Characterization of a three-electrodes surface corona actuator

Scuola di Ingegneria Industriale e dell’Informazione Dipartimento di Scienze e Tecnologie Aerospaziali

Characterization of a

three-electrodes surface corona

actuator

Advisor: Prof. Marco Belan

Co-advisor: Ing. Federico Messanelli

Master Thesis of:

Francesco Borghi, ID 856128

Sommario x

Abstract xi

Ringraziamenti xiii

1 Introduction 1

1.1 Flow control . . . 2

1.1.1 Flow control methods . . . 2

1.1.2 Flow control classification . . . 3

1.1.3 Passive control . . . 3 1.1.4 Active Control . . . 6 2 Plasma actuators 9 2.1 Plasma . . . 10 2.2 Corona actuators . . . 11 2.2.1 Corona effect . . . 11

2.2.2 Electrical properties and discharge regimes . . . 13

2.2.3 Corona performances . . . 19

2.2.4 External agents influence . . . 23

2.3 DBD actuators . . . 26

2.4 Multi-electrode actuators . . . 28

2.4.1 Multi-electrode corona actuators . . . 29

2.4.2 Volume discharge . . . 29

2.4.3 Surface discharge . . . 32

3 Experimental set-up 35 3.1 Ionic wind measurements . . . 35

3.1.1 Actuator . . . 35

3.1.2 Actuator positioning system . . . 36

3.1.3 Ionic wind measurements . . . 37

3.2.1 Ionic wind velocity . . . 45

3.2.2 Power . . . 46

3.3 Visualization of the discharge . . . 47

3.3.1 Camera . . . 47

3.3.2 Intensifier . . . 47

4 Results and discussion 49 4.1 Direct current voltage supply . . . 49

4.1.1 Dependence on geometric parameters . . . 50

4.1.2 Actuator performances . . . 55

4.2 Pulsed voltage supply . . . 57

4.2.1 Pulsed waveform . . . 58

4.2.2 Actuator performances . . . 58

5 Conclusions and future developments 73

Bibliography 77

1.1 Control strategies . . . 4

1.2 Riblets geometry. . . 4

1.3 Vortex generators working principles in two different configu-rations . . . 5

1.4 Predetermined control methodology. . . 6

1.5 Active control methodologies . . . 6

1.6 Synthetic jet actuators. . . 7

1.7 Traveling wave simulation. . . 8

2.1 Point-to-plate configuration . . . 12

2.2 Current-Voltage representation of a Needle-to-plate positive corona . . . 14

2.3 Current-Voltage representation of a Needle-to-plate negative corona . . . 15

2.4 Wire-to-plate surface corona configuration . . . 16

2.5 Generalized glow regime (Streamer regime) . . . 16

2.6 Line regime (Glow regime) . . . 17

2.7 Maximum velocity vs mean current density . . . 18

2.8 Velocity profile induced by the ionic wind . . . 18

2.9 Ionic wind effect on the boundary layer of a flow . . . 19

2.10 wire-to-wire . . . 20

2.11 wire-to-plate . . . 20

2.12 Schematic of the DC surface electric wind. . . 20

2.13 Electrodes diameter effect . . . 21

2.14 Velocity field induced by a serrated edge corona actuator . . . 21

2.15 Velocity profiles for three different inner-electrodes distances . 22 2.16 Influence of different materials . . . 23

2.17 V-I values at different pressure . . . 24

2.18 Current values with respect to relative humidity . . . 25

2.20 Current with respect to the electric field for different external flow velocities. . . 27

2.21 Different velocity profile obtained with actuator on and off and

U∞ equal to 5, 10 and 17 m/s . . . 27

2.22 Schematic DBD configuration . . . 28

2.23 Three electrodes actuator proposed by Colas . . . 30

2.24 Numerical simulation of the electric field lines . . . 31

2.26 Thrust with respect to the current for the design in Fig. 2.25b with two different values of d1 and with V2 on and off . . . 32

2.27 Three electrodes surface corona configuration and parameters 33 2.28 Comparison of velocity profiles: 3-electrodes corona measured 40 mm downstream of the needle tip and 4 serrated edge ac-tuator (two corona C11 and C12 and two DBD D4 and D5) measured 17 mm downstream of a tip. . . 34

3.1 Three electrodes actuator configuration . . . 35

3.2 Actuator positioning system . . . 37

3.3 Ionic wind measurement set-up . . . 37

3.4 Manual linear positioning system. . . 38

3.5 Span position of the measurements. . . 40

3.6 DC electric circuit configuration. . . 42

3.7 Glassman PS/FC20R06. . . 42

3.8 Particulars of the setup for velocity measurements at the bench 43 3.9 Electric circuit pulsed power supply. . . 44

3.10 DALSA Genie HM640 . . . 47

3.12 Hamamatsu C9548 . . . 48

4.1 Induced velocity for different values of the control distance. . . 50

4.2 Geometric parameters. . . 51

4.3 Induced velocity with respect to an increasing value of dacc2− dacc1 with Vcon = 2 kV and Vacc = 14 kV . . . 52

4.4 Induced velocity with respect to an increasing value of dacc2− dacc1 with Vcon = 3 kV and Vacc = 15 kV . . . 53

4.5 Three different configuration tested . . . 54

4.6 Ionic wind profile in the three different configurations. . . 54

4.7 Ionic wind profile with two different plates. . . 55

4.8 Velocity profiles and ionic wind map in m/s for Eacc= 1.03 kV /mm and Econ = 1.4 kV /mm . . . 56

4.9 Electric power as a function of Vacc for different values of Vcon. 57 4.10 Comparison of the ionic wind maps at Vacc= 14 kV . . . 60

4.11 Maximum velocity map in m/s in the parameter space Eacc and Econ. . . 61

4.12 Comparison of the induced ionic wind at Vcon = 1.5 kV . . . 62

4.16 Streamer discharge visualization. . . 66 4.17 Streamer discharge visualization with bigger disks. . . 67 4.18 Velocity map in m/s at Vacc = 16 kV and Vcon = 1 kV . . . 68

4.19 Ionic wind comparison between streamer and glow regime with Vcon = 1 kV and Vacc= 17 kV . . . 69

4.20 Velocity profiles and ionic wind map in m/s for Vacc= 18 kV

and Vcon = 1.5 kV . . . 70

4.21 Electric power comparison between streamer and glow regime as function of Vacc at Vcon = 1.5 kV . . . 71

4.22 Luminosity map with dcon = 2 mm, dacc1 = 15 mm, dacc2 =

14 mm , Vcon = 1 kV and Vacc = 15 kV . . . 71

A.1 CAD of the protection tunnel. . . 83 A.2 Flyback circuit. . . 84

Lo scopo di questo lavoro di tesi, di carattere sperimentale, `e lo studio delle prestazioni di una nuova configurazione di attuatore al plasma di tipo corona, composto da tre elettrodi. Per comprendere come si sviluppa la scar-ica tridimensionale vicino agli elettrodi vengono effettuate delle misurazioni della velocit`a indotta dall’attuatore al plasma disposto su lastra piana, in aria calma. Ci`o `e stato svolto per diverse geometrie e con diversi tipi di alimentazione, in tensione continua ed impulsata, con lo scopo di compren-dere come venga influenzato il campo di moto indotto dall’attuatore. Viene inoltre visualizzata la scarica attraverso delle immagini scattate ad alta fre-quenza per comprenderne le caratteristiche e viene analizzato il consumo energetico dell’attuatore. Le buone prestazioni in termini di velocit`a in-dotta dell’attuatore a tre elettrodi rispetto alle configurazioni degli attuatori corona a punte sono confermate. Il passaggio ad una alimentazione in ten-sione impulsata non ha portato, al contrario di quanto ci si aspettava, ad una maggiore stabilit`a della scarica a tensioni maggiori ma ha tuttavia permesso di generare una scarica in regime glow molto stabile e performante in termini di velocit`a indotta e con un basso consumo energetico.

Parole chiave: Attuatori al plasma, Corona, Attuatore a tre elettrodi, Vento ionico, Controllo attivo del flusso.

The aim of this thesis work is to characterize the performance of a new three-electrodes surface corona plasma actuator. In order to understand how the three-dimensional discharge is developed near the electrodes, some mea-surements of the induced velocity have been done with the plasma actuator placed on a flat plate, in still air. This has been performed for different ge-ometries and two types of power supply, continuous and pulsed voltage, with the purpose of understanding how the flow field induced by the actuator is controlled. To understand the discharge patterns, the discharge has been visualized with high frequency images and, in addition, the energy consump-tion of the plasma actuator has been evaluated. The good performances in terms of induced speed of the three-electrode actuator with respect to clas-sical and serrated edge corona configurations are confirmed. The passage to the pulsed power supply, in contrast to what expected, did not lead to a better stability of the discharge at higher voltages. Nevertheless, it allowed to generate a very stable glow discharge with high performances in terms of induced speed velocity and with low energetic consumption.

Keywords: Plasma actuators, Corona, Three-electrodes actuators, Ionic wind, Active flow control.

Ringrazio sinceramente il relatore, Professor Marco Belan, per la pas-sione e l’esperienza messe a disposizione, risultate fondamentali in questi mesi trascorsi in laboratorio.

Vorrei inoltre ringraziare l’Ing. Federico Messanelli per l’infinita disponibilit`a ed i preziosi suggerimenti.

Ringrazio la mia famiglia per il supporto e la fiducia dimostrati in questi anni.

Ringrazio infine i compagni di laboratorio, Francesco, Edoardo, Marco e Lorenzo, che hanno reso pi`u piacevoli questi mesi di lavoro, sempre disponi-bili per un sorriso ed una parola di sostegno.

Introduction

This work aims to continue the experimental investigation performed in our department in the field of plasma actuators.

Plasma actuators belongs to the category of Electrohydrodynamic flow con-trol devices, they exploit electrical fields and ionized molecules to interact with the surrounding flow field.

In fact, by applying a sufficient potential difference between some properly located electrodes in a fluid, such fluid is ionized and plasma generation oc-curs; it is then possible to take advantage of the plasma and its interactions with the electrical field in order to modify the flow and to obtain some ben-eficial effects.

In the recent past, many research groups focused on plasma actuators be-cause they represent a good substitute for the traditional flow control meth-ods. They are simple to manufacture and do not include moving parts, which would add complexity and weight to the structure, and their response time is very short making them suitable to control high speed and high frequency phenomena.

The aim of this thesis work is to continue the development of a new three electrodes surface corona actuator introduced by Baselli and Peronaci; in [1] they presented and characterized the behaviour of the actuator powered by a DC voltage supply. In this thesis work further studies on the influence of some geometrical parameters in case of direct current supply are conducted and the performances of the actuator in case of pulsed voltage supply are tested.

In this chapter the problem of flow control and some of the techniques adopted are introduced concisely. In Chapter 2 the main characteristics of plasma actuators are reported and the reasons behind this thesis work are presented. In Chapter 3 the experimental setup adopted is described. In Chapter 4 all the results obtained are reported and analyzed and in Chapter 5

conclusions are presented and possible future developments are suggested.

1.1

Flow control

Flow control is a rapidly evolving field of fluid dynamics; it consists in the ability to effect a change in the flow field to obtain a benefit. Since the dawn of aeronautics, attention toward this field has been very high. In-deed, the profit gained with efficient flow control systems allows saving in fuel consumption, to increase flight range, to reach higher cruise speed and would allow the possibility of takeoff and landing with heavier aircraft or with shorter runways.

Nowadays, the theme of efficiency has expanded to all the processes involv-ing fluid flows and flow control has gained very high interest also in the field of biomedical devices, land and sea vehicles and in gas and oil distribution systems, not only for economic reasons but also because many environmen-tal regulations are pushing toward the reduction of atmospheric and acoustic pollution.

1.1.1

Flow control methods

The fluid dynamics phenomena on which it is possible to act to control a flow are:

ˆ Laminar to turbulent transition control ˆ Flow separation control

ˆ Turbulence control

The delay of the transition is very effective to obtain a reduction of the skin frictional drag; in a laminar flow indeed, drag can be about an order of magnitude lower than in the case of turbulent flow and since almost 50% of an aircraft’s resistance is due to viscous forces, it is simple to understand the great interest on this theme. A delay of the transition also reduces noise production and improves comfort. On the contrary, in other situations, the transition may be anticipated on purpose in order to generate a turbulent boundary layer, which is able to withstand in a better way the adverse pres-sure gradient thanks to its higher energy content, resulting in a postponed stall and in an increase of the maximum lift. The laminar flow generates less drag but it is prone to the separation due to its low energy content.

layer from the surfaces in some particular conditions. Once separation oc-curs, it causes vortex generation, which produces an impressive increase in drag, limiting the design and the performances of devices involving fluid flow. Lastly, depending on the application, it can be useful to modify the turbu-lence level of a flow. For instance, an increase in the turbuturbu-lence level could be useful in combustion processes to facilitate mixing. On the other hand, a decrease in turbulence level leads to a noise reduction.

1.1.2

Flow control classification

Flow control methods may be classified in many different ways. First, we can distinguish between techniques that are applied at the wall or away from it. The interaction between the wall surface and the flow is of fundamental importance and the most important parameters include roughness, shape, wall motion, curvature, porosity and temperature of the wall. A second clas-sification scheme makes a distinction between methods that directly act on the shape of the instantaneous/mean velocity profile or selectively influence the small dissipative eddies. However, the most adopted classification is the one that considers energy consumption, dividing the control devices in active and passive depending on whether they require energy input into the system or not (Fig. 1.1).

1.1.3

Passive control

Passive control does not require an energy input to operate, this makes it quite simple to implement and cheap. However, its simplicity leads to devices that cannot sustain big changes in the working conditions and it could be even possible that, in off-design conditions, the overall effect of the system results deleterious.

Hereafter the most important techniques of passive control are briefly pre-sented:

ˆ Riblets: small grooves, inspired by the skin of the sharks, dug on the wall surface that interact with the turbulence wall-cycle stabilizing the quasi-streamwise vortices and reducing the production of turbulent ki-netic energy. Generally, they are aligned to the free stream direction and their common cross-sectional shape is triangular with sharp tips, as shown in Fig.1.2. They have been widely studied and different ge-ometries have been tested ([4], [5], [6]). The drag reduction obtained is of the order of 10%. Recently, sinusoidal riblets have been devel-oped and their performances are even better ([7]). This technology

Figure 1.1: Control strategies. [2].

Figure 1.2: Riblets geometry. [3].

has been successfully used in aeronautical and naval applications but their sensitivity to external agents makes them of little practicality. Indeed, riblets are very sensitive to ultraviolet light and they have the tendency to get easily dirty due to dust: those aspects degrade their performances and force frequent maintenance.

ˆ Surface roughness: modifying the pattern and/or the heights of sur-face protrusion with respect to the ideal sursur-face of an object located in a fluid stream, laminar-to-turbulent transition can be anticipated or

delayed.

ˆ Compliant coatings: special adaptive coatings that allow to delay the laminar-to-turbulent transition due to the Tollmien-Schlicting in-stability [8].

ˆ Polymer injection: addition of long-chain molecules or micro bubbles to liquid flows allows the reduction of the turbulent skin-friction. These substances act in the buffer layer, where velocity fluctuations extend the polymer chains, locally increasing the viscosity and leading to a suppression of the production of the Reynolds stresses. This technique allows to obtain a reduction of frictional drag up to 80% [9].

ˆ Vortex generators: mainly used to delay flow separation; they are typically constituted by rectangular or triangular blades placed behind the leading edge and their height is usually about 80% of the boundary layer thickness. These blades cause the formation of vortices, which carry fast and high-energy air from the outer stream to the boundary layer near the wall, contributing to energize it, as represented in Fig 1.3. The energy addition allows to the flow to win the adverse pressure gradient, delaying the separation and postponing the stall. The main disadvantage associated with this type of technique is the increase of aerodynamic drag due to vortex production: as a passive device it cannot be activated at will and, therefore, if the flow is attached the only effect is to increase the drag force.

Figure 1.3: Vortex generators working principles in two different configu-rations [10].

1.1.4

Active Control

On the contrary of passive control, active control involves an energy input in the flow. As shown in Fig. 1.1, active control is divided in two subcate-gories:

ˆ Predetermined control is effectuated in an open loop and no sensors are required. An energy input is supplied to the system without the actual knowledge of the particular state of the flow (Fig. 1.4).

Figure 1.4: Predetermined control methodology. [2]

ˆ Reactive control, conversely, adapts the control to flow parameters as a result of the evaluation of the external variables by means of sensors. In feedforward control, the measured variable differs from the controlled one (Fig. 1.5a), while in feedback control the controlled variable is measured, fed back and compared with a reference input (Fig. 1.5b).

(a) Reactive, feedforward, open loop.

(b) Reactive, feedback, closed loop.

Hereafter the most important techniques of active control are briefly pre-sented:

ˆ Boundary layer blowing: a stream of high speed air is injected into the flow tangentially to the contour surface; this injection increases the energy and the momentum of the boundary layer and allows to increase the maximum angle of attack before stall.

ˆ Boundary layer suction: the slowest part of the boundary layer, the one closer to the wall, is aspired using micro-porous walls or slots on the surface connected with a pump that generates a depression. The suction of the layer with less energy allows to move the separation point forward and to retard the stall.

ˆ Synthetic jets: it combines the two previous techniques, through suc-tion and blowing acsuc-tion exerted by some pistons on the airfoil (Fig. 1.6). This technique increases the mixing of fluid layers with different amount of energy. The low momentum fluid near to the wall is aspired and the same quantity of fluid is blown into the flow with an higher level of energy [11].

Figure 1.6: Synthetic jet actuators.

ˆ MEMS (Micro-Electro-Mechanical-Systems): miniaturized devices placed on the aerodynamic surface that can perform several functions with-out introducing severe passive disturbances to the flow field. By the integration of mechanical and electronic components, they are able to manipulate coherent structures in a nonintrusive way. For example, they can act on the fluid by applying an appropriate oscillatory mo-tion that promotes flow reattachment and delays separamo-tion. This is only one of the many different ways by which those devices can act to control the flow, a complete review on MEMS for flow control may be found in [12].

ˆ Spanwise wall oscillation: imposing cyclic surface motion in a wall-bounded turbulent flow causes interesting effects. The most practically appealing is a significant reduction of the mean streamwise wall friction, first reported by [13]. Numerical simulations with sinusoidal waveforms have shown drag reductions up to 34% ([14]). Nevertheless, as many of those active techniques, wall oscillation effect decreases when Reynolds number grows.

ˆ Traveling waves: with the same principles of the spanwise oscilla-tions, waves of spanwise velocity are modulated in the flow direction (Fig. 1.7), causing an interesting drag reduction. Numerical results in [14] showed an abatement in drag of 48%, whilst an experimental test performed in our laboratory obtained a drag reduction of 33%.

Figure 1.7: Traveling wave simulation. [15]

ˆ EMHD (Electro-Magneto-Hydro-Dynamic): devices that provide the variation of momentum in the flow through Lorentz force generated by magnets and electrodes.

ˆ EHD (Electro-Hydro-Dynamic): similar to the EMHD devices but in this case the protagonist is the Coulomb force. Plasma actuators, which will be analysed in next chapter, belong to this category.

Plasma actuators

Plasma actuators are simple devices that, by exploiting the formation of plasma, are able to impart some desired modifications into a fluid flow. Before the 2000s, studies about plasma actuators were quite rare although plasma was exploited in several industrial applications. There were some preliminary researches in the ’50s and the ’60s about the air movement pro-duced by corona discharge ([16]), but the first application of plasma actua-tors as boundary layer control devices was studied by Velkoff and Ketcham in 1968 [17].

The first developed plasma actuators were the corona actuators (Sec. 2.2.1), and were extensively studied from the 1990s. Nevertheless, corona discharge resulted to be unstable, generating dangerous sparks, thus research tried to find an alternative solution. In the middle of ’90s, Roth’s group developed the DBD (Dielectric Barrier Discharge) actuator that, nowadays, is the most common type of plasma actuator (Sec. 2.3).

Both types of plasma actuators, corona and DBD, generate a flow, called ionic wind, near the wall that modifies the boundary layer velocity profile with benefits that can be exploited in various areas.

For instance, effects on the flow field in the wake of a cylinder were studied by the group of Y.Sung in [18]. They obtained, through a proper plasma actuation, an impressive reduction of the wake size and a reduction of the vortex shedding. Effect of plasma were studied also in terms of noise reduc-tion: interesting results have been obtained in [19]; the beneficial effects of plasma can be exploited in the power production sector, by applying actua-tors on wind turbines ([20], [21]) or on gas turbines ([22]). In addition, many research groups focused their efforts on studying the benefits of plasma ac-tuation on separation control and on laminar-to-turbulent transition of the boundary layer.

experi-ments concerning separation control on airfoils at high angles of attack, in sta-tionary and periodically oscillating aerodynamic conditions ([23], [24], [25]); several tests were also conducted on their application on jet manipulation ([26], [27]) and on various bluff bodies ([28], [29]).

Plasma actuators versatility is due to the advantages of this technology, that are:

ˆ lack of mechanical moving parts, so that the application of the actuators does not imply an increase in weight and complexity of the structure; ˆ short time response, which makes them able to control high speed and

high frequency phenomena;

ˆ reliability, due to their simple manufacturing;

ˆ small size, which implies negligible flow disturbances. On the contrary, the weaknesses of the plasma actuators are: ˆ energy conversion, which is not very efficient;

ˆ their performances, that are very sensitive to ambient conditions, in particular for corona actuators;

ˆ generation of dangerous gases, such as ozone (O3), nitrogen oxide (NO),

nitric oxide (N O2) and thus nitric acid if water vapour is present;

ˆ the main limitation is that their beneficial effect decreases with high flow velocities.

2.1

Plasma

Plasma is the most abundant state of matter in the Universe, however on Earth it is naturally visible only in lightning and in the aurora borealis. Historically, the phenomenon of plasma was discovered by Sir William Crookes, in 1879, but the name plasma was assigned to it later by Irving Langmuir, in 1928, which introduced this term to describe a ionized gas region consisting of electrons and ions globally neutral.

Currently, with the term plasma we refer to a ionized gas with an energy density as high as to dissociate a large population of electrons from atoms or molecules and to allow both species, ions and electrons, to coexist; since the positive and the negative particles generated are approximately equal in number, the gas results globally neutral. Its characteristics are remarkably

different from those of ordinary neutral gases, indeed it is considered a dis-tinct fourth state of matter.

Plasma can be classified in ”thermal” or ”non − thermal” based on the rel-ative temperatures of the electrons, ions and neutrals; in fact, because of the large difference in mass, the electrons come to thermodynamic equilibrium amongst themselves faster than they come into equilibrium with the ions and the neutral atoms: if the thermodynamic equilibrium among all the particles is reached it is called ”thermal” plasma, on the contrary, if it is not reached it is called ”non − thermal” and the ions and the neutral particles are at much lower temperature (nearly room temperature) with respect to electrons. Nowadays, plasma is being studied for various industrial applications, such as ozone production, pollution agents removal, surface treatments, plasma welding, plasma cutting and neon tubes. In addition to this, even aerospace industries are interested in plasma, in order to utilize it in propulsion and in flow control technologies.

2.2

Corona actuators

2.2.1

Corona effect

Corona discharge

The corona discharge is an electrical discharge brought on by the ioniza-tion of a fluid surrounding a conductor that is electrically charged.

The formation of this discharge is based on Townsend mechanism, it is also known as electrons avalanche. Considering two planar electrodes at ambi-ent pressure and progressively providing them a voltage gradiambi-ent, until the potential difference stays below a threshold, we do not see any phenomenon and there is no passage of current; when the dielectric strength value of the air is overcome, atoms and molecules of the fluid undergo a process of ioniza-tion. Ionization consists in making the neutral particles become positive ions by snatching an electron from them and it happens due to photo ionization in the gap between the electrodes; subsequently, the charged particles inter-act with the electric field and, if the voltage is high enough, an avalanche of charged particles is generated, leading to the formation of plasma, as it will be deepened in the next section. The discharge is perceived by human eye as a blue-violet glow concentrated in the regions where the electric field is greater. Exploiting the definition made by Loeb in [30]: ”The expres-sion corona will be used to describe the general class of luminous phenomena appearing associated with the current jump to some microamperes at highly stressed electrode preceding the ultimate spark breakdown of the gap”.

Typically, to generate a corona discharge in atmospheric conditions the point-to-plate configuration is utilized, as in Fig. 2.1. The electric breakdown oc-curs locally, close to the pointed shape electrode provided with high voltage (HV). The distribution of the electrical field then decreases, with a minimum in correspondence of the ground or negative electrode. Therefore, primary ionization occurs near the HV electrode, forming a luminous active region and, after ionization, Coulomb forces attract electrically charged particles towards the opposite charged electrode, determining the drift region.

Figure 2.1: Point-to-plate configuration. [31]

Positive and negative corona

It is possible to distinguish two different kinds of corona discharges, de-pending on the voltage polarity provided by the power supply on the sharp electrode. The discharge is called a positive corona if the HV applied to the low curvature radius electrode is positive, on the contrary if it is negative it is called negative corona.

The physics mechanism that generates the two discharges is extremely dif-ferent.

ˆ Positive corona: in the region of high potential gradient an exoge-nous ionization occurs due to photo ionization of the neutral molecules. The electrons resulting from the ionization are attracted towards the sharp electrode, the anode, and the positive ions are repelled from it. A series of collision, closer and closer to the anode, generates the ioniza-tion of other molecules, producing an electron avalanche, as expressed in Eq. (2.1)

A + e− → A+_{+ 2e}−

As shown from the reaction, the number of electrons increases at every collision; secondary electrons are created by the ionization caused by the photons that are generated due to the thermal energy liberated in the collisions of the electrons. The electrons that are created are then accelerated toward the anode from the electrical field and will hit other neutral molecules, triggering the discharge mechanism.

ˆ Negative corona: ionization process occurs at the cathode, where a negative HV is applied, while the anode is grounded. In negative corona discharge the formation and sustenance process is much more complex with respect to the positive corona. Primary electrons are generated close to the cathode tip and they possess low kinetic energy, often their kinetic energy is not sufficient to overcome the ionization energy of the gas molecules ([32]) and they result to be not useful in sustaining the negative corona process. For negative corona, instead, the dominant process generating secondary electrons is the photoelectric effect from the surface of the electrode. Furthermore, due to the cathode repulsion, the electrons tend to escape towards the discharge volume and they bind themselves to electronegative molecules (like oxygen and water steam) generating negative ions that are attracted by the anode to close the circuit and which significantly contribute to the momentum exchange with neutral air molecules.

2.2.2

Electrical properties and discharge regimes

The regimes of the corona discharge depends on a multiplicity of factors: the working gas, the pressure of the gas, the geometrical configuration of the discharge (volumetric or surface), the polarity of the voltage provided and the geometry of the electrodes.

An accurate description of the electrical properties and regimes of volumetric needle-to-plane corona discharges, both positive and negative, was published by Gallo in [33]. A schematic representation of the V-I relation in positive corona is presented in Fig. 2.2.

The initial low background current is due to intermittent pulses that correspond to the drift in the electric field of the few electrons and posi-tive ions formed by natural radioactivity; the electric field is low and the electrons do not acquire sufficient energy to produce subsequent ionization. As the voltage is increased, a time-averaged saturation current will be at-tained and subsequently, at higher voltages, the energy of the electrons be-comes sufficiently high to ionize the gas by collisions and the formation of the Townsend ionization avalanche occurs generating a rapid rise of the current;

Figure 2.2: Current-Voltage representation of a Needle-to-plate positive corona. [33]

the Townsend ionization avalanche takes the form of irregular current pulses called onset-streamers and, as the voltage increases, this pulsed discharge becomes self-sustained by ionization of the gas itself due to the collisions of the electrons with neutral molecules. As the voltage is increased, the an-ode first becomes covered with an uniform corona glow and subsequently the breakdown streamers appear. Streamers are preferential channels between the two electrodes that imply a considerable increase of the current value. When the voltage across the gap rises to a critical value, the breakdown streamers succeed in creating ionization across the entire gap, creating an unstable transition region that evolves into a destructive, high current arc or spark.

In case of negative corona the current with respect to the voltage is rep-resented in Fig. 2.3; the main difference in the case of negative discharge is that the Townsend ionization implies the appearance of irregular Trichel pulses, formed by an electrons avalanche which is then extinguished by the formation of a negative ions charge cloud that is swept away by the electric field, this re-establishes the original situation and the process goes on repeat-edly. The next stage of negative corona is the pulseless glow where a steady

Figure 2.3: Current-Voltage representation of a Needle-to-plate negative corona. [33]

corona current is obtained; this happens when the negative ions clouds be-come numerous and begin to overlap so that the entire gap results full of negative ions. Subsequently, an increase in voltage generates the formation of a pulsating component superimposed on the steady glow, which then leads to retrograde streamers. At this stage, an unstable transition region is en-tered and finally arcs or sparks develop in the gap; these three pulsed phases in negative corona were recently studied in [34] and [35].

Typically, the corona discharges exploited in the aeronautical sector are realized between two parallels electrodes, wires or metallic foils, flush mounted on a non-conducting surface (Fig. 2.4) and are called surface corona.

Regarding this discharge configuration, it is possible to distinguish five dif-ferent regimes by increasing the electrical field intensity [36]:

ˆ Spot type regime: the discharge is concentrated in some visible spots of the HV electrode. An increase in the voltage difference implies an increase of the number of spots. This regime corresponds to currents lower than 0.2 mA/m, with power of about 150 W/m2 and a negligible production of ionic wind.

Figure 2.4: Wire-to-plate surface corona configuration. [31]

ˆ Generalized glow regime: at higher voltage, it is possible to ob-serve an homogeneous luminescence in the gap between the electrodes. The discharge appears as a thin film of ionized air on the flat surface (Fig. 2.5). The discharge is quite stable in time, produces an audible noise and is largely dependent on the quality of the finishing of the two electrodes. The power involved is between 150 and 400 W/m2 and the current is between 0.2 and 0.5 mA/m.

Figure 2.5: Generalized glow regime (Streamer regime). [31]

ˆ Line regime: there is an important number of luminous points that form luminous lines on both the electrodes, with the disappearance of the thin blue layer of ionized air in the gap between them, as showed in Fig. 2.6. This regime involves powers between 400 and 1600 W/m2_,

current between 0.5 and 1.5 mA/m. The effect of humidity becomes very important.

ˆ Filament type regime: electrical charge is concentrated in some points on the electrode as filaments, with the possibility of temporary sparks if the voltage increases. The power is greater than 600 W/m2

(0.6 mA/m).

ˆ Spark regime: due to the high power the discharge becomes very unstable with many electrical arcs, whose energy may be dangerous both for the material of the surface and for the generator.

Figure 2.6: Line regime (Glow regime). [31]

This classification, made by Artana et al. [36] has been subsequently mod-ified by Moreau in [31]. He did not modify the definitions and characteristics of the spot, the filament and the spark regimes, but he defined as streamer discharge the regime previously called generalized glow regime, characterized by an homogeneous luminescence between the electrodes. Furthermore, he gave the name glow discharge to the regime characterized by the presence of the blue luminous lines near the electrodes, the line regime. From now on, for clarity in the discussion, it will be adopted the nomenclature of the regimes introduced by Moreau in [31].

Ionic Wind

The ignition of the plasma discharge generates an airflow, called ionic wind, due to ionized species that drift between the electrodes under the elec-tric field effect. A good definition of the phenomenon of the ionic wind is the one given by Robinson in [16]:”The phenomenon known as the electric wind, corona wind and electric aura refers to the movement of gas induced by the repulsion of ions from the vicinity of an high-voltage discharge electrode” . Robinson was one of the first scientists to study the corona discharge mech-anism in order to generate an airflow and he found that the induced velocity is proportional to the square root of the current (Eq. (2.2)):

vG = k

s I

ρµ (2.2)

where ρ is the gas density, µ is the ionic mobility of the gas and k is a geo-metrical parameter.

Subsequently, Sigmond et al. in [37] completed the previous relation (Eq. (2.2)) with d, the distance between the electrodes, and AG, the transversal section

vG =

s Id ρµAG

(2.3) Experimental results by various authors verified the proportionality of the gas velocity to the square root of I (Fig. 2.7) measuring a maximum induced velocity of 5 m/s. Electric wind is due to the collisions between the ions that

Figure 2.7: Maximum velocity vs mean current density. [31]

drift and the neutral particles in the electrode gap and causes a motion of the fluid near to the wall, as illustrated in Fig. 2.8.

Figure 2.8: Velocity profile induced by the ionic wind. [31]

Various research groups focused on the study of the ionic wind and its application to control a fluid flow; indeed, the maximum speed of the induced

Figure 2.9: Ionic wind effect on the boundary layer of a flow. [38]

wind is very close to the wall and it can be exploited to act in a beneficial manner on the boundary layer, as represented in Fig. 2.9.

Moreau et al. introduced in [39] a model to compute the mechanical power introduced by the actuator in the fluid under the assumption of stationary flow and known the velocity profile of the ionic wind (Eq. (2.4)):

Pmech = 1 2ρL Z ∞ 0 v3_G(y) dy (2.4)

The ratio between the mechanical power of the ionic wind, Pmech, and

the Pelec = V I is then exploited to obtain the electro-mechanical efficiency

of the actuator (Eq. (2.5)).

η = Pmech Pelec

(2.5) Generally, the value of η is very low in surface discharge; indeed, the skin friction at the wall reduces significantly the electric wind velocity. Despite of this low value, beneficial effects are obtained also for a low energy input in the fluid flow.

2.2.3

Corona performances

Classical corona actuator configurations for flow control on aerodynamic surfaces contemplate the utilization of two planar electrodes placed on an insulating material plane, seeking to minimize the disturbance to the external flow.

The mostly studied configurations are:

ˆ wire-to-wire configuration, where anode and cathode are wires flush mounted on the surface (Fig. 2.10).

ˆ wire-to-plate configuration, where one electrode is a wire and the second one consists in a conductive material plate (Fig. 2.11).

Figure 2.10: wire-to-wire

Figure 2.11: wire-to-plate

Electrodes dimensions and shape

In order to obtain better performances the asymmetry of the two elec-trodes has to be as great as possible; indeed, a greater asymmetry of the electrodes implies an higher divergence of the electric field and it favours the ionization process. Taking a positive corona as example, one uses usually a thin anode and a wider cathode; indeed, in the thin anode configuration the space charge between the electrodes is mainly positive and electric wind is due to the positive ions motion (Fig. 2.12a); if anode and cathode are re-versed the electric wind is composed of two opposites components; in fact, the thinner cathode leads to the ionization of the air near to it, which implies the appearance of a negative electric wind (Fig. 2.12b).

(a) Thin anode and wide cathode repre-sentation.

(b) Thin cathode and wide anode repre-sentation.

Figure 2.12: Schematic of the DC surface electric wind.. [31]

This effect was verified by Labergue et al. in [40] by testing three different wire-to-wire configurations with different diameters for the cathode and the anode. The maximum ionic wind velocities were measured with the smallest anode and the greatest cathode configuration (Fig. 2.13a); the diameter of the electrodes affects also the discharge current, which increases when the electrode diameter decreases (Fig. 2.13b).

(a) Electrodes diameter effect on the ionic wind.

(b) Electrodes diameter effect on the discharge.

Figure 2.13: Electrodes diameter effect. [40]

The previous considerations brought to test some electrodes with a ser-rated edge shape in order to obtain larger electric fields near the tips. Belan and Messanelli in [41] investigated various serrated edge geometries of the electrode and verified that an increase of the sharpness of the tips allows to obtain more stable discharge with higher local velocities and larger mass flow in comparison to planar electrodes (Fig. 2.14).

Distance between the electrodes

Another parameter that affects the actuator performance is the distance between the electrodes; by looking at Fig. 2.15 it is possible to notice that with constant applied voltage, the maximum velocity decreases when the gap increases because it implies a reduction of the electric field. On the contrary, an excessive vicinity of the electrodes tends to make the discharge unstable and to continuously generate electric arcs. Thus, there is an optimal compromise value for the gap between the electrodes.

Figure 2.15: Velocity profiles for three different inner-electrodes dis-tances. [40]

Furthermore, an increase of the gap allows to increase the value of the supply voltage provided to the actuator before the occurrence of electric arcs.

Dielectric material

An important influence on the discharge behaviour is given also by the insulating material on which the electrodes are mounted. In [40] a study with different material (PMMA, PVC and MDF) has been performed by Labergue et al. and the different behaviour of the discharges have been evaluated. Results are shown in Fig. 2.16, where it is clearly noticeable that different materials allow to obtain different discharge characteristics and performances.

(a) Discharge current as function of the applied electric field for three different materials

(b) Velocity profile obtained with three different materials

Figure 2.16: Influence of different materials. [40]

2.2.4

External agents influence

In addition to geometrical parameters, the corona discharge is influenced in a non-negligible manner by external agents, such as pressure, temperature, humidity and external flow velocity.

Pressure

In aeronautical applications the effect of pressure cannot be neglected, since it can vary considerably. A study on the behaviour of the discharge at different pressure levels was conducted by Moreau et al. in [42] (Fig. 2.17); they noticed that when the pressure decreases, the discharge needs a lower electric field and it results to be more stable and homogeneous until about 104 P a. On the contrary, with pressure lower than that threshold the dis-charge is more concentrated in some visible points on the electrodes such as a filamentary discharge and it is very difficult to get an homogeneous discharge. Temperature

A rise of the air temperature increases the current discharge linearly up to 30◦C [43]; on the contrary, the variation of the dielectric material temperature between 20◦C and 65◦C has no effect on the discharge behaviour [42]. Humidity

Humidity affects widely the discharge stability and behaviour. Partic-ularly critical is the relative humidity, which determines the degree of ion

Figure 2.17: V-I values at different pressure (in 105 _{P a). [42]}

hydration; indeed, high values of relative humidity are linked to the ten-dency of generating little water drops with low ionization potential on the electrodes surface, which inhibit the emission of the electrons [44]. An high concentration of water molecules in the air promotes the production of OH− ions and the drift of these negative ions towards the anode has a direct effect on the quantity of the ionic wind produced [45]. Relative humidity has a direct influence on the behaviour of the discharge (Fig. 2.18), Leger et al. in [46] found that, generally, relative humidity lower than 45% generates a thin and unstable range of streamer regime and a very wide range of glow regime; values higher than 45% allows to obtain a more stable and homoge-neous streamer regime; when the relative humidity overcome the 55%, the discharge is very unstable, and the formation of arc results to be very fre-quent.

Subsequently, Mestiri et al. in [47] verified a peak value of the ignition voltage of the discharge for relative humidity values between 50% and 60%; the voltage at which electric arcs are formed, indeed, decreases with higher humidity values.

These considerations are valid in general but, in addition, the effect of hu-midity on corona discharges is different with respect to the material utilized for the electrodes, particularly in negative corona (Fig. 2.19b) and with re-spect to the insulating material on which the corona discharge is generated (Fig. 2.19a), due to their different attitudes of water absorption. Rickard et al. in [49] observed that changes in atmospheric humidity were directly responsible for day-to-day variation in the actuator performances.

Figure 2.18: Current values with respect to relative humidity. [46]

External flow velocity

An increase in the velocity of the fluid in which the actuator is ignited makes more difficult the transition from glow regime to the electric arc and leads to a more stable discharge than in still air; indeed, convective external velocity prevents an excessive local accumulation of charges that may gen-erate sparks. The local current density depends on both a diffusion and a convective term, which usually are neglected in electrohydrodynamic theory because they are generally much lower than the Coulomb forces. However, in aerodynamic applications the external velocity is high and the convective term cannot be neglected. The corona discharge results to be more stable in presence of an external flow, it allows to reach higher electric fields values and the density charge increases [50]. This is showed in Fig. 2.20, where the current with respect to the electric field is presented for different values of the electric field. Despite stabilizing the discharge, external velocity is one of the main limiting factors for plasma actuators. In fact, by increasing the velocity of the flow U∞ the power of the fluid rises while the power of the

actuator remains constant, implying a reduction of the effect of the ionic wind on the external flow [38]. Moreau et al. in [45] verified the decrease of the effect of the actuator for increasing values of U∞; as shown in Fig. 2.21

the difference in the boundary layer velocity profiles when the actuator is on and off is noticeable in case of U∞ = 5 m/s while for higher velocities the

(a) Maximum current values in respect to relative humidity for different insulating ma-terial. [48].

(b) Current in respect to relative humidity for different electrode materials.

Figure 2.19: Relative humidity effects

2.3

DBD actuators

Nowadays, corona actuators have been substituted by Dielectric Barrier Discharge actuators, which at present times are the most common plasma actuators; DBD actuators have replaced the coronas due to a more stable induced discharge. The main difference between corona and DBD actuators is that the latter exploits a layer of insulating material between the two elec-trodes to limit the electric current and to prevent the formation of sparks. The phenomenon of a discharge through a dielectric layer was described by Ernst Werner von Siemens at first, in 1857. Subsequently, after the work by Roth et al. ([51] and [52]), which called this technique OAUGDP (One

Figure 2.20: Current with respect to the electric field for different external flow velocities. [50]

Figure 2.21: Different velocity profile obtained with actuator on and off and U∞ equal to 5, 10 and 17 m/s. [45]

Atmosphere Uniform Glow Discharge Plasma), DBD actuators began to be exploited for fluid dynamics applications in air at atmospheric pressure. DBD plasma actuators are composed of two electrodes: one is exposed to the air and is fed with an high voltage supply while the other electrode is covered by the dielectric material and is grounded. The presence of the dielectric material layer does not allow the passage of a direct current, thus the DBD actuators are fed in alternating voltage (typically a sinusoidal waveform) that at high enough levels, causes the ionization of the air over the covered elec-trode (Fig. 2.22); the ionized air, in presence of the electric field, results in a body force vector that acts on the ambient air and can be exploited for aerodynamic control. The main strength of DBD actuators is the stability of the discharge; DBDs can sustain a large volume discharge without

col-Figure 2.22: Schematic DBD configuration. [53]

lapsing into electrical arcs. This is governed by the build-up of the charges on the dielectric surface; during the negative AC half-cycle of the voltage the exposed electrode is more negative then the dielectric surface and, when the electric potential is large enough, electrons are emitted from the exposed electrode and deposited onto the dielectric surface. As the charge on the di-electric builds up it opposes the applied voltage on the uncovered electrode. This process is similar on the opposite half of the AC cycle, but in this case the electrons are emitted from the dielectric surface and deposited on the exposed electrode. This phenomenon inhibits an overgrowth of the differ-ence of potential and it is called self-limiting effect of the discharge. On the contrary, the main weaknesses of DBD actuators are:

ˆ a limited extension of the generated plasma, which imply a limitation in the induced ionic wind velocity.

ˆ the power consumption, which is greater than in corona actuator to give the same aerodynamic performances.

As said, recently DBD actuators have been the most studied plasma ac-tuators and in literature it is possible to find thousands of papers concerning their performances and their applications. However, in order to not weight the treatment down, since this thesis works concerns corona actuators DBD actuators will not be described further.

2.4

Multi-electrode actuators

As it has be shown in the previous sections, one of the most severe limit for the performances of plasma actuators is the external freestream velocity. Indeed, despite the optimization of all geometrical and electrical parameters,

an increase of the flow velocity is typically accompanied by a reduction of the benefits of plasma actuation. This is due to a rise of the power of the flow, which increases with the cube of the velocity, while the power provided to the fluid by the actuator remains constant when the supply voltage is fixed. Re-cently, this requirement pushed the research, aiming to obtain higher values of induced-velocity, exploiting various electrodes shape or particular voltage supplies as it has been analysed in past sections.

A further step forward has been made by increasing the number of elec-trodes of the actuators, modifying their configuration. This innovative tech-nique was tested, with good results, first on DBD actuators, called sliding discharge in this configuration, ([54], [55], [56], [57], [58]) and, recently, also on corona actuators. Indeed, corona actuators, with respect to DBD, allow to obtain the same control performances with an order of magnitude lower power ([59], [41]). In the next section (Sec.2.4.1) the focus will be on multi electrode corona actuators.

2.4.1

Multi-electrode corona actuators

The first development of an innovative corona actuator was made by Colas et al. in [60], where, to generate higher ionic wind velocities, a new multi-electrode configuration is presented. The principle that they want to exploit is the decoupling of the mechanism of ions generation from the one of ions acceleration. Lately, other research groups focused on multi-electrode corona configuration, Moreau et al. in [61] and Johnson et al. in [62], as it will be presented in the next section (Sec. 2.4.2). Their works, however, were on volumetric discharge actuators, useful in various industrial processes but of little interest for flow control on airfoil. A new configuration exploiting this innovative principle on a surface corona discharge was introduced in [1] (Sec. 2.4.3).

2.4.2

Volume discharge

Classical configurations of corona actuators, composed by two electrodes, the cathode and the anode, are not able to produce high ionic wind veloci-ties; for example, despite of the serrated edge shape optimization performed in [41] and [63] the maximum measured velocity in our laboratories was about 3.5 m/s at a distance of 17 mm from the active electrode. In [60], in order to increase the magnitude of the actuator-induced ionic wind velocity, Colas et al. presented a new idea of three electrodes volumetric corona. They consid-ered as a major problem in the classical DC corona actuators the fact that the ionization and the acceleration processes are coupled, which implies that

the energy deposited in the flow is limited, because an increase in voltage causes the appearance of sparks. The aim of the new configuration was to increase the velocity of the flow by enhancing the number of charged parti-cles or the electric field. They proposed a wire-cylinder-plate configuration able to increase the flow velocity up to 10 m/s exploiting the decoupling of the ionization and the acceleration processes, they measured a rise of the generated thrust up to 0.35 N/m, i.e. 40% higher than in all previous tests with DBD or corona actuators, with a raise in the electric power of only 16% compared to standard coronas. The configuration they proposed is shown

(a) 2D experimental setup

(b) 3D experimental setup

Figure 2.23: Three electrodes actuator proposed by Colas. [60] in Fig. 2.23, they created a configuration in which there is a ionization zone between the wire, provided with a positive voltage V1, and a pair of

cylindri-cal grounded electrodes. They set the voltage V1 just below the breakdown

electric field value in order to maximize the ionization process. Behind the ionization region they created an acceleration region, between the grounded cylinders and two parallel plates fed with a negative voltage value V2. The

voltage V2 was selected in order to maximize acceleration, by performing a

numerical simulation and adopting a voltage value that allowed to generate electric field lines as parallel to the x-axis as possible. The effect of the volt-age V2, computed through 2D numerical simulations, is shown in Fig. 2.24; it

is possible to notice the creation of the lines of the electric field parallel to the x-axis, the flow direction, promoting a region of strong acceleration between the cylinders and the plates. The secondary power supply V2 increases the

(a) Electric field lines with V1 = 15 kV

and V2= 0 kV

(b) Electric field lines with V1 = 15 kV

and V2= −8 kV

Figure 2.24: Numerical simulation of the electric field lines. [60]

electric field in the space between the plates and the cylinders by almost one order of magnitude and the momentum of the charged particles is increased along the direction of the electric field lines resulting in a rise of the induced flow velocity.

The idea of separating the ionization zone from the acceleration region in corona actuators has been studied also by Moreau et al. in [61]. They made a comparison study between two different configurations of wire-to-cylinders actuators (Fig. 2.25). They highlighted that a fundamental geometrical pa-rameter in case of multi-electrodes actuators is the distance between the HV electrode and the grounded one. Indeed, they obtained a great effect due to the presence of the second voltage supply only for little distances between the HV wire and the two grounded cylinders, as it is shown in Fig. 2.26; this allowed the formation of a strong ionization zone and a good decoupling from the acceleration mechanism.

(a) Three electrodes design (b) Five electrodes design

Figure 2.25: Configuration of the corona actuators tested. [61]

Figure 2.26: Thrust with respect to the current for the design in Fig. 2.25b with two different values of d1 and with V2 on and off. [61]

2.4.3

Surface discharge

As for the classical corona actuators, in order to exploit the discharge for aerodynamic purposes, it is necessary to minimize the disturbances of the actuator on the flow field. This is the reason why the volumetric discharge corona are not serviceable for flow control on an airfoil.

Inspired by Colas’s paper, Baselli et Peronaci in [1] made some preliminary tests on a new three-electrode surface corona actuator. Recalling that the corona effect is favored by the difference between the curvatures of the elec-trodes and since experimental results by Belan and Messanelli in [41] and

Modugno and Mulone in [63] verified that serrated-edge electrodes with high h/w ratio are the most performing, they utilized a needle as main electrode, a grounded disk, with small thickness with respect to the diameter, as ionizer and an aluminium foil as accelerator electrode, as illustrated in Fig. 2.27. They conducted some studies on the effect of some parameters:

Figure 2.27: Three electrodes surface corona configuration and parame-ters. [1]

ˆ the angle β;

ˆ the diameter of the disk D;

ˆ thickness of the aluminium foil tALL;

They highlighted that the best configuration in terms of induced velocity was with a perfectly perpendicular needle (β = 0), that the disk diameter effect was almost negligible, with a slight rise in induced-velocity for bigger disks and that a thin aluminum foil did not allow to obtain good performances. They then added a second disk and characterized the behaviour of this new actuator powered by DC voltage supply, observing a promising effect in the separation of the ionization and acceleration process. Their optimization process allowed them to measure high values of induced velocity overcoming all the previously tested actuators in our laboratories, both DBD and corona (Fig. 2.28).

Figure 2.28: Comparison of velocity profiles: 3-electrodes corona measured 40 mm downstream of the needle tip and 4 serrated edge actuator (two corona C11 and C12 and two DBD D4 and D5) measured 17 mm downstream of a tip. [1]

Experimental set-up

3.1

Ionic wind measurements

3.1.1

Actuator

As previously presented, the particular plasma actuator under study is composed by three electrodes: a needle powered by a negative HV, a plate supplied by a positive HV and two grounded disks, as represented in Fig. 3.1. This configuration forms a double negative corona configuration and it has been chosen with the purpose of separating the ionization and the accelera-tion processes. X = 0 Y X Y = 0 d con d acc 2 d acc 1 D Needle Disk Disk Plate +HV -HV GND GND

Figure 3.1: Three electrodes surface actuator configuration.

curvature radius of the electrodes, here as cathode we utilize a steel needle with a tip radius of about 0.04 mm. We believe that the ionization of the fluid is mainly due to the electric field between the needle and the disks and, to favor this electric field, we chose two steel disks with rounded edges and a small thickness with respect to the diameter; in particular, the disks have a diameter of 9 mm and a thickness of 1 mm, the same order of magnitude of the needle thickness. On the contrary, the plate is responsible of the acceleration process; a steel plate with dimensions 15 x 120 mm and 1 mm thick has been selected. The electrodes are placed on a glass surface, which has been preferred to plexiglass or other insulating materials because of its resistance to electric arcs; indeed, plexiglass is damaged by the occurrence of electric arcs and a continuous maintenance is necessary; on the contrary, glass is able to guarantee higher reliability.

Some of the most important geometric parameters of the new three elec-trodes plasma actuator are represented in Fig. 3.1:

ˆ dcon: distance between the needle and the disks;

ˆ dacc1: distance between the needle tip and the plate;

ˆ dacc2: distance between the disks and the plate;

ˆ D: diameter of the disks; ˆ t: thickness of the plate; ˆ td: thickness of the disks.

3.1.2

Actuator positioning system

The relative positions between the needle and the disks can be precisely tuned by means of a very accurate self-built positioning system (Fig. 3.2). The positioning system is composed by two different mechanisms: the main body is a micro linear positioning system that allows to move the needle in the x-axis direction with an accuracy of 0.01 mm; a second mechanism is able to modify the y-axis distance between the needle and the disks (in accordance with the axis reference illustrated in Fig. 3.1, whose origin is in the needle tip). The region between the needle and the disks is the zone where the ionization process is expected to occur making the distance dcon

Figure 3.2: Actuator positioning system.

3.1.3

Ionic wind measurements

The main objective of this thesis work is to evaluate the performances of the three electrodes corona actuator; to make a comparison between the various configurations the value of the induced velocity is measured on a plane surface, as illustrated in Fig. 3.3. The velocity of the induced ionic wind is

+ V

GND

GND

- V

Y

X

To pressure

transducer

Z

Figure 3.3: Ionic wind measurement set-up.

obtained measuring the pressure difference between the static pressure in the room and the stagnation (or total) pressure at the open tip of a Pitot probe and exploiting then the Bernoulli’s theorem (Eq. 3.1) considering the low Reynolds number effect and other corrections linked to the measurement

setup to obtain a more accurate result (Sec. 3.1.3). Ptot = Ps+

1 2ρV

2 _(3.1)

The probe is constituted by a thin capillary (external diameter of 1 mm and internal diameter of 0.5 mm) with the purpose of minimizing the interference to the flow and to have a good spatial resolution. In addition, to prevent elec-trical arcing from the plasma region to the tip of the tube a Pyrex capillary is selected. The capillary is connected to a double manual linear positioning device, built by Modugno et al. in [63] (Fig. 3.4), that permits the handling and the positioning of the probe in the y-axis and z-axis directions with an accuracy of 0.01 mm.

The pressure difference is measured, via the capillary, by a micro-manometer with an adjustable range of ±20 P a or ±200 P a, a ±5 V DC analog output and an accuracy of ±0.5% of the full scale value. The manometer works in a differential way so the stagnation pressure at the Pitot probe tip is related to the room pressure, which represent a good approximation of the reference static pressure.

Figure 3.4: Manual linear positioning system.

The measurement of the dynamic pressure is acquired through an oscillo-scope with a time window of 4 s. The mean value over this observation time

window is considered the dynamic pressure of the flow.

Furthermore, to prevent undesired disturbances in the measurements of the stagnation pressure, a partial box was built to protect the discharge. Indeed, to obtain a correct measurement of the actuator induced velocity it is impor-tant to protect the measurement zone from the possible presence of external disturbances. The protection is a sort of tunnel with a plexiglass optical ac-cess to the discharge on the upper side and openings in the x-axis direction; in fact, a totally closed box around the actuator would generate some draw-backs on the measurement: first, the induced ionic wind bounded inside a closed case would imply a recirculatory motion of the air, making impossible to distinct the real induced velocity value; second, the chemical composition of the air inside a closed box would be altered in an unpredictable manner from the discharge effect on the air molecules.

Measurements acquisition

To measure the velocity profile of the ionic wind induced by the actuator, the Pitot probe is placed 40 mm downstream of the tip of the needle in order to compare the results with those measured in previous works ([1]). With the purpose of obtaining a better comprehension of the global effect of the actuator, the velocity profiles are acquired at four different span position in the y-axis direction (Fig. 3.5) starting from the needle tip: on the centerline (y = 0 mm), at the middle distance between the needle and the disks in the ionization region (y1), at the middle of the disk (y3) and at a fourth distance intermediate between the second and the third (y2); in the vertical z-axis direction, the measurements are acquired from z = 0.5 mm to z = 4.5 mm with a pace of 0.25 mm and from z = 4.5 mm to z = 7.5 mm with a pace of 0.5 mm.

The magnitude of the velocity at measurement points is given by Bernoulli’s equation (Eq. 3.1), which is indeed valid along a single streamline in steady, inviscid flows where the continuum approximation holds; those requirements cannot be respected in total, and thus it is necessary to introduce some cor-rections on the measured quantities.

First, the finite size of the probe violates the condition of measuring the to-tal pressure of a single streamline, but it will measure an uniform pressure imposed by the flow at its nose. The single-streamline condition is approxi-mated and it is considered valid since the very small diameter of the capillary tip.

However, the small dimension of the probe tip makes necessary a correction on the assumption of inviscid flow. In fact, the local Reynolds number of the

Y = 0

y1

y0 y2 y3

Disk Needle

Figure 3.5: Span position of the measurements.

probe tip results to be low making the viscosity not negligible. The viscos-ity affects the flow around the probe tip generating an increase of the total pressure reading and resulting in an higher velocity measure.

The correction adopted is the one proposed by Zagarola [64]: Cp = 1 +

10 Re1.5

d

(3.2) where Redis the Reynolds number calculated considering the external

diam-eter of the probe tip (1 mm). The utilization of a Pitot probe near a solid boundary requires an additional correction; indeed, the presence of the probe hampers the uniform flow generating a deflection of the current towards the region of higher velocity away from the wall. Thus the MacMillan correction is applied [64]:

∆U

U = 0.015 ∗ e

−3.5 z/d−0.5

(3.3) where z is the vertical position of the probe tip with respect of the wall position (z = 0) and d is the probe diameter; this correction is applied when z/d < 2.

The value of the air density ρ is obtained at first by applying the perfect gas relation, then the humidity value is measured through an hygrometer T-Logg 160 and used to calculate the relevant density variation.

The empirical relation Eq. 3.4 allows the calculation of the saturated pressure steam by knowing the temperature T in the room:

log ps =

A · T

where A, B and C are empirical constant (A = 17.438, B = 239.78 and C = 6.4147).

Subsequently, the specific humidity x is computed through the relation Eq. 3.5: x = 0.62198 · φ · ps

p − φ · ps

(3.5) where φ is the relative humidity read on the hygrometer and p is the value of the ambient pressure. Finally, the specific humidity allows to correct the density of the air in absence of water vapor ρs and to compute the correct

value of ρ by exploiting the Eq. 3.6: ρ = ρs· 0.622 ·

1 + x

0.622 + x (3.6)

3.1.4

Power supply

Direct current

In the first phase of this work, the analysis of the influence of some geo-metrical parameters of the actuator in case of direct current supply is done. In particular, the actuator is fed by a DC voltage on the electrodes: a posi-tive voltage, Vacc, is provided to the plate, whereas the needle is supplied by

a negative voltage, Vcon, and the disks are grounded; a scheme of the electric

circuit for the actuator is shown in Fig. 3.6:

The plate is fed with a positive voltage, provided by a Glassman PS/FC20R06 (Fig. 3.7) high voltage power supply; the Glassman is capable of 6 mA in a voltage range from 0 to 20 kV . This power supply unit (PSU) is equipped with a safety circuit to protect the instrument in case of sparks appearance. Indeed, the connection to the actuator is implemented through an RC filter that limits the voltage fluctuations in case of the occurrence of arcs. The ”T ” symmetric RC filter has an 8.8 M Ω total electrical resistance and a 0.9 nF capacity. These particular values have been chosen after a study on the sparks time constant and frequency, in order to avoid interruptions in the power supply.

The negative HV voltage to the needle is supplied by a Leybold 521 721, a double polarity high voltage PSU capable of providing a range of voltage from 0 to 25 kV with a maximum current of 0.5 mA. The Leybold is connected to the needle through a 1 M Ω ballast resistor in order to limit the peaks of the current and to protect the power supply in case of short circuits due to the appearance of electric arcs.