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PECyT - Plasma Enhanced Cycloidal Thruster

Carlos M. Xisto,∗Jos´e C. P´ascoa,†M. Abdollahzadeh‡and Jakson A. Leger§

Universidade da Beira Interior, Covilh˜a, 6201-001, Portugal

Pierangelo Masarati¶and Louis Gagnon k

Politecnico di Milano, 20156 Milano, Italy

Meinhard Schwaiger∗∗and David Wills ††

IAT21-Innovative Aeronautics Technologies GmbH, A-4050 Traun, Austria

In the following paper we introduce PECyT system for enhancing the aerodynamic

eﬃciency of cycloidal rotors. For that purpose the incorporation of Dielectric Barrier

Discharge plasma actuators for active ﬂow control on a pitching airfoil, under deep-stall

conditions, will be assessed using a numerical tool. Two diﬀerent arrangements of DBD

actuators will be analysed, namely single- and multi-DBDs conﬁgurations. For the single-

DBD plasma actuator the eﬀect of diﬀerent modes of actuation on the lift coeﬃcient will

also be studied. We will show that the multi-DBD actuator, in a steady-actuation mode,

could delay stall and allows for a faster reattachment of the ﬂow. However during the

downstroke phase of the pitching cycle the unsteady operation of a single-DBD gives us

the best results in terms of lift coeﬃcient.

I. Introduction

Acyclorotor, also known as a cyclocopter or a cyclogiro, is a rotating wing machine where the axis of

rotation is parallel to the blade span, see Fig. 1-a). It consists of a set of blades that are connected to

a mechanical system with the ability to deﬁne a periodic pitching schedule for the wings as they preform

one revolution around the horizontal axis. This allows us to deﬁne a periodic variation of the angle of

attack (AoA) on each blade and to control the direction and magnitude of the resultant thrust vector almost

instantly in 360 radial direction, thus allowing for a substantial increase in ﬂight control.

Cyclorotors were studied in the 1920’s by Kirsten with the cooperation of Boeing1as a mean of propulsion

for aerial and marine crafts. In the mid 30’s they were deeply study, under contracts for the National

Advisory Committee for Aeronautics, by Strandgren2who developed an analytical model able to predict the

amount of lift and propulsion that could be generated by a cyclorotor, and by Wheatley3,4who conducted

experimental activities and also theoretical studies on the eﬃciency of cyclorotors in hovering and forward

ﬂight conditions. Wheatley tested a four-blade rotor with a span and diameter of 8 feet (2.4384m) and chord

length equal to 0.312 feet (0.0950976m) in a 20-foot (6.09600m) wind tunnel, showing that the tested rotor is

able to take-oﬀ vertically and hover in air, ﬂy horizontally and auto-rotate in the case of main engine failure.

Wheatley concluded that cyclorotors could have a practical application into aeronautical propulsion, but

that the probable achievable performance is very poor when compared with the available screw propellers of

that period. However, only one rotor geometry was analysed and several aspects related to the ﬂow around

pitching airfoils were not fully comprehended during that time.

∗Research Fellow, Dep. de Eng. Electromecˆanica, Rua Mqs D’ ´

Avila e Bolama, xisto@ubi.pt, AIAA Member

†Professor Auxiliar, Dep. de Eng. Electromecˆanica, Rua Mqs D’ ´

Avila e Bolama, pascoa@ubi.pt

‡Ph.D. Student, Dep. de Eng. Electromecˆanica, Rua Mqs D’ ´

Avila e Bolama, mm.abdollahzadeh@yahoo.com

§Ph.D. Student, Dep. de Eng. Electromecˆanica, Rua Mqs D’ ´

Avila e Bolama, leger mec@hotmail.com

¶Associate Professor, Dip. di Scienze e Tecnologie Aerospaziali, via La Masa 34, pierangelo.masarati@polimi, AIAA Member

kResearch Associate, Dip. di Scienze e Tecnologie Aerospaziali, via La Masa 34, louis.gagnon@polimi.it

∗∗General Manager, IAT21, Langholzstraße 16, meinhard.schwaiger@iat21.at

††Business Director, IAT21, Langholzstraße 16, davidwills@fastmail.fm

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50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference

July 28-30, 2014, Cleveland, OH

AIAA 2014-3854

Copyright © 2014 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Propulsion and Energy Forum

(a) (b)

Figure 1. a) 3D representation of a cyclorotor with six NACA0012 blades and a maximum pitch angle of 40

degree. b) IAT21 D-DALUS concept uses four contra-rotating cycloidal rotors for propulsion.

Such system was never accepted in the aeronautical industry due to the lack of technology and due to

the fact that old days analytical tools were unable to analyse the complex ﬂow that was associated with

the interaction between the pitching rotating blades. New advancements in technology are now opening

the possibility of introducing the cyclorotor concept in the aeronautical market as a propulsion system for

airships5,6,7and into disruptive aircrafts, see Fig. 1-b).

During the last decade several research teams are working on the applicability of cyclorotors in MAV-

scale (Micro Air Vehicles) concepts. Iosilevskii and Levy8performed experimental and CFD studies on

the eﬃciency of a MAV-scale four-blade cyclorotor with span and chord length equal to 0.110 and 0.022 m,

respectively. They found out that in terms of performance the cyclorotor is comparable with an heavy-loaded

helicopter rotor. Sirohi et al.9analyzed the hoover performance of a cyclorotor with a diameter and span

of 6 inches (0.1524 m). In their research they have also included an analytical model able to predict rotor

performance, where vertical axis wind turbine theory was adapted in the context of aeronautical propulsion.

A comparison between the tested rotor and a conventional rotor, of the same diameter, showed that the

cyclorotor was able to achieve higher power loading. Hwang et al.10,11 developed a four-rotor cyclocopter

with elliptic blades that produces a spanwise uniform distribution of the induced velocity, that could open

the possibly of exploiting aeroelastic tailoring in such a way that the aerodynamic loads themselves induce

twist changes, which will improve the distribution of induced velocity for diﬀerent operating conditions. A

throughout study on the understanding of cyclorotors was taken by Benedict et al.12,13,14,15 They have

study12 the inﬂuence of the number of blades on the performance of a 0.152 m in diameter/span cyclorotor

composed by NACA0010 airfoils with a uniform chord of 0.0254 m. Their main conclusion was that, for

small scale cyclorotors with a number of blades up to ﬁve and a maximum pitching amplitude of 40 deg,

the power loading increases with the increasing number of blades. Diﬀerent rotor parameters, like airfoil

section, blade ﬂexibility, blade camber, rotor radius, blade span, rotor aspect-ratio, rotor solidity, blade

planform and blade kinematics were also analysed by Benedict et al.13,15 They found out that for low-

Reynolds numbers the airfoil section does not plays a signiﬁcant role in the aerodynamic performance of a

cyclorotor, since the inverted NACA0010 airfoil produces similar values of eﬃciency when compared with

the baseline NACA0010, cambered blades resulted in lower eﬃciency when compared with symmetrical ones.

They also concluded that the virtual camber eﬀect and the chord-to-radius ratio play a signiﬁcant role in the

aerodynamic eﬃciency. Regarding the pitching schedule, they observed that using an asymmetric pitching

could be beneﬁcial if one selects an higher pitching amplitude on the top blade.

The EU-FP7 funded CROP (Cycloidal Rotor Optimized for Propulsion) project strives to design a

cycloidal propulsion system that is suitable for manned and unmanned aerial vehicles. In order to asses

the applicability of cyclorotors in large scale, several studies have been taken using pure analytical16,17

and CFD18,19 approximations. It was concluded that CROP could introduce into the aeronautical market

several advantages in comparison with traditional VTOL, ﬁxed wing air vehicles and hybrid aircrafts. It uses

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common surfaces to achieve lift and thrust along the full range of ﬂight speeds. The problem of retreating

blade stall of helicopters is not so severe in cycloidal rotors, meaning that they can achieve higher subsonic

speeds. The use of a wing rotating around the axial axis creates lift, and thrust, when the blades move

backward in relation to the vehicle direction of ﬂight. This makes possible to use the intermittent, but very

high, lift value generated by the unsteady pitching of the blades. Further, each blade of the cycloidal rotor

operates at similar conditions (angle of attack, velocity, Reynolds number) so, in principle, the blades are

easier to optimize in terms of aerodynamic performance.20

The unsteady ﬂow mechanism that is generated by the pitching movement of the blades also plays a

signiﬁcant role in the aerodynamic eﬃciency of the cyclorotor, since it can delay blade stall, thus increasing

the amount of lift that can be produced by each blade. This phenomenon is known as dynamic stall and

its predominant feature is the creation and convection of a vortex disturbance on the suction surface of the

airfoil that will resist to the adverse pressure gradients that are responsible for ﬂow separation. This eﬀect

as been extensively studied using experimental techniques21,22 and CFD tools.23,24,25,26

Since the main aerodynamic component of a cycloidal rotor comprises a pitching airfoil, any ﬂow control

techniques that could increase the aerodynamic eﬃciency dealing with stalled ﬂow over the airfoil could be

beneﬁcial. Several active and passive ﬂow control mechanisms had been reported in literature for controlling

the ﬂow around pitching airfoils, among them Dielectric Barrier Discharge (DBD) plasma actuators are

considered a promising technique.27,28,29,30 DBD plasma actuators31,32,33 are novel means of controlling

ﬂow which imparts momentum to the ﬂuid by creating an ionic-wind beside the control surface. These

actuators have several advantages in comparison to other ﬂow control systems, which includes being fully

electronic, having a fast response time, less complexity and easy integration into the system. In the following

paper we intend to study the idea of possible inclusion of DBD actuators for active ﬂow control in cycloidal

rotors, where here after we call it PECyT (Plasma Enhanced Cycloidal Thruster). We will show that the

combined eﬀect of the leading edge vortex (LEV) with the PECyt system could delay separation at high

angles of attack. Using numerical models for gas dynamic34,35 with a suitable multiphysic CFD models,36,37

numerical analysis of such complex ﬂows was performed. For that purpose we will consider an individual

airfoil performing a sinusoidal pitching movement (the most simple aerodynamic equivalent system). The

results will provide information for design an optimization of DBD plasma actuators that could control the

ﬂow for cycloidal rotors.

II. Numerical Model

To model the eﬀect of plasma actuation, we will consider a simple phenomenological model, which will

consider the eﬀect of the actuator as a body force. Thus, the Unsteady Reynolds Averaged Navier-Stokes

(URANS) equations under the inﬂuence of a body force are given by:

∂ρ

∂t +∇ · (ρU) =0

∂ρU

∂t +∇ · (ρUU) = − ∇p+∇ · τ+F

(1)

Where Frepresents the external eletrodynamic body force generated by the plasma actuator. In Eq. (1)U

is the velocity ﬁeld vector, pis the static pressure, ρrepresents the density of air and τis the viscous stress

tensor. The body force is here added under the assumption that the plasma formation and ﬂow response

are decoupled from each other. Such approximation can be applied due to the big disparities between the

characteristic velocities associated to each physical process.32

The external body force in the momentum equation is given by:

F=ρcE,(2)

where ρcis the net charge density and Eis the electric ﬁeld vector. The Maxwell equations for a quasi-steady

plasma, with the assumption of negligible time variation of the magnetic ﬁeld, are the following:

∇ · (ε0εrE) = ρc,∇ × E= 0.(3)

Where εrand ε0are the relative permittivity of the medium and permittivity of free space, respectively.

The electric ﬁeld can be derived from the gradient of a scalar potential,

E=−∇Φ,(4)

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and

∇ · (εr∇Φ) = −ρc

ε0

.(5)

Since the gas particles are weekly ionized, we can decouple the potential in two parts,38

Φ = ϕ+φ, (6)

where φis the potential due to external electric ﬁeld and ¯ϕis related to the potential due to net charge

density in the plasma. For the potential due to the external ﬁeld,

∇ · (εr∇φ) = 0.(7)

The charge density could be related to the electrical potential with the Debye length,

ρc

ε0≈ − 1

λ2

d

ϕ, (8)

where λdis de Debye length. An equation for the charge density can now be written by using Eq. 9, 7 and

6,

∇ · (εr∇ρc) = ρc

λ2

d

.(9)

The value for the Debye length is estimated with the relation proposed by,39

λd= 0.20.15 ×10−6Vpp −7.42 ×10−4(10)

where Vpp is the applied peak-to-peak voltage.

The above described model assumed a Gaussian distribution of charge density in accordance to experi-

mental observations,

ρc,w (t) = ρmax

cG(x)f(t) (11)

G(x) = exp "−(x−µ)2

2σ2#(12)

where µis a location parameter that indicates the position of the function maximum, and σrepresents the

rate of decay of charge density. We note that Eq. 11 as a signiﬁcant eﬀect on the accuracy of the numerical

simulations. In Suzen et al.38 a value for ρmax

cwas selected accordingly with experimental data. In the

present work we apply the modiﬁcation of Abdollahzadeh et al.33 that has scaled ρmax

cand the electric ﬁeld

with the following functions:

ρmax

c= 2fCeq.

Vpa −Vbd

fcorr λd

, fcorr =1

2√2πσ

lp"erf 1

2

µ√2

σ!+ erf 1

2

√2 (lp−µ)

σ!#; (13)

E=E0E∗, E0=(Vpa −Vbd)

lp

.(14)

In Eq. 13 fis the AC voltage frequency, Vpa =Vpp/2 is the applied voltage peak amplitude, Ceq is the

equivalent capacitance of the DBD actuator, Vbd represents the critical breakdown voltage where ionization

occurs and lpis an estimation of the length of the plasma region. These scaling functions were proposed by

Abdollahzadeh et al.33 in order to reduce the dependence on empirical ﬁtting parameters and to improve

the applicability of the model into diﬀerent practical applications.

We note that Eqs.(7) and (9) do not have any temporal derivative term, only Eq. 11 is time dependent.

We can then solve them in terms on normalized variables,

ρ∗

c=ρc

ρmax

c

, φ∗=φ

φmaxf(t)E∗=∇φ∗=lp∂φ∗

∂x i+∂φ∗

∂y j,(15)

where f(t) is the shape of the applied voltage. We can return to the dimensional variables by multiplying

the electric ﬁeld and charge density distributions by the corresponding normalization factor.

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III. Results and Discussion

In the following section we apply the numerical model of section II into the analysis of DBD plasma

actuation in the ﬂow of a pitching airfoil. We start by validating the numerical model in the computation

of a purely gas dynamic ﬂow (no-actuation) under deep-stall conditions. Afterwards in section Bthe eﬀect

of plasma actuation will be assessed in terms of number of DBD actuators and operation mode.

A. Validation

We start by validating the gas dynamic model without the inclusion of plasma actuation. For that purpose

we selected the pitching NACA0012 airfoil experimental test case of Lee and Gerontakos21 in deep-stall

conditions. This experiment was preformed in a suction type low-speed wind tunnel with 0.9 m×1.2 m×2.7 m

operating at a turbulent intensity of I= 0.08% at U∞= 35 m/s. The aluminium NACA0012 airfoil had

a chord length, c, equal to 0.150 m and a span length, s, equal to 0.375 m, the pitching axis was located

at a quarter of the chord length (0.25c). In order to minimize the three-dimensional ﬂow eﬀects at the

measurement location (airfoil midspan), two circular end plates with 0.3 m of diameter were ﬁtted into the

experiment, the gap between the endplates and the airfoil tip was less than 1 mm. By using a 5 µm hot-wire

probe the two-dimensional uniformity of the ﬂow was measured, and was found that the 2D non-uniformity

was around ±4% of the free-stream value, the wind tunnel maximum blockage was around 5%. The pitching

movement was controlled by a four-bar-linkage and ﬂywheel mechanism that is capable to oscillate the airfoil

at several amplitudes and frequencies, the instantaneous pitching amplitude,

α(t) = αm+ ∆αsin (ωt) (16)

is a function of time deﬁned by a mean pitching angle, αm, an oscillating amplitude, ∆α, and a circular

frequency, ω= 2πf. Here the deep-stall condition was used for validating the gas dynamic numerical model:

αm= 10 deg; ∆α= 15 deg; and ω= 18.67 rad/s for a reduced frequency of k=ωc/(2U∞) = 0.1. The mean

free-stream velocity was U∞= 14 m/s corresponding to a chord Reynolds number, Re = U∞c/ν = 1.35×105.

Figure 2shows an overall and partial views of the numerical domain. It has a circular shape with R= 50c

and it is composed by an hybrid mesh with a O-type structured mesh in the boundary layer region and an

unstructured mesh in the remanding domain. The structure mesh was used in order to achieve a desirable

value for the y+, in our case less than one. Three diﬀerent regions were created: an outer-region, a reﬁned

region for the wake and a blade region. The blade region is a circular shaped domain with center located

at a quarter of the chord length, prescribing the movement that is given by Eq. 16. This region exchanges

information with the outer and wake regions through a numerical interface. Regarding boundary conditions,

in the outer boundary we have speciﬁed an inlet-outlet BC where we impose U∞= 14 m/s in the xdirection,

a turbulent intensity of I= 0.08% and a turbulent length scale of 0.02c.

For solving the incompressible Unsteady Reynolds Averaged Navier-Stokes equations a pressure-based

coupled solver was used, where a Courant number of 100 was selected within each time step. The desirable

time and space accuracy were achieved by using the second-order implicit and second-order linear-upwind

interpolation schemes, respectively. For turbulence modelling, since the experimental data21 was showing

clear signs of transition the k-ω-SST transition model40,41,42 was selected. It was shown by Wang et al.25

that URANS with k-ω-SST transition is capable to capture major ﬂow features of dynamic stall, namely the

formation and development of the LEV and the hysteresis loop, the dynamic loading acting on the airfoil

and also the unsteady behaviour of the lift coeﬃcient in post-stall conditions.

A grid sensitivity study was taken in order to achieve a ﬁnal solution that is independent from the

mesh dimension. Four diﬀerent grids were build with increasing size: Grid-0 with ∼89,000 cells; Grid-1

with ∼180,000 cells; Grid-2 with ∼582,000 cells; and Grid-3 with ∼873,000 cells. In Fig. 3-a) we show the

experimental results for the lift coeﬃcient (CL) and the computed values obtained with the four diﬀerent

grids as a function of the pitching angle. For all the cases we have computed 8 complete cycles (only the

curves of the 8th cycle are displayed), although a time-converged solution was found after 4 cycles. The

time-step that was used in the grid independence study was dt2 = Tc/1000, where Tc= 2π/ω is the cycle

period. We can see that in the upstroke phase the curves of CLalmost overlap with each other in the entire

half-cycle. The biggest discrepancy for the upstroke phase is located in the peak region, see Fig. 3-b).

Here the results obtained with Grid-2 and Grid-3 show a good agreement, while the results of Grid-0 and

Grid-1 are slightly diﬀerent. In the downstroke phase the ﬂow is signiﬁcantly unsteady, thus we have a more

pronounced discrepancy between the curves. Nevertheless the results obtained with Grid-2 and Grid-3 are

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= 50

Wake Region: 300,000 cells

Blade Region: 200,000 cells

Interface

Grid-2: 582,381 cells

∞

y

x

Figure 2. Numerical grid (grid-2) used for the computation of Lee and Gerontakos21 pitching airfoil in deep-

stall conditions.

very similar in terms of average values. Based on these observations we assume that the results obtained

with Grid-2 are acceptable and we will use this mesh for the remaining part of this paper. For all the four

grids a time-step independence study was also preformed. In Fig. 3-c) we show the results obtained for

CLin grid-1 for three consecutively reﬁned time-steps: dt1 = Tc/500; dt2 = Tc/1000; dt3 = Tc/2000. We

can observed that there isn’t a signiﬁcant diﬀerence in the plots dt2 and dt3, thus, and following the same

conclusions of the grid independence study, we will use the dt2 time-step for the remaining part of this paper.

Let’s now compare the experimental data with the numerical results obtained with grid-2 and dt2. Figure

3-a) shows that the numerical model is able to predict with some accuracy the time-dependent values of CL

even in the downstroke phase of the cycle, when the ﬂow is completely separated. The biggest discrepancy is

found in the peak region, where the numerical model is predicting the stall onset to occur sooner. This eﬀect

should be related to a non-well resolved LEV in terms of size and intensity. The formation and convection of

this vortex structure induces pressure ﬂuctuations that keep the ﬂow attached at high angles of attack, when

the LEV leaves the trailing edge and goes into the wake the ﬂow completely separates and there is an abrupt

decrease in Lift and an increase in Drag coeﬃcients. Figure 4-a) shows the instantaneous non-dimensional

vorticity (ω∗

z=ωzc/U∞) contour plots for the upstroke and downstroke phase of the cycle. We can see that

the current model is able to capture the formation and convection of the LEV. When the LEV leaves the

top surface of the blade the ﬂow becomes completely separated and it will remain in stall conditions for

almost the entire downstroke phase until reatchament is achieve at 5.4 deg. Although over-predicting Drag

in several pitching positions, the computed result of drag coeﬃcient CDwith the transition-SST model is

showing in general a good agrement with experiments, see Fig. 3-d).

B. DBD plasma actuators for active ﬂow control

Dielectric Barrier Discharge plasma actuator is a very promising technology for active ﬂow control at reduced

cost and weight. Plasma-based devices exploit the momentum coupling between the surrounding gas and

plasma to manipulate the ﬂow. When compared with other ﬂow control techniques, these devices require low

power consumption and do not require any moving mechanical parts. They are suitable for incorporation

in thrust vectoring propulsion systems43 since they have a very fast frequency response, that allows a real-

time control of the ﬂuid ﬂow. Figure 5-b) shows a single-DBD, it consists in two electrodes separated by

a dielectric material usually glass, Kapton or Teﬂon. One electrode is exposed to the air and the other

is fully covered by a dielectric barrier. The exposed electrode is loaded by an high AC voltage signal, of

suﬃcient amplitude (5-40kV) and frequency (1-20 kHz), whereas the covered electrode is grounded. The

intense electric ﬁeld partially ionizes the surrounding gas producing non-thermal plasma on the dielectric

surface. The ionized air (plasma) in the presence of the electric ﬁeld produces an attraction/repulsion force

on the charged particles. The ionized particles are then accelerated and transmit their momentum, through

collisions, to the neutral air particles in the plasma region over the covered electrode.44 The result is the

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-1

-0.5

0

0.5

1

1.5

2

2.5

3

-5 0 5 10 15 20 25

CL

α (º)

Experimental

Grid-0

Grid-1

Grid-2

Grid-3

(a)

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

20 21 22 23 24 25

CL

α (º)

Experimental

Grid-0

Grid-1

Grid-2

Grid-3

(b)

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-5 0 5 10 15 20 25

CL

α (º)

Experimental

Grid-1-dt1

Grid-1-dt2

Grid-1-dt3

(c)

0

0.2

0.4

0.6

0.8

1

1.2

-5 0 5 10 15 20 25

CD

α (º)

Experimental

SST-Transition

(d)

Figure 3. a) Lift coeﬃcient as a function of the pitching angle computed on several grids. b) Detail of CL

in the upstroke phase (20-25 degs). c) Time-step independence study computed on grid-1. d) Comparison

between experimental data and computed values (grid-2) for the drag coeﬃcient.

creation of an induced velocity (ionic wind) in the proximity of the dielectric surface.

At critical values of pitching amplitude, the cyclorotor blades could experience ﬂow separation. In stall,

lift coeﬃcient rapidly decreases and drag coeﬃcient increases. The main goal of PECyT is to delay stall

at high pitch amplitudes thus increasing the lift and the eﬃciency of the rotor. The PECyT-DBD induced

ﬂow can play a signiﬁcant role in delaying boundary layer separation. However, for an eﬃcient ﬂow control,

the location of the actuator needs to be optimized based on the chord position where separation occurs.

Such position will vary with several ﬂow parameters, such as the pitch angle and rotation speed. For an

eﬃcient control of the aircraft the pitch angle and rotation speed of the rotor will be continuously modiﬁed,

so the rotor blade could experience stall at diﬀerent chord locations. Because of this, the usage of a single-

DBD might not be enough for providing an eﬃcient mean of ﬂow control. In Fig. 5-a) we show a possible

conﬁguration of a rotor blade with a multi-DBD plasma actuator (Fig. 5-c). Such system could be adjusted

using a suitable control-loop to activate a single or a combination of DBD actuators, thus controlling the

boundary in the most optimum manner.

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1.2 deg

12.3 deg

22.1 deg

23.4 deg

24.8 deg

25 deg

/∞

10 deg

5.4 deg

18.8 deg

20.6 deg

24.8 deg

23.4 deg

22.1 deg

20.6 deg

18.8 deg

1.2 deg

LEV formation

LEV

Separated flow

LEV

LEV

Reattachment

(a)

1.2 deg

12.3 deg

22.1 deg

23.4 deg

24.8 deg

25 deg

/∞

10 deg

5.4 deg

18.8 deg

20.6 deg

24.8 deg

23.4 deg

22.1 deg

20.6 deg

18.8 deg

1.2 deg

(b)

Figure 4. Instantaneous vorticity contour plots for a pitching cycle obtained with: a) the baseline case (without

plasma actuation); b) unsteady actuation St= 0.5with leading edge actuation.

1. Steady actuation

Firstly we will considerer the application of DBD actuators under a steady-actuation condition. In this case,

since the AC frequency is much more higher than ﬂuid response frequency, the ﬂow will sense a constant

body force. Two diﬀerent arrangements of DBDs were selected for the steady-actuation analysis. In the ﬁrst

conﬁguration only one single-DBD located at the leading edge (x/c = 0) was activated. For the second case

a multi-DBD conﬁguration was selected, which is composed by three pairs of electrodes that are placed 2

mm apart from each other in the suction surface of the airfoil. The idea behind the usage of multi-DBD

conﬁgurations is that one could achieve a multiplication factor that will increase the maximum induced

velocity per actuator and also cover a larger surface of the airfoil by actuator zone. Such eﬀect is only

possible in steady-actuation conditions where a quasi-steady ionic wind is achievable, see Figure 6-c) and d).

Each one of the DBDs consisted in two electrodes, one being exposed to the air and the other being

covered with a dielectric material. The exposed electrode is 3 mm wide and the covered electrode as a

length equal to 4 mm. For the dielectric material we have assumed a thickness equal to td= 0.1×10−3m,

which is a common thickness for two layers of Kapton ﬁlm,30 for a more detail picture of the dimensions

see Fig. 6-a). The signal supplied to the plasma actuator was a 7kHz sinusoidal wave with Vpp = 8 kV. For

the steady-actuation case this voltage was provided in a continuously way to the electrodes, allowing the

creation of a quasi-steady induced ﬂow.

Figure 6-a) shows a detail of the grid near the electrodes. The mesh is very similar to grid-2 but it

further reﬁned near the actuation zones that are given by the intersection point between the exposed and

cover electrode. This was done because the computational cells need to be small enough to properly compute

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Multi-DBD Dielectric

Plasma

Exposed Electrode

AC voltage

Covered Electrode

(a) (b)

(c)

Figure 5. a)Possible arrangement of a multi-DBD plasma actuator on a NACA airfoil. Graphical representation

of a single- (b) and multi- (c) Dielectric Barrier Discharge plasma actuator.

the thickness of the plasma region (body force region) that, depending on the operating conditions, could

be some tens of λd.

In Fig. 6-b) we show the speciﬁed boundary conditions for the DBD model and the computed distribution

of the non-dimensional electric potential ﬁeld. In the exposed electrode we specify the maximum value of

φ∗= 1 and in the covered electrode we impose a zero value for the electric potential. For the dielectric

surface we assumed a coupled boundary condition, by forcing the gradient of the electric potential to be

equal at the sides of the surface of the dielectric layer. In the remanning walls we assume that they are

perfect insulators of electricity. Regarding the boundary conditions for the charge density we specify a proﬁle

for the discharge surface with Eq. 11 and a zero gradient boundary condition for the remanning boundaries.

In Fig. 7we show the CLresults with and without actuation. Figure 7-a) shows that for almost the

entire upstroke phase of the pitching cycle the inclusion of DBD actuators in steady actuation mode, with a

single- or multi-DBD arrangement, do not inﬂuence the lift coeﬃcient proﬁle as the pitching angle increases.

This was also observed experimentally by diﬀerent authors.28,30 The eﬀect of the plasma actuation is more

strong in the stall region where we can observe that the ﬂow separation is slightly delayed. We note that

this eﬀect is more pronounced with the multi-DBD conﬁguration, see Fig. 7-b). However the maximum

lift is also slightly reduced. From Fig. 7we can observe that the intersection point between the upstroke

and downstroke points is occurring sooner for the actuation case, again this eﬀect is more pronounced in

multi-DBD conﬁguration, since more momentum is being applied to the ﬂow. For the downstroke phase

it is visible that higher steady actuation is obtained with the multi-DBD, thus promoting separation and

reducing the generated lift force.

2. Unsteady actuation

The second case that we have analysed is related to the unsteady operation mode of the DBD. In this case the

AC signal that is supplied to the electrodes was cycled oﬀ and on with an unsteady period. The time that the

AC voltage is activated within that period is called duty-cycle and is normally given in terms of percentage

of the unsteady period, in our case the duty-cycle percentage was set at 10%. This unsteady actuation

promote the creation of non-stationary disturbances that, if generated near the separation point, will lead to

vortical structures. These vortices will increase the momentum on the suction surface of the blade, allowing

the ﬂow to withstand the adverse pressure gradients, which are responsible for ﬂow separation. We still need

to select the optimal forcing frequency that should be selected in a way that the DBD could generate and

convect 2-3 vortical structures over the separated zone of the airfoil.28 This could be attained if the Strouhal

number,

St=fc

U∞

,(17)

is equal to one. This empirical relation is appropriate for static airfoils, however for pitching airfoils it was

found that under certain conditions a lower forcing frequency (lower St) could be more beneﬁcial in terms of

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4 mm

3 mm

2 mm

NACA0012

y

x

= 0.1 mm

Covered Electrode

Exposed Electrode

(a)

Covered Electrode

Exposed Electrode

(V)

∗= 1

∗

= 0

∗= 0

∗

∗

= 0

∗=,

(b)

(m/s)

DBD

Single-Actuation

(c)

(m/s)

DBD-1

DBD-2 DBD-3

Multi-Actuation

(d)

Figure 6. a) Detail of the grid used for the computation of ﬂow with DBD plasma actuation. b) Boundary

conditions imposed for the DBD numerical model and the computed distribution of the non-dimensional

electric potential ﬁeld. c) Quasi-steady ionic wind obtained with a single DBD. b) Induced ﬂow computed

with the multi-DBD arrangement.

ﬂow control. It was shown by Post and Corke28 that a St= 0.25 was responsible for an increase of the CL

in almost the entire pitching cycle. The work performed by Mitsuo et al.30 have shown that the best results

in terms of eﬃciency were obtained for a St= 0.5. For the pitching airfoil setup of Lee and Gerontakos21

that we are using here (c= 0.150 m and U∞= 14 m/s) the optimal forcing frequency for a St= 1 is equal

to f=U∞/c = 93.3 Hz. In this paper we compute the unsteady actuation for St= 0.5, meaning that the

applied forcing frequency is equal to f= 46.67 Hz.

Figure 7-a) shows the lift coeﬃcient as a function of the pitching angle, where the values for steady and

unsteady actuation could be compared with the case with no-actuation. We can see that the CLremains

unchanged for the unsteady actuation in almost the entire half-pitching cycle. Here the ﬂow is completely

attached to the suction surface of the airfoil and the introduction of small disturbances will not aﬀect the

generated force. In Fig. 7-b) we can see that the stall angle is similar to the one where there isn’t any

actuation but the maximum lift is slightly reduced. This could be related to a small perturbation of the

LEV that at this point could not be beneﬁcial. Such perturbation is visible in Fig. 4-b) for the upstroke

angle of 23.4 deg (near stall). The biggest visible eﬀect is perhaps in the downstroke cycle, when the ﬂow

is completely separated. We can see in Fig. 7-a) that the unsteady actuation can improve the aerodynamic

eﬃciency of the airfoil for certain pitching angles (20-15 deg). For angles within this range, namelly 20.6

deg and 18.8 deg a visible reduction of the separtaion bubble is observed in Fig. 4-b). The intersection point

between the half-cycles is similar to that obtained with no-actuation.

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-1

-0.5

0

0.5

1

1.5

2

2.5

3

-5 0 5 10 15 20 25

CL

α (º)

No Actuation

Steady SDBD

Steady Multi-DBD

Unsteady SDBD

(a)

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

20 21 22 23 24 25

CL

(º)

No Actuation

Steady SDBD

Steady Multi-DBD

Unsteady SDBD

(b)

-0.1

-0.05

0

0.05

0.1

0.15

0.5 1 1.5 2 2.5

CL

(º)

No Actuation

Steady SDBD

Steady Multi-DBD

Unsteady SDBD

(c)

Figure 7. a) Lift coeﬃcient as a function of the pitching angle with and without plasma actuation. b) Detail

of CLin the stall region. c) Detail of the intersection between the upstroke and downstroke CLlines.

IV. Conclusion

In the present paper we have analysed with numerical tools the inﬂuence of plasma actuation in pitching

airfoils under deep-stall conditions. Two modes of actuation were analyzed, namely steady actuation and

unsteady actuation. For the steady actuation case diﬀerent arrangements of DBDs were studied, namely a

single-DBD, positioned at the leading edge, and a multi-DBD conﬁguration.

We have demonstrated that the inclusion of multi-DBDs could be more beneﬁcial than using a single

DBD for delaying stall and to obtain a faster reattachment of the ﬂow. However an optimal arrangement

of actuators in terms of position need to be selected in order to obtain a maximum multiplication eﬀect

of the induced ﬂow velocity. A control algorithm similar to the one of Lombardi et al.29 should also be

implemented in the steady actuation mode in order to shutdown the actuation in most of the downstroke

cycle where the DBDs were reducing the aerodynamic eﬃciency of the airfoil.

The unsteady actuation have demonstrated a superior performance on the downstroke phase of the cycle.

Although not being able to delay stall it was responsible for an increase of CLwithin a relevant portion of

the downstroke phase.

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Acknowledgments

The present work was performed as part of Project CROP, supported by European Union within the 7th

Framework Programme under grant number 323047, and also supported by C-MAST, Centre for Mechanical

and Aerospace Science and Technology Research Unit No. 151.

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