Surface Actuated Variable-Camber and Variable-Twist...

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American Institute of Aeronautics and Astronautics

Surface Actuated Variable-Camber and Variable-Twist

Morphing Wings Using Piezocomposites

Onur Bilgen,* Michael I. Friswell

†

College of Engineering, Swansea University

Singleton Park, Swansea SA2 8PP, UK *Corresponding author, e-mail: [email protected]

and

Kevin B. Kochersberger‡, Daniel J. Inman,

§

Center for Intelligent Material Systems and Structures

Virginia Tech, Blacksburg, VA 24061, USA

A surface actuated variable-camber morphing airfoil employing a type of piezoceramic

composite actuator known as Macro-Fiber Composite is presented. The proposed airfoil

employs two cascading active surfaces and a pair of optimized pinned boundary conditions.

The optimized locations of pinned boundary conditions and the geometric features allow for

a variable and smooth deformation in both directions from a flat camber line. The continuity

of the airfoil surface is achieved by using a single substrate that wraps around the airfoil

shape. This substrate forms the surface of the airfoil and it serves as the host material for the

two cascading bimorph actuators. The cascading bimorphs are pinned together at the

trailing edge with a compliant hinge, which is also formed by the substrate material. The

paper focuses on the theoretical static-aeroelastic response characterization. A parametric

study of the fluid-structure interaction problem is employed to optimize the geometric

parameters and the boundary conditions of the variable-camber airfoil. The coupled

treatment of the fluid-structure interaction allows the realization of a design that is not only

feasible in a bench top experiment, but that can also sustain large aerodynamic loads. The

paper identifies the effects of four important structural parameters to achieve the highest

possible lift coefficient and lift-to-drag ratio. Practical recommendations are presented to

achieve a working prototype.

Keywords: Variable-camber airfoil, morphing, bimorph, Macro-Fiber Composite, piezoceramic, low RE number

I. Introduction

HE desire for smaller and lighter aircraft has driven a need to investigate the use of smart materials for flight

and flow control. For example, field-deployable aircraft have flexible wings that can be folded during

transportation, and they can be unfolded for operation. These compliant wings can be realized with the integration of

smart materials. Piezoelectrics remain the most widely used smart material because they offer actuation and sensing

over a wide range of frequencies. Specifically, piezoelectrics have been employed in aerospace structures to perform

shape and flow control. A Macro-Fiber Composite (MFC) is a type of piezoelectric device that offers structural

flexibility and high actuation authority (up to 0.2% in-plane strain). A challenge with piezoelectric actuators is that

they require high voltage input. In contrast, the current drain is low which creates small power consumption and

* Post-doctorate researcher, College of Engineering, AIAA Member.

† Professor, College of Engineering.

‡ Research Associate Professor, Department of Mechanical Engineering, AIAA Associate Fellow.

§ George R. Goodson Professor, Department of Mechanical Engineering, AIAA Fellow.

T

52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
19th4 - 7 April 2011, Denver, Colorado

AIAA 2011-2072

Copyright © 2011 by Onur Bilgen. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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requires relatively lightweight electronic components. For smart material actuated devices, another challenge is

found in operating a relatively compliant, thin structure (desirable for piezoelectric actuators) in situations where

there are relatively high external (aerodynamic) forces. Establishing a wing configuration that is stiff enough to

prevent flutter and divergence, but compliant enough to allow the range of available motion is the central challenge

in developing a piezocomposite airfoil. Novel methods of supporting the airfoil can take advantage of aerodynamic

loads to reduce control input moments and increase control effectiveness. The next section presents a selection of

research that deals with camber morphing in aircraft using piezoelectric materials.

A. Aerodynamic Camber Morphing with Piezoelectric Materials Piezoelectric materials offer relatively high force output over a wide frequency range. Although the strain

output is very small for low excitation levels, the response is relatively linear. In the linear regime, the fast response

of Lead-Zirconate-Titanate (PZT) actuators caused initial interest in the field of aerodynamic vibration control.

Many researchers focused on the application of piezoelectrics to the blades of rotary wing aircraft to improve their

performance and effectiveness. Steadman et al. [1] showed an application of a piezoceramic actuator for camber

control in helicopter blades. Giurgiutiu et al. [2] has researched performance improvement on rotor blades using

strain-induced actuation methods (using PZTs). Wind tunnel experiments proved the control authority of the PZT

actuators. Giurgiutiu [3] presented a comprehensive review on the application of smart material actuation to

counteract aeroelastic and vibration effects in helicopters and fixed wing aircraft. Other “smart rotor” concepts have

also been presented: leading- and trailing-edge flaps actuated with smart material actuators, controllable

camber/twist blades with embedded piezoelectric elements/fibers, and active blade tips actuated with tailored smart

actuators. For flap actuation, devices range from piezobimorphs (Koratkar and Chopra [4,5]), piezostacks (Lee [6],

Lee and Chopra [7,8], Straub et al. [9,10], Janker et al. [11]), and piezoelectric/magnetostrictive-induced composite

coupled systems (Bernhard and Chopra [12], Rogers and Hagood [13], Derham and Hagood [14], Cesnik and Shin

[15], Cesnik et al. [16], Shin [17], Shin et al. [18], Kovalovs [19]).

In addition to the research in vibration control applications, “static” control of aerodynamic surfaces using

piezoelectric materials started in early 90‟s for large aircraft. In static-aeroelastic control, researchers employed both

the low amplitude (mostly linear) and high amplitude (non-linear) excitation ranges of piezoelectric material.

Lazarus et al. [20] examined the feasibility of using representative box wing adaptive structures for static-aeroelastic

control. Pinkerton and Moses [21] discussed the feasibility of controlling the wing geometry employing a

piezoelectric actuator known as the thin layer composite-unimorph ferroelectric driver and sensor (THUNDER).

Hysteresis nonlinearity was observed in the voltage-to-displacement relationship. Barrett and Stutts [22] proposed

an actuator that uses a pair of piezoceramic sheets arranged in a push-pull assembly to turn a spindle of an

aerodynamic control surface. Wind tunnel testing showed the feasibility of the concept. Geissler et al. [23] adopted

piezoelectric materials as the actuation element for a morphing leading edge: however, in this case the leading edge

is an independent element able to rotate around an internal hinge. Munday and Jacob [24] developed a wing with

conformal curvature, driven by a THUNDER actuator internally mounted in a position so to alter the upper surface

shape of the airfoil, resulting in a variation of the effective curvature. Wang et al. [25] presented results from the

DARPA/AFRL/NASA Smart Wing Phase 2 Program which aimed to demonstrate high-rate actuation of hingeless

control surfaces using several smart material-based actuators including piezoelectric materials. Grohmann et al.

[26,27] presented the active trailing edge and active twist concepts applied to helicopter rotor blades. The paper

presented the optimization of sizing and placement of piezo-composite patches so that desired wing weight and

pitching moment output is obtained.

The rapid development and the reduced cost of small electronics in the last decade led to the interest of using

piezoelectric materials in small unmanned (and/or remotely piloted) fixed wing, rotary and ducted fan aircraft. The

2002 Virginia Tech Morphing Wing Design Team (Eggleston et al. [28], of the Department of Aerospace and Ocean

Engineering) experimented with the use of piezoceramic materials (THUNDER), shape-memory alloys (SMAs), and

conventional servomotors. Wind tunnel testing showed the feasibility of the smart material systems. Barrett et al.

[29] employed piezoelectric elements along with elastic elements to magnify control deflections and forces. The so-

called Post-Buckled-Precompression (PBP) concept was employed as guide vanes in a small rotary aircraft. The

PBP concept, in its earliest incarnation, was primarily intended to increase the coupling coefficient exhibited by

piezoelectric transducer elements (Lesieutre and Davis [30]). Vos et al. [31,32] conducted research to improve the

PBP concept for aerodynamic applications. Roll control authority was increased on a 1.4 meter span unmanned air

vehicle. Kim and Han [33,34] designed and fabricated a smart flapping wing by using a graphite/epoxy composite

material and an MFC actuator. A twenty percent increase in lift was achieved by changing the camber of the wing at

different stages of flapping motion. Bilgen et al. [35,36] presented a unique application for piezo-composite

actuators on a 0.76 meter wingspan morphing wing air vehicle. In this application, two MFC patches are bonded to

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the wings of a small demonstration vehicle, and the camber of the wing is changed with voltage. Adequate roll

control authority is demonstrated in the wind tunnel as well as in flight. All electronics, including MFC power

electronics, are powered by an 11.1 V Lithium-Polymer battery, a common choice for remotely controlled aircraft.

Bilgen et al. presented static flow vectoring via an MFC actuated thin bimorph variable-camber airfoil [37], and an

MFC actuated cascading bimorph variable-camber airfoil [38]. Wind tunnel results and analytical evaluation of the

airfoils showed comparable effectiveness to conventional actuation systems and no adverse deformation due to

aerodynamic loading. Paradies et al. [39] implemented MFCs as actuators into an active composite wing. A scaled

prototype wing was manufactured and models were validated with static and preliminary dynamic tests of the

prototype wing. Wickramasinghe et al. [40] presented the design and verification of a smart wing for an unmanned

aerial vehicle (UAV). The proposed smart wing structure consists of a composite spar and ailerons that have

bimorph active ribs consisting of MFC actuators.

The 2010 Virginia Tech Wing Morphing Design Team (Butt et al. [41,42], of the Department of Aerospace and

Ocean Engineering; Bilgen et al. [43], of the Department of Mechanical Engineering) have developed a completely

servo-less, wind-tunnel and flight tested remotely piloted aircraft. The MFC actuators were used to form variable-

camber, continuous, piezo-composite wings instead of the traditional servomotor controlled (and discrete) control

surfaces. The team was able to develop lightweight control surfaces and the necessary driving high-voltage DC-DC

converters, culminating in a landmark first flight of the completely MFC controlled aircraft on April 29, 2010. An

electric motor driven propulsion system was used to generate thrust and all systems were powered with a single

Lithium-Polymer battery. This vehicle became the first fully MFC controlled, flight tested aircraft. It is also known

to be the first fully piezoelectric controlled, non-tethered, flight tested fixed-wing aircraft.

B. Current Research Motivation There are several benefits of employing continuous shape (or more specifically camber) control via active

materials over the discrete trailing edge control using conventional control surfaces in small aircraft. The term

camber control simply refers to the change of the curvature of the airfoil by means of actuators. First, the low

Reynolds number flow regime can result in flow separation that reduces the effectiveness of a trailing edge control

surface. Second, small aircraft cannot afford to lose energy through control surface drag because of their severe

power limitations. Finally, the opportunity for flow control is inherent in the active material due to its direct effect

on circulation and its high operating bandwidth. Smart actuators are effective in dynamic laminar separation bubble

control (also referred to as flow control).

The motivation for the current research is to determine the aerodynamic effectiveness of a variable-camber

airfoil concept. The proposed concept employs piezoceramic materials that provide the actuation forces and

moments, and they also form the surface of the airfoil. The research focuses on fundamental (and isolated) airfoil

characteristics, quantified in terms of conventional two-dimensional aerodynamic coefficients. First, a previously

presented variable-camber airfoil design is introduced as a baseline to the current concept. Next, the present concept

for variable-camber airfoil is introduced. The static-aeroelastic response of the airfoil is theoretically evaluated for

lift and lift-to-drag performance for range of structural configurations. The paper concludes with a brief discussion

of the results.

II. Baseline Variable-camber Airfoil

A variable-camber airfoil was previously presented by Bilgen et al. [38] and it serves as a baseline to the design

proposed in this paper. The baseline design employs two cascading active bimorph actuators (which form the top

and bottom trailing surfaces of the airfoil) that are pinned at the trailing edge. These active surfaces are chosen to be

MFC actuated bimorph laminates. The Macro-Fiber Composite actuator was developed at NASA Langley Research

Center [44,45]. An MFC is a layered, planar actuation device that employs rectangular cross-section, unidirectional

piezoceramic fibers embedded in a thermosetting polymer matrix. The in-plane poling and subsequent voltage

actuation allows the MFC to utilize the 33 piezoelectric effect, which is higher than the 31 effect used by traditional

PZT actuators with through-the-thickness poling [46]. There has been extensive analytical and experimental

research focused on utilizing MFC as an actuator (or sensor) for structural control. Williams [47] and Bilgen [48]

provide a detailed linear and nonlinear characterization of the mechanical and piezoelectric behavior of the MFC

actuator.

A compliant parallelogram (box structure) is used to create the desired boundary conditions to the leading end

of the active bimorph surfaces. Figure 1 shows the kinematic model and the parameters of the airfoil. In the figure, β

is the leading edge (LE) incidence angle and MCL is the mean-camber-line. The compliant box can simply be

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described as a four-bar mechanism. The two parallel bars that connect the top and bottom surfaces have constant

length (L).

Figure 1: Baseline airfoil design and geometric parameters. Morphed state is illustrated.

The airfoil can be mounted to the vehicle either at the center or at the ends of the vertical bars. The change in

camber of the active surface of the airfoil causes the box to comply and generate a shear-like motion while keeping

the end-slope of the bimorphs equal to each other. When the airfoil is in the non-actuated state, the link length (L) is

equivalent to the LE thickness (T) of the airfoil. The initial percent thickness (Th=L/chord*100) is calculated at the

zero volt state. The LE geometry is chosen to be elliptic in the actual prototype of this concept (discussed later). The

airfoil thickness is determined depending on the application, where an optimum configuration can be achieved for a

desired function of various aerodynamic coefficients.

A. Theoretical Aerodynamic Response The method for theoretical analysis is presented in detail in Ref. [38]. Figure 2 shows the theoretical change in

lift coefficient and lift-to-drag ratio for the airfoil with 127 mm chord. The airfoil is subjected to 15 m/s free-stream

velocity.

Figure 2: Theoretical (2D) a) lift coefficient and b) lift-to-drag ratio for novel airfoil subjected to free-stream velocity of 15

m/s. Rechord = 1.27x105.

The 2% thick airfoil reaches a CLmax value of 1.12 at 1400 V due to early flow separation. In contrast, the 6%

thick airfoil shows the highest lift trend. The 12% thick airfoil shows the lowest drag coefficient trend (not shown

here). Considering the stiffness of the airfoil, the flow induced deformation is assumed negligible at 15 m/s. A

smooth surface is assumed for the analysis which is the main reason for the deviation of the lift curve from the

actual performance around CLmax. As reported in the literature, XFOIL predicts slightly high lift coefficients and low

drag coefficients when compared to experimental results and therefore the predictions must be viewed as an upper

boundary to actual performance. The maximum theoretical L/D is 42.6 for the 10% thick airfoil at 1300 V. This

operation point corresponds to a camber of 4.12% and an AOA of 7.21°. The 2% thin airfoil shows the lowest L/D

trend due to early stall and LE separation. Overall, the aerodynamic analysis clearly shows that a single bimorph

airfoil (which is approximately 1% thick) is not as effective as generating lift force when compared to a thick airfoil

at the same surface curvature (and excitation voltage).

B. Measured Structural Response Using the theoretical predictions above, two prototypes are manufactured with two active surfaces (cascading

bimorphs made with four MFC M8557-P1 [49] actuators each) and a single four-bar (box) mechanism as the

internal structure. The airfoil has 127 mm chord, 133 mm span and 15 mm thickness. The two bimorphs used in the

TE

β=LEα MCL

AOA

Bimorph

surfaces

L

Thickness (T)

Compliant box

100 700 1400 17000

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1.5

Lift C

oe

ffic

ien

t (2

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Voltage, V

Th=2%c

Th=6%c (max)

Th=10%c

Th=15%c

a) b)100 700 1400 1700

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Th=2%c

Lift/D

rag

(2

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Th=15%c

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0.5

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1.5

Lift C

oe

ffic

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Th=2%c

Th=6%c (max)

Th=10%c

Th=15%c100 700 1400 17000

0.5

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1.5

Lift C

oe

ffic

ien

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Voltage, V

Th=2%c

Th=6%c (max)

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Th=15%c100 700 1400 1700

0

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Lift C

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ffic

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Voltage, V

Th=2%c

Th=6%c (max)

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Th=15%c

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airfoil are fabricated by sandwiching a 27 µm thick stainless-steel material with the MFC actuators. The MFC

actuators have a voltage range of approximately -500 V to 1500 V. Since the airfoil has two surfaces, both in a

bimorph configuration, the MFCs on the opposite sides are actuated with an opposite field and with 3:1 fixed ratio.

First, bench top experiments were conducted to reveal the displacement-to-excitation relationship. During this test,

the actuation voltage is swept from -1400 V to 1400 V and swept back to -1400 V. The effect of piezoelectric

hysteresis is relatively large; however, it should also be noted that the deflection is repeatable. A non-linear analysis

was not conducted; instead the shape of the airfoil at each test condition is measured directly. This measurement is

also necessary to observe the additional deformation (if any) due to aerodynamic loading (for wind tunnel tests

discussed next). It is also observed that the actual airfoil outline does deviate from the theoretical (and desired)

airfoil. Most of this deviation occurs due to the interface between the active section and the rapid-prototyped elliptic

LE. In summary, the airfoil achieved a peak -4.14% camber and -6.3° AOA at -1400 V excitation. The airfoil

achieved a peak +5.24% camber and 7.01° AOA at +1400 V excitation.

C. Measured Aerodynamic Response Wind tunnel experiments are conducted to compare the prototype variable-camber airfoil to other similar (in

shape) fixed-camber airfoils. Four airfoils are presented: 1) Novel, variable-camber airfoil; 2) NACA 0009 airfoil; 3)

NACA 0013 airfoil; 4) A rapid prototyped (RP) airfoil generated from the profile of the variable-camber prototype

(at zero camber state.) The fourth airfoil is tested to determine the effects of the surface roughness. The NACA 0009

has a maximum thickness of 11.3 mm, and the NACA 0013 airfoil has a maximum thickness of 16.5 mm. The

variable-camber and the RP airfoils have an equivalent thickness of 15 mm. The rapid-prototyped airfoils have 133

mm span, 127 mm chord and a finite trailing edge (TE) thickness of 1.0 mm. The lift and drag measurements are

conducted at 15 m/s and at a chord Reynolds number of 127,000. For the variable-camber airfoil, the true AOA (the

voltage-induced AOA) is given as the independent variable. The mounting angle ( ) is zero. In other words, there is no rotation of the airfoil supports for the morphing airfoil data presented. This allows a “fair” comparison between

the fixed and variable-camber airfoils. The lift coefficient and lift-to-drag ratio (L/D) comparison is presented in

Figure 3. Note that the arrows in the legend specify the direction of sweep of voltage (Volt) and AOA (α).

Figure 3: Measured a) lift coefficient and b) lift-to-drag ratio (2D) comparison at 15 m/s. Rechord=1.27x10

5.

There is a significant increase in lift due to camber induced by voltage input. A lift curve slope of 0.144 per-

degree is measured which exceeds the NACA 0009 lift slope (0.083 per-degree) by 72%. The plot shows the clear

advantage of the lift generation by coupled camber-AOA change induced by voltage. The NACA 0013 and the RP

airfoils develop similar lift-curve-slope; however the NACA 0013 achieves a slightly higher . The overall performance comparison of the airfoils is done by looking at the lift-to-drag ratio presented in Figure 3b. The

variable-camber airfoil produces a maximum L/D ratio of 13.4 at 1500 Volts (α=5.78°) and an L/D ratio of -11.2 at -

1500 Volts (α=-5.20°). The NACA 0009 airfoil produces a maximum L/D ratio of 16.3 at α=4.21° and an L/D ratio

of -12.3 at α=-4.97°. The variable-camber airfoil has higher L/D performance when compared to the fixed-camber

airfoils with similar thickness (NACA 0013 and RP). In comparison to the conventional airfoils, the morphing

airfoil generates a comparable change in lift-to-drag ratio. A relatively high experimental drag was observed for the

morphing airfoil due to its blunt (elliptical) LE when compared to the LE of NACA 0009 airfoil. The variable-

camber prototype does not have a continuous surface as desired due to in-house fabrication limitations and this is

one of the issues addressed by the current paper. This is evident when the drag performance of the morphing airfoil

-20 -10 0 10 20

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Angle of Attack, degrees

Lift C

oe

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2*

Morphing (Volt )

Morphing (Volt )

NACA 0009 ( )

NACA 0009 ( )

NACA 0013 ( )

NACA 0013 ( )

RP ( )

RP ( )

a) b)-20 -10 0 10 20

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-10

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0

5

10

15

20

Angle of Attack, degrees

Lift o

ve

r D

rag

(2

D)

Morphing (Volt )

Morphing (Volt )

NACA 0009 ( )

NACA 0009 ( )

NACA 0013 ( )

NACA 0013 ( )

RP ( )

RP ( )

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at zero AOA is compared to its rapid-prototyped replica airfoil (RP) with a continuous and relatively smooth

surface. Since the variable-camber airfoil is aimed at generating lift forces for vehicle control, performance in lift is

considered more important than the performance in drag.

III. Proposed Airfoil Concept

The high structural deflection requirement (of aerodynamic applications) creates the need for semi-solid-state

mechanisms and distributed boundary conditions to be employed along with piezoelectric actuation. The baseline

concept presented in the previous section generates a significant amount of deformation and lift change induced by

excitation voltage. On the other hand, the design still has a discontinuity between the leading section geometry and

the variable-camber trailing section. In the prototype of the baseline design, this gap (with variable-length) is

covered using a flexible strip of plastic which allows the active bimorph surface to slide forward and backwards

with respect to the fixed LE geometry. Another issue is that the solid-state compliant box mechanism (formed by

four “live” hinges) introduced extra weight and complexity due to limited in-house fabrication capabilities.

In the current concept, illustrated in in Figure 4, the authors propose a continuous airfoil surface and a set of

“simpler” boundary conditions to remedy these problems. The continuity in the airfoil surface is achieved by using a

single substrate that wraps around the airfoil shape. This substrate forms the surface of the airfoil and it serves as the

host material for the two cascading bimorph actuators. This airfoil is attached to the three-dimensional spar structure

(e.g. a rectangular spar box with spanwise taper) at two locations. In Figure 4, the locations of these two boundary

conditions (Pin1 and Pin2) are exaggerated to aid visibility.

Figure 4: A simplified illustration of the variable-camber airfoil design. Actuated and non-actuated states are shown.

In Figure 4, the label “AOA” represents the angle-of-attack. The boundary conditions in the design are pinned-

pinned (similar to a simply-supported beam) for ease of implementation; however one can choose the second

boundary condition (Pin2) as a slider (allowing motion in the chordwise axis and restricting motion in the lift axis).

A pair of pinned-pinned boundary conditions theoretically creates a nonlinear displacement response but this is not

dominant in an actual implementation of the airfoil geometry and the pin locations. Starting with the baseline design,

multiple configurations can be generated by changing the location of the pins. The two extreme configurations occur

when: 1) the first pin is moved to the LE and the second pin is moved to the TE which is similar to a sail or a

simply-supported beam; 2) both the first and second pins are moved to the leading edge, hence the airfoil becomes

equivalent to a cantilevered beam.

The airfoil examined here (without electrical excitation and aerodynamic loading) has an elliptical leading edge

(with 2:1 ratio) and a circular-arc trailing section. The TE is formed by pinning the two bimorph surfaces and it is

assumed to have a finite thickness of 0.05% chord. A constant curvature is assumed for the bimorph trailing section

due to the uniform chordwise coverage of the active material (MFC actuator). The nonlinear voltage-displacement

relationship of a single cantilevered MFC bimorph actuator is experimentally quantified (previously) with laser

displacement measurements (see Ref. 37). Figure 5 presents the measured chordwise deformation of a thin bimorph

airfoil in response to electrical excitation. Since the airfoil is in a bimorph configuration, the MFCs are actuated

asymmetrically with an opposite field and with a 3:1 fixed ratio. The higher of the two supply voltages (V) is used

for labeling in the figure. A negative sign simply indicates actuation in the reverse direction as indicated in Figure 5.

The AOA and the effective camber are calculated by fitting a 127 mm circular-arc to the measured data points. The

percent-camber (C) is the percentage of the height over the chord of the circular-arc.

020

4060

80100

120

-50

0

50Num. Nodes=54324. Max UY=-2.2234 mm at 100.2067 % chord.

x axis, mm

y ax

is, m

m

AOA

Pin2Pin1

TE

7


Figure 5: An MFC bimorph displacement measurement with a digital camera. Legend shows test order, voltage (V) and

camber (C) of the circular-arc fit (shown by solid lines).

In Figure 5, the actuation voltage is swept from -1400 V to 1400 V and swept back to -1400 V. The effect of

piezoelectric hysteresis can be observed in the difference between the deflection at zero voltage during the positive

and negative voltage sweeps. However, the deflection is very repeatable, as seen at the maximum positive and

negative voltage levels. Figure 5 also shows that a circular-arc is a good approximation; however the actual shape

does deviate from a circular arc. The peak-to-peak camber-voltage relationship (deduced from the data of Figure 5)

of a single bimorph is used to determine the material properties in the finite-element (FE) model.

A. Static-Aeroelastic Analysis Method A thin shell-like morphing airfoil (with reasonable chordwise stiffness and displacement output) is possible with

an MFC actuator given that the boundary conditions and structural features are favorable. Therefore, the support

system for the variable-camber device is determined here using a parametric analysis. A MATLAB [50] based

program is used to solve the static fluid-structure interaction (FSI) problem by iterating between a panel method

software XFOIL [51,52], and a finite element code ANSYS [53]. Before the iteration starts, the non-aero-loaded

airfoil shape is analyzed in XFOIL to initialize the FSI. XFOIL calculates lift and drag coefficients and the pressure

distribution and the program enters the iteration loop. First, the pressure distribution is applied to the airfoil

geometry in ANSYS which calculates the aero-loaded (deformed) airfoil shape. Second, the deformed airfoil shape

is analyzed in XFOIL to calculate change in the lift and drag due to the change in pressure induced deformation.

These two steps are continued until no change is observed in the parameters of interest (i.e. deformation and

aerodynamic coefficients). Due to the static nature of the problem, the solution converges with a few iterations. Note

that the dynamic effects are known to be negligible (and ignored in the analysis) because of previous experimental

observations. The analysis in this paper considers only chordwise distribution of aerodynamic loads and structural

deformations.

For XFOIL simulations, a 0.85% (of the mean velocity) turbulence level is assumed, which is consistent with

the measured turbulence level in the previous wind tunnel data. It must be noted that XFOIL predictions for AOA

above maximum lift angle are not accurate [52]. Due to the limitation of the deflection of the piezo-composite

bimorph, the XFOIL analysis presented here (for a 9.0% thick airfoil) never passes beyond this AOA limit (see

Figure 2). Approximately 400 panels are used in XFOIL to achieve numerical convergence for the airfoils

considered in this section. As reported in literature [51,52], XFOIL predicts slightly higher lift coefficients and

lower drag coefficients when compared to experimental results; therefore the predictions must be viewed as an

upper boundary to actual lift and lift-to-drag performance.

The passive material in the airfoil is modeled as a homogeneous 2D area mesh using PLANE82 high-order

quadrilateral (Q8) type element in ANSYS. The MFC actuator is modeled as a monolithic piezoelectric layer using a

homogeneous 2D area mesh consisting of PLANE223 high-order quadrilateral (Q8) coupled-field elements. The

plane element type is chosen (instead of the beam element type) because of the dense, non-uniform and distributed

loading at the leading edge with significant components in the in-plane direction as well as the out-of-plane

direction. The material properties used in the finite element model are checked using previous experimental data.

Approximately 20,000 elements are used to ensure convergence of the finite element model for all airfoil models

0 20 40 60 80 100 120-10

-5

0

5

10 (1) V=-1400, C=-5.67 %

(2) V=0, C=-2.06 %

(3) V=1400, C=4.71 %

(4) V=1400, C=4.91 %

(5) V=0, C=1.87 %

(6) V=-1400, C=-5.75 %

Streamwise Axis, mm

Dis

pla

ce

me

nt, m

m

8


evaluated in the parametric study. The number of elements chosen is relatively high to accommodate the highly non-

uniform pressure distribution data from XFOIL. Figure 6 shows an example of the finite element model used in the

parametric study. There is a high concentration of aerodynamic loading (shown with arrows normal to the surface)

at the leading edge. Note that the most of the features on this figure are exaggerated to aid the visibility. In reality,

the thickness of the substrate and the PZT layer is very small compared to the maximum thickness of the airfoil.

Figure 6: Example of the finite element model used in the parametric study. a) Complete model. b) Zoomed image of the

leading edge and pressure distribution. c) Transition from passive leading section to the active trailing section. d) Zoomed image of the live hinge that connect the cascading active surfaces at the TE.

The figure shows the whole airfoil and zoomed images of important areas. In addition to the effect of the

location of boundary conditions, the substrate thickness is an important parameter assuming that the PZT layer

thickness (tpzt) is fixed. The MFC actuator has a fixed thickness of 300 µm. The leading section of the airfoil has a

constant thickness of tsubs. This “stiff” substrate overlaps with a fraction of the active trailing section. This substrate

is then reduced to a thickness of tpzts. This arrangement is due to several reasons. First, the non-uniform aerodynamic

pressure distribution has a much higher magnitude close to the LE. A thick (and therefore stiff) substrate is required

around the LE. At the trailing section, the laminate formed by the active material and a thinner substrate has enough

bending stiffness to carry aerodynamic loads. Another important reason for the stepped thickness is that the

“optimum” leading section substrate thickness is more likely to be different than the “optimum” substrate thickness

for a bimorph (or unimorph) actuator. These are expected results, however since these structural parameters are

coupled with the aerodynamic state, a parametric analysis is presented next to understand the coupled behavior.

B. Parametric Analysis Results The main parameters of interest are 1) Pin1 location, 2) Pin2 location, 3) leading section substrate thickness,

and 4) thickness of the substrate under the active material. The substrate material is assumed to be stainless-steel.

The first pin is fixed in both axes; in contrast the second pin is restrained only in the lift axis. The top MFC actuator

is subjected to an effective +1500 V and the bottom MFC actuator is subjected to an effective -500 V. Note that the

actual applied electric field is adjusted so that the unimorph FE model has a matching transverse displacement

response to the actual bimorph device. In addition, the electric field is also corrected for the fact that the 33 mode

interdigitated MFC actuator is modeled as a 31 monolithic piezoceramic.

First, the effects of pin locations on the lift coefficient and lift-to-drag ratio are investigated. A fixed leading

section substrate thickness (tsubs = 203 µm) and a fixed trailing section substrate thickness (tpzts = 25.4 µm) is

assumed. Figure 7 presents the lift coefficient and lift-to-drag ratio for the proposed airfoil subjected to free-stream

velocity of 15 m/s. The plots represent the aerodynamically loaded (and converged) response.

a)

b) c) d)tpzt

tpzts

tsubs

9


Figure 7: Theoretical (2D) a) lift coefficient and b) lift-to-drag ratio for proposed airfoil subjected to free-stream velocity of

15 m/s. Rechord = 1.27x105.

The analysis shows that placing Pin1 close to the leading edge results in the highest lift output. The highest lift

coefficient and the lift-to-drag ratio is achieved for the configuration with Pin1=10%c and Pin2=20%c. The actual

displacement of this configuration is presented in Figure 8. Note that the x and y axes are equally scaled.

Figure 8: Morphed airfoil that corresponds to both highest lift coefficient and lift-to-drag ratio subjected to free-stream

velocity of 15 m/s. Rechord = 1.27x105.

The remainder of the parametric analysis considers the cases with Pin1 located at 10% chord. Now, the effects

of the leading section substrate thickness and Pin2 location on the lift coefficient and lift-to-drag ratio are

investigated. A fixed trailing section substrate thickness (tpzts = 25.4 µm) and a fixed Pin1 location (Pin1 = 10%c) is

assumed. Figure 9 presents the lift coefficient and lift-to-drag ratio for the proposed airfoil subjected to free-stream

velocity of 15 m/s.


15 m/s. Rechord = 1.27x105.

The analysis shows that placing Pin2 at 55%c and using a leading section thickness of 50.8 µm results in the

highest lift output and placing Pin2 at 35%c and using a leading section thickness of 178 µm results in the highest

lift-to-drag ratio. The highest lift coefficient achieved is 1.77 and the highest lift-to-drag ratio achieved is 40.3. The

actual displacements of these configurations are presented in Figure 10.

20 40 60 80 1000.2

0.4

0.6

0.8

1L

ift C

oe

ffic

ien

t (2

D)

Pin 2, %c

Pin1=5Pin1=10Pin1=20Pin1=30

Pin1=05%c

Pin1=10%c

Pin1=20%c

Pin1=30%c

a) b)

0 20 40 60 80 10010

15

20

25

30

35

40

45

Pin1=5

Lift/D

rag

(2

D)

Pin 2, %c

Pin1=10Pin1=20Pin1=30

Pin1=05%c

Pin1=10%c

Pin1=20%c

Pin1=30%c

0 20 40 60 80 100 120

-50

-40

-30

-20

-10

0

10

20

30

40


x axis, mm

y a

xis

, m

m

0

50

100 0

2

4

x 10-4

0

0.5

1

1.5

tsubs

, mmPin 2, %c

Lift C

oe

ffic

ien

t (2

D)

0

50

1000

2

4

x 10-4

0

20

40

tsubs

, mmPin 2, %c

Lift/D

rag

(2

D)

a) b)

10


Figure 10: Morphed airfoil that corresponds to highest a) lift coefficient and b) lift-to-drag ratio subjected to free-stream


Finally, the effects of the trailing section substrate thickness and Pin2 location on the lift coefficient and lift-to-

drag ratio are investigated. A fixed leading section substrate thickness (tsubs = 25.4 µm) and a fixed Pin1 location

(Pin1 = 10%c) is assumed. Figure 11 presents the lift coefficient and lift-to-drag ratio for the proposed airfoil

subjected to free-stream velocity of 15 m/s.


15 m/s. Rechord = 1.27x105.

The analysis shows that placing Pin2 at 55%c and using a trailing section thickness of 50.8 µm results in the

highest lift output and placing Pin2 at 45%c and using a trailing section thickness of 10.2 µm results in the highest

lift-to-drag ratio. The highest lift coefficient achieved is 1.79 and the highest lift-to-drag ratio achieved is 40.2. The

actual displacements of these configurations are presented in Figure 12. As noted earlier, the x and y axes are equally

scaled.

Figure 12: Morphed airfoil that corresponds to highest a) lift coefficient and b) lift-to-drag ratio subjected to free-stream


0 20 40 60 80 100 120-60

-50

-40

-30

-20

-10

0

10

20

30

40

Num. Nodes=58307. Max UY=-22.109 mm at 100.2067 % chord.

x axis, mm

y a

xis

, m

m

0 20 40 60 80 100 120

-50

-40

-30

-20

-10

0

10

20

30

40


x axis, mm

y a

xis

, m

m

a)

b)

0

50

100

0

2

4

6

x 10-5

0

0.5

1

1.5

Pin 2, %ctpzts

, m

Lift C

oe

ffic

ien

t (2

D)

0

50

100

0

2

4

6

x 10-5

0

20

40

Pin 2, %ctpzts

, m

Lift/D

rag

(2

D)

a) b)

0 20 40 60 80 100 120-60

-50

-40

-30

-20

-10

0

10

20

30

40


x axis, mm

y a

xis

, m

m

0 20 40 60 80 100 120

-50

-40

-30

-20

-10

0

10

20

30

40


x axis, mm

y a

xis

, m

m

a)

b)

11


IV. Conclusions

This paper proposed a variable-camber airfoil that employs surface-induced deformations instead of the more

typical internal actuation. The coupled treatment of the fluid-structure interaction allows the realization of a design

that is not only feasible in a bench top experiment, but that can also sustain large aerodynamic loads. The effects of

four important structural parameters are studied to achieve the highest possible lift coefficient and lift-to-drag ratio.

The highest lift coefficient of 1.79 is achieved by a configuration with 1) Pin1 at 10%c, 2) Pin2 at 55%c, 3) leading

section substrate thickness of 25.4 µm and 4) trailing section thickness of 50.8 µm. The highest lift-to-drag ratio of

40.3 is achieved by a configuration with 1) Pin1 at 10%c, 2) Pin2 at 35%c, 3) leading section substrate thickness of

178 µm and 4) trailing section thickness of 25.4 µm. The substrate material is assumed to be a stainless-steel, and

the active material electromechanical properties are equivalent to the Macro-Fiber Composite actuator. The results

are presented for a free-stream velocity of 15 m/s, chord Reynolds number of 127,000 and an assumed turbulence

level of 0.85%. In comparison to the baseline variable-camber airfoil (with solid-state internal hinges and 9.0%

chord thickness), the proposed airfoil (with a pair of pinned-sliding boundary conditions) produce higher lift

coefficient and slightly lower lift-to-drag ratio. The advantages of the new concept are: 1) it has a continuous surface

and 2) it requires more practical internal boundary conditions when compared to the baseline design.

Acknowledgments

This work is supported by the European Research Council grant number 247045 entitled "Optimisation of

Multi-scale Structures with Applications to Morphing Aircraft".

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