1. No category

Journal of Fluids and Structures 49 (2014) 687–704
Contents lists available at ScienceDirect
Journal of Fluids and Structures
journal homepage: www.elsevier.com/locate/jfs
Experimental study of wings undergoing active root flapping
and pitching
Norizham Abdul Razak a, Grigorios Dimitriadis b,n
a
b
School of Aerospace Engineering, Universiti Sains Malaysia 14300 Nibong Tebal, Pulau Pinang, Malaysia
Aerospace and Mechanical Engineering Department, University of Liège, 4000 Liège, Belgium
a r t i c l e i n f o
abstract
Article history:
Received 24 November 2013
Accepted 7 June 2014
Available online 1 July 2014
This paper presents the results of experiments carried out on mechanical wings undergoing active root flapping and pitching in the wind tunnel. The objective of the work is to
investigate the effect of the pitch angle oscillations and wing profile on the aerodynamic
forces generated by the wings. The experiments were repeated for a different reduced
frequency, airspeed, flapping and pitching kinematics, geometric angle of attack and wing
sections (one symmetric and two cambered airfoils). A specially designed mechanical
flapper was used, modelled on large migrating birds. It is shown that, under pitch leading
conditions, good thrust generation can be obtained at a wide range of Strouhal numbers if
the pitch angle oscillation is adjusted accordingly. Consequently, high thrust was
measured at both the lowest and highest tested Strouhal numbers. Furthermore, the
work demonstrates that the aerodynamic forces can be sensitive to the Reynolds number,
depending on the camber of the wings. Under pitch lagging conditions, where the
effective angle of attack amplitude is highest, the symmetric wing was affected by the
Reynolds number, generating less thrust at the lowest tested Reynolds value. In contrast,
under pure flapping conditions, where the effective angle of attack amplitude was lower
but still significant, it was the cambered wings that demonstrated Reynolds sensitivity.
& 2014 Elsevier Ltd. All rights reserved.
Keywords:
Flapping flight
Unsteady aerodynamics
Wind tunnel testing
Dynamic stall
1. Introduction
Flapping flight has been the subject of research since the dawn of the science of aerodynamics; early examples of analysis
include work by Von Karman and Burgers (1935) and Garrick (1937). Recently, due to growing interest in Micro Air Vehicles
(MAV), flapping flight has re-emerged as a popular research area. A number of works have been published since the 1990s,
aiming at understanding and optimising flapping flight for low Reynolds numbers. In general, flapping flight research can be
grouped into insect-based and bird-based. Insect flapping is characterised by higher frequencies and by persistent flow
separation over significant parts of the wings (Ellington et al., 1996). Bird flapping involves lower frequencies and the flow
can be fully attached at all times for specific flight conditions. Nevertheless, dynamic stall is generally thought to play a
significant role even in bird flight; several mechanisms involving separated flow have been reported, such as the Leading
Edge Vortex (LEV) (Hubel and Tropea, 2010; Yu et al., 2013) or clap and fling (Bennett, 1997). Such mechanisms are discussed
in detail by Shyy et al. (2010), albeit mostly within the context of insect and hovering bird flight.
n
Corresponding author.
E-mail address: [email protected] (G. Dimitriadis).
http://dx.doi.org/10.1016/j.jfluidstructs.2014.06.009
0889-9746/& 2014 Elsevier Ltd. All rights reserved.
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Research on plunging and pitching 2D airfoils has shown that the best propulsive efficiency is obtained when the pitch
leads the plunge by a phase difference or around 901 (Anderson et al., 1998; Platzer et al., 2008). This type of flapping
kinematics is commonly referred to as pitch-leading and can result in propulsive efficiencies of up to 75%. Nudds et al.
(2004) and Schouveiler et al. (2005) showed that, for plunging and pitching wings, maximum propulsive efficiency is
achieved at Strouhal numbers of 0.21–0.25. The experiments by Schouveiler et al. (2005) also demonstrated that the thrust
force increases continuously with the Strouhal number. However, this result concerned a symmetric airfoil pitching.
As the phase difference between the pitch and the plunge moves away from 901, thrust production reduces significantly
because of the occurrence of dynamic stall (Isogai et al., 1999). On the other hand, dynamic stall has been known to increase
the instantaneous lift to up to three times the maximum static lift (Francis and Keesee, 1985). It has been theorised (Lighthill,
1975) that this mechanism is used by large birds in order to generate additional lift during some flight phases, such as
takeoff. Usherwood et al. (2003) measured the pressure on the wings of Canada geese during takeoff and observed double
peaks in pressure at the wingtip during the downstroke. Such peaks may be evidence of the passage of a LEV. One of the
most complete experimental investigations of root flapping was carried out by Hubel and Tropea (2009, 2010) on a gooselike flapping wing model featuring wings that could flap but not pitch. The work showed that very high lift forces could be
generated during parts of the flapping cycle and the authors demonstrated that this phenomenon is due to the development
of a leading edge vortex.
Actively flapping and pitching 3D wings have been recently studied experimentally for insect-like flight (see for example
Seshadri et al., 2013) but such work is still rare for bird-like wings. Malhan et al. (2012) studied experimentally a flapping
wing at both hover and forward flight conditions but at smaller scales and higher frequencies than typical of most birds.
The purpose of the present work is to investigate experimentally the effect of a few key parameters on the generation of
aerodynamic forces of a bird-like mechanical model that flaps and pitches its wings. The parameters are the kinematics,
reduced frequency and wing profile. As mentioned above, the phase difference between flapping and pitching that gives the
best performance is well known. However, the effect of the pitch angle limits (i.e. pitch angle mean and amplitude) has not
been as thoroughly investigated. Furthermore, birds have cambered wing sections and a lot of the previous work on
propulsion has concentrated on symmetric airfoils. In this work, an asymmetric airfoil is used to investigate pitch leading
aerodynamics and the pitch angle range can be altered to determine which range gives the best thrust.
Pitch lagging is the opposite of pitch leading, i.e. a wing motion whereby the pitch lags the flap. Pitch lagging and pure flap
kinematics are studied in order to determine the effect of wing camber on separated flapping flows. The frequency, airspeed, phase
between pitch and lag can all be varied. Three different wing sections are tested, one symmetric and two cambered. Detailed
measurements of the aerodynamic forces acting on the model are carried out by means of an aerodynamic balance. Furthermore,
the flowfield around the wing is visualised using Particle Image Velocimetry at distinct instances of the flapping cycle.
2. Experimental setup
The experiments described in this work were conducted in the Multi-Disciplinary Low Speed Wind Tunnel of the
University of Liège. The tunnel's aeronautical test section was used, which has dimensions of 2 m 1.5 m 5 m (width
height length) and is capable of achieving airspeeds of up to 60 m/s in the closed loop configuration. The turbulence
level is 0.15% of the windspeed on average. The test section is equipped with a rotating turntable for controlling the model's
orientation and a three-component aerodynamic force balance measuring total lift, drag and side force.
2.1. Flapping wing model
The flapping wing wind tunnel model developed for this work is referred to as the Metal Bird (Razak and Dimitriadis,
2009, 2011). Its general specifications are consistent with a medium-sized bird, such as a duck, albeit simpler in kinematic
terms. The total wingspan (tip to tip) is 1.3 m and the total aspect ratio is 8.6. The flap angle, γ, was designed to flap between
Fig. 1. Diagram of the flapping and pitching mechanical model, front and top view.
N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
689
301 and þ301, as shown in Fig. 1, to reflect the flap amplitude of several large migrating birds under cruise conditions.
The nominal maximum pitch angle is specified as 7201 but can be changed by means of a special adaptor.
The design of the 3-D flapping and pitching apparatus makes use of the tandem dual crank mechanism arrangement
shown in Fig. 2. The dual crank is used to achieve root flapping of the wing while the tandem setup causes the pitching
motion. The latter is allowed for by setting an offset in the initial position of the two crank mechanisms with respect to each
other. Both crank mechanisms are driven by a single drive shaft, so that the phase between the forward and aft flapping
arms remains the same throughout the upstroke and downstroke motions. This design, adapted from Kim et al. (2003),
allows a single motor to be used to achieve both flapping and pitching. Similar designs were employed by Mazaheri and
Ebrahimi (2011) and Seshadri et al. (2013). The geometric angle of attack of the wing, αs, can be set to any desired value. The
complete flapping system is driven by a single direct current (DC) brushless motor that comes with a reduction gear of 5:1
ratio. The rotation speed is further reduced using a gear train (combination of pinion and spur gears) to achieve lower
rotational speed values to suit the test flapping frequency range. The reduction in rotational speed also increases the torque
required to flap and pitch the wings. The complete Metal Bird installed in the wind tunnel is shown in Fig. 2.
2.2. Wings
The wings were rapid prototyped in laser sintered polyamide. In order to minimise their weight, the wings were designed to be
hollow, consisting mainly of the skin and a central rectangle, as well as some local reinforcement at the leading and trailing edges.
Short aluminium bars were passed through the central rectangle and acted as spars to further reinforce the wings' structural
strength at the wing root. The wings' surface was treated with epoxy to provide a smooth finish before being painted mat black for
flow field measurements. Three sets of wings with different profiles were built for this study. Three classes of profile were chosen: a
symmetric airfoil, a medium cambered airfoil and a highly cambered thin airfoil. The airfoils used were NACA 4-digit i.e. 0012, 4412
and 6409 respectively. The wing chord, c, is 0.146 m and the span, b, is 0.48 m for the 12% thick airfoils while for the NACA6409 the
chord is 0.16 m and the span 0.4 m. The distance from the flapping axis to the wing root, d, is 0.19 m for the NACA 0012 and 4412
and 0.15 m for the 6409 wing. The characteristics of all three wings are summarised in Fig. 3.
2.3. Particle Image Velocimetry
Time resolved Particle Image Velocimetry (PIV) was used to capture the instantaneous velocity-field in a vertical plane
parallel to the wing chord during the flapping cycle. The PIV interrogation area was illuminated by a twin 10 mJ Litron
Fig. 2. A close-up of the tandem dual crank mechanism (left) and the complete flapping and pitching mechanical model in the wind tunnel (right).
Fig. 3. Wing dimension.
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double-pulse laser, producing a pulse width of 10 ns with a 30 μs duration between pulses. The wind tunnel was seeded
using a Laskin nozzle fog generator placed downstream of the test section to ensure a homogeneous distribution of particles.
Corn oil was used to generate suitably sized particles.
The PIV images were captured using a CCD camera (Phantom V9.1, 1600 1200 Pixels) mounted on a traversing system
outside the test section. The camera was installed on the side of the wind tunnel's working section, looking through a
Perspex window. The vector field was calculated using the adaptive correlation function in the standard two-dimensional
PIV software system supplied by Dantec Dynamics (Dynamic Studio). The interrogation window used for the analysis was
32 32 pixels with a 65% overlap; an additional validation area was used that included subpixel interrogation to improve
accuracy. All further processing was carried out using the Matlab software.
The first image captured during the oscillation was manually triggered in the PIV software. All subsequent images were
triggered via a pre-set time stepping signal. The triggered signal was also captured by the National Instruments (NI) data
acquisition box used to acquire the force measurements. Measurements were performed at three spanwise positions at
midstroke (during both downstroke and upstroke) as shown in Fig. 4. Midstroke is the best position to undertake PIV
measurements since it provides minimum reflection because the wing's surface is perpendicular to the laser plane.
2.4. Kinematics
The instantaneous flap and pitch angles were measured by means of two calibrated linear rotary potentiometers
installed on the starboard flapping arm. The data sampling rate for all sensors was set to 1.0 kHz. The instantaneous angles
were then differentiated using a central difference scheme to obtain the flapping velocities. For all tests, the starboard and
port wings were set at the same geometric angle αs.
Fig. 5 shows the flapping and pitching angle variation of the wings for a flapping frequency of 1.2 Hz over one complete
cycle. The y-axis represents the angle in degrees while the x-axis represents the time normalised by the period. It should be
noted that the motion is not purely sinusoidal; the downstroke period is shorter compared to the upstroke due to the effect
of gravity. The kinematics are also partly dependent on the wind tunnel airspeed. Fig. 5(a) plots the kinematics for pure
flapping cases. Fig. 5(b) plots the kinematics for combined flapping and pitching motions; the curve labelled ‘flapping’
denotes the variation of the flap angle in time. The other two curves denote the variation of the pitch angle for two different
kinematic cases, pitch leading (solid line) and pitch lagging (dashed line).
The wing's effective angle of attack, αeff , is the result of the combination of the pitching motion and the plunge velocity
due to flapping, Vz, which is perpendicular to the free stream. The value of αeff is given by
Vz
þ αp ;
U1
αeff ¼ αs þ arctan
ð1Þ
where αs is the wing's geometric angle of attack, Vz is the instantaneous plunge velocity at each spanwise section, U 1 is the
freestream velocity and αp is the wing's instantaneous pitch angle, calculated from the phase difference between the fore
and aft flapping arms. Clearly, the effective angle of attack varies in the spanwise direction but the estimates of αeff
presented in this paper are taken at the midspan section unless stated otherwise. The instantaneous plunge velocity is
computed from the measured instantaneous flapping angle data and is given by
V z ¼ γ_ r s ;
ð2Þ
where γ_ is calculated numerically using central differences and rs is the distance from the rotational axis of the flapping
arms to the midspan of each wing.
The unsteady flow characteristics of flapping flight are categorised using either the reduced frequency or the Strouhal
number. The reduced frequency, k, is defined as k ¼ π fc=U 1 , where f is the flapping frequency, c is the chord length and U 1
is the free stream velocity. The flapping frequency is defined as the inverse of the period of a complete flap cycle and is
obtained from an optical encoder which measures the drive shaft's rotational speed, which is equal to four times the
flapping frequency. The flapping frequency values obtained from the optical encoder were compared to the frequency values
measured from the rotary potentiometers. The difference was found to be less than 2%. The reduced frequency shows to
what degree transient phenomena are important when flapping and pitching motions force the fluid particles around the
wing. Ames et al. (2001) stated that 0 r k r 0:03 indicates quasi-steady flow where wake effects are unimportant.
Fig. 4. Measurement plane positions along the span on the flapping wing model.
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691
30
Angle, deg°
20
Pure flapping
10
downstroke
0
Upstroke
−10
−20
−30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.9
1
t/T
30
downstroke
flapping
20
Angle, deg°
Pitch (lag)
10
0
−10
Pitch (lead)
−20
Upstroke
−30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
t/T
Fig. 5. Instantaneous flapping and pitching angle for both cases for one full period. (a) Pure flapping. (b) Flapping and pitching.
Table 1
Reynolds numbers, Strouhal numbers and reduced frequencies of all the test cases.
U 1 (m/s)
f (Hz)
NACA 0012, 4412
Re 10
6
6
6
6
9.4
9.4
9.4
9.4
14.8
14.8
14.8
14.8
0.8
1.0
1.2
1.5
0.8
1.0
1.2
1.5
0.8
1.0
1.2
1.5
0.55
0.55
0.55
0.55
0.86
0.86
0.86
0.86
1.36
1.36
1.36
1.36
5
NACA 6409
St
k
Re 105
St
k
0.089
0.111
0.134
0.168
0.057
0.071
0.086
0.107
0.036
0.045
0.054
0.068
0.061
0.076
0.092
0.115
0.039
0.049
0.059
0.073
0.025
0.031
0.037
0.047
0.60
0.60
0.60
0.60
0.95
0.95
0.95
0.95
1.49
1.49
1.49
1.49
0.073
0.092
0.110
0.138
0.047
0.059
0.070
0.088
0.030
0.037
0.045
0.056
0.067
0.084
0.100
0.126
0.043
0.054
0.064
0.080
0.027
0.034
0.041
0.051
For 0:03 rk r 1 the flow is quasi-unsteady; added mass is negligible but wake effects are crucial. The fully unsteady flow
regime lies at k Z 1 and is dominated by acceleration effects.
Three airspeeds were tested in this work: 6.0 m/s, 9.4 m/s and 14.8 m/s. For each airspeed, four flapping frequencies were
tested: 0.8 Hz, 1.0 Hz, 1.2 Hz and 1.5 Hz. These combinations of airspeed and frequency correspond to reduced frequency
values between 0.03 and 0.13, as seen in Table 1, which tabulates all the airspeed, frequency, k and Strouhal values for each
wing. The Strouhal number is defined as St ¼ 2y0 f =U 1 , where y0 is the flapping amplitude at the wingtip in m, i.e.
y0 ¼ ðd þ bÞ sin 301. Table 1 shows that the experiments lie in the 0.03–0.17 range, i.e. slightly lower than the optimal
propulsion efficiency value of St¼0.21 suggested by Nudds et al. (2004). The reason for limiting the maximum Strouhal
number to 0.17 is related to measurement issues and will be explained in the next section.
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3. Inertia and added mass measurements
The forces measured by the aerodynamic balance under flapping conditions consist of the sum of unsteady aerodynamic,
inertial and added mass forces. The inertial forces must be subtracted from the measured loads in order to estimate the
aerodynamic forces (Dickinson and Götz, 1996; Wilkin and Williams, 1993). The inertial contribution was measured by
flapping the wings under wind-off conditions. This measurement was repeated for each flapping frequency of interest, after
replacing the wings by thin metal bars with the same inertial characteristics. We also installed extension springs on the top
of the flapping arms in order to fine tune the flapping kinematics of the wind-off tests with metal bars so that they match as
40
30
10
Z
F (N)
20
0
−10
F
−20
(U=14.8ms )
F (U=0ms )
FZ (F
−30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
−F )
0.9
t/T, deg
Fig. 6. Measured vertical forces at wind-on and wind-off conditions and their difference for U 1 ¼ 9:4 m=s, F ¼1.23 Hz and αs ¼ 01.
2
1.5
NACA0012, Re = 86370
NACA0012, Re = 135980
NACA4412, Re = 86370
NACA4412, Re = 135980
NACA6409, Re = 94650
NACA6409, Re = 149020
CFZ
1
0.5
0
−0.5
−1
−25
−20
−15
−10
−5
0
5
10
15
20
25
αS, deg°
0.45
0.4
0.35
NACA0012, Re = 86370
NACA0012, Re = 135980
NACA4412, Re = 86370
NACA4412, Re = 135980
NACA6409, Re = 94650
NACA6409, Re = 149020
CFX
0.3
0.25
0.2
0.15
0.1
0.05
−25
−20
−15
−10
−5
0
5
10
15
20
αS, deg°
Fig. 7. Static vertical (CFZ) and horizontal force coefficients (CFX) for NACA 0012, 4412 and 6409 wings between Re¼ 86 370 and Re¼149 020. (a) CFZ vs αs.
(b) CFX vs αs.
N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
693
closely as possible the kinematics of the wind-on experiments with wings at all parameter values of interest. Fig. 6 shows an
example of the vertical forces recorded at wind-off and wind-on conditions, along with their difference for a pure flapping
case oscillating at 1.2 Hz and αs ¼ 01.
As the flapping frequency increases, the ratio of inertial amplitude to aerodynamic amplitude also increases; at high
enough flapping frequencies it may become impossible to distinguish the aerodynamic force from the noise. This
phenomenon is dependent primarily on the mass undergoing the flapping motion and the flapping frequency. Rival et al.
(2009) found that the ratio of aerodynamic to inertial forces is inversely proportional to k2. When this ratio is equal to or
lower than the sensitivity of the measurement instrument, the estimation of the aerodynamic forces becomes impossible.
In the present work, the aerodynamic balance sensitivity is 0.05 N so the maximum flapping frequency tested had to be
limited to 1.5 Hz in order to maintain measurement accuracy.
All the force measurements presented in this work are based on cycle averages over 25 cycles. The cycle averaging
procedure produced smooth time responses over a single cycle that represents the noisy raw signals measured over the
entire recording period. The same procedure was applied to all recorded signals, i.e. flap angle, pitch angle, horizontal force
and vertical force.
4. Static wind-on tests
The first wind-on tests were carried out under static conditions, i.e. without flapping. The wings were secured in the
horizontal position. The objective of these tests was to determine the static lift and drag curves of the wings by varying the
angle of attack and the Reynolds number. The geometric angle of attack αs was set by rotating the wing at its joint by angles
ranging from 201 to 201 in increments of 11. The test airspeeds were 9.4 m/s and 14.8 m/s. The measured lift and drag
values were averaged over 20 s of measurement time. The tests were repeated for the three different wing profiles
mentioned earlier. A set of tests was also carried out without wings to estimate the drag of the fuselage and support
structure. The force coefficients are defined as
C FZ ¼
C FX ¼
2F Z
;
ð3Þ
;
ð4Þ
ρU 21 S
2F X
ρU 21 S
where FZ and FX are the measured vertical and horizontal forces respectively, ρ is the air density, U 1 is the airspeed and S is
the wing area for any of the wings. The vertical force is defined positive upwards and the horizontal force positive
backwards (i.e. in the free stream direction). In this work, the term vertical force is used to denote either lift or downforce.
The term horizontal force denotes either drag or thrust.
Fig. 7(a) shows that the NACA 0012 generates the lowest maximum vertical force coefficient values while the NACA 6409
wing section gives the highest maximum vertical force coefficient, peaking at 1.3. The linear angle of attack range for all the
wings extends from 81 to þ81, except for the NACA 4412 wing, whose linear region extends up to around 131. Fig. 7(b)
shows the static horizontal force coefficient curves for all the wings. The minimum drag coefficient ranges from 0.05 to 0.1
for the three different wings.
Table 2
Maximum and minimum static force coefficient measured.
Wing
Max CFZ
Corresponding αs (deg)
Min CFZ
Corresponding αs (deg)
NACA 0012
NACA 4412
NACA 6409
0.8
1.2
1.4
15
15
15
0.8
0.4
0.1
16
12
10
Table 3
Pitch angle limits for pitch leading tests on the NACA 6409 wing.
NACA 6409
Downstroke (deg)
Upstroke (deg)
αs (deg)
12
10
8
6
4
0
2
4
6
8
6
4
2
0
2
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N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
1.2
Pitch Amplitude = −12 to 0
Pitch Amplitude = −10 to 2
Pitch Amplitude = −8 to 4
Pitch Amplitude = −6 to 6
Pitch Amplitude = −4 to 8
1
0.8
CFZ
0.6
0.4
0.2
0
−0.2
−40
−30
−20
−10
0
10
20
30
40
Flapping angle, deg
Pitch Amplitude = −12 to 0
Pitch Amplitude = −10 to 2
Pitch Amplitude = −8 to 4
Pitch Amplitude = −6 to 6
Pitch Amplitude = −4 to 8
0.06
0.04
CFX
0.02
0
−0.02
−0.04
−0.06
−0.08
−6
−4
−2
0
2
4
6
Effective angle of attack, deg
Fig. 8. Horizontal and vertical force coefficient for different pitch amplitudes for NACA 6409, f ¼1.2 Hz and U 1 ¼ 9:4 m=s. (a) CFZ vs γ. (b) CFX vs αeff .
1.2
Pitch Amplitude = −10 to 2
Pitch Amplitude = −8 to 4
1
Pitch Amplitude = −6 to 6
Pitch Amplitude = −4 to 8
0.8
CFZ
0.6
0.4
0.2
0
−0.2
−30
−20
−10
0
10
20
30
40
Flapping angle, deg
0.08
Pitch Amplitude = −10 to 2
0.06
Pitch Amplitude = −8 to 4
Pitch Amplitude = −6 to 6
0.04
Pitch Amplitude = −4 to 8
0.02
C
FX
0
−0.02
−0.04
−0.06
−0.08
−0.1
−10
−5
0
5
10
15
Effective angle of attack, deg
Fig. 9. Horizontal and vertical force coefficient for different pitch amplitudes for NACA 6409, f ¼1.2 Hz and U 1 ¼ 6:0 m=s. (a) CFZ vs γ. (b) CFX vs αeff .
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695
Table 2 summarises the results of Fig. 7(a), tabulating the maximum and minimum CFZ values for each wing, along with
the corresponding geometric angles of attack. This data will be referred to in later sections, as the dynamic lift values will be
compared to the static values in order to assess whether dynamic stall may be occurring.
5. Pitch leading tests
As mentioned in the Introduction, previous research on pitching and plunging 2D airfoils has shown that the best
propulsive efficiency is optioned when the phase difference between pitching and plunging is 901. Furthermore, the best
Strouhal number range for thrust production is between 0.21 and 0.25. However, the effects of root flapping, wing camber
and pitch angle limits on thrust production are also of interest and have not yet been thoroughly discussed. These effects are
investigated in the present section, albeit at the suboptimal Strouhal range of 0.3–0.17. The highly cambered and thin NACA
6409 wing is flapped in pitch leading configuration at different pitch angle limits, airspeeds and frequencies. The pitch angle
limits selected for these tests are shown in Table 3. The first column shows the minimum instantaneous value of pitch, the
second the maximum value and αs in this case denotes the mean between minimum and maximum. The minimum pitch
1
0.8
Mean CFZ
0.6
U = 6.0m/s, F =0.8Hz
U = 6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U = 9.4m/s, F =0.8Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,m/s, F = 1.2Hz
U = 14.8m/s, F = 0.8Hz
U =14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
0.4
0.2
0
−0.2
−0.4
−8
−6
−4
−2
0
2
4
Mean α , deg
S
U = 6.0m/s, F =0.8Hz
U = 6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U = 9.4m/s, F =0.8Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,/s, F = 1.2Hz
U = 14.8m/s, F = 0.8Hz
U =14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
0.1
0.08
0.06
Mean C
FX
0.04
0.02
0
−0.02
−0.04
−0.06
−0.08
−6
−4
−2
0
2
4
Mean αS, deg
Fig. 10. Mean force coefficients for NACA 6409 at different αs for all pitch leading cases. (a) Mean CFZ vs αs . Mean CFX vs αs .
Table 4
Pitch angle limits for pitch lagging case.
NACA 0012
NACA 4412
Upstroke (deg)
Downstroke (deg)
αs (deg)
Upstroke (deg)
Downstroke (deg)
αs (deg)
12
5
3
4
6
–
0
7
9
16
18
–
6
1
3
10
12
–
12
6
3
0
4
6
0
6
9
12
16
18
6
0
3
6
10
12
696
N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
angle is increased from 121 to 41 in increments of 21 and the pitch amplitude is always 121. The phase difference
between pitch and flap is always set to 901.
Fig. 8(a) plots the variation of vertical force with flapping angle for the different pitch amplitudes at U 1 ¼ 9:4 m=s and
f ¼1.2 Hz (St ¼0.07). The lowest mean pitch angle yields the lowest vertical force. Increasing the limits of the pitch motion
shifts the vertical force coefficient values upward. Almost all cases show positive vertical force coefficient values during both
downstroke and upstroke, i.e. even at negative pitch angles, the wing generates an upward vertical force. The only exception
is the 121 to 01 pitch angle case, for which downforce is produced over some parts of the cycle. This generation of
downforce can be explained by looking at the effective angle of attack values, which are lower than the zero lift angle of the
wing over a certain wing area during the upstroke.
Fig. 8(b), which plots the horizontal force coefficient against effective angle of attack at midspan for U 1 ¼ 9:4 m=s and
f ¼1.2 Hz, shows that the horizontal force is negative for large parts of the cycle for all pitch amplitudes. Negative horizontal
force coefficient values indicate thrust generation. In fact, thrust occurs only during downstroke, while upstroke generates
drag. Reducing the mean pitch angle increases thrust generation during downstroke but it can also increase drag during
upstroke.
Fig. 9 plots the vertical and horizontal force variation of the NACA 6409 for different mean pitch angles at the same
frequency of 1.2 Hz but at a lower airspeed of 6.0 m/s (St¼0.11). The vertical force plot of Fig. 9(a) is similar to the one
obtained at 9.4 m/s (Fig. 8(a)). Fig. 9(a), which plots the horizontal force against αeff at midspan, shows that thrust is
produced over most of the cycle for all the configurations. Clearly, the increase in Strouhal number from 0.07 to 0.11 has a
beneficial effect on thrust production, as the increase is in the direction of the optimal Strouhal value of 0.21–0.25.
Nevertheless, even at the lower Strouhal value, there are some mean pitch angles that give good thrust characteristics. It is
therefore interesting to determine the variation of total thrust over the complete cycle.
Mean vertical and horizontal forces for each test were obtained by calculating the time integral of the cycle averaged
force signals and dividing by the period. Fig. 10(a) and (b) shows the mean values of the vertical and horizontal force
coefficients plotted against αs at all airspeeds and frequencies tested for the NACA 6409 wing. The three plotted airspeeds
are differentiated by line type. Solid lines represent values measured at U 1 ¼ 9:4 m=s, dash-dot lines represent U 1 ¼
6:0 m=s and dashed lines represent U 1 ¼ 14:8 m=s. For each airspeed four different flapping frequencies are plotted,
denoted by different marker types. Frequencies of 0.8 Hz, 1 Hz, 1.2 Hz and 1.5 Hz are denoted by circles, squares, diamonds
and triangles respectively.
Pitch Amplitude = −12 to 0
1.5
Pitch Amplitude = −5 to 7
Pitch Amplitude = −3 to 9
Pitch Amplitude = 4 to 16
Pitch Amplitude = 6 to 18
0.5
C
FZ
1
0
−0.5
−1
−30
−20
−10
0
10
20
30
40
Effective angle of attack, deg
0.5
Pitch Amplitude = −12 to 0
Pitch Amplitude = −5 to 7
0.4
Pitch Amplitude = −3 to 9
Pitch Amplitude = 4 to 16
Pitch Amplitude = 6 to 18
C
FX
0.3
0.2
0.1
0
−30
−20
−10
0
10
20
30
Effective angle of attack, deg
Fig. 11. Vertical and horizontal force coefficients for different pitch limits for NACA 0012, f ¼1.2 Hz and U 1 ¼ 9:4 m=s. (a) CFZ vs αeff . (b) CFX vs αeff .
N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
697
Fig. 10(a) shows that the mean vertical force coefficient depends monotonically on αs , the mean pitch angle, for all airspeed
and frequency cases. Clearly, as far as lift is concerned, the best results are obtained at the highest mean pitch angle. In contrast,
Fig. 10(b) shows that good thrust values can be obtained both at the lowest and the highest mean pitch angle; the difference is
Strouhal number. The St¼0.05 case (U 1 ¼ 9:4 m=s, f¼0.8 Hz) results in a mean thrust equal to that of the St¼0.11 case
(U 1 ¼ 6 m=s, f¼1.2 Hz). For the St¼ 0.05 case the optimal pitch angle range is 41 to 81 while for St¼0.11 the optimal range is
121 to 01. Previous experimental work by Schouveiler et al. (2005) showed a monotonic increase in thrust with increasing
Strouhal number but these results concerned symmetric airfoils and symmetric pitch motion. The present experiments show
that decreasing the Strouhal number does not necessarily affect negatively the amount of thrust produced, as long as the mean
pitch angle is adjusted accordingly. Furthermore, Fig. 10(a) shows that the St¼0.05 case is in fact preferable from a lift
generation point of view because it produces a mean lift of 0.4, while the St¼0.11 setting produces a mean downforce of 0.1.
6. Pitch lagging tests
Pitch leading motion leads to low values of the effective angle of attack, as already seen in Figs. 8(b) and 9(b), where the
effective angle of attack at midspan oscillates between 761 and 7101 respectively. Consequently, the flow remains
attached over most of the wing's surface and most of the flapping cycle. In contrast, pitch lagging leads to very large
amplitudes of effective angle of attack, which in turn causes massive dynamic stall effects. This section aims to investigate
the effects of dynamic stall on the horizontal and vertical force variation.
The NACA 0012 and NACA 4412 wings were tested in the pitch lagging configuration. The test frequencies were 0.8 Hz,
1.0 Hz and 1.2 Hz and the test airspeeds were 6.0 m/s, 9.4 m/s and 14.8 m/s. The pitch angle limits and centre values, αs ,
chosen for the two profiles are given in Table 4. As in the pitch leading case, the amplitude of the pitch oscillation is always
121 and the phase difference between the pitch and the flap is 901.
Fig. 11 plots the horizontal and vertical force coefficients measured on the NACA 0012 wing for a frequency of 1.2 Hz and
an airspeed of 9.4 m/s. Fig. 11(a) shows the variation of vertical force coefficient plotted against effective angle of attack at
midspan. For both the upstroke and the downstroke, as the pitch angle limits are increased, the vertical force coefficient also
increases. The maximum vertical force coefficients measured for the αp ¼ 41 to 161 and αp ¼ 61 to 181 cases are significantly
higher than the maximum static lift coefficient. It can be seen that the αeff at midspan range lies between 201 and 301. In
fact, the 61 to 181 case results in a maximum CFZ value that is nearly twice as high as the corresponding maximum static lift
of Table 2. This stall delay effect is caused by the dynamic stall phenomenon.
2
1.5
Pitch Amplitude = −12 to 0
Pitch Amplitude = −6 to 6
Pitch Amplitude = −3 to 9
Pitch Amplitude = 0 to 12
Pitch Amplitude = 4 to 16
Pitch Amplitude = 6 to 18
C
FZ
1
0.5
0
−0.5
−30
−20
−10
0
10
20
30
40
Effective angle of attack, deg
0.4
C
FX
0.3
Pitch Amplitude = −12 to 0
Pitch Amplitude = −6 to 6
Pitch Amplitude = −3 to 9
Pitch Amplitude = 0 to 12
Pitch Amplitude = 4 to 16
Pitch Amplitude = 6 to 18
0.2
0.1
0
−0.1
−30
−20
−10
0
10
20
30
Effective angle of attack, deg
Fig. 12. Vertical and horizontal force coefficients for different pitch limits for NACA 4412, f¼ 1.2 Hz and U 1 ¼ 9:4 m=s. (a) CFZ vs αeff . (b) CFX vs αeff .
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N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
Fig. 11(b) plots the horizontal force coefficient measured during the pitch lagging tests of the NACA 0012 wing. The
αp ¼ 41 to 161 and αp ¼ 61 to 181 cases generate roughly twice as much drag as the other cases. The horizontal force peaks
even before the mid downstroke position is reached. For nearly all the pitch angle limits, the minimum drag occurs at the
endstroke. Clearly, no thrust is generated at any point during the cycle.
Fig. 12 plots the vertical and horizontal force coefficients measured on the NACA 4412 wing for a frequency of 1.2 Hz and
an airspeed of 9.4 m/s. As for the NACA 0012 wing, the effective angle of attack at midspan ranges between 201 and 301.
The maximum instantaneous vertical force is obtained at αp ¼ 61 to 181, which is around 50% higher than the corresponding
maximum static lift. Therefore, dynamic stall has a smaller amplification effect on the lift of the NACA 4412 wing than that of
the NACA 0012 wing at this airspeed and frequency. The peak vertical force coefficient values occur towards the end of the
downstroke. Fig. 12(b) shows that, again no thrust is produced over any part of the flapping cycle, except for the 121 to 01
test, which generates a small amount of instantaneous thrust.
The fact that the maximum instantaneous vertical force coefficient exceeds the static maximum lift in the examples of
Figs. 11 and 12 suggests that stall delay is occurring, i.e. that a Leading Edge Vortex is generated. It is interesting to note that
the corresponding instantaneous horizontal force coefficient values lie within the static drag coefficient range of the wings,
as seen in Fig. 7(b). This phenomenon was also observed by Hubel and Tropea (2009), who showed that LEVs occur during
pure flapping oscillations, leading to instantaneous lift coefficients exceeding the maximum static lift values but the
dynamic drag coefficients remained within the static drag coefficient range.
Fig. 13 shows the variation of the mean horizontal and vertical force coefficients for the NACA 0012 wing with all the test
parameters. The symbol conventions are the same as those of Fig. 10. It can be seen that the biggest effect on both forces is
caused by the pitch angle limits. Interestingly enough, the mean lift forces measured at 6 m/s are lower than those observed
at the other two airspeeds for all frequencies and pitch angle limits. In contrast, the airspeed does not appear to have a clear
effect on the mean drag. This phenomenon suggests a sensitivity of the lift coefficient to Reynolds number; it will be
discussed further in the next section on the pure flapping tests, where the phenomenon was more pronounced.
Fig. 14 shows the variation of the mean horizontal and vertical force coefficients for the NACA 4412 wing with all the test
parameters. In this case, there is no significant effect of the airspeed (and therefore Reynolds number) on the mean lift or
1
0.8
Mean CFZ
0.6
U = 6.0m/s, F =0.8Hz
U = 6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U = 9.4m/s, F =0.8Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,m/s, F = 1.2Hz
U = 14.8m/s, F = 0.8Hz
U =14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
0.4
0.2
0
−0.2
−0.4
−5
0
5
10
15
Mean α , deg
p
0.35
Mean C FX
0.3
0.25
U = 6.0m/s, F =0.8Hz
U = 6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U = 9.4m/s, F =0.8Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,/s, F = 1.2Hz
U = 14.8m/s, F = 0.8Hz
U =14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
0.2
0.15
0.1
−5
0
5
10
15
Mean α , deg
p
Fig. 13. Mean force coefficients for NACA 0012 at different αp undergoing pitch lagging oscillations. (a) Mean CFZ vs mean αp . (b) Mean CFX vs mean αp .
N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
U = 6.0m/s, F =0.8Hz
U = 6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U = 9.4m/s, F =0.8Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,m/s, F = 1.2Hz
U = 14.8m/s, F = 0.8Hz
U =14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
1
0.8
FZ
0.6
Mean C
699
0.4
0.2
0
−0.2
−0.4
−8
−6
−4
−2
0
2
4
6
8
10
12
14
6
8
10
12
14
Mean αp, deg
0.35
U = 6.0m/s, F =0.8Hz
U = 6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U = 9.4m/s, F =0.8Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,/s, F = 1.2Hz
U = 14.8m/s, F = 0.8Hz
U =14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
Mean CFX
0.3
0.25
0.2
0.15
0.1
−6
−4
−2
0
2
4
Mean αp, deg
Fig. 14. Mean force coefficients for NACA 4412 at different αp undergoing pitch lagging oscillations. (a) Mean CFZ vs mean αp . (b) Mean CFX vs mean αp .
α = −2
1.5
α = 0
α = 2
α = 4
CFZ
1
α = 6
α = 8
α = 10
0.5
0
−0.5
−15
−10
−5
0
5
10
15
20
Effective angle of attack, deg
0.25
α = −2
α = 0
α = 2
α = 4
α = 6
α = 8
α = 10
0.2
CFX
0.15
0.1
0.05
0
−15
−10
−5
0
5
10
15
20
Effective angle of attack, deg
Fig. 15. Force coefficients against αeff at midspan for NACA 6409 at different αs for pure flapping at f¼ 1.5 Hz and U 1 ¼ 9:4 m=s. (a) CFZ vs αeff . (b) CFX vs αeff .
700
N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
mean drag. Therefore, this cambered wing is less sensitive to Reynolds number effects than the symmetric NACA 0012 wing
at pitch lagging conditions. As will be shown in the next section, pure flapping reverses this situation.
7. Pure flapping tests
As mentioned in the introduction, Hubel and Tropea (2009, 2010) carried out a series of experiments on a flapping model
of similar dimensions to the one used in the present investigation. Their model could only flap at different geometric pitch
angles, it could not pitch actively through the cycle. Furthermore, they only tested one wing section. In this work, pure
flapping kinematics is investigated in order to determine the effect of different airfoil shapes. All three sets of wings were
tested at 4 different frequencies and 3 different airspeeds. The flapping frequencies were 0.8 Hz, 1.0 Hz, 1.2 Hz and 1.5 Hz
and the airspeeds 6.0 m/s, 9.4 m/s and 14.8 m/s. All these tests were repeated for geometric angles of attack, αs , ranging
from 21 to 101 with an increment of 21.
Fig. 15 plots the cycle averaged vertical and horizontal force coefficient variation with instantaneous αeff at midspan for
the NACA 6409 wing at f ¼1.5 Hz, U 1 ¼ 9:4 m=s and all static angles of attack. It can be seen that the static angle of attack
causes both C F Z and C F X to increase steadily. This effect of the static angle of attack, which was also reported by Hubel and
Tropea (2009) for a Wortmann wing section, was observed for all three tested wings, airspeeds and frequencies. The effects
of all the test parameters can be identified more clearly by looking at mean forces over complete cycles.
Fig. 16 shows the mean forces measured over the entire flapping cycle for the NACA 0012 airfoil in pure flapping for all
static angles of attack, airspeeds and frequencies. The symbol conventions are the same as those of Fig. 10. The lift increases
nearly linearly with static angle of attack; the drag increases very slowly for αs values from 21 to 81 but jumps abruptly at
αs ¼ 101. Note that the airspeed has a small effect on the mean forces.
This is not quite the case for the two cambered wings. The mean forces measured over the entire flapping cycle for the
NACA 4412 airfoil in pure flapping are summarised in Fig. 17. It is interesting to note that this airfoil produces significantly
less lift at 6 m/s than at 9.4 m/s or 14.8 m/s for all tested flapping frequencies and mean pitch angles. Take for example the
U 1 ¼ 6 m=s, f ¼0.8 Hz case, for which St ¼0.089, and the U 1 ¼ 9:4 m=s, f¼1.2 Hz case, for which St¼0.086 (see Table 1).
The two Strouhal numbers are very close but the former case generates less lift. As mentioned in the pitch lagging section,
0.8
Mean CFZ
0.6
0.4
0.2
U = 6.0m/s, F =0.8Hz
U =6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U =6.0m/s, F =1.5Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,/s, F = 1.2Hz
U = 9.4m/s, F = 1.5Hz
U = 14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
U = 14.8m/s, F = 1.5Hz
0
−0.2
−0.4
−2
0
2
4
6
8
10
6
8
10
αS, deg
0.4
0.35
Mean C FX
0.3
0.25
0.2
U = 6.0m/s, F =0.8Hz
U =6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U =6.0m/s, F =1.5Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,/s, F = 1.2Hz
U = 9.4m/s, F = 1.5Hz
U = 14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
U = 14.8m/s, F = 1.5Hz
0.15
0.1
0.05
0
−2
0
2
4
αS, deg
Fig. 16. Mean force coefficients for NACA 0012 at different αs undergoing pure flapping oscillations. (a) Mean CFZ vs αs . (b) Mean CFX vs αs .
N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
701
this phenomenon is due to Reynolds number effects; at the lowest Reynolds number the flow may still be laminar over
significant areas of the wing's surface. This situation may in turn cause a different separation mechanism than in higher
Reynolds number cases.
The NACA 6409 wing is also affected by the Reynolds number but in a different way. Fig. 18 shows that this wing
produces significantly more drag at 6 m/s, although the lift is unaffected by the airspeed. At U 1 ¼ 6 rmm=s, f¼0.8 Hz, the
Strouhal number is 0.073, while at U 1 ¼ 9:4 m=s, f ¼1.2 Hz, St ¼0.070. Again, the two Strouhal numbers are very similar but
the drag at 6 m/s is higher due to the difference in Reynolds numbers. A PIV investigation was carried out in order to
attempt to understand the increased drag of the NACA 6409 wing at 6 m/s. As the flow was visualised only at mid-stroke,
the PIV results consist of single snapshots taken twice per cycle.
Fig. 19 shows snapshots of the flowfield at mid-stroke at two different spanwise positions (50% spans and 75% span) and
different frequencies and static pitch angles, all at the airspeed of 6 m/s. Fig. 19(a)–(d) shows the flow during the
downstroke; there is clear evidence of flow separation in all these flowfields. Fig. 19(e) plots the flow during the upstroke,
which is fully attached. Snapshot 19d, taken at 75% span, f ¼1.5 Hz and αs ¼ 61 shows a very clear region of recirculation near
the leading edge. This flow feature may be evidence of a Leading Edge Vortex that has just lifted off the surface. A second
area of recirculation can be seen higher up in the flow.
Collectively, the results of Fig. 19 show that the flow on the upper side of the NACA 6409 wing at 6 m/s is fully separated
at mid-downstroke. The separation is more extensive (i.e. reaches further up into the flowfield) towards the wingtip and as
the frequency is increased. This is also the case for the other two wings, so the PIV results do not demonstrate any clear
difference between the three wing sections at 6 m/s. It is possible that the difference lies on the flow over the lower side of
the wing during the upstroke. Hubel and Tropea (2010) showed that a LEV can develop on the lower surface during the
upstroke phase around the outer wing region. However, this flow could not be visualised during the course of the present
experiments, as the PIV laser was installed above the wind tunnel's working section.
The comparison of Figs. 16–18 shows an interesting dependence of the mean aerodynamic forces on wing profile. These
forces are unaffected by the Reynolds number for the NACA 0012 symmetric wing. In contrast, the increased camber of the
NACA 4412 wing appears to cause lower mean lift but the same mean drag at low Re. The even higher camber and thinner
section of the NACA 6409 wing causes increased drag but the same lift at low Reynolds numbers. It should be kept in mind
0.8
Mean CFZ
0.6
0.4
U = 6.0m/s, F =0.8Hz
U =6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U =6.0m/s, F =1.5Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,/s, F = 1.2Hz
U = 9.4m/s, F = 1.5Hz
U = 14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
U = 14.8m/s, F = 1.5Hz
0.2
0
−0.2
−2
0
2
4
6
8
αS, deg
0.35
Mean CFX
0.3
0.25
U = 6.0m/s, F =0.8Hz
U =6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U =6.0m/s, F =1.5Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,/s, F = 1.2Hz
U = 9.4m/s, F = 1.5Hz
U = 14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
U = 14.8m/s, F = 1.5Hz
0.2
0.15
0.1
−2
0
2
4
6
8
α , deg
S
Fig. 17. Mean force coefficients for NACA 4412 at different αs undergoing pure flapping oscillations. (a) Mean CFZ vs αs . (b) Mean CFZ vs αs .
702
N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
0.7
0.6
Mean CFZ
0.5
0.4
U = 6.0m/s, F =0.8Hz
U =6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U =6.0m/s, F =1.5Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,/s, F = 1.2Hz
U = 9.4m/s, F = 1.5Hz
U = 14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
U = 14.8m/s, F = 1.5Hz
0.3
0.2
0.1
0
−2
0
2
4
6
8
10
α , deg
S
0.4
0.35
Mean CFX
0.3
0.25
U = 6.0m/s, F =0.8Hz
U =6.0m/s, F =1.0Hz
U =6.0m/s, F =1.2Hz
U =6.0m/s, F =1.5Hz
U = 9.4m/s, F = 1.0Hz
U =9.4,/s, F = 1.2Hz
U = 9.4m/s, F = 1.5Hz
U = 14.8m/s, F = 1.0Hz
U = 14.8m/s, F = 1.2Hz
U = 14.8m/s, F = 1.5Hz
0.2
0.15
0.1
0.05
−2
0
2
4
6
8
10
α , deg
S
Fig. 18. Mean force coefficients for NACA 6409 at different αs undergoing pure flapping oscillations. (a) Mean CFZ vs αs . (b) Mean CFX vs αs .
that the NACA 6409 wing has a larger chord and shorter span than the 12% thick wings, so a direct comparison of the
aerodynamic forces generated by the three wings would not be useful.
The dependence of the aerodynamic force on Reynolds number has an equivalent in flow over static airfoils. Lutz et al.
(2001) and Poirel et al. (2008) showed that airfoils can have low lift curve slopes (as low as π instead of 2π ) at low Reynolds
numbers and angles of attack, due to trailing edge separation. Furthermore, Lutz et al. (2001) show that, under low Reynolds
number laminar flow conditions, the drag of airfoils may be significantly higher than under turbulent conditions. They
attribute this phenomenon to the existence of a laminar separation bubble on the suction side. Even though these results
only concern static airfoils, they may also be linked to dynamic flow phenomena. For example, several authors have
suggested that the bursting of a laminar separation bubble is a possible mechanism for the occurrence of dynamic stall
(Johnson and Ham, 1972; Fukushima and Dadone, 1977).
8. Conclusions
This paper presents the results of wind tunnel tests on an actively flapping and pitching mechanical wing model. The
objective is to determine the effect of active pitching and airfoil geometry on the aerodynamic forces. Two major
conclusions were drawn from the work, one concerning thrust generation and one concerning Reynolds sensitivity at
separated flow conditions.
Net thrust generation was observed mainly during the flapping and pitching experiments, whereby the pitch angle was
leading the flap angle by 901. It was found that, for a cambered wing section, high thrust can be obtained at both low and
high Strouhal number values. At low Strouhal numbers, the pitch oscillation must be centred around a positive pitch angle.
Conversely, at high Strouhal values the pitch oscillation must be centred around a negative pitch angle. Consequently, high
thrust values were obtained at both St¼0.05 and St¼ 0.11. Previous work on 2D symmetrically pitching and plunging airfoils
has shown that thrust increases monotonically with the Strouhal number (Schouveiler et al., 2005). The present results
show that, for a 3D flapping wing that pitches asymmetrically, the thrust can in fact decrease with the Strouhal number, as
seen for example in Fig. 10(b) for αs ¼ 21.
N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
703
Fig. 19. Instantaneous vector fields at midstroke for different flapping frequencies, spanwise positions and αs for the NACA 6409 wing at U 1 ¼ 6:0 m=s.
(a) f¼ 0.8 Hz at midspan and αs ¼ 101, downstroke. (b) f ¼1.2 Hz at midspan and αs ¼ 101, downstroke. (c) f¼ 1.5 Hz at midspan and αs ¼ 101, downstroke.
(d) f¼ 1.5 Hz at 75% span and αs ¼ 61, downstroke. (e) f¼ 1.5 Hz at 75% span αs ¼ 101, upstroke.
The reason for the dependence of thrust on pitch angle limits when St is varied can be found in the effective angle of
attack. As the Strouhal number increases, so does the amplitude of the effective angle of attack. Therefore, the limits of the
pitch angle oscillation must be reduced in order to ensure that the flow remains attached throughout the cycle. Conversely,
at low Strouhal numbers the effective angle of attack amplitude is also low and therefore the limits of the pitch angle
oscillation can be higher.
The second major conclusion of the present work concerns the sensitivity to Reynolds number. It was found that, under
pitch lagging and pure flapping conditions, i.e. when flow separation occurs over significant sections of the wing's surface
and flap cycle, some of the wing sections can be sensitive to Reynolds number effects. In pitch lagging oscillations only the
symmetric NACA 0012 wing showed this type of sensitivity; its lift was lower than usual at the tested airspeed. In contrast,
under pure flapping conditions, it was the cambered wings that demonstrated Reynolds number sensitivity while the
symmetric wing was unaffected. The lift of the NACA 4412 wing decreased and the drag of the NACA 6409 wing increased at
the lowest tested airspeed.
PIV flow visualisations confirmed that flow separation occurs under both pitch lagging and pure flapping. However, they
were insufficient to explain the Reynolds number sensitivity. The phenomenon may be related to laminar flow separation at
the lowest Reynolds number but the exact mechanism needs to be further investigated. Nevertheless, it is clear that
704
N.A. Razak, G. Dimitriadis / Journal of Fluids and Structures 49 (2014) 687–704
Reynolds sensitivity is related to camber, although the effect of camber is dependent on kinematic conditions. For pitch
lagging, whereby the amplitude of the effective angle of attack is very high, only the uncambered wing was affected by the
Reynolds number. For pure flapping, at lower (bust still significant) effective angle of attack amplitudes, only the cambered
wings were affected.
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