Dielectric barrier Discharge Plasma Actuator Characterization and Application

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ANOSECOND

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IELECTRIC

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ARRIER

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ISCHARGE

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L ASMA

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CTUATOR

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ANOSECOND

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IELECTRIC

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ARRIER

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ISCHARGE

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L ASMA

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CTUATOR

CHARACTERIZATION AND

APPLICATION

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K. C. A. M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op Maandag 8 februari 2016 om 10:00 uur

door

Giuseppe C

ORREALE

Master of Science in Aerospace Engineering Delft University of Technology, The Netherlands

Copromotor: Dr. M. Kotsonis Samenstelling promotiecommissie:

Rector Magnificus, voorzitter

Prof. dr. F. Scarano, Technische Universiteit Delft, promotor Dr. M. Kotsonis, Technische Universiteit Delft, copromotor Independent members:

Prof. dr. ir. L. L. M. Veldhuis, Technische Universiteit Delft Prof. dr. J. Little, Arizona State University, US Prof. dr. J. P. Bonnet, Universite de Poitiers, FR

Dr. P. Leyland, Ecole Polytechnique Federale de Lausanne, CH Prof. dr. N. Benard, Universite de Poitiers, FR

v

Keywords: ns-DBD Plasma Actuator

Printed by: Ipskamp Drukkers

Front & Back: Wheatfield with Crows, Vincent Van Gogh Graphic by:

Copyright © 2016 by Giuseppe Correale ISBN 978-94-6186-603-5

An electronic version of this dissertation is available at

I shall either find a way either make one. Hannibal

S

UMMARY

A

Nexperimental investigation about nanosecond Dielectric Barrier Discharge (ns-DBD) plasma actuator is presented in this thesis. This work aimed to answer fun-damental questions on the actuation mechanism of this device. In order to do so, para-metric studies in a quiescent air as well as laminar bounded of free shear layers were performed. Amplitude and location of the input with respect to the receptivity region as well as frequency of flow actuation were investigated. This work required the im-plementation of acquisition techniques such as Schlieren, Particle Image Velocimetry (PIV), infrared thermography, back current shunt technique and balance measurements. Moreover, tools of analysis were employed such as Linear Stability Theory (LST), Proper Orthogonal Decomposition (POD) and Inverse Heat Transfer Problem (IHTP).

Results revealed that the effect of a ns-DBD is that of “enhancing” the development of natural hydrodynamic instabilities of the specific field of motion. Therefore, in case of a laminar boundary layer, the effect of a ns-DBD plasma actuator was to amplify Tollmien–Schlichting waves according to linear stability theory. Such results led to un-derstand the influence of the actuator position on the achievement of a specific flow control task.

A ns-DBD is capable of producing several effects: a shock wave, a small body force and a thermal gradient within the discharge volume. Thus, three were the possible causes of flow actuation. The shock wave was found to be too weak to be capable of introducing an appreciable disturbance. As the shock wave, also the momentum injec-tion induced by the body force produced by the pulsed discharge was found to be rela-tively too small to justify a control authority based on momentum redistribution within the boundary layer, for cases of relatively high freestream velocity. Thus, the thermal gradient induced within the discharge volume by the energy deposition of a high volt-age nanosecond discharge is the effect capable of inducing a relatively large disturbance into the field of motion. Nevertheless, a thermal gradient within a gaseous flow induces two effects, it reduces density and increases viscosity. At the moment it is still unclear which of these two effects is more relevant. Once identified the thermal gradient as the main cause of flow control mechanism, a characterization study was performed aimed to identify the properties of a ns-DBD plasma actuator (thermal, electrical and geomet-rical) important to maximize the induced thermal gradient within the discharge volume. In general, a higher efficiency is achieved by a strong dielectric material concerning thermal energy deposition. A barrier of a ns-DBD plasma actuator should be as thin as possible. However, the thickness affects also the lifetime of the barrier itself.

Nanosecond pulsed DBD plasma actuators have shown to have the capability to de-lay leading edge separation. However, in the relevant literature, an influence of the ac-tuation frequency on the achieved results is always reported. In order to investigate this frequency effect, a parametric study on a Backward Facing Step was performed. This geometry was selected because it mimics a fixed point laminar separation, the flow

nario of interest. Such flow scenario is unstable at high frequencies close to the step and low frequencies downstream the step and it naturally develops a most unstable mode within it. However, when a flow is actuated, its stability changes, so do the most unsta-ble frequencies naturally developed within it. Results showed that the effect of actuation is the redistribution of energy among modes and that the optimal frequency of actua-tion must be based on the new stability achieved by the flow due to the actuaactua-tion itself. Moreover, results indicated that the optimal frequency of actuation is not related to the most unstable frequencies naturally present within the base non-actuated flow.

A method to quantify the efficiency of ns-DBDs in depositing energy within the dis-charge volume is proposed. This energy is the one that eventually contributes to the formation of the thermal gradient responsible of the flow control capabilities shown by these devices. Such method is based on simultaneous implementation of infrared ther-mography and back-current shunt techniques. Results showed that the overall efficiency of a ns-DBD plasma actuator is inversely proportional to the thickness of the dielectric barrier.

Last part of this thesis is concerned with a demonstrative application of a ns-DBD plasma actuator on a two element airfoil, at Reynolds numbers ranging between 0.2·106 and 2 · 106. Results demonstrated its capability to delay separation, increase lift and re-duce drag in the post stall regime. Moreover, the plasma actuator showed the capability to eliminate both a laminar bubble separation for small angles of attack and the hystere-sis behaviour of the selected airfoil.

In conclusion, this work shed some light on the flow actuation mechanism of a ns-DBD plasma actuator and deepened its basic knowledge.

S

AMENVAT TING

In deze thesis wordt een experimenteel onderzoek naar de nanosecond Dielectric Bar-rier Discharge (ns-DBD) plasma actuator gepresenteerd. Het onderzoek had als doel de fundamentele fysische werking van het actuatie mechanisme te bepalen. Hiervoor werd zowel in stilstaande lucht, in een laminaire grenslaag en in een losgelaten grens-laag een parameter studie uitgevoerd. De actuatie frequentie, en de amplitude en lo-catie van de ontlading met betrekking tot de gevoeligheidsregio van de grenslaag zijn onderzocht. Voor dit onderzoek zijn de visuele technieken Schlieren, Particle Image Ve-locimetry (PIV) en infrarood thermografie gebruikt. Daarnaast, zijn ook de back current shunt techniek en een krachtenbalans gebruikt. De analytische methodes Lineare sta-bility theorie (LST), Proper Orthogonal Decomposition (POD) en Inverse Heat Transfer Problem (IHTP) zijn toegepast bij de data verwerking. De resultaten hebben aangetoond dat de ns-DBD de natuurlijke hydrodynamische instabiliteit versterkt. Hierdoor worden in een laminaire grenslaag volgens de lineaire stabiliteit theorie de Tollmien-Schlichting golven versterkt. Dit resultaat geeft ook een indicatie waar de actuator geplaatst dient te worden voor het uitvoeren van stromingsbeïnvloeding.

Een ns-DBD een schok golf, een kleine volume kracht en een thermische gradiënt binnen het ontladingsvolume kan produceren. De schok golf blijkt te zwak om signi-ficante verstoringen te kunnen veroorzaken. Door gepulseerde actuatie ontstaat een kleine volume kracht. Echter, in hoge snelheid stromen waar stromingsbeïnvloeding gebaseerd is op momentum herverdeling in de grenslaag, blijkt deze kracht een te kleine momentum injectie te veroorzaken. De energie afzetting van een hoog voltage ns-DBD naar het ontladingsvolume veroorzaakt een temperatuur gradiënt welke relatief grote verstoringen in het stromingsveld kan veroorzaken. Echter, een temperatuur gradiënt in een gasvormige stroming heeft twee effecten; het verlaagt de dichtheid en verhoogt de viscositeit. Op dit moment is nog niet bevestigd welk van deze twee effecten do-minant is. Na het vaststellen van de beïnvloeding van de temperatuur gradiënt als het meest dominante stromingsbeïnvloeding mechanisme is een parametrische studie ge-start. Deze studie had als doel het identificeren van de eigenschappen van een ns-DBD plasma actuator (thermisch, elektrisch en geometrisch) welke het meest significant zijn in het maximaliseren van de geïnduceerde temperatuur gradiënt. Een sterk isolerend barrière materiaal is efficiënter in het produceren van de energie afzetting dan een min-der sterke isolator. Hiernaast, moet de barrière dun zijn voor maximale efficiëntie, ter-wijl een dikkere barrière een verhoogde levensduur heeft. In literatuur wordt er vaak een correlatie tussen de actuatie frequentie en de stromings-beïnvloeding resultaten gerap-porteerd. Ns-DBD plasma actuators zijn specifiek goed in het uitstellen van laminaire loslating van de voorrand van de vleugel. Daarom is er een onderzoek gedaan naar de invloed van de ontladings frequentie op een achterwaarts gerichte stap . Deze geometrie is gebruikt omdat het een vast punt van laminaire loslating heeft. Dit stroming patroon is instabiel met hoge frequentie verstoring vlak voor het loslaat punt en voor lage

tie verstoring stroomafwaarts ervan. Daarnaast ontwikkeld het een instabiele eigenmo-dus. Echter, de stabiliteit van de stroming veranderd wanneer deze onder invloed is van de actuatie van een ns-DBD plasma actuator. Hiermee worden ook de meest onstabiele frequenties in de stroming veranderd. De resultaten laten zien dat de invloed van de ac-tuatie een herverdeling van de energie in de verschillende eigenmodes tot stand brengt. Het blijkt dat de optimale actuatie frequentie gebaseerd moet worden op de nieuw tot stand gekomen stroming met bijbehorende stabiliteit eigenschappen. Hiernaast laten de resultaten zien dat de meest optimale frequentie voor actuatie geen correlatie heeft met de meest onstabiele frequenties aanwezig in de niet beïnvloedde stroming.

In deze studie wordt een methode voorgesteld om de efficiëntie van de energie af-zetting naar het ontladings volume te kwantificeren. Deze energie afaf-zetting is de oor-zaak van de gevormde temperatuur gradiënt welke weer verantwoordelijk is voor het stromings beïnvloeding mechanisme van de ns-DBD plasma actuator. De voorgestelde methode van efficiëntie kwantificeren is gebaseerd op infrarood thermografie en back-current shunt techniek. De resultaten toonden aan dat de algehele efficiëntie van een ns-DBD plasma actuator is omgekeerd evenredig met de dikte van de diëlektrische sper-laag.

Het laatste deel van deze thesis bevat een toepassing van een ns-DBD plasma ac-tuator op een dubbel element vleugel profiel bij een Reynolds nummer tussen 0.2 · 106 en 2 · 106_{. De resultaten toonden aan dat de actuator de laminaire loslating uitstelt, en}

daarnaast de opwaartse kracht (lift) verhoogd en luchtweerstand verminderd wanneer de stroming los gelaten is. Hiernaast werd de laminaire loslating bubbel bij lage invals-hoeken verwijderd, net als de hysterese van het geteste vleugelprofiel.

Kortom, dit werk werpt enig licht op de fysieke stroom bedieningsmechanisme van een NS-DBD plasma actuator en hebben de basiskennis verdiept.

P

REFACE

T

HISbook represents the final achievement of a seven years long journey in the world of plasma actuators. I first got exposed to them in 2009, working at NEQlab Research B.V. as junior researcher on projects of volumetric ignition, syngas reforming, detonation and flame propagation control. At the same time, until 2011, I carried out a preliminary investigation of ns-DBDs applied as active flow control means. Then, I have spent the last four years as Ph.D. researcher performing a basic research on their physical working principles. The main results of this research are summarized and reported in this thesis. Characterization of flow actuation mechanism and the problem of energy deposi-tion are the main topics treated here. A method to quantify efficiency is proposed as well. Moreover, a demonstrative application, at Reynolds number in the order of 106, is reported. Results demonstrate the positive effect that ns-DBDs can induce on the aero-dynamics performances of a wing.

Writing this thesis took me about nine months and it caused me a lot of stress and fatigue. However, it is not only the result of my efforts. Gratitude is due to my promoter Fulvio Scarano, who has been a good mentor and a guide from professional and personal points of view. Gratitude to Marios Kotsonis, my supervisor and friend, constant source of inspiration, who kept challenging me until the very end of this dissertation. Working side by side with him has been an unmatched honour and a pleasure. Gratitude to my colleagues, family and friends as well, who have been supporting me all the way through this adventure. I could not have done it without them.

Hoping the readers will enjoy reading this thesis, I leave them hoping to have con-tributed to the basic knowledge of plasma actuators, which can bring along improve-ments in many technological fields such as transportation and energy production. In this way I hope I have contributed to the progress of science and by extension to the progress and wellness of the whole human kind.

Giuseppe Correale Delft, December 2015

C

ONTENTS

Summary ix Samenvatting xi Preface xiii Prologue 1 1 Introduction 3 1.1 A sustainable future. . . 4 1.2 Flow control. . . 4 1.3 Governing equations . . . 5 1.4 Boundary layer . . . 7

1.5 Free shear layer. . . 9

1.6 Flow control goals. . . 10

1.7 Governing equations at the wall. . . 11

1.8 Techniques classification . . . 12

1.9 Flow control techniques . . . 13

1.10Dielectric Barrier Discharge Plasma Actuators . . . 14

1.11Open questions regarding ns-DBDs. . . 18

1.12Motivations and Objectives. . . 19

1.13Thesis outline. . . 20

2 Principles of Plasma Actuators 23 2.1 Plasma and plasma technologies . . . 24

2.2 DBD plasma actuators . . . 25

2.3 Historical background of ns-DBD. . . 28

2.4 DBD mechanisms. . . 31

2.5 State of the art of ns-DBDs . . . 34

3 Measurements techniques and data analysis 43 3.1 Experimental Methods . . . 44

3.1.1 Particle Image Velocimetry. . . 44

3.1.2 Schlieren. . . 48

3.1.3 Infrared thermography. . . 49

3.1.4 Back-current shunt technique . . . 53

3.1.5 Flow Visualization Technique . . . 54

3.1.6 Lift and drag measurements . . . 55 xv

3.2 Analysis Methods. . . 56

3.2.1 Proper Orthogonal Decomposition . . . 56

3.2.2 Linear Stability Theory. . . 58

3.2.3 Inverse Heat Transfer Problem. . . 60

I Characterization 63 4 Effect of actuation on a laminar boundary layer 65 4.1 Introduction . . . 66

4.2 Experimental setup. . . 67

4.2.1 Model and facility . . . 67

4.2.2 Actuator . . . 67 4.2.3 Schlieren imaging . . . 69 4.2.4 PIV measurements. . . 70 4.2.5 Electrical measurements. . . 70 4.2.6 Test cases . . . 70 4.3 Results . . . 71 4.3.1 Quiescent conditions . . . 71

4.3.2 Laminar boundary layer . . . 74

4.3.3 Electrical measurements. . . 78

4.4 Discussion . . . 79

5 Characterization of actuator orientation 81 5.1 Introduction . . . 82

5.2 Experimental Setup. . . 83

5.2.1 Test facility. . . 83

5.2.2 Wind-tunnel model . . . 84

5.2.3 Plasma actuator . . . 84

5.2.4 Particle Image Velocimetry. . . 85

5.2.5 Pulse energy measurements . . . 86

5.3 Results . . . 86 5.3.1 Baseline flow. . . 87 5.3.2 Actuated flow . . . 87 5.3.3 Energy deposition . . . 89 5.3.4 Density calculations . . . 90 5.4 Conclusions. . . 94

6 Control of a Backward Facing Step flow: Frequency effect 95 6.1 Introduction . . . 96

6.2 Experimental Setup. . . 97

6.2.1 Model and facility . . . 97

6.2.2 Actuator . . . 98

CONTENTS xvii

6.3 Results . . . 100

6.3.1 Base Flow . . . 100

6.3.2 Reattachment length. . . 104

6.3.3 Frequency analysis. . . 106

6.3.4 Proper Orthogonal Decomposition analysis . . . 108

6.3.5 Vorticity thickness . . . 110

6.3.6 Stability analysis. . . 112

6.4 Conclusions. . . 114

7 Influence of dielectric material on energy deposition 117 7.1 Introduction . . . 118

7.2 Experimental Setup. . . 119

7.2.1 Test Facility . . . 119

7.2.2 Nanosecond plasma actuator . . . 120

7.2.3 Selection of Materials . . . 121

7.2.4 Schlieren imaging . . . 121

7.2.5 Power measurements . . . 121

7.2.6 Discharge light intensity. . . 122

7.2.7 Material tests . . . 122

7.3 Results . . . 123

7.3.1 Material properties . . . 123

7.3.2 Electrical power characteristics . . . 124

7.3.3 Discharge imaging. . . 125

7.3.4 Energy deposition characteristics . . . 127

7.4 Calibration of the qualification method. . . 132

7.5 Discussion . . . 133 8 Quantification of ns-DBD efficiency 135 8.1 Introduction . . . 136 8.2 Experimental Setup. . . 138 8.2.1 Plasma actuator . . . 138 8.2.2 Back-current shunt . . . 139 8.2.3 Schlieren imaging . . . 139 8.2.4 Infrared thermography. . . 140

8.2.5 Heat Transfer Data Reduction . . . 140

8.3 Results . . . 142

8.3.1 Electrical efficiency . . . 142

8.3.2 Fluid mechanic efficiency . . . 144

8.4 Conclusions. . . 147

II Application 149 9 Airfoil Leading Edge Separation Control 151 9.1 Introduction . . . 152

9.2 Setup . . . 152

9.3 Results . . . 153

9.3.2 Force measurements. . . 154 9.3.3 PIV. . . 156

9.4 Conclusions. . . 163

Epilogue 169

10Conclusions and Recommendations 171

10.1Conclusions. . . 172 10.2Recommendations . . . 174 References 177 Biographical Note 197 List of Publications 199 Acknowledgements 203

P

ROLOGUE

1

I

NTRODUCTION

A man sees in the world what he carries in his heart. Doctor Faust - Johann Wolfgang von Goethe

In this chapter an introduction to the topic of ns-DBD plasma actuators is given together with its motivations and relevance. Open questions are summarised and objectives are outlined and discussed. An outline of the thesis structure is given as well.

1

T

HElimited amount of resources on the planet and the increment of the world pop-ulation have increased the awareness about the need to pursuit a sustainable devel-opment. For this reason researches are directed towards the development of efficient and sustainable technologies. In the aerodynamic field, large industries such as aircraft manufacturers are trying to improve their technologies to make them more efficient and less pollutant. To this end, the development of technologies aimed to improve aircraft performances has become more and more popular in past 50 years. One among such technologies is called “flow control”, which is the focus of the present thesis.

1.1.

A

SUSTAINABLE FUTURE

Scientific progress driven by the economy development of a growing world population is nowadays oriented towards a sustainable use of resources. The increasing demand of renewable energy and the need to reduce emission of greenhouse gases have imposed strict limitations on the technologies implemented until the end of the last century. Due to this reasons, the energy production and transportation industries have to address top-ics such as efficiency of implemented technologies and pollution factors respectively. In the field of transportation, aeroplanes, cars and trucks producers have focussed their efforts to develop more efficient and green vehicles. In the field of airborne energy, a constant effort is spent developing technologies more and more efficient and capable of being implemented on large scales. It can be foreseen that these topics will be the focus of researchers for many years to come.

From a fluid dynamic point of view, the need to move towards a sustainable use of resources has many implications. In particular, research in the field of aerodynamics performances is driven by the need to reduce fuel consumption and improve efficiency. To that end, researchers address the possibility of controlling or managing a flow around an object so to gain from its manipulation. This branch of the aerodynamics field is called “flow control”. Thus, flow control technologies have been developed in the past decades with the sole purpose to help solving one of the most pressing worldwide prob-lems. However, a flow control technology simple, inexpensive and without unwanted side effects does not exist. This is due to the complexity of the task of controlling a flow itself. For this reason, new flow control technologies are developed and it is important to keep pushing the envelope. This work is an effort towards the further development of a new flow control technology, called plasma actuator. A short description of the theory behind flow control is presented in the next section.

1.2.

F

LOW CONTROL

Flow control can be defined as “the attempt to favourably alter the character or dispo-sition of a flow field” [81]. The capability to control a fluid flow is desired in any flow-related industrial application because of the potential benefits it brings along. In gen-eral, manipulation of flows can increase efficiency, reliability and/or safety of industrial processes involving fluid flows as well as water or air vehicles. Flow control reduces to the control of bounded or free shear flows defined as “boundary layer control includes any mechanism or process through which the boundary layer of a fluid flow is caused to

1.3.GOVERNING EQUATIONS

1

5

behave differently than it normally would” by Flatt [77]. Thus, modification of natural fluid motion is the final goal of flow control.

All the means designed to achieve this task are called flow control techniques. Modifi-cation of fluid motion can be generated mechanically, thermally, electrically or by other means. Pioneer of this field was Ludwig Prandtl who introduced the concept of bound-ary layer. During the third International Congress of Mathematicians (Heidelberg, Ger-many, 1904) [194] he presented results of suction applied to delay boundary layer sepa-ration on a cylinder. However, the development of this scientific discipline had to wait until the second world war in order to gain attention [145,271].

An example of what the result of flow control by a plasma actuator could be is pre-sented in figure1.1[80]. In this figure a visualization technique yields the flow stream-lines around an airfoil. At larger incidence the flow naturally separates above the airfoil (left) and a formation of a large wake is visible (figure1.1a). When the flow is controlled, it reattaches on the suction side of the airfoil, thus reducing the wake that the airfoil generates (figure1.1b).

Figure 1.1: Leading edge separation control, NACA0015, α = 12◦_{. (a) Natural flow with actuator OFF and (b)}

with flow control ON [80].

For about a century researchers have pushed the envelope in the field of flow control. Many different techniques were developed in order to achieve tasks that span between transition delay [148], separation prevention [92,149], lift production enhancement [82,

269], noise reduction or suppression [170,180], drag reduction [213] and more [81].

1.3.

G

OVERNING EQUATIONS

The motion of a fluid is governed by constitutive laws known as Navier-Stokes equations, which are a set of non-linear, partial differential equations that express conservation of mass, momentum and energy. These equations require initial and boundary conditions before they can be solved. The derivation of these equations is beyond the scope of this paragraph, the interested reader is addressed to textbooks of fundamental fluid dynam-ics [225,274]. In their most generic form, expressed in a Cartesian tensor notation, they read as: ∂ρ ∂t + ∂ ∂xk (ρuk) = 0 (1.1)

1

∂ ∂t(ρui) + ∂ ∂xk (ρuiuk) = ∂Σki ∂xk + fvol ume (1.2) ∂ ∂t(ρe) + ∂ ∂xk (ρeuk) = − ∂qi ∂xk+ Σki ∂ui ∂xk+ Ψ (1.3) where fvol umeindicates all the forces acting on the whole mass of fluid, energy e is ex-pressed per unit of mass, ui is the instantaneous velocity component in three different directions (u, v, w), Σkiis general deformation law for newtonian viscous fluids and in-dicates the sum of forces acting on the surface of a control volume, qi is the heat flux, ρ is the density and Ψ is a source term. Time t and space coordinates (x, y, z) are the independent variables.

Considering that the stress tensor is symmetric with only 6 independent compo-nents, the system of equations1.1-1.3has 14 unknown in 5 equations. Then, to close the system it is necessary to define a relation between the heat flux vector and the tem-perature, the stress tensor and deformation rate and an appropriate equation of state.

For a newtonian, isotropic, ideal gas, equations1.1-1.3can be simplified and rewrit-ten as: ∂ρ ∂t + ∂ ∂xk (ρuk) = 0 (1.4) ∂ ∂t(ρui) + ∂ ∂xk (ρuiuk) = − ∂p ∂xk+ ∂ ∂xk · µµ ∂ui ∂xk+ ∂uk ∂xi ¶ + δkiλ ∂uj ∂xj ¸ + fg+ fe (1.5) cp µ ∂ ∂t(ρT ) + ∂ ∂xk (ρTuk) ¶ = ∂ ∂xk µ κ∂T ∂xk ¶ + φ + Ψ (1.6)

where, in addition to the former set of equations (equations1.1-1.3) there is the ther-modynamic pressure p, the dynamic and dilatational viscosity coefficients µ and λ, T is the temperature field, κ and cp are the thermal conductivity and specific heat respec-tively, δki is the Kronecker delta, which is equal to one when k = i and equal to zero when k 6= i , φ is a dissipation function expressing the irreversible process of mechanical energy converted to internal energy and Ψ is a source term. Moreover, the term fvol ume has been decomposed in volumetric forces due to gravity fg and forces due to applied electromagnetic potentials fe. The latter is usually neglected, but for the specific case of plasma actuators it cannot be neglected [67,68]. The system of equations1.4-1.6is still open having 5 equations and 7 unknowns ρ, ui, fe, p and T . Moreover, the equation of state for ideal gas is:

p = ρRT (1.7)

with R representing the universal gas constant.

The system of equations1.4-1.7, coupled with an adequate number of boundary and initial conditions and without considering fe, constitute a well-posed problem and can be solved. For the case of plasma actuators, fecan be modelled or found experimentally [113,139].

1.4.BOUNDARY LAYER

1

7

Considerable simplification of the problem can be obtained in certain cases such as incompressible or steady flows. The Navier-Stokes equations are often written in non-dimensional form. In such shape, dimensionless coefficients appear in front of several of the terms within the equations system. Those dimensionless parameters determine the relative importance of different terms within the equations, thus allowing further sim-plification. The most relevant parameters used in aerodynamics and within the scope of the present work are Reynolds (Re), Mach (M a) and Strouhal (St) numbers.

Re =LU ν (1.8) M a =U a (1.9) St = f L U (1.10)

The first one, defined in equation1.8as the ratio between a characteristic length (L) and velocity (U ) with respect to the kinematic viscosity coefficient (ν). It represents the relative importance of inertial forces with respect to viscous forces. The second one, defined in equation 1.9as the ratio between the local flow velocity (U ) and the local speed of sound (a). It gives an indication on the relative importance of compressibility effects. The third one, defined in equation1.10as the ratio between frequency (f ) and a characteristic length (L) with respect to a characteristic velocity (U ) of the physical system analyzed. It represents non-dimensional frequency and can be referred to the periodicity of specific flow structures.

1.4.

B

OUNDARY LAYER

The region of a wall-bounded flow where viscosity effects are not negligible is called boundary layer [194] and it is located in the proximity of walls. Thus, any object im-mersed in a moving fluid flow develops on its walls a boundary layer. A boundary layer can be classified according to the state of motion of the particles, i.e. it can be “laminar” or “turbulent”. A laminar boundary layer is characterized by a smooth flow that does not contain swirls or vortices. On the other hand, a turbulent boundary layer is character-ized by a more chaotic flow motion and the presence of rotating flow structures within it. The passage from a laminar state to a turbulent one is called “transition”. In figure1.2

a sketch of laminar, transitional and turbulent boundary layer is reported.

As shown in figure1.2, a turbulent boundary layer is further divided in viscous sub-layer, buffer layer and turbulent region, also called external layer [225,274].

Transition from laminar to turbulent is a process that passes through a series of stages [172] and is connected to the stability of the boundary layer [225,274]. Inde-pendently from the path of transition, its first stage begins in the receptivity region of a laminar boundary layer. The parameter that dominates the beginning of the receptivity region is the Reynolds number [225,274].

Independently from its nature, a boundary layer can separate from the wall where it forms if a strong enough adverse pressure gradient is present. This is the case of a boundary layer developing on the curved surface of an airfoil, as illustrated in figure1.3.

1

Figure 1.2: Sketch of a laminar-to-turbulent transition of a boundary layer [2].

Figure 1.3: Boundary layer in flow over a curved surface [72].

Figure1.3also illustrates that the velocity profile across the boundary layer exhibits an inflection point and the gradient of velocity at the wall in the wall-normal direction (in figure1.3indicated with y) is equal to zero. After that point the boundary layer sep-arates and a region of reverse flow is formed, also called recirculation region. Turbulent boundary layers are more energetic than laminar ones, with momentum more uniformly distributed across it. For this reason, turbulent boundary layers can stand higher adverse pressure gradient than laminar ones before separating. However, friction induced by a turbulent boundary layer is higher than that produced by a laminar one [72,274].

Two main goals of flow control on boundary layers are: reduction of skin friction and separation delay. The latter is of special interest since it represents a promising applica-tion for flow control based on ns-DBDs.

In general, the majority of flow control techniques rely on a manipulation of a bound-ary layer and its stability is a parameter that indicates how susceptible it is to manipula-tions. The shape of the velocity profile is an important factor to determine the stability behaviour of a boundary layer. More specifically, velocity profiles of boundary layer can be non-inflectional, thus stable according to the linear stability theory [203]. Stable pro-files are difficult to manipulate. On the other hand, velocity propro-files can also present an inflectional shape, which makes them unstable and easy to manipulate. Therefore, according to the shape of the velocity profile and the task to be achieved, different flow

1.5.FREE SHEAR LAYER

1

9

control techniques can be designed. Differently from separated flows (see paragraph

1.5), boundary layers are easily reachable being attached on a wall. Thus, flow control techniques can be distributed along the wall where the flow develops. This kind of con-trol is often coupled with a feedback concon-trol loop [37,264], given the possibility to have wall-distributed probes capable of measuring flow changes and change the control algo-rithm accordingly [266,267]. In chapters4and5, results of experimental investigations on manipulations of boundary layer are reported. More specifically, the effect of ns-DBD plasma actuators on laminar boundary layers is investigated.

In the context of an aircraft, flow separation delay allows to increase the angle of incidence (a.k.a. angle of attack) of a wing with the freestream. Therefore, high lift con-figurations can be achieved at relatively lower velocities than the case without control. Thus, flow control can allow aircraft to land at a lower speed, so increasing safety. More-over, wings can not operate to close to their CLM AX configuration because a sudden air

gust can separate the flow. A flow control technique capable of delaying separation can, therefore, increase the safety margins also during take-off.

1.5.

F

REE SHEAR LAYER

When a bounded shear flow separates from the wall where it develops, a region of reverse flow is formed and the portion of flow where the effects of viscosity are not negligible is called free shear layer. A free shear layer can also be created by a non-separated flow, as for the case of a mixing layer. A mixing layer is formed at the aft stagnation point of an airfoil for instance, where boundary layers of the suction and pressure sides merge together. In figure1.4two examples of free shear layers are given.

(a) (b)

Figure 1.4: Shear layer formed at the verge of a corner (a) and the wake induced by an airfoil (b). Figure adapted from [72].

As with the boundary layer, a free shear layer can be laminar or turbulent and transi-tion from one state to the other can happen within the free shear layer.

Shear layers have an inflectional mean velocity profile, thus they are unstable ac-cording to the inviscid linear stability theory [203] and susceptible to inviscid instabili-ties, thus they are easy to manipulate. Their control mechanism is based on induction of vorticity. Flow control tasks are mainly transition delay and mixing enhancement. The latter is of special interest since it presents a promising application for flow control techniques based on ns-DBDs.

Techniques and strategy of flow control are different according to the case. Free shear layers originate from surface or geometrical aberrations, nozzle, slitter plates and more in general from separated wall-flows. Independently from the way they are generated,

1

free shear layers are not bounded so not directly reachable. Therefore, in order to ma-nipulate them, flow control devices are placed upstream their separation point or on the corresponding wall, though far from the region to be controlled [75,95]. For this rea-son, feedback loop meant to operate on the flow control of a free shear layer are hard to implement without being intrusive into the flow field [76,94,276]. Both numerical and experimental works have tested shear layer control techniques on benchmark flows such as a flow over a Backward Facing Step [8,19,166], which can mimic flow separation typ-ically occurring in high lift devices such as airfoils at high angles of attack [26,97,126], even if the latter flow scenario is generated by an adverse pressure gradient over the suc-tion side of an airfoil instead of a geometrical perturbasuc-tion [39,92,110].

In this work, the effect of a ns-DBD plasma actuator on a free shear layer generated at the verge of a backward facing step is reported in chapter6. More specifically, results of an experimental investigation on the frequency effect of this device on a free shear layer are reported. Moreover, in chapter9results on an application of a ns-DBD for separation control are reported.

Reattachment of separated flow can be as important as delaying flow separation. In fact, at given flow conditions, a wing of an aircraft at high lift configuration, i.e. close to its CLM AX can experience flow separation due to a sudden air gust. Once the flow is

separated and the air gust is over, the wing is in what is called hysteresis, i.e. a charac-teristic part of lift polar of a wing. As consequence, the size of the wake generated by that wing increases and manoeuvrability reduces. Therefore, a flow control capable of reattaching a separated flow increases the safety margins of aircraft that fly at high lift configurations.

1.6.

F

LOW CONTROL GOALS

Several are the flow control goals that can be achieved by manipulating the bound-ary layer developed on the external surface of any object moving within a fluid flow. Tasks such as transition or separation delay [92,148,149], lift enhancement [82,269], skin-friction and pressure drag reduction [92,213], turbulence augmentation [279], heat transfer enhancement [38,281], or noise suppression [144,275] can be achieved. How-ever, all the flow control tasks are intrinsically interrelated to each other and whenever a goal is achieved other side effects are created. In figure1.5a schematic representation of the interrelations between flow control goals is given [81]. For instance, in the case of a flow over an airfoil, a turbulent boundary layer would become more resistant to sepa-ration, so angle of attack can be increased in order to generate more lift. However, skin friction of a turbulent flow is one order of magnitude higher than the one of a laminar flow. On the other hand, if turbulent flow is delayed, other interactions are induced. If transition is delayed skin friction and noise are reduced, but a laminar boundary layer is more susceptible to separation [81]. These examples are given in order to underline that flow control is never trivial, it is a trade off among potential conflicting effects. “An ideal method of control that is simple, inexpensive to build and operate, and does not have any trade-off does not exist” [81].

1.7.GOVERNING EQUATIONS AT THE WALL

1

11

Figure 1.5: Interrelations between flow control goals. Figure adapted from [81]

1.7.

G

OVERNING EQUATIONS AT THE WALL

Flow control of wall-bounded flows is basically a manipulation of the boundary layers that develop around solid boundaries. Therefore, it is interesting to look at the governing equation of motion (see paragraph1.3) at the wall, i.e. where a boundary layer develops. Considering the stream-wise component of an incompressible flow over a non-moving wall, in a Cartesian coordinate system having the positive x-axis aligned with the stream-wise direction, equation1.5can be written at y = 0 as [81]:

ρvw∂u ∂y ¯ ¯ ¯ ¯ y =0+ ∂p ∂x ¯ ¯ ¯ ¯ y =0− ∂µ ∂y ¯ ¯ ¯ ¯ y =0 ∂u ∂y ¯ ¯ ¯ ¯ y =0= µ ∂2u ∂y2 ¯ ¯ ¯ ¯ y =0 (1.11) The right hand side (RHS) of this equation represents the curvature of the velocity profile across the boundary layer. Its shape is an important factor which allows to dis-tinguish between laminar or turbulent flow. Moreover, from the curvature of the velocity profile of a boundary layer it is possible to determine the stability character of the flow [225,274], i.e. to determine whether and where/when it undergoes laminar-to-turbulent transition. In general, the fuller the velocity profile is the longer a boundary layer does not experience separation. In this description, negative curvatures implies a fuller ve-locity profile.

On the left hand side (LHS) of equation1.11the terms that affect the boundary layer profile are identified. The first term represents suction/blowing at the wall, with the

1

vertical component of the velocity at the wall vwnegative/positive respectively. The sec-ond term represents the contribution of the pressure gradient to the curvature of veloc-ity profile at the wall. In aerodynamics application, adverse pressure gradients in the stream-wise direction are a common cause of flow separation. The third term represents the contribution of viscosity. Wall viscosity smaller or larger than the one of the flow can affect the curvature of the velocity profile.

Therefore, according to the specific flow control task desired, the LHS of equation

1.11must be modified accordingly. For instance, in order to delay transition it is impor-tant to keep the velocity profile as full as possible (RHS of equation1.11), and this can be achieved by wall suction, positive pressure gradient or having a wall viscosity lower that the one above the surface. Therefore, knowing what is necessary to achieve a desired flow control task, techniques can be developed accordingly.

1.8.

T

ECHNIQUES CLASSIFICATION

Flow control techniques can be classified in different categories according to particular features of the control system itself. The most common distinction is based on the en-ergy expenditure and the control loop involved. Therefore, flow control techniques can be categorised in two main groups: passive and active. Passive techniques are those that do not require auxiliary power to work, practically they are always on. On the contrary, active techniques are those that require energy expenditure and are not always on, but need to be switched on when required by a user/control-loop. Active techniques are fur-ther divided into “predetermined” or “interactive”. A schematic representation is given in figure1.6

1.9.FLOW CONTROL TECHNIQUES

1

13

The differences between predetermined and interactive control is in the control loop. The former is applied when the flow situation is well known and a sure effect is expected. The control loop in this case is open and no sensors are required. The latter is employed when the flow conditions are time dependent and the control function is constantly ad-justed upon incoming conditions and post-actuation flow conditions. The control loop in this case can either be an open and feed-forward or closed and feed-back loop. Clas-sical control theory deals, for the most part, with interactive control.

Both categories (i.e. passive and active) have their pros and cons. In general a pas-sive technique is preferred because of its simplicity and reliability. However, in general it induces a constant contribution on the drag that represents a strong limit in optimiza-tion processes. Active techniques do not have this drawback. However, very often their mechanical complexity is such that to implement or retrofit them on existing designs is challenging.

1.9.

F

LOW CONTROL TECHNIQUES

Many examples of flow control techniques applied to the aerodynamic field can be re-ported. Passive techniques, as defined in the previous paragraph, are vortex generators, winglets, riblets, serrations and more [81]. In figure1.7examples of applications of these techniques are reported.

The mechanisms of flow actuation of all these devices can be related to a modifica-tion of the left hand-side terms in equamodifica-tion1.11. For example, vortex generators (figure

1.7a), generating vortices, redistribute momentum within the boundary layer, so affect-ing the first term on the LHS of equation1.11. While winglets (figure1.7b), affect the pressure distribution along a wing, so affecting the second term on the LHS in equation

1.11.

In general, active flow control techniques are more complex, from a mechanical and/or electrical point of view. Moreover, they require power to be activated and a sys-tem to manage and/or control them. Such syssys-tem can be of different kinds. Thus, ac-cording to the kind of control loop implemented within a device, an active flow control technique can further be categorized, as illustrated in figure1.6.

Example of active flow control techniques are blowing/suction at the wall, fluidic/ synthetic jet actuators (illustrated in figure1.8a), MEMS/piezoelectric actuators (illus-trated in figure1.8b).

As for passive techniques, also the mechanism of active flow control techniques can be related to a modification of the terms on the LHS of equation1.11. For instance, blow-ing/suction (figure1.8a) introduces a vertical wall-normal velocity component, i.e. vw in equation1.11. While MEMS/piezoelectric actuators (figure1.8b) modify the velocity gradient in the wall-normal direction, i.e. the first and third terms on the LHS of equa-tion1.11.

1

(a)

(b)

(d)

Vortex Generator

Figure 1.7: Examples of passive flow control techniques employed in the aerodynamics field (left column) and encountered in nature (right column). Vortex generators (a), winglets (b), riblets (c) and serrations (d). Figures adapted from the internet.

1.10.

D

IELECTRIC

B

ARRIER

D

ISCHARGE

P

LASMA

A

CTUATORS

Among the most recent developed techniques for flow control, a great deal of interest is aroused by dielectric barrier discharge (DBD) plasma actuators. The DBD technology was originally developed to synthesize chemicals [30,191] and clean/sterilize surgical tables or tools [119,284]. Later these devices were used to design active flow control techniques, but without the typical drawbacks of an active flow control technique, i.e. not adding mechanical complexity [207,210]. As a matter of fact, what makes these devices so appealing is the lack of mechanisms or moving elements. Moreover, they have a relatively simple layout that combined with a relatively low energy consumption make of them one of a kind. DBD plasma actuators can be perfectly flush mounted on the surface where flow control is desired, thus not inducing additional aerodynamic drag and their simple constructive requirements allow them to be implemented or retrofitted on existing designs.

1.10.DIELECTRICBARRIERDISCHARGEPLASMAACTUATORS

1

15

(b)

(a)

Power Input

Figure 1.8: Examples of active flow control techniques employed in the aerodynamics field. Synthetic jet (a) and piezoelectric MEMS actuator (b). Figures adapted from [4] and [254]).

According to the electrical waveform used to produce plasma, DBDs for flow control can be classified in two categories: ac-DBD and ns-DBD [43,171]. The former produces plasma by discharging an Alternative Current (AC) and it is the most used and studied, therefore its principle of operation and flow actuation are well known. A sketch illustrat-ing layout and discharge induced effects is reported in figure1.9. The latter produces plasma by discharging a nanosecond (ns) high voltage pulse with very short rising and fall period. A sketch illustrating layout and discharge induced effects is reported in fig-ure1.10. The two devices produce the same kind of plasma, namely what is called cold plasma [78]. However, given the different time scales involved, the physics phenomena developed within the plasma layer are different. This is the reason why the two plasma actuators have a different effect on a flow.

The flow actuation mechanism induced by an ac-DBD plasma actuator relies on the production of a body force [69,70] which imparts momentum into the lower layers of the bounded shear flow under control. Based on geometrical and/or electrical characteris-tics of this kind of plasma actuator, a wall jet with a maximum velocity of about 11m/s was reported in literature [22,43,171].

During the first half of the AC cycle, for example characterised by positive voltage, electrons move from the High Voltage (HV) electrode towards the grounded one, though not being capable of reaching it. During their motion, electrons colliding with molecules generate ions that are moved by the electrical field created by the voltage difference be-tween the electrodes. While ions motion generates a body force, electrons accumulate on the dielectric surface. This affects the electrical field generated by the second half of the AC cycle, creating ions that will be moved by a somehow smaller electrical field, inducing the typical push-pull mechanism [138] of ac-DBD, with an overall net force pointing from the HV (exposed) electrode to the grounded (covered) one. Electrons keep accumulating on the dielectric surface cycle after cycle, limiting the force generation

1

V Fb

Figure 1.9: Sketch illustrating ac-DBD plasma actuator layout, geometry and effects induced by the electrical discharge. Figure adapted from [263].

Figure 1.10: Sketch illustrating ns-DBD plasma actuator layout, geometry and effects induced by the electrical discharge. Figure adapted from [263].

mechanism.

Taken the discharge region as control volume, during the discharge the term in equa-tion1.5relative to a volumetric force induced by an electromagnetic field febecomes

1.10.DIELECTRICBARRIERDISCHARGEPLASMAACTUATORS

1

17

significant and is the key parameter of the flow actuation mechanism of an ac-DBD. Also the source term Ψ in equation 1.6becomes different than zero during the discharge. However, on typical time scales of flow motion, i.e. milliseconds, it is relatively small and can be neglected [113].

In order to overcome the self limiting behaviour of an ac-DBD, a sustained direct discharge should be employed, i.e. Direct Current (DC). However, the dielectric barrier does not allow to sustain such kind of discharge, for a long period of time. Some attempts to overcome this limit by modifying the dielectric nature of the barrier are reported [184,

244], however such idea has not been pursuit.

Meanwhile, a different kind of DBD actuator was used for flow control in supersonic aerodynamics applications [27]. It was the so called nanosecond DBD (a.k.a. ns-DBD). Given the reported results (see chapter2), it was thought to be capable of overcoming the self-limiting mechanism of the ac-DBD [182,217]. The first time that such actuator was employed in subsonic flow was in 2005, in a paper by Opaits et al. [182]. Ever since, research on this kind of plasma actuator has increased, demonstrating a large control authority for the case of laminar leading edge separation. However, a long debate was generated around the nature of its physical mechanism of flow actuation.

A plasma actuator, when driven by a nanosecond HV pulse, induces on a flow differ-ent effects that develop on differdiffer-ent time scales. Taking a control volume coinciding with the discharge volume, on the time scale of the discharge, i.e. nanoseconds, the fast dis-charge induces an impulsive energy deposition, thus the source term Ψ in equation1.6

becomes significant. Also a relatively small body force feis induced, but given the short time scale, no effect on the flow is shown yet, so fe can still be neglected in equation

1.5. On a microsecond time scale, a temperature gradient due to the energy deposition induces a density gradient within the discharge/control volume. The consequent ex-pansion happens adiabatically, since temperature rises but the gas does not have time to expand yet. This increases the first term on the RHS of equation1.5, i.e. the pressure gradient and generates a shock wave which becomes a sonic wave after few microsec-onds [287]. Due to the short time scales, the flow has not been capable yet to react to the energy deposited, body force and compressive wave. As time elapses, on millisecond time scales, the energy deposited diffuses non-adiabatically and induces a temperature gradient which affects the continuity equation1.4. As a result, the discharge/control vol-ume expands. Moreover, it affects also the viscosity coefficient µ in the second term of the RHS of equation1.5. On this time scale also the body force fein equation1.5 be-comes significant.

Therefore, the effect of a ns-DBD plasma actuator on a flow relies on the energy de-posited on a nanosecond time scale. Any flow manipulation achieved by applying this plasma actuator is a consequence of that.

In figure1.11the effect of the discharge on the discharge volume is shown on three different time scales. The light scattered by the discharge on nanosecond time scales highlights the discharge volume (figure1.11a). The gas within the discharge volume im-pulsively increases its temperature adiabatically, resulting in the generation of a shock wave on microsecond time scale (1.11b). When enough time is elapsed, the deposited energy induces a temperature rise of the ions and molecules present within the dis-charge volume which induces an expansion of the gas contained within it (1.11c).

1

a) nanosecond time scale b) microsecond time scale c) millisecond time scale

Figure 1.11: Schlieren image of ns-DBD plasma actuator on a nanosecond (a), microsecond (b) and millisec-ond (c) time scale. Experiment carried out in quiescent air cmillisec-ondition on a ns-DBD plasma actuator discharging a burst of 50 pulses with an amplitude of 10kV and a repetition rate of 10k H z, mean energy input per pulse about 10m J. Figures adapted from [46].

Results on flow control achieved by applying ns-DBD are shown in figure1.12. A NACA63618 is placed in an open jet flow at an incidence of 32◦_{and a Reynolds number}

in the order of 105. Due to the presence of relatively strong adverse pressure gradients the flow is separated (figure1.12a). After a single high voltage nanosecond pulse a shock wave propagates toward the far field (figure1.12b). When the flow has enough time to react, a coherent span-wise vortex propagates throughout the free shear layer (figure

1.12c). As a consequence, the shear layer transits from laminar to turbulent and since a turbulent flow is capable to stand a stronger pressure gradient, the flow reattaches on the suction side of the airfoil (figure1.12d).

a

b

c

d

Figure 1.12: Schlieren image of ns-DBD plasma actuator on the leading edge of a NACA63618 at α = 32◦_and Re = 4 · 105. Flow separated (a) and after the discharge a shock wave is visible (b). Then, a span-wise coherent vortex (i.e. a Kelvin-Helmholtz instability) propagates throughout the free shear layer (c) with a subsequent turbulization and flow reattachment (d). Figures adapted from [49].

1.11.

O

PEN QUESTIONS REGARDING NS

-DBD

S

Advancing the knowledge on ns-DBD plasma actuator is the main objective of this work. Prior to this research the great potential of this kind of plasma actuator was demon-strated [49,153,217], but the physical principles of flow actuation were unclear. Given the similarity with other kinds of actuators and the numerical and experimental results

1.12.MOTIVATIONS ANDOBJECTIVES

1

19

reported, the general opinion converged on a “thermal effect” capable of driving laminar-to-turbulent flow transition and/or excitation of a shear layer instability [154,217].

Therefore, while the effect was an acceleration on a laminar-to-turbulent transition, the cause of it was source of debate. Part of the ambiguity could be ascribed to the several possible routes toward transition of the boundary layer [172]. From an application point of view an open question was demonstrating the existence of an optimum for location, amplitude and frequency of actuation.

Although, electrical [23,53] and optical [23,251] characterizations of ns-DBD are found in literature, there is no sufficient information on the process of energy deposition due to a high voltage discharge, i.e. the “thermal effect”.

Methods that quantify the energy deposition are also under development. In litera-ture a method to quantify efficiency of ac-DBDs [140,143] is reported and the present study extends that method to the ns-DBD plasma actuators.

1.12.

M

OTIVATIONS AND

O

BJECTIVES

The understanding of the working principles of the flow actuation mechanism induced by a ns-DBD plasma actuator is the main driver of this research. Such understanding is important for using and exploiting it in industrial applications. Related to the mecha-nism effectiveness are the location, amplitude and frequency of actuation [47,120,280]. Moreover, the amount of energy deposited within the controlled flow is an important pa-rameter for optimization processes. Following from this, main objectives of this research can be formulated.

• The first objective of this research is the investigation of the effect that a ns-DBD plasma actuator induces on a flow. The flow response to ns-DBD actuation is in-vestigated. This is mainly done studying the interaction of a ns-DBD input with a laminar boundary layer. It is observed that Tollmien-Schlichting (TS) waves are induced. Such investigation clarifies the influence of the actuator location as well as the amplitude of its input on the effect induced on the controlled flow.

• The second objective is to find the cause of the flow perturbation induced by an ns-DBD. Such objective is as important as the first one from an application point of view and an experimental campaign is set up toward this goal. An induced den-sity/viscosity gradient is recognised to be the main cause of flow perturbation.

• The next objective is to understand the effect of actuation frequency on the control of a separated flow (Backward Facing Step). Forcing frequency is the only parame-ter investigated and its effect on the reattachment length afparame-ter the step is observed and used as reference for performance evaluation. It is observed that according to the frequency of actuation, different reattachment lengths after the step can be achieved.

• After the definition of the main objectives related to the basic knowledge of ns-DBDs, a next objective is the geometrical, electrical and thermal characterization of this kind of actuators. However, only a qualitative characterization is possi-ble, since there are no means to quantify the energy deposition efficiency of this

1

kind of plasma actuators in literature. To do so, experiments are performed, which demonstrate that the properties of the material used for the barrier can affect the energy deposition achieved by these actuators.

• A method to quantify energy deposition efficiency needs to be determined. In order to do so, experimental measurements are coupled with the solution of an Inverse Heat Transfer Problem (IHTP). Moreover, efficiency is determined as the product of two contributions, one purely electric and one thermodynamic.

• Last objective of this work is demonstrating the utility of ns-DBD with an aero-dynamic application. A two elements airfoil at high incidence develops relatively strong pressure gradients [6,178]. Experiments quantify the macroscopic effect of a ns-DBD plasma actuator over the aerodynamic performances of the airfoil, namely maximum lift and drag. The research was supported by AmpyxPower BV, interested in applying this technology to the Power Pl ane©project.

1.13.

T

HESIS OUTLINE

In chapter 1 background information and relevance of the topic to science and technol-ogy have been given, along with a summary of the thesis scope.

Chapter2defines the state of the art of ns-DBD plasma actuator prior this research. Historical development of ns-DBDs as a flow control technique is given. A general overview on the physical principles and a short introduction to plasma physic in general is given as well.

In chapter3a description of the measurement techniques as well as of the analy-sis tools employed during this research is given. More specifically, a detailed basic de-scription of the theory behind techniques such as PIV, Schlieren, infrared thermography, back-current shunt and aerodynamic measurements is given. Tools for data analysis such as Proper Orthogonal Decomposition (POD), Linear Stability Theory (LST)and In-verse Heat Transfer Problem (IHTP) are described as well. The description of the imple-mentation and setup of the acquisition techniques is found case by case in the specific chapters.

Chapter4presents the results concerning the basic understanding of the flow con-trol actuation mechanism. The experimental setup and the analysis tools employed are described as well.

Chapter5focuses on the effect of actuator orientation and a quantification of in-duced density perturbation is carried out. Experimental setup, numerical simulations and a method employed to enforce conclusions are described.

Chapter6describes the experimental and analytical efforts towards the understand-ing of the forcunderstand-ing frequency effect on the effectiveness of the control. A description of acquisition setup is given together with description of the analysis tool employed.

In chapter7results of a qualitative characterization study are reported. Setup and data post-processing procedure are described. The investigated parameters are the geo-metrical, electrical and thermal proprieties of the ns-DBD plasma actuator.

1.13.THESIS OUTLINE

1

21

and tested. Also in this chapter, the experimental setups and the analysis tool employed are given in details.

Chapter9presents the results of an application on a two elements airfoil. The em-ployed measurement techniques are described and motivated and results are discussed. Chapter10summarizes and concludes the work. Additionally, suggestions for possi-ble continuation of this research are elaborated.

2

P

RINCIPLES OF

P

L ASMA

A

CTUATORS

It is the mark of an educated mind to be able to entertain a thought without accepting it. Aristotél¯es

This chapter introduces the physical principles governing the operation of plasma actua-tors. The system is described in terms of its components and their function. The physical mechanism of air ionization is briefly described, followed by the distinction between the main two modes of operation. Ac-DBD is briefly addressed as it is not in the focus of this work. Ns-DBD is described with more detail and the current knowledge available from literature is surveyed.

2

2.1.

P

LASMA AND PLASMA TECHNOLOGIES

P

LASMAis commonly known as the fourth fundamental state of matter. Such is the state of stars, where temperature is such that all the matter is ionised. A plasma is characterized by strong Coulombian interactions between ions and molecules, but displaying overall a neutral behaviour [155]. On Earth it is possible to find it as result of high voltage arc discharges (like a thunderbolt) or gas heating by lasers or microwaves.

Plasma is classified as thermal or non-thermal according to the relative tempera-ture of the charge carriers within it [155,200]. The difference between the two is that in non-thermal plasma there is not a thermal equilibrium between negative charge carriers (typically electrons) and positive ones (typically ions, with a much greater mass).

In this work, with the term “plasma technology” is meant a technology that makes use of any kind of plasma, i.e. thermal and non-thermal plasma. Plasma technologies based on non-thermal plasma are characterised by the fact that only a small fraction of the gas molecules are ionized. This kind of plasma is most commonly used and applied in many technological fields because of its capability to scale temperature/density ac-cording to the application requirements.

Researchers over the years have developed different techniques to produce and ap-ply “cold” plasma. Regardless of the means of plasma generation, energy is required to produce it and a continuous energy input is necessary in order to sustain it [96,100]. Fields of applications range from metal cutting [177] and welding [33] to surface clean-ing and coatclean-ing [175].

The electrical potential field of non-thermal plasma can be calculated by its net charge density, assuming that electrons satisfy the Boltzmann relation [35]:

ne(φ2) ∝ ne(φ1)eeΦ/kBTe (2.1)

where neis the electron number density, kBis the Boltzmann constant ( approximately equal to 1.381×10−23_{[J/K ]), T}

eis the electron temperature of plasma and the difference of local electrostatic potential between two points is represented by Φ = φ2− φ1.

Differ-entiating equation2.1gives a formula to calculate the electrical field from the density of particles: −→ Ee=kBTe e ∇ne ne (2.2) where−E→eis the electron electric field.

For each application a typical technology and relative techniques of plasma produc-tion and applicaproduc-tion are developed. Each one of these technologies and/or techniques has its own characteristics and physical macroscopic properties [100]. For example, ap-plications like Silent Discharge CO2Laser, fluorescent lamps and Plasma TV require low

pressure in the range 10 − 70kPa [85,105] and a frequency between 50 and 200kH z [282,283]. While applications like flame stabilization, volumetric ignitions and ozone production work at high pressure 100 − 2000kPa [131,243] and lower frequencies, up to 10kH z [241,242]

In aerodynamics, hot and cold plasma are used, the former because of its capability of producing shock waves [89,112,129], the latter because of its capability of inducing

2.2.DBDPLASMA ACTUATORS

2

25

a body force within the discharge volume and its surroundings [131,155]. In particular, for the cold plasma used in aerodynamic applications a technology of great interest is the so called Dielectric Barrier Discharge (DBD) plasma actuator [207,208].

2.2.

DBD

PLASMA ACTUATORS

A non-thermal discharge generated by the application of a High Voltage (HV) between two electrodes separated by a dielectric material is typically called Dielectric Barrier Dis-charge (DBD) [100,131,155]. A schematic drawing of a micro-discharge channel is re-produced in figure2.1a, where the ground electrode is separated from the HV electrode by a dielectric barrier. The two electrodes are placed symmetrically with respect to the horizontal axis. In figure2.1b, an example of floating ground electrode is shown.

Dielectric Barrier Surface Discharge Microdischarge Channel Ground Electrode HV Electrode

a

b

Figure 2.1: The anatomy of a single DBD streamer with dielectric covering one electrode. Figure adapted from [151] and [17].

Once an electrical potential of sufficient amplitude is applied between the two elec-trodes, electrons leave the high voltage electrode moving towards the ground electrode, triggering a chain of chemical reaction that generates the typical blueish glow of the bar-rier discharge. The chemical reaction due to direct electron impact are reported in rela-tions2.3and2.4:

e + N2→ e + e + N2+ (2.3)

2

For a more detailed description of chemical processes due to indirect electron impact the interested reader is addressed to the relevant literature [5,188].

The presence of the barrier does not allow electrons to travel from one electrode to the other freely, thus no arc discharge is possible. The nature of the discharge depends on the kind of electrical potential applied (i.e. direct or alternate current) and the material between the electrode, it is however mainly diffusive or filamentary [79,130]. In figure

2.2a an example of filamentary discharge is illustrated and compared to an example of diffusive discharge in figure2.2b.

Figure 2.2: Filamentary (a) and diffusive (b) glow discharge. Figure adapted from [101].

The first attempts to produce dielectric barrier discharged plasma at atmospheric pressure, for surface cleaning and coating purposes, date back to 1988 [64,118,285]. In figure2.3, an example of an industrial coating application is illustrated with plasma off (a) and on (b).

a b

Figure 2.3: Atmospheric pressure DBD discharge on a coating process application. Figure adapted from [36].

It was found that the nature of this kind of cold plasma was unstable due to the self-limiting mechanism of the discharge [79]. The presence of the dielectric induces an ac-cumulation of electrons on the barrier surface, thus reducing the local electrical field and consequently quenching the discharge. Due to this, DC discharge cannot be sustained [79], therefore AC current is used for DBD applications. For this reason DBD plasma ac-tuators have been addressed for years as ac-DBD. Different geometrical configurations

2.2.DBDPLASMA ACTUATORS

2

27

of ac-DBD are possible [131,132], as illustrated in figure2.4. Electrodes can be straight (figures2.4a,2.4b and2.4c) or circular (figure2.4d) and they are placed in a symmet-ric fashion. The dielectsymmet-ric barrier can be attached on one electrode (figure2.4a) or both (figure2.4b) or be distant from both electrodes(figure2.4c).

a

b

c

d

Figure 2.4: Common dielectric barrier discharge configurations. Figure adapted from [132].

In particular, an asymmetric planar configuration induces a net motion of the air surrounding the discharge volume, as illustrated in figure2.5. This configuration typi-cally allows only a small overlap of the two electrodes. The covered electrode is longer than the exposed one as to allow the discharge to extend as much as possible, as shown in figure2.5.

Figure 2.5: Drawing of an ac-DBD plasma actuator (a) and its powered circuit (b) adapted from [60].