged and rms values of the primary velocity component (x/D = 0.1)

intensity curve is once again discontinuous due to the instabilities identified during the baseline experiment sessions. The mean turbulence intensity in the potential core is 3–4% like the natural air jet. The DBD has a global action in the flow structure and the modifications induced by the control device at the upper part of the diffuser are extended to the lower part of the airflow. The rms fluctuations in the potential core have a constant mean value for both the free and manipulated flows. The perturbations induced by the non-thermal plasma are introduced in the shear layer only unlike acoustic forcing for example (Cho et al. 1998). The increased turbulence levels at the upper position are

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consistent with the suppression of the large scale structures. Contrary to the reducing of the upper coherent structures, the reduced turbulence level at the lower part corresponds to an increase of the structure scale. The time-averaged and the rms distributions of the secondary velocity component are plotted in Fig. 15. The plasma effects are clearly visible on the mean velocity profiles with negative values for 75% of the cross-stream positions. This result confirms the flow deviation occurring under actuation. The air jet start to be deflected at y/D = 0.5, which confirms that airflow is detached of the upper bevel. The flow deviation remains more pronounced at lowest

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velocity but this deflection seems to be independent from the Reynolds number as velocities of 30 and 40 m s–1 produce similar velocity profiles. The rms fluctuations of the secondary velocity component are less intense than the primary one in the shear layer and in the potential core (maximal difference of 47 and 30%, respectively). The actuation enlarges the upper shear layer and increases the turbulence intensity as for the primary component; the lower part undergoes a reverse process. Since the turbulence intensity is also promoted in the upper part of the potential core, this region was subject to large oscillations of the upper deviation angle during the experiments. 4.6 The jet vectoring estimated using LDV The time-averaged velocity distributions showed in Fig. 16 present the spatial evolution of the cross-stream profiles with respect to their longitudinal positions (0.1 £ x/D £ 4). The potential core is reduced in width and in peak value when the longitudinal position is increasing. The end of the potential core occurs between x/D = 2 and 4. A jet deflection toward the lower part of the diffuser is apparent but the deviation angle declines when the primary airflow velocity increases. The deviation angle is computed using the radial position of the potential core centre. This centre is defined as the mean distance between the upper and lower shear layer thickness when possible (x/D £ 2) or using the radial position of the velocity peak (x/D ‡ 2). The corresponding radial position is denoted by ymax. The deviation angle is finally defined as:

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hdeviation ¼ Arc tan

y

max

x



;

where x correspond to the distance of the investigated stream-wise plan. The resulting deviation angles are summarized in Fig. 17. The vectoring of the air jet is not uniform over the Reynolds numbers range investigated. The deviation angle is directly related to the air jet velocity and to the longitudinal position. The maximal vectoring occurs for the lowest jet velocity (Uj = 20 m s–1) with an angle of 13.5 (8.5 and 5.5 for Uj = 30 and 40 m s–1, respectively). A linear regression of the results illustrated in Fig. 17 demonstrates that the deviation angle reduction with the longitudinal position is greater for the lower Reynolds numbers (–1.7) as the curve slope remains constant for larger velocity (–1.25). These results demonstrate that a jet vectoring is possible for velocities up to 30 m s–1 using this actuator and a 3-mm-thick PVC dielectric. For higher speed flow, the vectored jet is unstable and the jet alternatively attaches to the upper and the lower bevel of the diffuser. Labergue et al. (2007) have also demonstrated that the effects of a DBD actuator on the separation along the bevel of a rectangular diffuser (angle of 16) decreases with the primary jet velocity. They obtained a flow separation for velocity flow of 30 m s–1 using an electric power consumption increase via the augmentation of the signal frequency. The DBD actuator generates local air flow velocities smaller than the induced speed provided by other flow control devices. The obtained deviation angles are therefore very promising and are comparable with jet vectoring using

Fig. 15 Mean and rms distribution of the secondary velocity component (x/D = 0.1)

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Fig. 16 Time-averaged velocity profiles for different stream-wise positions (x/D = 0.1, 0.5, 1, 2 and 4) with the DBD actuator activated

consequently would be more difficult to realize and is based on the creation of low recirculating regions only. Thrust vectoring control is in most cases achieved using actuator inducing velocities greater than the one produced by the plasma actuator. The present results using a continuous actuation are however in a similar efficiency range and DBD actuators could consequently be a new alternative for manipulation of subsonic jet. 4.7 The DBD effects on the jet width by LDV

Fig. 17 Angle of deviation induced by the DBD actuator for the three tested velocities versus x/D

piezo-electric actuators (deviation angle of 7 for primary air flow of 18 m s–1) (Pack and Seifert 2001) or fluidic synthetic jets (deviation angle of 20 for a rectangular duct with a diffuser at air flow of 18 m s–1) (Ben Chiekh et al. 2003). Smith and Glezer (2002) using secondary synthetic jets to control a rectangular air jet noticed that larger primary jet velocities result in smaller vectoring angle and they obtained deviation angle of 30 and 12 for air flow of 7 and 17 m s–1, respectively. At 7 m s–1, the air jet is laminar and the comparison with our results is not relevant. Nevertheless, at higher velocity exhaust, the flow is fully turbulent and they obtain similar jet deflections than those presented in this study. However, one can notices that in their experiments apparatus, no extended surface are mounted on the jet exit and the control of the air jet

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The computation of the jet width is based on the radial position at which the velocity is half of the potential core velocity value (d1/2). These positions at unforced and forced jet conditions are plotted in Fig. 18 for upper and lower air flow. An asymmetry exists for the natural jet with a larger expanding rate in the upper part of the air flow certainly due to local perturbation of the active electrode in contact with air jet. An increase in primary air jet velocity induces a wider jet width. The natural upper flow is linearly enlarged with the Reynolds number increase contrary to the lower part which exhibits no width variation. Under the momentum addition generated by the DBD actuator, the upper flow is thinner (due to the increase of the turbulent intensity and the boundary layer thickness as demonstrated in Sect. 3.4) and the lower flow is enlarged for velocity up to 30 m s–1, the jet width is only slightly increased but the jet is vectorized. The rate at which a jet widens has a direct impact on the volume flux of the jet. For a velocity of 20 m s–1, the DBD actuator has few effect on the jet width (width increase between 2 and 6%) so the added volume flux is negligible (Fig. 19). For the higher speeds, the plasma interaction with the boundary layer induces more flux entrainment

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controller, resulting in a 6 m s–1 counter-flow wall jet. Despite of the large difference between the generated flow and the primary controlled air jet velocities, different innovative conclusions are expressed in this paper: •

•

Fig. 18 Jet boundary based on half the maximal velocity as a function of longitudinal position

•

•

•

Fig. 19 Jet width as a function of longitudinal position

(minimal and maximal width increase of 2 and 13%, respectively). A jet vectoring is not systematically achieved for jet velocity up to 30 m s–1, but in this case the DBD actuators could be more suitable in the perspective of an enhancement of the jet spreading. In particular a dual side excitation could constitute an efficient hyperspreading configuration (Ben Chiekh et al. 2003).

5 Concluding remarks The ionic wind generated by a non-thermal plasma actuator has proved to be sufficient for control of vortex shedding, control of the flow separation and reattachment over airfoils or control of the boundary layer occurring over a flat plate. The present study investigates a new application for the control of an axisymmetric air jet equipped with a small angle diffuser for primary jet velocity between 20 and 40 m s–1. A single DBD actuator is used as upper-side

A flow naturally attached to the diffuser bevels could be partially detached for velocities of 20 and 30 m s–1. The actual limit of the DBD effects occurs for velocity of 40 m s–1 which produces jet instabilities with successive separations to the upper or lower lips of the diffuser. The turbulent intensity is largely intensified at the manipulated diffuser side and the turbulent shear layer thickness is enhanced. The manipulation of the shear layer allows a maximal jet vectoring of 13.5 but the deviation angle remains strongly dependent on the Reynolds number. Actuation on 1/4 of the exit perimeter induced flow modifications on 1/2 perimeter and the air flow perturbations in the forced jet are 3D. In this single DBD configuration the width of the jet is lightly modified by the ionic wind along the diffuser lip, but a dual-side actuation could improve the jet spreading.

As previously published in the case of a rectangular jet, the DBD actuator creates 3D perturbations in the primary air jet. One of the future objectives of our team concerns the characterization of these 3D modifications using stereoscopic PIV. A second objective is to dynamically characterize a non-stationary DBD actuator synchronized on the jet response using spectral analysis. Indeed, a pulsed manipulation would periodically force the flow at a characteristic frequency and would constitute a less expensive technological solution in term of energy (use of a duty-cycle input signal), for identical (or better) results. Investigations are currently in development in order to first enhance the mixing and also vectored the air jet for primary velocity up to 80–100 m s–1. Acknowledgements The authors thank AIRBUS for its financial and technical support (contract #D05028043), under the scientific direction of Dr. Stephen Rolston, and J.P. Bonnet and J. Delville (CEAT, Poitiers) for helping us in designing the diffuser geometry and for theirs advices. We also acknowledge J.C. Jouvanneau for the fabrication of the experimental diffusers and P. Braud for the technical assist.

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