Aerodynamics of an airfoil with plasma actuators of different kinds and geometries

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Politecnico di Milano

Corso di Laurea Magistrale in Ingegneria Aeronautica Scuola di Ingegneria Industriale e dell’Informazione

Dipartimento di Scienze e Tecnologie Aerospaziali

Aerodynamics of an airfoil

with plasma actuators

of different kinds and geometries

Relatore: Prof. Marco Belan

Tesi di Laurea di:

Mattia Baselli Matr. 818753 Simone Peronaci Matr. 816978

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Sommario

Lo scopo di questo lavoro di tesi, di carattere sperimentale, è lo studio delle prestazioni degli attuatori al plasma, sia di tipo corona che DBD (Dielectric Barrier Discharge), nell’ambito del controllo della separazione su profili aerodinamici ad alti angoli di inci-denza. In particolare viene ottimizzata la geometria degli elettrodi a punte triangolari. I parametri geometrici delle punte sono ottimizzati in termini di efficacia nell’aumento di portanza e nella posticipazione dello stallo. Viene inoltre analizzato anche il consumo energetico. Per far ciò sono state effettuate prove di pesate aerodinamiche in galleria del vento su un profilo NACA0015 a quattro diversi numeri di Reynolds (85000, 170000, 255000 e 340000). I risultati ottenuti indicano una superiorità della geometria a punte triangolari rispetto alle configurazioni tradizionali, seppur con un maggior dispendio energetico.

Inoltre, è stato presentato un nuovo attuatore corona a tre elettrodi, basato sul principio dell’aumento della densità ionica. Da alcune misure preliminari della velocità indotta è stato possibile stimare come questo attuatore abbia grandi potenzialità future. Infatti, le misure effettuate mostrano velocità e portate superiori sia rispetto agli attuatori tra-dizionali che agli attuatori a punte.

Parole chiave: Attuatori al plasma, Corona, DBD, Controllo attivo del flusso, Ritardo dello stallo, Elettrodi a punte

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Abstract

The aim of this thesis work is to study the performances of plasma actuators, both corona and DBD (Dielectric Barrier Discharge) types, as flow control devices on an airfoil at high angles of attack. In particular, serrated-edge electrodes are investigated. A study on a NACA0015 airfoil is performed with the aim of improving its aerody-namic performances, with particular focus on lift coefficient increase and stall delay. The energy consumption of plasma actuators is also evaluated. To do this, lift and drag measurements have been done in a wind tunnel at four different Reynolds numbers (85000, 170000, 255000 and 340000). The results prove that the serrated-edge geometry, when properly designed, overcomes the performances of the straight actuators, although it has a higher energy consumption.

Furthermore, a new three-electrodes corona actuator is presented, based on the increase of the ion density. Some preliminary measurements of the induced velocity point out the future potentialities of this actuator. In fact, the new configuration seems to provide higher velocities and higher mass flow rates respect to serrated-edge and traditional geometries.

Keywords: Plasma actuators, Corona, DBD, Active flow control, Stall delay, Serrated electrodes

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List of Figures

1.1 Different kinds of riblets . . . 4

1.2 Vortex generators on a wing and different types of vortex generators . . 4

1.3 Active control methodology . . . 5

1.4 Graphical representation of the travelling waves of spanwise velocity . . 7

1.5 Standard configuration of an EMHD device . . . 8

1.6 Rail EMHD plasma actuator configuration . . . 8

1.7 Schematic view of the sparkjet actuator . . . 9

1.8 Effect of a corona actuator on an airfoil . . . 10

1.9 Effect of a DBD actuator on lift and drag . . . 10

2.1 Corona wire-to-plate actuator . . . 14

2.2 Generalized glow regime . . . 16

2.3 Line regime . . . 17

2.4 Filamentary regime . . . 17

2.5 Current: pressure dependency . . . 18

2.6 Corona: dependency on humidity . . . 18

2.7 Current: freestream dependency . . . 19

2.8 Velocity profiles for three values of electrodes gap . . . 20

2.9 Corona actuators with three types of dielectric material . . . 20

2.10 Corona: effect of wire diameter . . . 21

2.11 Serrated-edge corona: velocity field . . . 22

2.12 Section of a DBD actuator . . . 23

2.13 DBD: current versus time when the grounded electrode is encapsulated 24 2.14 DBD: effect of frequency . . . 25

2.15 DBD: effect of different waveforms . . . 26

2.16 DBD: effect of humidity on induced velocity . . . 28

2.17 Dielectric constant of a variety of materials . . . 29

2.18 DBD: dependancy on dielectric thickness . . . 30

2.19 Different plasma actuators shapes . . . 31

2.20 DBD: serrated edge . . . 31

2.21 Sketch of the gas flow generated by a multi-tip DBD actuator . . . 32

2.22 Induced velocity of a serrated-edge DBD . . . 32

2.23 Horizontal velocity profile above 4 DBDs in series . . . 33

2.24 DBDs in series with shield electrode . . . 34

2.25 DBDs in series HV and ground alternation . . . 34

2.26 Sliding discharge plasma actuator . . . 35

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2.27 Sliding discharge plasma luminescence . . . 35

2.28 Sliding discharge: alternative configurations . . . 35

2.29 Flow topology sliding discharge . . . 36

3.1 Red wind tunnel . . . 38

3.2 Wind tunnel calibration . . . 39

3.3 NACA0015 airfoil . . . 40

3.4 Planar representation of a multi-tip corona actuator . . . 41

3.5 Planar representation of a multi-tip DBD . . . 41

3.6 Set of coronas . . . 42

3.7 Set of DBDs . . . 43

3.8 Glassman PS/FC20R06 . . . 45

3.9 Electric setups for DBD and corona actuators . . . 46

3.10 DBD driver and its response curve . . . 47

3.11 OWIS rotary system . . . 48

3.12 Support structure for the airfoil . . . 49

3.13 Instrumented support system . . . 50

4.1 Corona discharge . . . 56

4.2 DBD discharge . . . 57

4.3 Aerodynamic curves of NACA0015 . . . 58

4.4 Comparison of clean aerodynamic curves . . . 59

4.5 Passive influence of corona actuators . . . 60

4.6 Passive influence of DBD actuators . . . 61

4.7 C6 performances . . . 63

4.8 D5 performances . . . 64

4.9 Coronas lift coefficient increase . . . 66

4.10 DBDs lift coefficient increase . . . 67

4.11 Stall delay in the parameter space . . . 70

4.12 Corona: voltage vs freestream Velocity . . . 72

4.13 Corona: power Vs freestream velocity . . . 73

4.14 Corona: power per unit length in W/m . . . 74

4.15 DBD: voltage and current waveforms . . . 75

4.16 DBD: power vs freestream velocity DBD . . . 75

4.17 DBD: power per unit length in W/m . . . 76

4.18 DBD: power per unit of perimeter in W/m DBD . . . 76

4.19 Corona: critical lift effectiveness parameter . . . 80

4.20 DBD: critical lift effectiveness parameter . . . 81

4.21 Corona: average lift effectiveness parameter . . . 82

4.22 DBD: average lift effectiveness parameter . . . 83

4.23 Lift coefficient curves for plate-to-plate DBD and wire-to-plate corona . 84 4.24 Corona: average drag efficiency . . . 85

4.25 DBD: average drag efficiency . . . 86

4.26 Lift and drag curves for C6 at U = 20m/s . . . 87

4.27 Lift and drag curves for D5 at U = 20m/s . . . 88

4.28 Lift augmentation as function of velocity . . . 89

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4.29 Maximum lift augmentation as function of velocity . . . 89

5.1 Plasma torch . . . 93

5.2 Plasmatron . . . 94

5.3 Experimental setup of Colas’ new three-electrodes actuator . . . 95

5.4 Electric field lines: numerical simulations . . . 96

5.5 Three-electrodes corona ionization regions . . . 97

5.6 3-electrodes corona electric circuit scheme . . . 98

5.7 New corona first configuration and parameters . . . 99

5.8 Velocity vs β . . . 100

5.9 Velocity vs washers diameter . . . 101

5.10 Velocity vs foil thickness . . . 102

5.11 Numerical simulations of the electric fields for different dACC2 . . . 103

5.12 Particulars of the setup for velocity measurements at the bench . . . 104

5.13 Preliminary velocity profile . . . 105

5.14 New corona “symmetric” configuration . . . 106

5.15 Actuator positioning system . . . 107

5.16 Comparison of the height of the high speed region . . . 109

5.17 Comparison of the span position of the high speed region . . . 110

5.18 Maximum velocity map . . . 111

5.19 Best velocity profiles and map . . . 112

5.20 Comparison of velocity profiles . . . 112

5.21 Vertical position of the velocity maximum . . . 113

5.22 Mass flow rate map at x = 40mm from needle tip . . . 114

A.1 Flow visualization around a cylinder . . . 126

A.2 Futuristic use of plasma actuators on trucks . . . 127

A.3 Dielectric-barrier-discharge vortex generator schematic . . . 128

A.4 Leading-edge plasma actuator . . . 129

A.5 Trailing-edge plasma actuator . . . 130

A.6 Gurney flap plasma actuator . . . 130

A.7 Effect of plasma Gurney flap on aerodynamics performances . . . 131

A.8 Plasma actuators for flight control . . . 132

A.9 Pair of plasma actuators used for roll control . . . 133

A.10 Example of distributed DBD flow control actuators on wind turbine blade 133 A.11 Example of dynamic stall control in oscillating airfoils . . . 134

B.1 C1 performances . . . 136 B.2 C2 performances . . . 137 B.3 C3 performances . . . 138 B.4 C4 performances . . . 139 B.5 C5 performances . . . 140 B.6 C6 performances . . . 141 B.7 C7 performances . . . 142 B.8 C8 performances . . . 143 B.9 C9 performances . . . 144 VI

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B.10 C10 performances . . . 145 B.11 C11 performances . . . 146 B.12 C12 performances . . . 147 B.13 C13 performances . . . 148 B.14 C14 performances . . . 149 B.15 C15 performances . . . 150 B.16 D1 performances . . . 151 B.17 D2 performances . . . 152 B.18 D3 performances . . . 153 B.19 D4 performances . . . 154 B.20 D5 performances . . . 155 B.21 D6 performances . . . 156 B.22 D7 performances . . . 157 B.23 D8 performances . . . 158 B.24 D9 performances . . . 159 B.25 D10 performances . . . 160 B.26 D11 performances . . . 161 B.27 D12 performances . . . 162 B.28 D13 performances . . . 163 B.29 D14 performances . . . 164 B.30 D15 performances . . . 165

D.1 Map VACC = 13.0kV and VCON = 2.4kV . . . 168

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List of Tables

3.1 Uncertainties of CL and CD . . . 55

4.1 Lift coefficient increase for coronas and DBDs . . . 65

4.2 Stall delay for coronas and DBDs . . . 71

C.1 Drag coefficient reduction for coronas and DBDs . . . 167

C.2 Aerodynamic efficiency augmentation for coronas and DBDs . . . 167

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Chapter 1

Introduction

The following thesis aims to continue the development of the plasma actuators through experimental tests in a wind tunnel. This technology belongs to the research field of flow control, typical area of interest of the aeronautical world. In particular in this work a study on a NACA0015 airfoil is performed with the objective of improving its aerodynamic performance, with a particular focus on stall control. The energy con-sumption of plasma actuators is also evaluated in order to quantify their efficiency as flow control devices. With this research we also would like to renew interest towards corona actuators, that, except in rare cases, the scientific community tends to neglect in favour of DBD actuators, because of their poor stability.

In this introductive chapter aerodynamic flow control problem is presented. Then it is dealt with the various adopted solutions and how plasma actuators are collocated within these solutions; the main benefits of this technology are presented.

In Chapter 2 plasma actuators are described from a physical point of view. DC coronas and AC DBDs are presented, and for each type advantages, disadvantages and geometrical and electrical optimizations are exposed.

In Chapter 3 the experimental set-up necessary for measurements acquisition is de-scribed.

The obtained results are reported and analyzed in Chapter 4.

In Chapter 5 a new 3-electrodes corona actuator is studied, from preliminary tests to ionic wind measurements.

In Chapter 6 conclusions of the research are presented and possible developments and future applications are suggested.

1.1 Flow control benefits

The ability to manipulate a flow field to impress a desired change is of immense prac-tical importance. The art of flow control probably has its origins in prehistoric times when streamlined spears and fin-stabilized arrows were empirically developed by archaic Homo Sapiens, but the real science of flow control originated with the aeronautical era. The research on the aerodynamic flow control, in particular in the boundary layer

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re-CHAPTER 1. INTRODUCTION

gion becomes indispensable. This broad area of research remains of great interest for its numerous potential benefits for both the military and civilian sectors. Today the attention of the aeronautical companies towards this field is very high.

Drag reduction on an aircraft allows to save in fuel consumption, to increase flight range and to reach higher cruise speed. Increasing the maximum lift would allow takeoff and landing with shorter runways or with a heavier aircraft. From a quantitative point of view, according to some market analysis, it has been estimated that an increase of 5% of the maximum CL during the taking off would allow an increase of the traffic load

by 20%; a drag reduction of 5% would guarantee a 40% increase of it, as well as a reduction in fuel consumption [1]. A total drag reduction of 1% could lead to a 0.2% decrease in operating costs of a large transport aircraft [2]. Therefore, the control of the aircraft flow allows both economic and performance advantages. Moreover, many environmental regulations oblige the aviation industry to continuous research in order to reduce atmospheric pollution (hence fuel consumption) and acoustic pollution.

1.2 Flow control methods

To control an air flow a system can act on three fluid dynamic phenomena: • laminar-to-turbulent transition;

• flow separation/reattachment; • turbulence level.

The delay of the transition allows mainly to reduce the frictional drag: drag in a laminar flow can be about an order of magnitude lower than in the turbulent case. Moreover turbulent flows generate much more acoustic noise than a laminar one. Instead, the transition advancement allows to increase the mixing phenomenon or the lift, post-poning the stall, since the most energetic turbulent boundary layer is able to better withstand the adverse pressure gradient.

Furthermore, the laminar flow has less drag, but it is also prone to the phenomenon called separation, which implies the detachment of the boundary layer from the surface in certain conditions, in particular at high angle of attack (AOA) when the flow has difficulties to follow the surface contour. Once separation of a laminar boundary layer occurs, drag rises dramatically because of vortices formation. A turbulent flow has more drag initially but also better adhesion, and therefore the separation is postponed with respect of a laminar flow in the same conditions. The reattachment of a separated flow on a wing allows to improve the performance in terms of lift and drag, as well as to increase the useful maximum angle of attack.

An increase in the turbulence level is used to facilitate the mixing. It is useful, for example, in combustion processes. Instead, a decrease in the turbulence level allows noise reduction.

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CHAPTER 1. INTRODUCTION

• passive control

• active control: characterized by - predetermined control ; - feedforward control ; - feedback control.

1.2.1 Passive flow control methods

A good solution to control problems might be to obtain the desired flow without spend-ing anythspend-ing in terms of energy. The passive control is based precisely on this strategy. Some techniques are able to interfere with the well-known wall cycle and its coherent structures, in order to break down the raising of the turbulence. Hereinafter the most important passive control technologies are described.

• Compliant coatings: inspired by dolphins skin, several researchers created an adaptive not-completely stiff surface, which allows an hydroelastical coupling be-tween the fluid and the surface on which it flows and an irreversible energy transfer from the fluid to the surface itself. It is a quite simple method since it does not require any internal device. The main task is to delay laminar-to-turbulent tran-sition caused by Tollmien-Schlichting instability. Compliant coatings reduce the frictional drag up to 7% and they also have sound-absorbing properties [3]. • Injection of additives: turbulent skin-friction drag can be reduced by the

ad-diction of several substances, such as long-chain molecules and micro bubbles in liquid flows. The addiction of these substances leads to a suppression of the Reynolds stresses production in the buffer region. They act in particular in the buffer layer, where velocity fluctuations extend polymer chains, locally increasing viscosity. Consequently the viscous length scale increases, leading to an increase of the buffer layer thickness, wall vortices process stops, turbulent kinetic energy production decreases and frictional drag decreases up to 80% [4]. Obviously this technique can be used only in wall-bounded flows.

• Riblets: inspired this time by the skin of sharks, engineers have modified the surface of a body, digging small grooves aligned with the freestream (Fig.1.1). Small longitudinal striations in the surface interact with the near-wall structures of turbulence stabilizing the QSV (Quasi-Streamwise Vortices) and reducing the production of turbulent kinetic energy. The drag reduction is about 10%. Over the last decades different geometries have been tried, such as rectangular, V-shaped, semicircular, and razor blade shaped. Tests were also performed with sinusoidal geometries not aligned with the mean flow and these geometries seem to work even better with drag reduction up to 20%[2][5][6].

• Vortex generators: using triangular or rectangular shaped vanes that have an height equal to about 80% of boundary layer thickness and placing them within a third of the airfoil chord, it is possible to create vortices that carry fast and highly

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Figure 1.1: Different kinds of riblets. [2]

energized air from the external flow toward the inner part of the boundary layer (Fig.1.2). In this way the boundary layer is energized and can better counteract the adverse pressure gradient responsible for the flow separation. Therefore, vortex generators are typically used to delay flow separations and, in the specific case of an airfoil, to delay stall. In a wing the trailing edge separation is postponed, allowing to increase the effectiveness of control surfaces at higher AOA. On a bluff body they are used mainly to reduce drag.

Figure 1.2: Vortex generators on a wing and different types of vortex generators.

• Surface roughness changes: modifying the quality of the surface finishing of an object located in a fluid stream, laminar-to-turbulent transition can be anticipated or delayed. The fundamental parameter is the height of the protrusions with respect to the ideal surface. This height changes substantially the behaviour of the inner boundary layer, dispersing or intensifying instabilities in order to alter the growth characteristics of the perturbations in the boundary layer. Maybe the most famous example of surface roughness effect is that on a golf ball. Dimples on the ball act as turbulators, so at high velocities the ball works at the “drag crisis zone” Reynolds, covering a greater distance than a smooth ball.

The main handicap of passive control is that it acts even when it is not strictly necessary and sometimes it can even cause unwanted side effects. For example, vortex generators are useful only at high angles of attack to prevent separation; at low AOA

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they only cause a drag increase, without other beneficial effects.

1.2.2 Active flow control methods

When using a mechanism activated by the use of a source of energy, we speak of active control. Usually there is a tendency to specify the control mode depending on how it is implemented.

The predetermined control (Fig.1.3(a)) is an open loop control, that does not involve the use of sensors and put into the system a quantity of energy decided a priori. Therefore, energy is supplied without having knowledge of the external real time variables. The reactive control instead requires the knowledge of the external variables through the use of sensors. Therefore, it allows to adapt the amount of input energy as a function of the current state of the system. If controlled variable and measured variable differ, it is called feedforward control (Fig.1.3(b)). If the controlled variable and measured one coincide, it is called feedback control (Fig.1.3(c)). In this case the variable is measured and compared with a reference value: according to the difference between the two val-ues, the control will intervene in a more or less resolved manner.

(a) Predeterminated, open ring.

(b) Reactive, feedforward, open ring.

(c) Reactive, feedback, closed ring. Figure 1.3: Active control methodology. [7]

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Hereinafter the most important active control technologies are described.

• Boundary layer blowing: the slowest particles of the boundary layer are accel-erated thanks to an increase of momentum caused by the release in the mean flow of a high-speed air jet in a more or less tangential to the wall direction. On an airfoil it mainly allows to increase the angle of attack at which the stall occurs. • Boundary layer suction: contrary to the other technique, the inner boundary

layer is not directly energized, but it is aspired in order to replace it with more energetic external boundary layer, with a higher momentum and thus more able to resist the adverse pressure gradients. Therefore, it allows to postpone the separa-tion point and to get lift coefficients up to four times bigger than the convensepara-tional ones. This type of control is obtained by means of microporous walls or with slots connected to a pump that creates depression. Because of the technological complexity, this technique is not used on civil aircrafts but only on prototypes or military ones.

• Spanwise wall oscillation: wall-bounded turbulent flows, both in planar and cylindrical geometry, exhibit interesting modifications when cyclic surface mo-tions are imposed in the spanwise direction. Perhaps the most interesting and practically appealing among the effects is the significant reduction of the mean streamwise wall friction, first reported by [8]. Among the possible types of os-cillations the most interesting is the sinusoidal one. Numerical tests have shown the possibility of reducing drag even of 34%. However, the wall oscillation effect decreases when Reynolds number increases.

• Travelling waves of spanwise velocity: it is a technique similar to the previous one and it is usable only for wall-bounded flows. Differently from oscillating wall, where the imposed spanwise velocity is homogeneous in stream and spanwise directions, here the spanwise velocity is a function not only of the time, but also of the streamwise coordinate. Waves are no longer stationary as in the case explained above, but they travel through the duct (Fig.1.4). Experimental tests show a decrease in drag around 33% against the 48% expected by numerical simulations [9][10].

• MEMS (MicroElectroMechanical System): they are a set of various kinds of devices (mechanical, electrical, electronic, ...) integrated in highly miniatur-ized form on a same substrate of semiconductor material, such as silicon. They combine multiple functions into a very small space, integrating the technology of sensors and actuators and the most different process management functions. The small size allows the installation on walls without introducing passive disturbances into the flow. When they are put into operation, through a vibratory motion they allow to promote a rapid laminar-to-turbulent transition, reducing the size of the laminar separation bubble, delaying the separation and anticipating the reattach-ment of the flow. They are advantageous also from an economic point of view. In fact they are quite inexpensive and require little power for operation [11].

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Figure 1.4: Graphical representation of the travelling waves of spanwise velocity. [3]

• MMMS (MicroMagnetoMechanical System) microvalves: they are very small electromagnetic actuated valves that can generate jets of micrometers order having local speeds up to 150m/s with variable frequencies up to 1kHz . Lines of these microvalves can be useful for separation flow control problems [12].

• EMHD (ElectroMagnetoHydroDynamic): magnetic fields are exploited to generate the volume forces able to control ionized flows. There are various con-figurations of these devices. The traditional design is characterized by long thin magnets and electrodes mounted immediately under the surface of the body in-vested by the flow. Each one is mounted with its axis aligned in the direction of the flow itself. In spanwise direction magnets and electrodes are alternately placed and with alternating polarity, as shown in Fig.1.5 [13].

Other researchers conceived different designs. For example the University of Austin, Texas [14], presented the Rail Plasma Actuator configuration (Fig.1.6). This configuration consists of two electrodes parallel to each other and to the di-rection of the mean flow, flush mounted on the upper surface of the body invested by the flow. The actuators rely on the current passing through the ionized air (plasma field ) between the electrodes inducing a magnetic field, which generates a strong Lorentz force on the plasma field. The Lorentz force has direction and orientation coincident with the mean flow one and therefore the plasma is accel-erated in this direction. Therefore, it transfers momentum to the surrounding air creating a high-speed pulsed air wall jet. As a consequence, flow near the wall can be periodically accelerated and the boundary layer separation can be delayed. Contrary to what we will see in this thesis (with the EHD plasma actuators), the MHD actuators operate at low voltages (order of volts) and high current levels (order of hundreds of amperes).

• EHD (ElectroHydroDynamic): in this case the protagonist is no longer the Lorentz force as in EMHD, but it is the Coulomb force. Plasma actuators of

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Figure 1.5: Standard configuration of an EMHD device. [13]

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Figure 1.7: Schematic view of the sparkjet actuator. [15]

our interest and of which we will discuss in this thesis belong to this group. This category also includes the Spark Discharge Actuators (also called plasma synthetic jet actuators or pulsed plasma jet actuators). A single cycle of sparkjet operation, as shown in Fig.1.7, consists of three distinct stages:

1. Energy deposition: the actuator is supplied by a high voltage power and when the cathode-to-anode potential is raised to the level required to initiate gas breakdown, a spark discharge is formed and ionizes the gas in the chamber, and the electrical energy is translated into heat;

2. Discharge: the energy deposition rapidly heats the chamber gas to high tem-perature with a corresponding rise in chamber pressure, the hot and pressur-ized gas being expelled from a small orifice in the chamber and a high speed jet being formed;

3. Recovery: the chamber pressure and temperature drop and fresh air outside of the device is drawn into the chamber, as the jet ejects and heat is lost through the wall. The cycle is complete, and the device is ready for operation again.

The sparkjet actuator only needs to consume electrical energy and the jet mo-mentum can be directed opportunely by changing the angle at which the jet is released into the flow [15][16].

1.3 Plasma actuators as flow control devices

Although plasma devices have been used in various industrial applications, before the 2000s the studies about plasma actuators were quite rare. There were some prelimi-nary researches in the ’50s with the Europeans J. Turck and A.G. Bahnson and the American G. Hill, but the first scientific publication did not come out until 1968 with Velkoff and Ketchmann [17]. At first, scientific community was very focused only on DC corona actuators. But corona configuration facilitated the creation of electric arcs not useful for flow control and potentially dangerous. Researchers discovered that the corona-to-spark transition might be prevented by employing a very short pulsed high voltage or an AC supply. Here focus shifted almost entirely on AC DBD actuators, leav-ing aside the DC corona technology. In the middle of the 1990s, Roth’s group perfected

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and developed an atmospheric pressure DBD (Dielectric Barrier Discharge) that is the basis of today’s DBD actuators for aerodynamic flow control [18][19]. Nowadays, new configurations and types of actuators are proposed, such as multiple DBDs (Sec.2.5.4) and sliding discharge (Sec.2.5.5).

All these kinds of plasma actuators, exploiting the air ionization, create an induced wind very close to the wall through which the air flow is accelerated tangentially, changing the velocity profile in the boundary layer. The first applications in the aeronautical field were separation control (Fig.1.8) on the leading edge of an airfoil, lift augmentation, drag reduction (Fig.1.9), angle of stall position control and control of the flow around bluff bodies. A full review of aerodynamic applications of plasma actuators is presented in Appendix A.

Figure 1.8: Effect of a corona actuator on an airfoil [20]. In the left figure the actuator is off, in the right figure the actuator is turned on.

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The benefits which motivate a growing interest in these actuators are numerous: - The small size and simple geometry ensure minimal interferences and disturbances

on the external flow.

- Their simplicity makes them reliable components and it ensures low fabrication and maintenance costs.

- The total absence of moving mechanical parts minimizes the weight of the struc-ture. In civil aviation this would allow an increased payload and a decrease in consumption, while in the military would be particularly suitable for high load factor manoeuvres.

- Being characterized by extremely short response times, they are indicated for the real-time feedback control of unsteady phenomena at high frequency and they could also replace control surfaces, such as ailerons, ensuring less power require-ments than electronic servos [22].

The main disadvantages of plasma actuators are:

- electric energy is directly converted into kinetic energy, without moving mechanical parts involved. Unfortunately, this energy conversion is not very efficient, and it is the main disadvantage of plasma actuators;

- production of gases: in air, plasma actuators generate gases such as ozone (O3),

nitrogen oxide (N O), and in turn nitric oxide (N O2), and thus nitric acid if

water vapour is present. Unless intentionally created (as for instance in ozone generators), these highly corrosive substances are undesired or hazardous;

- plasma actuators performances decrease in air with low concentration of oxygen, as it happens at cruising altitudes;

- stability problems for corona: in particular humidity is detrimental for stability (Sec.2.2.4);

- actuators authority decreases with freestream speed: nowadays this is the biggest limit in aeronautic applications.

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Chapter 2

Plasma actuators

This chapter presents the main features of the plasma actuators. Chemical and physical characteristics of plasmas are described in Sec.2.1. Then configurations of DC corona actuators (Sec.2.2) and of AC DBD actuators (Sec.2.4) are presented with their geo-metric and electrical optimizations (Sec.2.3, Sec.2.5).

2.1 Plasmas

A plasma is a ionized gas, with an energy density as high as to dissociate a large popula-tion of electrons from atoms or molecules and to allow both species, ions and electrons, to coexist. It consists of an approximately equal number of positively charged ions and negatively charged electrons, i.e. it is globally neutral. However its characteristics are significantly different from those of ordinary neutral gases so that plasmas are consid-ered a distinct fourth state of matter. For example, since they are made of free electric charges, they are strongly influenced by electromagnetic fields and they are good con-ductors of electricity. Plasma is the most abundant form of matter in the Universe, since 99% of the matter is in a plasma form; however on Earth it is naturally visible only in lightning and in the aurora borealis.

The first scientific studies on plasmas were made by William Crookes at the end of 19th century. More detailed studies were carried out by Nikola Tesla and Irving Langmuir. A systematic interest arose in the late 50s of the last century, the period in which research on the effects of magnetic fields on ionized gases and the first studies on nuclear fusion began. Nowadays, plasma physics is a booming industry and there are several industrial applications based on it, such as surface treatment, precision cleaning, plasma cutting, plasma welding, plasma screens, neon tubes. Even aerospace companies are interested in plasma physics to use it in propulsion and flow control (Sec.1.3).

Depending on the relative temperature of electrons, ions and neutral molecules, plasmas are classified into thermal and non-thermal. Thermal plasmas have electrons, ions and neutral molecules at the same temperature, i.e. they are in thermal equilibrium with each other. Non-thermal plasmas have instead ions and neutral molecules at a much lower temperature, often room temperature, whereas electrons are at a higher temper-ature. A plasma is sometimes called “hot” if it is nearly fully ionized, or “cold” if only

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CHAPTER 2. PLASMA ACTUATORS

a small fraction of the gas molecules are ionized. Cold plasmas are usually non-thermal plasmas. Plasmas used in technological applications are usually cold plasmas; also in this thesis only cold plasmas are considered because the energy fed into the flow by the actuator is mainly used to produce energetic electrons and not to heat the surrounding gas, which remains at a temperature close to the room one.

2.2 Corona actuators

2.2.1 Corona effect and induced ionic wind

A corona discharge is an electrical discharge brought on by the ionization of a fluid surrounding a conductor that is electrically charged.

Let us consider two planar electrodes located in still air at a certain distance from each other. Let us progressively apply a voltage gradient in direct current (DC). Until the potential difference remains below a certain threshold we do not see any kind of phenomenon and the passage of current does not occur. When the dielectric strength value of the air is overcome, atoms and molecules of the fluid undergo a process of ionization, forming electrically conductive plasma, that is perceived by human eye as a blue-violet glow concentrated in the regions where the electric field is greater. Increasing again the voltage gradient, an electric arc, that allows the closing of the circuit, will form. The electric arc is characterized by high current density, it can reach temperatures dangerous for the materials, both metallic and dielectrics, and cause electromagnetic interference to instrumentation.

For flow control applications we focus on electric fields regimes close to the air dielectric strength value, hence before electric arc formation. In fact, it is detected a regime in which there is a lower current (1 ÷ 103_{µA) than in the arc regime, with the advantage}

of being able to exploit without interruption the ionic wind that is established between the two electrodes. The ionic wind (or electric wind or corona wind ) is the main effect of a plasma actuator ignition. Gaseous ions generated in the discharge are accelerated by the electric field and undergo collisions with neutral gas molecules. This exchange of momentum, and the consequent cascading effect, generates a bulk fluid motion known as ionic wind. Its definition was proposed by Robinson in 1961 [23]: “The phenomenon known as ionic wind or corona wind refers to the gas-induced repulsion movement of the ions near a high voltage electrode”. Robinson also proposed a quantitative expression of the speed induced by the ions:

vG= k

s I

ρµ (2.1)

Where k is a geometric parameter, I is the average current discharge, ρ is the gas density and µ is the gas ionic mobility. Another expression was formulated by Sigmond and Lagstadt in 1993 [24] vG= s Id ρµAG (2.2)

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with d distance between electrodes and AG transversal section of discharge.

Several researchers have experimentally verified the proportionality of the induced speed with the square root of the average current, by measuring maximum speed in the order of 5m/s.

In order to generate a corona discharge, the electric field must have a divergence ex-ceeding a certain threshold. This depends on electrodes geometry, as the definition of Loeb [25] states: “Corona is a phenomenon that occurs in high electric field areas near sharp objects, edges or wires, in electrically stressed gases, immediately before the electric breakdown”. It is obvious that an appropriate selection of the electrodes shape may facilitate the ignition of the discharge and its stability, very important aspects for our technological purpose. To easily generate the corona effect it is commonly used a pointed or sharp electrode for increasing the ionization and one with low curvature. The corona discharge can manifest itself in the form of unipolar or bipolar corona, with the possibility that both types coexist. Furthermore, the discharge can be volumetric or superficial. In aeronautical flow control, superficial discharge is obviously preferred. It is generated between two parallel electrodes flush mounted on an insulating surface and perpendicularly placed with respect to the freestream. These electrodes can be wires or metal foils. A typical corona actuator is shown in Fig.2.1.

Figure 2.1: Section of a corona wire-to-plate actuator for the generation a superficial discharge. [26]

2.2.2 Positive and negative corona

Depending on the way in which the high voltage (HV) is applied, the physical mecha-nism that sustains the ionization near the HV electrode changes: positive corona and negative corona are possible. This is determined by the polarity of the voltage on the sharp electrode. If the curved electrode has a positive voltage with respect to the flat electrode, we have a positive corona, if it is negative, we have a negative corona. The physics of positive and negative coronas are strikingly different. In literature there are different opinions on which one works better.

Positive corona

A positive corona is initiated by an exogenous ionization event in a region of high potential gradient. The electrons resulting from the ionization are attracted toward the highly curved electrode, which serves as an anode, and the positive ions repelled from it. By undergoing unelastic collisions closer and closer to the anode, further molecules are ionized in an electron avalanche, which is expressed by the Eq.2.3.

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Secondary electrons, for further avalanches, are generated predominantly in the fluid itself, in the region outside the plasma or avalanche region. They are created by ion-ization caused by the photons emitted from the plasma in the various de-excitation processes occurring within the plasma itself after electron collisions; the thermal en-ergy liberated in those collisions creates photons which are radiated into the gas. The electrons resulting from the ionization of a neutral gas molecule are then electrically attracted back toward the anode, attracted into the plasma, and so begins the process of creating further avalanches inside the plasma.

The positive corona is divided into two regions, concentric around the sharp electrode: • Inner region contains ionizing electrons and positive ions, acting as a plasma; the electrons avalanche acts in this region, creating many further ion/electron pairs. It is known as plasma region;

• Outer region consists almost entirely of the slowly migrating massive positive ions, moving toward the uncurved electrode, which serves as a cathode, along with secondary electrons (close to the interface of this region), liberated by photons leaving the plasma, and being re-accelerated into the plasma. It is called unipolar region.

Negative corona

Negative coronas are more complex than positive ones. As with positive coronas, the establishing of a negative corona discharge begins with an exogenous ionization event generating a primary electron, followed by an electron avalanche. Electrons ionized from the neutral gas are not useful in sustaining the negative corona process by generating secondary electrons for further avalanches, as the general movement of electrons in a negative corona is outward from the curved electrode, which in this case serves as a cathode. The dominant process generating secondary electrons is the photoelectric effect from the surface of the electrode itself. The work function of the electrons (the energy required to liberate the electrons from the surface) is considerably lower than the ionization energy of air at standard temperatures and pressures, making it a more liberal source of secondary electrons under these conditions. Again, the source of energy for the electron-liberation is a high-energy photon from an atom within the plasma body relaxing after excitation from an earlier collision. However, the use of the ionized neutral gas as a source of further ionization is diminished in a negative corona by the high-concentration of positive ions clustering around the curved electrode. The collision of the positive species with the cathode can also cause electron liberation. Three radial areas around the sharp electrode can be identified:

• Inner region: high-energy electrons unelastically collide with neutral atoms and cause avalanches, whilst outer electrons (usually of a lower energy) combine with neutral atoms to produce negative ions;

• Intermediate region: electrons combine to form negative ions, because they typically have insufficient energy to cause avalanche ionization, but remain part of plasma owing to the different polarities of the species present, and the ability to take part in characteristic plasma reactions.

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• Outer region: only a flow of negative ions and, to a lesser and radially-decreasing extent, free electrons toward the positive electrode (anode) takes place.

The first two regions are known as the corona plasma. The inner region is an ionizing plasma, the middle one a non-ionizing plasma. The outer region is known as the unipo-lar region.

The difference between positive and negative coronas, in the matter of the genera-tion of secondary electron avalanches, is that in a positive one they are generated by the gas surrounding the plasma region, the new secondary electrons travelling inward, whereas in a negative corona they are generated by the sharp electrode itself, the new secondary electrons travelling outward.

A further feature of negative coronas is that, as the electrons drift outwards, they en-counter neutral molecules and, with electronegative molecules (such as oxygen and water vapour), combine to produce negative ions. These negative ions are then attracted to the positive uncurved electrode and significantly contribute to the momentum exchange with neutral air molecules.

2.2.3 Corona discharge types

In the case of surface coronas, five corona discharge regimes may be observed when the voltage between the electrodes is progressively increased.

• Spot regime: above the corona-starting voltage, the first regime is the spot regime. The discharge is concentrated within some visible spots on the sharp electrode. The current density is < 0.2mA/m and the electric wind is negligible. • Generalized glow regime: as the electric field is increased, a thin sheet of

blue ionized air between both electrodes may be observed (Fig.2.2). This mode is called generalized glow discharge (called streamer discharge in [26]). In this regime, the current density values vary around 0.2 ÷ 0.5mA/m and the electric power consumption is about 150 ÷ 400mW/m2 of plasma sheet.

Figure 2.2: Generalized glow regime. [26]

• Line regime: for higher voltage/gap ratios, current density 0.5 ÷ 1.5mA/m and power consumption 400 ÷ 600W/m2, the “line regime” (called glow discharge in [26]) is obtained. In this regime, there is no thin sheet of blue ionized air between the two electrodes but only a set of adjacent luminescent spots around both elec-trodes (Fig.2.3). This is a typical corona. Compared with the generalized glow discharge, the two main advantages of the line regime are its stability and the fact that high current values may be reached.

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Figure 2.3: Line regime. [26]

• Filamentary regime: if the voltage/gap ratio is further increased, the entire cur-rent is concentrated within few filaments (Fig.2.4); this is the filamentary regime. It has current density above 0.6mA/m and power consumption above 600mW/m2_.

Figure 2.4: Filamentary regime: discharge current. [26]

• Spark regime: thereafter, sparks appear and the discharge may become very difficult to control and dangerous since the electric arc may damage both the surface dielectric and the power supply.

2.2.4 Dependence on external factors

Corona actuators are not affected by the ambient temperature, until it is below 60°C. Instead, they are strongly dependent on the density of the fluid (Fig.2.5). In laboratory experiments the law of ideal gases is usually used, so the results are often presented as function of pressure. To be sustained, discharge needs smaller values of the electric field when the pressure decreases. While the pressure is decreased under 104P a, the discharge appears to be increasingly concentrated in a few, well visible points, in analogy with the filamentary regime [27]. In such condition it is difficult to obtain a homogeneous discharge.

Also the relative humidity has a dramatic role: when it grows, the actuator becomes progressively less stable. To obtain a stable discharge it is normally necessary to have low levels of relative humidity (< 50% [27]).

The surface of the dielectric material and the relative humidity have a large influ-ence on the intensity of the current flowing during the discharge of a corona actuator. As it can be seen in Fig.2.6, the steady state current intensity of the glow discharge

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Figure 2.5: Discharge current as a function of the applied electric field for different values of pressure. [27]

Figure 2.6: Maximum discharge current versus relative humidity values of air for three different materials. [28]

increases nearly linearly with the relative humidity of air on the glass surface as on the Pyrex surface. Conversely, the maximum current value decreases when the relative humidity increases on the PMMA surface. These dielectrics have different properties of surface water adsorption and this is probably the most important reason why the differ-ent dielectrics show a differdiffer-ent behaviour with humidity. It is very difficult to prove the direct relationship between the discharge current and surface water adsorption because measuring surface water adsorption is complex in practice.

The surface roughness was also suspected to have an influence on the initiation of the corona discharge but its effect is probably less important than the water adsorption, because the corona discharge could be obtained on a rugged surface, such as wood or paper, as well as on a smooth surface such as glass [28].

It was even noted that, when the actuator is ignited in an air stream, it is more stable, i.e. with less glow to spark transitions, than in still air. The tendency to form electric arcs is limited. The local current density depends on both a convective and a diffu-sion term that usually are neglected in electrohydrodynamic theory. This is justified

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by the fact that these terms are usually much lower than the Coulomb forces. How-ever, in aerodynamic applications the convective velocity is high and therefore the term associated with it cannot be neglected. The convective external velocity prevents an excessive local accumulation of charges that may cause the formation of a spark. Fig.2.7 [27] shows how the discharge current and the minimum voltage for the corona actuator ignition increase with the freestream velocity U0. The figure also shows that the current

increases with the the freestream velocity for the same value of applied electric field. In Eq.2.4 the linear dependency is provided, where Ji is the current density along the ith

direction, ρc is the free charge density, D is the coefficient of diffusivity of ions, µ the

ion mobility, Ei is the electric field and ui the convective velocity in ith direction.

Ji= D

∂ρc

∂xi

+ ρc(µEi+ ui) (2.4)

Figure 2.7: Left: Discharge current as a function of external speed for three different values of the applied electric field. Right: Discharge current as a function of the applied electric field for two different freestream speed values. [27]

2.3 Optimization of coronas geometry

2.3.1 Electrodes gap

From several experiments, it appears that the efficiency of corona actuators depends widely on the discharge properties and more especially on the discharge-induced ionic wind characteristics. The inter-electrode distance is one of the most important parame-ters that affect these properties. In Fig.2.8 velocity profiles for three different electrode gaps are shown for the same value of applied voltage [29]. It is possible to see that the lowest induced velocity is obtained with the largest gap (8cm). Regarding the other two configurations (4cm and 6cm) the same maximum speed was obtained, but at different heights (1mm and 2.5mm). Thus, at constant applied voltage, the maximum velocity decreases when the gap increases and it seems that the maximum velocity is obtained at higher height values when the gap increases. Therefore, the volume of momentum exchange between ions and neutral particles increases above the inter-electrode area.

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It must be said that there is a minimum distance below which the corona actuator tends to continuously form electric arcs, making the discharge unstable and unusable. Furthermore, although the maximum velocity decreases when the gap is increased and voltage is kept constant, a greater inter-electrode distance allows to use a higher supply voltage without incurring into electric arcs and hence to have a higher time-averaged current. Remembering that the velocity of the ionic wind is proportional to the square root of the current(Eq.2.1), it is surely convenient to increase the electrode gap as well as the input voltage.

Figure 2.8: Velocity profiles obtained for three different values of electrodes gap. [29]

Figure 2.9: Average discharge current for corona actuators with three different types of dielectric material. [29]

2.3.2 Dielectric

Another important parameter to be investigated is the nature of the insulating surface. In [29] Labergue and his team tested dielectric surfaces in PMMA, PVC and MDF

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(Medium Density Fiberboard ). Fig.2.9 shows clearly that higher currents are obtained with the plate in PMMA for the same value of applied electric field. Furthermore it is difficult to have a stable discharge with PVC and MDF plates. Other materials that can be used are Teflon, glass, quartz and other plastic and ceramic materials.

2.3.3 Electrodes shape

Another very important geometrical parameter is the shape of the two electrodes. The easiest case to be analyzed is the wire-to-wire configuration that consists of two wire electrodes flush mounted on an insulating surface. In [29] the discharge current and the maximum induced velocity are studied. Fig.2.10 shows the time-averaged discharge current per unit length I (mA/m) as a function of the applied reduced electric field E (kV /cm) for three different electrode diameters.

Figure 2.10: Corona: effect of wire diameter. [29]

The current increases when the HV electrode diameter decreases. Fig.2.10 also shows the velocity profiles of the ionic wind as function of the height at a given distance from the cathode and for a specific value of the current. It is possible to see that the maximum ionic wind velocity is obtained for the corona with the smallest anode and the greatest cathode. The other two profiles are quite similar. Therefore the asymmetry of the two electrodes has to be as great as possible. In general, when the curvature radius is low, the electric field gradient increases and the ionization is favoured.

The serrated edge electrode seeks to exploit precisely this property. In fact, in case of two planar electrodes, triangular tips may imply large electric fields near the tips. A parametric investigation of corona serrated edge plasma actuators was made by Belan and Messanelli [30]. They showed that the stability of corona actuators grows with the tip sharpness. In fact undesired transient sparks become rare for high tip sharpness. Furthermore they studied the induced ionic wind of a set of actuators with different tip sharpness and all actuators showed the same qualitative behaviour, as shown in Fig.2.11. The flow pattern is an array of jets spreading from tips and merging at large distances.

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The maximum local velocity within the set was given by an actuator with very sharp and separate, not numerous tips. Also the largest mass flow has been recorded for high sharpness and moderate tips number.

Another possible configuration is the wire-to-plate, where a wire is the anode and a foil is the cathode. Also in this case plasma forms near the wire and expands towards the cathode. This configuration, as well as the wire-to-wire, is very hard to ignite in case of a long wire and no external flow.

Figure 2.11: Velocity field induced by a serrated-edge corona actuator. [30]

2.4 DBD actuators

Dielectric Barrier Discharge (DBD) actuators consist of two electrodes, usually asym-metrically located, separated by a dielectric material. One of the electrodes is exposed to air, the other is completely covered by dielectric material (Fig.2.12). The electrodes are powered by alternating current (AC), usually with voltages of the order of kV , with frequencies from 50Hz to 50kHz and with currents in the range of 1 ÷ 104µA. When current is sufficiently large and the electric field exceeds a certain threshold value, known as breakdown electric field and function of the set frequency, the air ionizes in the area where the electric potential is larger. This generally begins at the edge of the exposed electrode widening towards the covered electrode. Once the actuator is turned on, in order to maintain a continuous operation, the electric field can also be lower than the breakdown value, but must be above a minimum threshold, known as electric field of sustenance. The ionization process takes place on the typical time scales of the applied alternating voltage, of the order of milliseconds or even lower.

This configuration is known in the literature [31] with the name of Single Dielectric Barrier Discharge (SDBD) to differentiate it from the case of multiple DBD, in which several DBDs are arranged one after another to obtain a larger flow control authority,

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Figure 2.12: Section of a DBD actuator.

albeit with a greater energy expense, as proposed in [32].

For a single DBD, in [33], it was demonstrated that the consumed power is proportional to V7/2 _{and to f}3/2_{, but other values for the exponents have been proposed in other}

works such as [34]. Also the DBD performances increase with both the voltage amplitude and frequency

The ionized air in the presence of an electric field gradient produces a body force on the ambient air. Many researchers have tried to develop a model to express this volume force. Orlov et al.[35] developed a lumped circuit model from which the time-space-dependent body force can be computed, taking into account the dynamic nature of the plasma formation process. A simpler and more used formulation [36] expresses the body force as: fb = −Eϕ( 0 λ2 D ) (2.5)

where ϕ is the electric potential, E is the electric field magnitude, λD is the Debye

length and 0 is the air permittivity. The Debye length is a characteristic distance of

a plasma beyond which the electric field of a charged particle is shielded by particles having charges of the opposite sign. Inside a sphere whose radius is the Debye length, charges feel the potential due to the central charge. Outside the sphere, the potential falls off and charges are no longer aware of the presence of the central charge. λD is also

known as Debye-Huckel screening radius, Debye shielding length or shielding distance.

2.4.1 DBDs operating with sinusoidal input voltage

The most studied and used input voltage waveform is the sinusoidal one. In Fig.2.13 typical discharge waveforms for a DBD with an encapsulated lower electrode are repre-sented. If the grounded electrode is not encapsulated, there is an undesired formation of plasma even on the lower surface with a resulting symmetrical current waveform.

Current is not symmetrical in the positive and negative half-cycles, and it has the most intense peaks in the positive half-cycle. In addition there is a capacitive component of the current that is out of phase by 90 degrees with respect to the voltage signal. The asymmetric behaviour of the current corresponds to two types of discharge:

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Figure 2.13: DBD: current versus time when the grounded electrode is encapsulated. [26]

• Streamer regime: during the positive half cycle, characterized by small filaments of more intense plasma;

• Glow regime: during the negative half cycle, with a more uniform and widespread plasma.

Assuming that each peak corresponds to a streamer, the number of streamers increases with the amplitude of the voltage. However, an unbounded increase of voltage can lead to an excessive accumulation of charges on the dielectric and finally to the destabilization of the discharge.

Actually, beyond a certain voltage threshold, intense plasma filaments, called breakdown streamers, can form. Further increasing the voltage would not lead to an increase in the magnitude of the ionic wind and induced force; instead, this breakdown streamers would dissipate energy by heating the dielectric up to damage it and eventually perforate it. It is said that the DBD has reached a saturation state.

2.4.2 Frequency optimization

The AC frequency plays a fundamental role on DBDs operation. As the input signal frequency increases, the saturation voltage decreases and also the body force of satura-tion decreases. The optimum AC frequency that maximizes the body force depends on the capacitance of the circuit, hence on the thickness of the dielectric and the size of the electrodes.

Thomas et al. in [37] investigated the frequency dependence, by using a 6.35mm thick glass dielectric actuator. The results are shown in Fig.2.14. For this actuator design, the 8kHz AC frequency gives the lowest maximum thrust, and the 1kHz frequency gives the highest thrust. For an equal value of the applied voltage, a larger frequency may give a higher thrust (body force). But for a higher frequency, saturation is reached at lower voltages, so that a proper optimization of voltage and frequency should be performed. Saturation voltage has a linear dependence with frequency and breakdown streamers are more numerous and intense for higher values of frequency as it can be seen in Fig.2.14.

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Figure 2.14: (a) Induced thrust from a single-dielectric barrier discharge plasma actuator with a 6.35mm thick glass dielectric for different AC frequencies of the applied voltage. (b) Corresponding images of plasma for each frequency at maximum thrust (saturation), showing the ionized air produced by the actuator. [37]

2.4.3 Electrical waveform optimization

As the force production relates to the discharge regimes, a change in the distribution of streamer and glow regimes may affect the resulting body force. This has been verified by applying different types of input voltage waveform.

Investigation on the influence of the waveform started in 2004 with the work of Van Dyken et al.[38]. They compared the maximum thrust produced by sine, square, tri-angular and positive and negative-sawtooth waveforms, and they concluded that the thrust production at constant power is maximized when using a negative sawtooth. However, in many researchers opinion, a higher mean thrust is prefereable, than higher values of instantaneous thrust. In fact, in Benard and Moreau [39], it is said that sym-metric waveforms produce a larger mean thrust. Therefore, if one wants to optimally use DBD actuators in terms of mean force at constant electrical power consumption, sine waveform as input voltage is recommended.

Results presented in Fig.2.15 show that periods of U velocity production (horizontal velocity) correspond to the negative-going cycles of the applied HV, whatever the HV waveform. In contrast, the U velocity decreases during the streamer discharge occur-ring in the positive-going cycle of the discharge. It results that the U horizontal velocity component is a mirror of the input electrical waveform. For most of the investigated waveforms, vertical induced speed component V remains negative indicating that the mean flow is deviated toward the dielectric wall. In contrast, for a positive ramp some periods of the time history of V exhibit positive values indicating that flow can be repelled from the wall.

Optimizing the sinusoidal electrical waveform is a promising approach to obtain a more performing DBD, but up to now no remarkable improvement has been achieved. Attempts were made by Abe et al.[40]. In this work the authors proposed as electrical

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Figure 2.15: Time-resolved electric wind U (horizontal, i.e., in the plasma layer direction) and V (normal direction) velocity for a) a sine waveform input, b) a square waveform, c) a positive ramp voltage and d) a negative ramp voltage. [39]

input a sine wave where the slope of the negative-going cycle has been increased. This modification showed a small benefit for the produced thrust (+10%).

In Kotsonis and Ghaemi [41], the authors looked at the effects of combinations of sine and square waveforms on the produced thrust and electric wind velocity. They defined an optimal waveform that could improve the efficiency up to 30% by comparison with the same actuator operated by a sine input waveform. The improvement in thrust production was also significant (+45%).

2.4.4 Modulated input signal and nanosecond pulse driven DBDs

Plasma actuators driven by burst modulation of the AC carrier signal are more effective for improving the control performances. A square modulating signal is generally used. It is defined as duty cycle the percentage of time in which the actuator is turned on. For example, a duty cycle of 20% means that the actuator is turned off for the 80% of the time. This is a method to drastically reduce the electrical power consumption. In [42] the authors argue that the implementation of a non-stationary actuation of a DBD becomes particularly effective when a frequency of modulation equal to that of vortex shedding is applied. They state that a DBD working in this way is able to ensure considerable results even at high mean stream velocities, although it produces a lower ionic wind velocity. In fact it seems that it excites the natural instabilities of the free shear layer, producing counter-rotating vortices within the nascent wake shear

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layer that delete coherent vortices of opposite sign, reducing the level of turbulence. In conclusion it seems that burst modulation may allow to achieve comparable or higher performances with respect to traditional waveforms, but with a consistent power saving. A new type of actuation is the nanosecond pulsed supply. Unlike standard DBDs, the nanosecond pulse driven DBD plasma actuator transfers very little momentum to the neutral air, but generates compression waves likewise localized arc filament plasma actu-ators. A complex pattern of quasi-planar and spherical compression waves is observed in still air. Measurements suggest that some of these compression waves are gener-ated by discharge filaments that remain fairly reproducible pulse-to-pulse. This type of actuation seems to be very effective also at high free stream speeds [43].

2.4.5 Dependence on external factors

In [44] preliminary experiments were conducted in a laboratory to examine the effects of water (simulated rain) and sand (simulated dust) on the operation of a DBD plasma actuator. When the DBD actuator is completely soaked with water, it shuts off tem-porarily, only at the location where the water is present; however, within seconds, as most of the water is either evaporated or pushed away by the plasma, the actuator resumes its normal operation, with no change in its amplitude or frequency settings. However in presence of water, the air relative humidity is high. As shown in Fig.2.16, the induced airflow is reduced when the air is wetted from 70% down to 98%, regard-less of the voltage amplitude. The shape of the velocity profiles is also affected by the external air condition. It appears that a decreasing humidity leads to thicker profiles, with maximal velocities obtained at higher y.

Moreover, it is widely known that the maximal electric wind velocity is usually reached at the end of the plasma region. The present results indicate that, at high RH (i.e, here higher or equal than 85%), the maximal induced electric wind velocity is located at x = 20mm from the exposed electrode, while at lower RH level, the maximal ve-locity is reached further upstream. This indicates that the ambient humidity acts on the extension of the plasma region. Further investigations are required, but it seems that the increase in RH leads to a longer plasma region. At 98% of relative humidity, the actuator performance significantly drops in terms of produced velocity and induced mass flow rate. This may limit the use of plasma discharge as a fluid dynamic control device in real-flight conditions. However, this drawback can be overcome by increasing the amplitude of the applied voltage.

With regard to the sand experiment, there were no negative effects whatsoever. Even after completely burying the actuator in sand, it continued to function normally. The plasma abruptly pushed the sand away from the actuator, indicating that the DBD is not affected by the presence of dust or sand. Instead, coronas suffer much the presence of dust and their performances are compromised, particularly as regards the ignition time and the discharge stability.