1 Department of Aerospace Engineering, Korea Advanced Institute of Science and ... 2 Aerodynamics Department, Korea Aerospace Research Institute.
Experimental Investigation on the Aerodynamic Characteristics of a Bio-mimetic Flapping Wing with Macro-Fiber Composites Dae-Kwan Kim, 1 Hong-Il Kim, 1 Jae-Hung Han1,* and Ki-Jung Kwon2 1 Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology Daejeon, 305-701, Republic of Korea 2 Aerodynamics Department, Korea Aerospace Research Institute Daejeon, 305-333, Republic of Korea
< Article Info. > Publication Title
Journal of intelligent material systems and structures
Journal Homepage
http://jim.sagepub.com/
Publication Year
2008
Volume/Issue
v.19 no.3
Paginations
pp.423-431
DOI
http://dx.doi.org/10.1177/1045389X07083618
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http://sss.kaist.ac.kr/
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This PDF file is based on the final submission to the publisher, and there might be slight change from the final form provided by the publisher.
Experimental Investigation on the Aerodynamic Characteristics of a Bio-mimetic Flapping Wing with Macro-Fiber Composites Dae-Kwan Kim, 1 Hong-Il Kim, 1 Jae-Hung Han1,* and Ki-Jung Kwon2 1 Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology Daejeon, 305-701, Republic of Korea 2 Aerodynamics Department, Korea Aerospace Research Institute Daejeon, 305-333, Republic of Korea
Abstract This paper describes the development of a bio-mimetic flapping wing and the aerodynamic characteristics of a flexible flapping wing. First, the flapping wing is designed to produce flapping, twisting and camber motions by using the bio-mimetic design approach. The structural model for macro-fiber composite (MFC) actuator is established, and the structural analyses of the smart flapping wing with the actuator are performed to determine the wing configuration for the maximum camber motion. The analysis model is verified with the experimental data of the smart flapping wing. Second, the aerodynamic tests are performed for the smart flapping wing in a subsonic wind tunnel, and the aerodynamic forces are measured for various test conditions. Additionally, the effects of camber and chordwise wing flexibility on unsteady and quasi-steady aerodynamic characteristics are discussed. The experimental results demonstrate that the effect of the camber generated by the MFC produces sufficient aerodynamic benefit, the chordwise wing flexibility is one of the important parameters affecting to the aerodynamic performance, and the lift produced in quasi-steady flow condition is mostly affected by the forward speed and effective angle of attack.
KEYWORDS: bird flight, flapping wing, macro-fiber composites (MFC), bio-mimetic design
1. INTRODUCTION Flapping flight is one of the nature’s finest locomotion experiments, and has fascinated humans for many centuries. The imitation of the nature’s flying mechanism was the motive power for the development of modern aeronautical technology over the past 100 years. Numerous efforts have been made to make flapping-wing vehicles named ornithopters. They can fly like birds, apparently with a large positive trim angle produced by adjusting the mass center or stabilizer to increase lift. However, birds and bats fly with horizontal flapping axes in equilibrium cruising flight, and their flight efficiency is fairly higher than that of the ornithopters [1]. For the efficient
maneuverability, the nature’s flyers utilize not only flapping and twisting motions but also complex wing motions such as folding, modification and reversal of camber, wing area expansion and contraction, and transverse bending. In order to generate the complex wing motions, they use an adaptation in skeletal and muscular systems like a human arm and muscles [2]. Due to the complicated wing motions and corresponding aerodynamic characteristics, the flapping flight has not been completely analyzed. One of the methods to make a successful flapping vehicle is to evaluate and mimic the flapping flight mechanism of the nature’s flyers. There have been many attempts to develop flapping wing mechanisms by using bio-mimetic or bio-morphic design. Pornsin-sirirak et al. [3,4] developed a palm-sized ornithopter. Its wings were manufactured by using MEMS technology, and the aerodynamic forces of the wings were measured from static and dynamic tests. Shape memory alloy (SMA) wires were used as muscle wires to control the elevator and rudder. Liger et al. [5,6] manufactured the flapping wings on which surfaces’ passive or adaptive valves manufactured by using MEMS technology were distributed to control the distribution of the pressure on the wings during up and down strokes. Jones et al. [7-9] developed a micro air vehicle which was propelled by a pair of flapping wings behind a main fixed wing. Because the wings flapped in counter phase, ground and stall suppression effects could be generated additionally. Cox et al. [10] developed three kinds of piezoelectrically actuated flexure-based flapping mechanisms which were operated at each system resonant frequency to increase the wing tip motions. Park et al. [11,12] manufactured flapping devices actuated by ionic polymer metal composite (IPMC) and lightweight piezo-composite actuator (LIPCA) of which actuation displacements were amplified by a linkage system. Some ground tests were performed to investigate the performances of the flapping devices. Lin et al. [13] designed a
four-bar linkage flapping mechanism driven by a DC motor. Some wind tunnel tests were performed for the flapping device and the aerodynamic characteristics were discussed. In this study, a bio-mimetic flapping wing was designed and manufactured. In order to generate an adaptive camber motion, the structural modeling of the macro-fiber composite (MFC) actuator was performed, and the flexible flapping wing was embedded with the MFC as surface actuators. Some aerodynamic tests were performed for the flapping wing to measure the lift and thrust for various test conditions, and the aerodynamic characteristics were investigated.
2. WING DEVELOPMENT 2.1 Wing Design A flexible flapping wing is designed to mimic the flapping motion of the nature flyers. The wing consists of composite frames and flexible thin skin. The flapping, twisting and adaptive camber motions are selected as the main wing motions. The flapping motion is generated by using an electric DC motor and a transmission system which converts the rotary motion of the motor into the flapping motion. The twisting motion is induced automatically by the flexibility of the wing during up and down strokes. The camber motion of local wing section is generated by the MFC actuator. The design parameters of the flexible wing are determined by some design constraints and the flight parameters of some birds. Due to the length of the MFC actuator (11 cm) and the width of a wind tunnel test section (10.16 cm), the design constraints are selected as max. chord > 11 cm, and max. span < 60 cm. Using the design constraints and the flight parameters of Table 1. Design parameters of smart flapping wing model. Parameters
Values
Expected total mass, W
200 g
Span, b
54 cm ( < 60 cm )
Max. chord, cmax
12.5 cm ( > 11 cm ) 2
Wing area, S
522.5 cm
Aspect ratio, AR
5.58
Wing loading, W S
0.383 g/cm2
Stall speed, VS
8 m/sec
Max flapping freq, Fmax
8 Hz
magpie and little grebe [14], the design parameters of the flexible wing are determined as shown in Table 1. The maximum flapping frequency is determined by the operating limitation of the driving motor and the transmission system.
2.2 Wing Modeling 2.2.1 Piezoelectric-thermal analogy In order to design a surface actuator module which can maximize the deformation of the variable wing camber, the structural modeling for the MFC actuator is performed for the basis of the analogy between thermal strains and piezoelectric strains using MSC/NASTRAN [15]. The MFC actuator consists of a sheet of aligned rectangular piezoceramic fibers, two structural epoxy layers and two interdigitated electrode layers, and exhibits converse and direct piezoelectric effects like PZT, PVDF, etc. The piezoelectric effects can be expressed mathematically by the constitutive equations as follows:
{T } = ⎡⎣c E ⎤⎦ {S} − [e] {E}
(1)
{D} = [e]{S} + ⎡⎣ε S ⎤⎦ {E}
(2)
T
⎡⎣c E ⎤⎦ , [ e ] and ⎡⎣ε S ⎤⎦ are a stress vector, an electric displacement vector, a strain vector, an electric field vector, an elastic stiffness coefficient matrix, piezoelectric coupling coefficient matrix and a dielectric coefficient matrix, respectively. By using the piezoelectric coupling matrix [ d ] which represents the relationship
where
{T } , {D} , {S } , {E} ,
between the piezoelectric strains and electric field strength, [ e ]
can be obtained as follows:
[e]
T
= ⎡⎣c E ⎤⎦ [ d ]
T
(3)
Generally, the thermoelastic constitutive equations can be expressed by the generalized Hook’s law in the form of
where
{α }
{T } = ⎣⎡c E ⎦⎤ {S} − ⎣⎡c E ⎦⎤ {α } ∆Θ
(4)
∆Θ = Θ − Θ0
(5)
, ∆Θ and Θ0 are a thermal expansion
coefficient vector, a temperature difference and a reference temperature, respectively. The substitution of Equation (3) into Equation (1) and comparison with Equation (4) gives
[ d ] {E} = {α } ∆Θ T
(6)
d 3i
∆ϕ3 = α i ∆Θ, ( i=1, 2, 3 ) t
(7)
where d3i , ∆ϕ3 , t and α i are a piezoelectric coupling coefficient, a electric voltage difference, a electric field thickness between the electrodes and the thermal expansion coefficient per each direction ( i ) of the resulting normal strain, respectively. 2.2.2 Structural wing model
Using the wing design parameters and the thermal analogy for piezoelectric materials, the structural modeling of the flexible wing is carried out. The wing model consists of graphite/epoxy composite frames and the MFC actuator as shown in Figure 1. The surface actuator to change the local wing camber is supported by two parallel composite rods, and some frames are constrained by the multi point constraints (MPC). The frames and the MFC actuator are represented with cbar and quad-4 elements, respectively. Table 2 shows the engineering properties of the MFC (M8557P1-d33 type, Smart Material Co.) and the graphite/epoxy composite. From some structural analyses of the wing model, the configuration of the frames, the location of the actuator module and the thickness of the supporting composite rods are determined to maximize the deformation of the wing camber. In order to verify the structural wing model, a transient response analysis is conducted by using MSC/NASTRAN, and the analysis result is compared with experimental data. The load case, which applied at the MFC actuator in this structural analysis, is a time dependent temperature field with the excitation frequency of 0.1Hz, as follows:
(
)
∆Θ(t ) = 2000 500 + 1000sin ( 2π × 0.1× ( t - 0.8333) ) (8)
The dynamic excitation test is performed for the real wing model without the skin, of which configuration is described in the following section. The sinusoidal excitation input voltage from -500V to 1500V is applied to the MFC actuator by using a high voltage amplifier (trek-623B), and the vertical displacement of the node 406 position is measured by using a laser sensor (LK081/2101). Figure 2 shows the comparison of the vertical displacements obtained from the experiment and the structural analysis. This result clearly demonstrates that the structural wing model is in good agreement with the dynamic test data, and that the piezoelectric strains induced by the electric fields can be estimated from the equivalent thermal analysis.
Table 2. Orthotropic linear elastic engineering properties of MFC and graphite/epoxy composite. Properties
MFC
Piezoelectric constant, d33 (pC/N)
Gr/Ep 2
4.6ｘ10
2
0
Piezoelectric constant, d31 (pC/N)
-2.1ｘ10
0
Tensile modulus, E1 (GPa)
30.336
119
Tensile modulus, E2 (GPa)
15.857
8.67
Poisson’s ratio, ν12
0.31
0.31
Shear modulus, G12 (GPa)
5.515
5.18
Density, ρ (kg/m )
6386
1570
Structural damping coeff., c
0.2
0
Electric field thickness, t (mm)
0.5
/
3
Figure 1. Analysis model of smart-flapping-wing without surface skin.
10
Experiment NASTRAN 5
Veritical Displacement(mm)
If only the out-of-plane electric field is applied on a piezoelectric actuator, Equation (6) can be reduced as follows:
0
-5
-10
-15
Measurement: node 406 U = 0.1Hz, 500 VDC, 2000 Vpp -20 -500
0
500
1000
1500
MFC Input Voltage, U(V)
Figure 2. Comparison of vertical displacements induced by MFC actuator (node 406).
2.3 Smart Flapping Wing
3. AERODYNAMIC TESTS
The flapping wing with the MFC actuator, named smart-flapping-wing in this paper, is manufactured on the basis of the design parameters and the analysis results. As outlined in the preceding section, the frames are made of the graphite/epoxy laminates which have unidirectional ply angle of 0º as shown in
3.1 Experimental Setup
Figure 3. The wing skin is a flexible PVC film, and the MFC (M8557P1) is embedded between the skin and frames at the distance of 8.5 cm from the flapping axis. The variations of the wing camber for different DC input voltages are measured by using laser displacement sensor. Figure 4 shows the camber lines of the maximum chord. The maximum camber of the chord line is linearly varied from -0.026c (-500V) to 0.044c (1500V), and these maximum cambers are located at ~ 0.498c from the leading edge. The vertical displacement of the trailing edge is varied from 1.676 mm (-500V) to -19.257 mm (1500V). The mean pitch angle of the chord, θ w , with respect to the flapping axis is linearly changed from -0.724º (-500V) to 9.056º (1500V). The flapping wing has the initial pitch angle 1.721º (0V).
In order to measure the aerodynamic forces of the smart-flapping-wing in static and dynamic wind tunnel tests, a test stand is manufactured. The test stand consists of a driving part, a test mount and a measurement part as shown in Figure 5. In the driving part, an electric DC motor and a transmission, which are the same parts as used in Cybird-P2 made by Neuros Co. in Korea, are used to generate the flapping wing motion. The pitch angle of the flapping axis, θ a , with respect to the free stream velocity V can be changed by adjusting the test mount which supports the driving part. In the measurement part, the lift L and the thrust T are measured simultaneously by the horizontal and vertical load cells, respectively. Using the test stand, some aerodynamic tests are performed in a subsonic wind tunnel with a 1,016ｘ762ｘ1,524 m test section. The test stand is located at the center of the test section as shown in Figure 6. In order to reduce the drag effect of the test stand, the measurement part is shielded by an aluminum fairing mounted on the bottom of the test section. The flapping angle φ is measured by the use of a laser Doppler vibrometer (OFV-3001/303). The input signals to the DC motor D and to the MFC actuator U are applied by a DC power supply (toe-8852) and a high voltage amplifier (trek-623B), respectively. In these aerodynamic tests, the static camber effects induced by three DC input voltages (-500, 0, 1500 V) are only considered.
Figure 3. Configuration of the smart-flapping-wing.
0.15
upper surface lower surface polynomial fit
0.10
leading edge 0.05
camber line flapping axis
0.00
-500V
z/c
0V -0.05
ch o rd l ine
-0.10
750V
θw
-0.15 -0.20 -0.25 -0.2
Flow velocity V: 0 m/s o Pitch angle θ a: 0 Flapping freq. F: 0 Hz 0.0
0.2
1500V trailing edge
0.4
0.6
0.8
1.0
1.2
x/c
Figure 4. Camber lines of the maximum chord line for the DC input voltages.
Figure 5. Configuration of flapping system and test stand. The inset is the front view of the transmission.
(a)
1.4
U=-500V U=0V U=1500V Curve Fit
1.2 1.0
∆CL
be r
0.6
am
0.4
Ef fe ct of C
Lift Coefficient, CL
0.8
downward cambered
0.2 0.0
symmetrical
α1
-0.2 -0.4
upward cambered
-0.6 -0.8
Velocity = 4m/s
-1.0 -15
-10
-5
0
5
10
15
20
25
Pitch Anlge of Flapping Axis, θ a (deg)
(b)
0.30
Figure 6. Experimental setup for aerodynamic tests.
U=-500V U=0V U=1500V Curve Fit
0.25
downward cambered
The static wind tunnel tests are performed for the smart-flapping-wing without the flapping motion. The flapping wing is fixed parallel to the flapping axis. That is, the flapping angle, φ , is set to zero. The free stream velocity is changed from 2 m/s to 10 m/s, and the pitch angle of the flapping axis is changed from -10º to 20º. To clarify the aerodynamic
r be am
0.15
fC
3.2 Static Results and Discussions
upward cambered CD1
0.10
∆CD
Ef fe ct o
Drag Coefficient, CD
0.20
symmetrical
0.05
0.00
α1
Velocity = 6m/s -0.05 -15
-10
-5
0
5
10
15
20
25
Pitch Anlge of Flapping Axis, θ a (deg)
characteristics, some selected experimental data are shown in Figure 7 and Figure 8. Figure 7 shows the variations of the lift and drag coefficients for the different MFC input voltages. In order to investigate the aerodynamic characteristics, the coefficients are fitted by polynomials. The lift and drag coefficient curves are shifted by the variation of the camber like the aerodynamic characteristics due to high-lift devices such as a trailing edge flap in a conventional airplane. As expected, with increasing the MFC input voltage, the lift and drag coefficients increase. The maximum lift and drag are 233 g and 49.6 g, which are obtained at V = 10 m s , θ a = 20ο and U = 1500V . These values
Figure 7. Effect of camber in static lift (a) and drag (b) results.
are greater than those measured in the symmetrical wing condition (0V) up to 24.4 % and 25.8 %, respectively. Figure 8 shows the variations of the coefficients due to the chordwise wing flexibility. The slopes of the lift and drag coefficient curves decrease with the increasing flow velocity. The pitch angle of the chord with respect to the flow velocity can be expressed as follows:
(b)
θ = θ a + θ w + δθ f
(9)
where δθ f is the variable pitch angle of the chord with respect to the flapping axis induced by the chordwise wing flexibility. Because δθ f plays a role in reducing the absolute value of θ ,
(a)
1.0
U=0V symmetrical
0.8
V=6m/s
0.6
Lift Coefficient, CL
V=10m/s 0.4
∆CL
0.2
Effect of Flexibilty 0.0
α1 αL0
-0.2 -0.4 -0.6 -15
-10
-5
0
5
10
Pitch Anlge of Flapping Axis,
15
θa
20
25
(deg)
0.25
U=0V symmetrical V=6m/s
Drag Coefficient, CD
0.20
0.15
V=8m/s CD1 ∆CD
0.10
V=10m/s
0.05
Effect of Flexibilty 0.00
α1 -15
-10
-5
0
5
10
15
20
25
Pitch Anlge of Flapping Axis, θ a (deg)
Figure 8. Effect of flexibility in static lift (a) and drag (b) results.
(a)
3.3 Dynamic Results and Discussions The dynamic wind tunnel tests are performed for the smart-flapping-wing with the flapping motion in the same test conditions as in the static tests. The flapping frequency is varied from 1 Hz to 8 Hz by controlling the frequency of the flapping ® angle measured at the root of the wing. The dSPACE DS1103 Controller and Real-Time Interface are used in this process. The flapping angle φ alternates between −25° and 32° . Figure 10 shows the mean lift and thrust measured in 8 Hz flapping frequency, 0° and 20° pitch angles. The mean lift values (Figure 10. a) are linearly proportional to the flow velocity V . The maximum mean lift is changed from 229 g (-500V) to 304.6 g (1500V) by the MFC actuator at V = 10 m s and θ a = 20° . These values are greater than
(b)
that measured in the symmetrical wing condition (0V) up to -9.2 % and 20.8 %, respectively. This camber effect can be utilized for controlling the roll moment of the flapping vehicle by applying different MFC input voltages to the left and right wings. Because the lift under the 6.2 m/s flow velocity is less than the expected total mass (200 g), however, the smart-flapping-wing can not sustain level flight in the lower Figure 9. Force increments due to the effects of camber (a) and flexibility (b) in static tests.
(a)
Mean Lift, Lmean(g)
250
150
θ a = 0ο
100
0
Flapping Freq. = 8 Hz -50 0
2
4
6
8
10
Velocity, V(m/s)
(b)
100
U=-500V U=0V U=1500V nd 2 Order Fit
75
Mean Thrust, Tmean(g)
reference coefficients. Figure 9 shows the aerodynamic force increments due to these effects. It is evident from the figure that the camber, which generated by the MFC actuator, effectively produces the positive force increment in almost the entire test conditions, but the chordwise wing flexibility produces the negative benefit in the test conditions except the high pitch angle and the high flow velocity regions at which the wing flexibility resists stall.
200
50
(10)
where ∆L and ∆D are the lift and drag increments, respectively. To calculate the force increment due to the camber effect, the aerodynamic forces measured in symmetrical wing condition ( U = 0V ) are used as the reference lift and drag. To calculate the force increment due to the wing flexibility, the lift and drag coefficients measured at V = 2 m s are used as the
θ a = 20ο
U=-500V U=0V U=1500V st 1 Order Fit
300
the effective angle of attack is reduced by the chordwise wing flexibility. Therefore, the lift and drag coefficients decrease with the increasing flow velocity. In order to investigate the aerodynamic benefits from the effects of camber and the wing flexibility, the force increment is defined as follows: ∆F = ∆L − ∆D
350
50
25
θ a = 0ο 0
-25
-50
θ a = 20ο Flapping Freq. = 8 Hz 0
2
4
6
8
10
Velocity, V(m/s)
Figure 10. Dynamic mean lift (a) and thrust (b). Flapping frequency = 8 Hz.
6
V=2m/s U=0V symmetrical
5
F=8Hz extension
Lift Coefficient, CL
4 increment
3 2
∆C L
F=4Hz
Unsteady Effect
1
F=1Hz 0
α1
αL0
-1 -2 -15
-10
-5
0
5
10
Pitch Anlge of Flapping Axis,
(b)
15
θa
20
25
(deg)
8
V=2m/s U=0V symmetrical
7
Mean Thrust Coeff., CT
6
Unsteady Effect
5
unsteady effect [16]. The smaller leading edge vortex may be stabilized by base-to-tip spanwise flow in the form of a spiral vortex, or the small effective angle of attack which is reduced by downward flow induced from tip vortices and wake vorticity [17]. As mentioned in preceding section, the chordwise wing flexibility also reduces the effective angle of attack. Therefore, additional aerodynamic force increment due to the unsteady effect can be generated by using a flexible wing unlike in the static results. From the different features of the aerodynamic characteristics of the wing flexibility in the static and dynamic test conditions, it seems desirable for higher flight efficiency to adaptively adjust the chordwise stiffness of the wing on the flight condition using some smart structures. The unsteady effect of the smart-flapping-wing can be found obviously in Figure 12, which shows the variation of the mean
F=8Hz
4
4.0
3
∆CT
1
3.0
F=5Hz 0
α1
F=2Hz
-1 -2 -15
-10
-5
0
Experiment Exponential Fit
3.5
2
5
10
Pitch Anlge of Flapping Axis,
15
θa
20
25
(deg)
Figure 11. Unsteady effect in dynamic lift (a) and drag (b) coefficients. The wing camber is symmetrical.
Mean lift coeff., CL mean
(a)
C L mean = 7.18e(
2.5
− J 0.53 )
2.0
+ 0.51
Velocity = 2~10 m/s MFC Input = -500, 0, 1500 V O Pitch Angle = const (10 ) Flapping Freq. = 1~8 Hz
1.5 1.0 0.5 0.0
The variations of the thrust values generated by the camber effect are smaller than those of the lift values. Figure 11 shows the variations of the mean lift and thrust coefficients according to the flapping frequency. Though the flow velocity is constant, the lift and thrust coefficients remarkably increase with the flapping frequency, and moreover, the stall angle increases. While the maximum lift coefficient obtained in the static tests is almost equal to 1, the dynamic results exhibit the maximum lift coefficient of more than 5. This aerodynamic benefit may be caused by the relative flow velocity and the effective angle of attack which are increased by the flapping motion, and the unsteady aerodynamic effect which is generated by a leading edge vortex attached on the wing surface. A smaller leading edge vortex allows the fluid separated from the wing surface to reattach more easily, and the wing can sustain this reattachment for a long time. Thus, the maintenance of a stable leading edge vortex plays an important role in the
-0.5 -2
0
2
4
6
8
10
12
14
16
18
20
Advance ratio, J
Figure 12. Unsteady aerodynamic effect of mean lift coefficients. Advance Ratio, J 0
0.93
0.47
1.40
1.86
2.33
100 90
Percentage of Lift Compnent, %
flight speed. The mean thrust values (Figure 10. b) decrease with the flow velocity, and the decrements are proportional to square of the flow velocity. The maximum mean thrust is 99.5 g, which are measured at V = 0 m s , θ a = 0ο and U = −500V .
80
Flapping Freq. = 8Hz ο Pitch Angle = 20 MFC Input = 1500V
70
Effective AOA
60 50 40 30 20 10
Camber Effect
0
Normal Force
-10 -20 0
2
4
6
8
10
Velocity, V(m/s)
Figure 13. Percentage of lift components measured at F = 8Hz, θ a = 20° , U = 1500 V.
lift coefficient according to the advance ratio. The advance ratio J is defined as follow: J = V 2ΦFb
(11)
where Φ , F and b are the amplitude of the flapping angle, the flapping frequency and the wing semi-span, respectively. This value means the ratio of the flight speed to the speed of the wing tip. It is evident from the figure that as the advance ratio decreases, the lift coefficient increases exponentially. Especially, the lift coefficient rises remarkably in the advance ratio of less than 1, which means that the wing is exposed to the unsteady flow regime. In the advance ratio of more than 1, however, the coefficient decays less than 1 like the static test results, which means that the flow condition is the quasi-steady flow regime. In spite of the aerodynamic benefit from the unsteady effect, the lift of the smart-flapping-wing operated below the stall speed (6.2 m/s) is not enough for the level flight. The lift L generated in the dynamic tests can be divided into three lift components as follows: L = Lnormal + Lcamber + Leffect
(12)
where Lnormal , Lcamber and Leffect are the normal force of the average resultant aerodynamic force vectored by adjusting the pitch angle, the adaptive lift produced by the camber effect, and the effective lift component due to the effective angle of attack and the relative flow velocity, respectively. Figure 13 shows the contribution of these lift components measured at F = 8Hz, θ a = 20° , U = 1500 V. This figure clearly demonstrates that in the quasi-steady flight condition, the main lift is generated by the effective angle of attack and the flight speed, but in the unsteady flight condition, the lift is mostly affected by the normal force Lnormal and the camber effect. Therefore, in the insufficient flight speed conditions such as the stall speed, take-off and landing, additional wing motions are necessary like birds or bats which utilize the higher pitch angle, the higher flapping frequency, the camber of the entire wing, the folding motion, etc, for their higher flight efficiency.
4. CONCLUSIONS In the present study, we developed the smart-flapping-wing with the MFC as the surface actuator. For the design of the flapping wing, the structural model of the MFC actuator was established by using the piezoelectric-thermal analogy, and the structural analyses of the wing were carried out. In order to measure the aerodynamic forces of the smart-flapping-wing, the test stand was manufactured, and the static and dynamic tests
were performed in the subsonic wind tunnel. In the static tests, the aerodynamic characteristics due to the effects of the camber and the chordwise wing flexibility were investigated. In the dynamic tests, the unsteady aerodynamic effect was discussed. The experimental results demonstrate that the effect of the camber generated by the MFC actuator can produce the sufficient lift variation of up to 24.4 % in the static condition and 20.8 % in the dynamic condition. The chord-wise wing flexibility is one of the important parameters to affect the aerodynamic performance. Especially, the wing flexibility can help the wing to stabilize the small leading edge vortex in the unsteady flow condition. The lift component induced by the forward speed and the effective angle of attack becomes dominant up to 70% in quasi-steady flight condition. In order to compensate the lift in the low speed flow condition, the additional wing motions should be adopted to utilize the unsteady aerodynamic benefit.
Acknowledgements This work was supported by grant No. R01-2005-00010848-0 from the Basic Research Program of the Korea Science & Engineering Foundation. The first author would like to thank the Brain Korea 21 Project in 2006.
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