RESEARCH ARTICLE

Experimental study of pitching and plunging airfoilsat low Reynolds numbers

Yeon Sik Baik • Luis P. Bernal

Received: 3 January 2012 / Revised: 28 September 2012 / Accepted: 3 October 2012 / Published online: 22 November 2012

� Springer-Verlag Berlin Heidelberg 2012

Abstract Measurements of the unsteady flow structure

and force time history of pitching and plunging SD7003

and flat plate airfoils at low Reynolds numbers are pre-

sented. The airfoils were pitched and plunged in the

effective angle of attack range of 2.4�–13.6� (shallow-stall

kinematics) and -6� to 22� (deep-stall kinematics). The

shallow-stall kinematics results for the SD7003 airfoil

show attached flow and laminar-to-turbulent transition at

low effective angle of attack during the down stroke

motion, while the flat plate model exhibits leading edge

separation. Strong Re-number effects were found for the

SD7003 airfoil which produced approximately 25 %

increase in the peak lift coefficient at Re = 10,000 com-

pared to higher Re flows. The flat plate airfoil showed

reduced Re effects due to leading edge separation at the

sharper leading edge, and the measured peak lift coefficient

was higher than that predicted by unsteady potential flow

theory. The deep-stall kinematics resulted in leading edge

separation that led to formation of a large leading edge

vortex (LEV) and a small trailing edge vortex (TEV) for

both airfoils. The measured peak lift coefficient was sig-

nificantly higher (*50 %) than that for the shallow-stall

kinematics. The effect of airfoil shape on lift force was

greater than the Re effect. Turbulence statistics were

measured as a function of phase using ensemble averages.

The results show anisotropic turbulence for the LEV and

isotropic turbulence for the TEV. Comparison of unsteady

potential flow theory with the experimental data showed

better agreement by using the quasi-steady approximation,

or setting C(k) = 1 in Theodorsen theory, for leading

edge–separated flows.

1 Introduction

Flapping wing aerodynamics is a complex problem char-

acterized by unsteady flow features and fluid structure

interaction (Shyy et al. 2008). The study of flapping wing

aerodynamics has attracted the interest of scientists and

engineers as possible propulsion and lift generation

mechanism for future micro air vehicles (MAVs) and nano

air vehicles (NAVs). The problem is characterized by small

length scales and flow speeds which typically result in a

Reynolds number range between O(102) and O(104).

Unsteady flow at low Reynolds numbers may include

laminar, transitional, and turbulent flows that are difficult

to probe experimentally and computationally. Recent

advances in technology have enabled various experimental

and computational techniques that aid understanding of

flapping wing aerodynamics (Platzer et al. 2008; Pines and

Bohorquez 2006). However, there still exist tremendous

challenges in the design of flapping wing–controlled

vehicles due to a lack of understanding of the aerodynamic

performance of flapping wing motions.

The number of control parameters in flapping wing

aerodynamics ranges from wing size and material proper-

ties to wing motion kinematics and flow conditions. To

understand how different physical processes contribute to

aerodynamic performance, it is useful to simplify the

problem by reducing the number of independent variables

Electronic supplementary material The online version of thisarticle (doi:10.1007/s00348-012-1401-6) contains supplementarymaterial, which is available to authorized users.

Y. S. Baik (&) � L. P. Bernal

Department of Aerospace Engineering,

University of Michigan, Ann Arbor, MI, USA

e-mail: yeon.baik@gmail.com

L. P. Bernal

e-mail: lpb@umich.edu

123

Exp Fluids (2012) 53:1979–1992

DOI 10.1007/s00348-012-1401-6

while retaining the relevant physical processes. Many

previous studies have simplified flapping wing kinematics

by considering infinite aspect ratio wings undergoing

pitching and plunging motions. This setup limits wing

motions to two degrees of freedom, and the infinite aspect

ratio reduces the complexity of spanwise variations of

force and associated 3-D flows. Effects of the free-end

condition on the aerodynamics of flapping wings have been

studied numerically (Shyy et al. 2009) and experimentally

(David et al. 2011). Pitching and plunging wing motions

may include laminar, transitional and turbulent flows

depending on Reynolds number and large-scale separation.

Numerous experimental studies of pitching and plunging

wings have found that the Strouhal number (St) is an

important parameter that governs formation of LEVs and

the wake structure behind the wing (Freymuth 1988; Ko-

ochesfahani 1989; Jones et al. 1996; Lai and Platzer 1999;

Young and Lai 2004; Lua et al. 2007). The St is also

important in considering propulsive efficiency of an

oscillating wing (Triantafyllou et al. 1992; Anderson et al.

1998; Read et al. 2003; Hover et al. 2004).

An important unsteady flow feature found in flapping

wing aerodynamics is the formation of large vortical

structures at the leading and trailing edges. Formation of

leading edge vortex (LEV) is found to be critical to lift

generation in insect flight, and studies document that an

attached LEV produces higher lift coefficient compared to

the steady-state conditions (Ellington 1984; Dickinson and

Gotz 1993; Birch et al. 2004). The formation of LEV and

trailing edge vortices (TEV) is observed in numerous bio-

logical flyers at low Reynolds number (Ellington et al.

1996; Maxworthy 1981; Birch and Dickinson 2001). For-

mation of large vortical structures is also found in dynamic

stall of rotor blades and in high-pitch-rate maneuvers, in this

case at Reynolds number O(106) (McCroskey 1981, 1982).

The dynamic-stall vortex is analogous to the LEV observed

in flapping wing aerodynamics, and it temporarily increases

the lift coefficient of the airfoil as the vortex convects along

the chord. The LEV or dynamic-stall vortex alters the

pressure distribution on the airfoil surface causing the

increase in lift (Maxworthy 1979; Sane and Dickinson

2001). However, other features contribute to unsteady force

generation of flapping wings. There are studies that illus-

trate the importance of wing kinematics on the formation of

LEVs (Dickinson 1994; Dickinson et al. 1999; Rival et al.

2009) and document the changing role of LEV for different

flow conditions and wing kinematics (Shyy and Liu 2007).

The present study was motivated by the work of Ol et al.

(2009) who studied the aerodynamics of a pitching and

plunging SD7003 airfoil undergoing two kinematics: a

shallow-stall kinematic where the effective angle of attack

produced by the plunging motion is reduced by the pitch

motion and a deep-stall kinematic with the same plunge

motion as the shallow-stall case but without the pitch

motion which results in an effective angle of attack history

that exceeds the steady-stall angle of attack by a large

amount during the cycle. They consider a Reynolds number

of 60,000 and report computational results, flow visuali-

zation, PIV measurements, and lift force measurements

which show attached flow for the shallow-stall case during

the cycle and formation of a LEV during the down stroke

for the deep-stall case. Of interest also is the effect of

airfoil shape on the aerodynamics of pitching and plunging

airfoils. A comprehensive computational study of a flat

plate airfoil undergoing shallow- and deep-stall kinematics

has been performed by Kang et al. (2012). They also

consider a finite span wing and note that the flat plate’s

sharp leading edge promotes formation of a LEV. They

document the force time history and flow evolution history.

Baik et al. (2012) report a comprehensive investigation of

the deep-stall kinematics for a flat plate airfoil at Reynolds

numbers in the range 5,000–20,000. They document the

LEV dynamics and report force measurements for varying

plunge motion amplitude and reduced frequency. They find

small Reynolds number effects and determine that flow

topology is controlled by reduced frequency, whereas force

time history is primarily controlled by the St. The present

experimental study explores Re effects on pitching and

plunging airfoils at Re = 1 9 104, 3 9 104, and 6 9 104.

Shallow- and deep-stall kinematics are considered for

SD7003 and flat plate airfoils in order to (1) elucidate

Reynolds number effects on flow topology for different

effective angle of attack histories and (2) determine the

effect of different airfoil shapes. The lift force time histo-

ries are measured and compared to Theodorsen (1935)

linear potential flow theory. We report detailed experi-

mental measurements using particle image velocimetry

(PIV) with emphasis on providing (1) a detailed exami-

nation of the flow field around pitching and plunging air-

foils by computing the vorticity and turbulence statistics,

(2) measured unsteady force time histories to examine the

effect of Re on unsteady force generation, and (3) provide

detailed experimental data for validation of computational

and theoretical models.

2 Airfoil kinematics

A brief description of airfoil kinematics used in the current

study is described in this section. A detailed description on

the origin of the kinematics can be found in Ol et al.

(2009). The equations for the plunging and pitching

motions are shown in Eqs. 1 and 2, respectively. The

effective angle of attack resulting from the combined

pitching and plunging motion is shown in Eq. 3. h0 is the

non-dimensional plunge amplitude, h0 = h/c, where h is

1980 Exp Fluids (2012) 53:1979–1992

123

the amplitude and c is the chord length. f denotes motion

frequency which is kept the same for both plunge and pitch

motions. h0 is the pitch amplitude in radians, and / is the

lag between the plunging and pitching motion. a0 is aver-

age angle of attack in radians and St is defined as 2fh/U?.

The arctangent function in Eq. 3 is approximately

sinusoidal for St below 0.15 (Baik 2011). Furthermore, the

lag between the plunging and pitching motion (/) is set as

a constant value of p/2 radians for all cases, which results

in the contribution of the pitch motion to the effective

angle of attack to be in phase and opposite direction to the

contribution from the plunge motion.

hðtÞ ¼ h0c cosð2pftÞ ð1ÞhðtÞ ¼ h0 cosð2pft þ /Þ ð2ÞaeffðtÞ ¼ a0þ h0 cosð2pftþ/Þþ arctan pSt sinð2pftÞð Þ ð3Þ

The shallow-stall kinematic is a combined pitching and

plunging motion with effective angle of attack range

between 2.4� and 13.6�. The pitch amplitude is 8.42� and

the non-dimensional plunge amplitude is kept constant at

h0 = 0.5. The deep-stall kinematic is the shallow-stall

kinematic without the pitching motion, resulting in a purely

plunging airfoil with effective angle of attack ranging from

-6� to 22�. The effective angle of attack time histories for

both kinematics are shown in Fig. 1. Both kinematics have

reduced frequency k = 0.25 and St = 0.08, and the motion

frequency was varied with flow speed to preserve the k and

St values. k is defined as pfc/U? in the current study.

The SD7003 airfoil is designed for low Reynolds number

applications and features a laminar separation bubble at low

Reynolds number (Ol et al. 2005) with stall angle of attack

equal to approximately 11� and zero angle of attack to -1� at

Re O(104) (Selig et al. 1995). For the present flow conditions,

the airfoil approaches static stall during the down stroke of the

shallow-stall kinematic. For the deep-stall kinematic, a large

separation is expected for the SD7003 airfoil. In the current

study, a flat plate airfoil is also investigated that is more rep-

resentative of airfoil sections found in biological flyers which

commonly have small thickness.

3 Experimental setup

Experiments were conducted at the University of Michigan

low-turbulence water channel. A detailed description of the

flow facility and instrumentation can be found in Baik

(2011). A brief description of the flow facility, PIV, and

force measurement techniques are highlighted here. The

water channel facility has a test cross-section 61 cm wide

by 61 cm high with free stream velocity that ranges from 6

to 40 cm/s. The measured turbulence intensity at a free

stream velocity of 6 cm/s is approximately 1 % and 0.1 %

for free stream velocities greater than 20 cm/s.

The current study explores two airfoil cross-sections:

SD7003 and a flat plate. Both models span the depth of the

water channel test section to simulate an infinite aspect ratio.

The model installation and instrumentation is illustrated in

Fig. 2. The SD7003 airfoil model has a chord length of

152 mm, and it was fabricated using stereo lithography of a

transparent resin (DSM Somos 11122) to minimize laser

reflection at the surface of the airfoil. Three different flat

plate models were used in the current study: 152-mm chord

with 2.3 % chord-to-thickness ratio (t/c), 76-mm chord with

t/c = 6.25 %, and 51-mm chord with t/c = 6.25 %. All the

flat plates have rounded leading and trailing edges with

radius equal to half the thickness. The flat plate models were

fabricated from stainless steel plate and polished to mini-

mize glare in the PIV images. As illustrated in Fig. 2, the

models were mounted vertically in the channel test section,

with the span axis normal to the water-free surface. An end

plate attached to the model is used to minimize free surface

effects. The cantilevered mounting scheme resulted in some

deflection of the plate due to the aerodynamic loading. The

plate thickness was selected to minimize model tip deflec-

tion at the bottom of the channel, which was 1 mm at the

highest Re tested. The SD7003 model tip deflection was

approximately 5 mm also at the highest Re tested. The

deflection at the half-span location where the PIV images

were taken was found to be negligible.

The airfoil motion was produced by a rotary stage

(Velmex B4872TS Rotary Table) for the pitch motion, a

linear traverse (Velmex 20-inch BiSlide) for the plunge

motion, and the associated control system (Velmex VXM-

1-1 motor controller). The motors were stepper motors with

accuracy of ±0.0125� (B4872TS) for the rotary stage and

±25 lm for the linear traverse.Fig. 1 Effective angle of attack profiles for shallow- and deep-stall

cases

Exp Fluids (2012) 53:1979–1992 1981

123

The flow visualization system consists of seven uni-

formly distributed dye streams introduced half chord in

front of the leading edge of the model. Two syringe pumps

are used to adjust the dye speed at the injection point in

order to match the water channel flow speed and minimize

disturbances produced by the wake of the dye injection

system. The dye streams were held fixed and the airfoil was

pitched and plunged within the width of the dye streams.

The PIV system includes a double-pulsed Nd-YAG laser

(Spectra Physics PIV 300), light sheet forming optics, two

dual frame CCD cameras (Cooke Corp. PCO.4000 equip-

ped with Nikon 105-mm Micro-Nikkor lenses, 4,008 9

2,672 pixels), a mechanical shutter, a signal generator, a

delay generator, computer image acquisition system, and

custom-built control box. The PIV system and model

motion apparatus were precisely synchronized using the

custom-built control box to capture the desired phases of

the motion. Phase-averaged PIV measurements were

computed using 200-image ensemble averages. The PIV

system and the airfoil motion periods were matched with

accuracy better than 0.1 ms, which resulted in a maximum

relative displacement of the airfoil between the first and

last images less than 7 pixels. The optical magnification

was 25 px/mm, which resulted in a field of view 160 by

107 mm in the flow. Each experimental run consisted of 12

motion cycles, and the first 2 cycles were discarded in

order to remove transient effects in the phase averages.

The PIV images were analyzed using an in-house-

developed MATLAB-based PIV analysis software. The

particle displacement is determined in two steps using

cross-correlation analysis of displaced interrogation win-

dows. The location of the cross-correlation peak, which

gives the particle displacement, is measured with sub-pixel

resolution using a Gaussian fit of the cross-correlation

function around the peak. In the first low-resolution step, a

fixed displacement of 20 pixels and an interrogation win-

dow of 64 9 64 pixel were used; in the second high-res-

olution step, the particle displacement measured in the first

step and an interrogation window size of 32 9 32 pixels

were used. This corresponds to an approximate spatial

resolution of the PIV measurements of ±0.64 mm. A

square grid with 8 pixel spacing (0.32 mm in physical

space) was used for all the images. Near the surface of the

airfoil, data points within 32 pixels from the boundary were

discarded because the interrogation window would include

pixels in the airfoil. This corresponds to four data points in

the measurement grid. A median filter based on velocity

vector values on spatially adjacent points was used to find

the particle displacement at the points where the PIV val-

idation failed. In addition, a 3-sigma filter was imple-

mented to remove outliers associated with large sample-to-

sample fluctuations. The 3-sigma filter was implemented in

two steps. In the first step the ensemble mean and standard

deviation are computed at all the points in the flow field.

Then, each sample was compared to ±3 standard devia-

tions of the mean value, and it was discarded if the sample

lied outside the 3-sigma range. The highest number of

outliers was located in the high shear region near the

leading edge, and the maximum number of data points

removed from the 3-sigma filter was approximately 10 %

of the sample size. Turbulence statistics were computed at

each phase and at each point in the field using the filtered

data.

The direct force measurement system consisted of a

force/torque sensor (ATI industrial automation Mini40

force/torque sensor), interface power supply (ATI indus-

trial automation 9105-IFPS-1), a data acquisition card

(National Instrument PCI-6625), and a computer. The

Fig. 2 Experimental setup at the University of Michigan water channel

1982 Exp Fluids (2012) 53:1979–1992

123

Mini40 F/T sensor is a 6-component sensor capable of

measuring forces in the plane of the airfoil cross-section up

to ±80 and ±240 N in the orthogonal direction. It also

measures torque up to ±4 Nm in all 3 axes. The published

resolution is 1/50 N for force and 1/2,000 Nm for torque.

For these measurements, the sensor axes were aligned with

the airfoil chord and chord-normal directions, and the

results were converted to the lift and drag directions using

the known pitch angle from case descriptions.

At each experimental condition, two different experi-

ments were performed to obtain the hydrodynamic force

time history: a tare experiment and a force experiment.

The tare experiments were performed in air to measure the

inertial load on the force/torque sensor due to mass of the

model and model attachment hardware. In these experi-

ments, the water level in the channel was lowered below

the bottom of the channel without changing any other

experimental parameters. The tare experiment results were

subtracted from the force test results to obtain the hydro-

dynamic loading on the wing model. Similar to the PIV

data acquisition, the force measurements were phase-

averaged for each wing kinematics. A typical force

measurement experiment consisted of 100 cycles with

5 seconds of pre-trigger data. The purpose of the pre-trig-

ger data was to eliminate sensor bias. The first 5 and the

last 5 cycles were discarded in order to remove transients

introduced by the low-pass filter; the force data were low-

pass filtered using a zero-phase sharp-frequency-cutoff

Fourier filter which introduced significant initial and end

transients lasting approximately three cycles. All the data

sets were sampled at 2,000 Hz and low-pass filtered with a

cutoff frequency equivalent to approximately 5 times the

motion frequency. The filter cutoff frequency was chosen

to remove force sensor signal associated with the structural

resonance of the cantilevered wing, which was measured at

approximately 6 Hz. Typical motion frequencies in these

experiments were in the range 0.035–0.21 Hz.

4 Results

4.1 Shallow-stall kinematics

Figure 3 shows side-by-side comparison of flow visuali-

zation and normalized vorticity contours for the SD7003

airfoil under shallow-stall kinematics at Re = 1 9 104,

3 9 104, and 6 9 104. The dye streams show small-scale

features for Re = 6 9 104 due to disturbances introduced

by the dye injector. Re effects are apparent during the down

stroke, 0 B t/T B 0.5. In this Reynolds number range, the

boundary layer is laminar at the leading edge. As the flow

develops, flow separation and transition to turbulent flow

occur, but the transition process differs depending on

Reynolds number. At Re = 10,000 and the beginning of

the down stroke (t/T = 0.00), the boundary layer on the top

surface of the airfoil is laminar. Laminar separation occurs

at approximately the 75 % chord location. During the ini-

tial part of the down stroke, t/T B 0.25, laminar separation

moves rapidly upstream to the leading edge and an unstable

separated shear layer develops. Kelvin–Helmholtz insta-

bility waves produce a vortex pattern on the top surface of

the airfoil. These instability waves are phase locked to the

airfoil motion, and the transitional vortex pattern is cap-

tured in the phase-averaged results. Streamlines at

t/T = 0.25 terminate on the suction side of the airfoil due

to the large plunge speed and pitch rate and form a closed

recirculation region particularly noticeable at Re = 10,000.

However, an organized LEV with closed streamlines cen-

tered in a region of high vorticity does not form. The

high vorticity region remains in the shear layer formed

at the separation point. At higher Reynolds numbers

(Re = 30,000 and 60,000), the boundary layer on the

suction side is unstable and phased-locked instability dis-

turbances are found at the beginning of the down stroke

motion (t/T = 0.00) for x/c [ 0.5. As the flow develops,

instability and transition moves upstream and small vorti-

cal structures are observed near the leading edge at

t/T = 0.25, which indicate laminar separation and reat-

tachment of the turbulent boundary layer. In all cases, the

boundary layer on the suction side reattaches and becomes

laminar during the up stroke motion of the airfoil.

Measured turbulence statistics are shown in Fig. 4. At

t/T = 0.25 and Re = 10,000, large values of the normal

components (u02=U21 and v02=U2

1) as well as the shear

component (u0v0=U21) of the Reynolds stress are found at

the same location as the transitional vortical features,

which suggest that an important contribution to the Rey-

nolds stress is cycle-to-cycle fluctuations in position of

these features. Similarly, high values of all component of

the Reynolds stress in the thin separated shear layer at the

leading edge (t/T = 0.33–0.5) suggest cycle-to-cycle fluc-

tuation in the position of the separated shear layer. High

values of u02=U21, exceeding 0.15, are measured at the

shear layer location. In contrast, the values of v02=U2

1 are

much lower, which is attributed to cycle-to-cycle move-

ment of the high shear region causing very large changes in

the u component compared to the v component of the

velocity. It is interesting to note that the shear component

of the Reynolds stress associated with the transitional

vortical features is relatively small compared to the shear

Reynolds stress in the separated region found at later

phases. However, these results clearly show turbulent flow

in the wake created by the leading edge separation at

Re = 10,000. At higher Reynolds number (Re = 30,000

and 60,000), the boundary layer is attached throughout the

Exp Fluids (2012) 53:1979–1992 1983

123

Fig. 3 Flow visualization and normalized vorticity contours of SD7003 undergoing shallow-stall kinematics at Re = 1 9 104, 3 9 104, and

6 9 104 (refer Supplementary material for high resolution figures)

Fig. 4 Contours of normalized turbulence statistics of SD7003 undergoing shallow-stall kinematics at Re = 1 9 104, 3 9 104, and 6 9 104

(refer Supplementary material for high resolution figures)

1984 Exp Fluids (2012) 53:1979–1992

123

down stroke, and the normal and shear components of the

Reynolds stress are significantly lower than that at the

lower Reynolds number. The turbulence is anisotropic for

all Re with values of u02=U2

1 greater than v02=U2

1.

Figure 5 shows side-by-side comparison of flow visu-

alization and normalized vorticity contours for a flat plate

airfoil undergoing shallow-stall kinematics at Re = 1 9

104, 3 9 104, and 6 9 104. The boundary layer separates at

the leading edge at all Reynolds numbers, and comparison

of flow fields shows small Reynolds number effects. At

t/T = 0.00, transition is observed near the leading edge;

small vortical structures are captured near the leading edge,

and the boundary layer remains attached aft of these

structures at all Re. The difference between the SD7003

airfoil and the flat plate is that the leading edge curvature

and thickness of the SD7003 airfoil delay boundary layer

separation at the leading edge, whereas the small radius of

curvature of the flat plate leading edge facilitates boundary

layer separation. Close examination at t/T = 0.42 and 0.50

suggests small Re effects in the development of recircula-

tion region at the end of the down stroke. At Re = 10,000,

the recirculation region on the suction side of the airfoil is

open, while it remains closed at the higher Re. It should be

noted that these recirculation region do not coincide with

regions of high vorticity and therefore cannot be associated

with formation of a LEV. Regions of high vorticity remain

in the shear layer formed at the leading edge by separation

of the boundary layer. During the up stroke, transitional

flow features are observed at Re = 10,000, while a turbu-

lent boundary layer is observed at the higher Reynolds

numbers.

Similar to the SD7003 airfoil, the turbulence in the

separated region of the flat plate airfoil is anisotropic as

shown by the u02=U2

1 and v02=U2

1 contours in Fig. 6. The

high values of u02=U2

1 near the leading edge shear layer are

comparable to the SD7003 airfoil. The u02=U2

1 contours

Fig. 5 Flow visualization and normalized vorticity contours of flat plate undergoing shallow-stall kinematics at three different Reynolds number

(refer Supplementary material for high resolution figures)

Exp Fluids (2012) 53:1979–1992 1985

123

show development of regions of high u02=U21 values that

coincides with the recirculation region captured by the

streamlines and into the near wake. This region progres-

sively increases in size as Re is increased. The v02=U2

1contours show similar features with higher values of

v02=U21in the wake near the trailing edge of the flat plate. In

this region, the streamlines show predominantly v-com-

ponent velocity, and cycle-to-cycle variation of the recir-

culation region would contribute to the large values of

v02=U21. The u0v0=U2

1 contours show similarity as well as

differences between low Re flow (Re = 10,000) and high

Re flow (Re [ 30,000). The magnitude of u0v0=U21 is

similar for all Re flows, but the concentration of u0v0=U21

varies with Re. For Re = 10,000 case, high values of

u0v0=U21 are shown at the shear layer formed by the leading

edge of the flat plate, and the distribution is correlated with

the vorticity contours shown in Fig. 5. In comparison, high

concentration of u0v0=U21 are located near the trailing edge

of the flat plate for higher Re flows with very small amount

of u0v0=U21 observed near the leading edge.

The results of force measurements for the SD7003 and

the flat plate airfoils under shallow-stall kinematics at

Re = 10,000 and 30,000 are shown in Figs. 7 and 8,

respectively. The plots show phase-averaged mean lift

and drag coefficients as function of phase. The phase

averages are computed using 100 cycles. The length of the

error bars shown at t/T = 0.25 and 0.75 are two standard

deviations computed using the same samples. The mag-

nitude of the error bars is within the measurement

uncertainty of the force sensor. At these low Reynolds

numbers, the measurement uncertainty of the sensor is

large compared to the magnitude of the drag force due to

drift of the sensor output, and therefore the drag coeffi-

cients plotted in Fig. 7 are referenced to the drag coeffi-

cient at zero phase. In contrast, the lift force is an order of

magnitude larger than the sensor measurement uncer-

tainty. Force measurements at Re = 60,000 are not

Fig. 6 Contours of normalized turbulence statistics of flat plate undergoing shallow-stall kinematics at three different Reynolds number (refer

Supplementary material for high resolution figures)

Fig. 7 Force time history of

SD7003 airfoil undergoing

shallow-stall kinematics at

Re = 10,000 and 30,000

1986 Exp Fluids (2012) 53:1979–1992

123

reported because the aerodynamic load exceeded the

capacity of the sensor at this Re.

The down stroke motion of the SD7003 airfoil for

shallow-stall kinematics produces thrust and lift. The

transition process at Re = 10,000 has significant effects on

the aerodynamic forces. The minimum drag coefficient is

lower (increased thrust) by approximately 20 % compared

to the higher Reynolds number results. The peak lift

coefficient at Re = 10,000 is approximately 25 % greater

than the Re = 30,000 case. Both maxima are found at

t/T = 0.25 which corresponds to the mid-point of the down

stroke motion when the effective angle of attack is maxi-

mum. Although these changes in lift and drag for the low

Reynolds number may appear contradictory, it seems that

the delayed reattachment of the boundary layer at

Re = 10,000 results in loss of leading edge suction and a

separated flow with closed streamlines and significant

streamline curvature. These effects combine to produce

aerodynamic force directed normal to the airfoil and of

larger magnitude than at higher Reynolds number. It should

be noted that the increased aerodynamic force is produced

as a result of the separated flow on the suction side of the

airfoil even though a LEV is not formed at these flow

conditions. During the up stroke motion, Re = 10,000 case

shows lower drag and lift values compared to Re = 30,000

case. There exists laminar separation near the trailing edge of

the airfoil at t/T = 0.75 for Re = 10,000 case (see Fig. 3),

whereas higher Re cases show attached turbulent boundary

layer. The separation can cause a loss of lift while turbulent

boundary layer at high Re increases the drag.

Figure 7 also shows comparison of the present mea-

surements with unsteady linear potential flow theory

(Theodorsen, 1935). Theoretical results shown in Fig. 7

include Theodorsen’s classical result as well the quasi-

steady approximation in which the Theodorsen function is

assumed unity, C(k) = 1 (Bisplinghoff et al. 1996). Ol

et al. (2009) report good agreement between the measured

lift coefficient time history of a SD7003 at Re = 60,000

and linear potential flow theory. In the current study, the

Re = 30,000 case show good agreement with the Theod-

orsen theory, which is consistent with findings by Ol et al.

(2009), and together support the conclusion of the present

flow visualization and PIV studies of negligible Re effects

in the range Re = 30,000–60,000. For Re = 10,000, the

higher lift coefficient is in better agreement with the quasi-

steady approximation. It should be noted that the angle of

attack for zero lift of the SD7003 airfoil is -1� because of

the mean camber, and therefore, the mean angle of attack

used in the calculations of theoretical results is 9� rather

than 8�. The change in effective angle of attack due to

airfoil cross-section is implicit, and it should be considered

part of the airfoil shape effect.

The flat plate airfoil produces qualitatively similar force

time history as the SD7003 airfoil. Measurement uncer-

tainty for the Re = 10,000 case is lower than for the

SD7003 airfoil. The down stroke generates thrust which

peaks at t/T = 0.25 and is comparable to the thrust pro-

duced by the SD7003 airfoil, although for the flat plate the

maximum thrust does not depend on Reynolds number.

The lift coefficient shows Re effects in the down stroke

with peak value of the lift coefficient at Re = 30,000

approximately 15 % greater than at Re = 10,000. The

increase in lift from higher Re can be associated with the

pitch rate, where the pitch rate for Re = 30,000 case is 3

times faster than Re = 10,000 case. Baik et al. (2012)

discuss the effect of pitch rate on force generation by

performing circulation analysis on the formed LEV.

Although there is no LEV present in the shallow-stall

kinematics, the shear layer formed from the leading edge is

Re dependent which can be observed from u0v0=U21 con-

tours. In addition, the recirculation region found near the

trailing edge of the airfoil at higher Re flows may also

contribute to the higher lift.

Comparison with linear potential flow theory shows

good agreement for the quasi-steady approximation from

t/T = 0.00 to 0.20. Between t/T = 0.20 and 0.50, there is a

Fig. 8 Force time history of flat

plate airfoil undergoing

shallow-stall kinematics at

Re = 10,000 and 30,000

Exp Fluids (2012) 53:1979–1992 1987

123

significant increase in the measured lift compared to theoret-

ical values. Although no LEV is formed in these cases, leading

edge separation and closed streamlines with significant cur-

vature on the leeward side of the flat plate result in a significant

increase in lift. During the up stroke motion, the measure-

ments show good agreement with the quasi-steady linear

potential flow theory. Clearly, the standard unsteady potential

flow theory underpredicts the magnitude of the lift coefficient

oscillations by a significant amount even during the up stroke

when the boundary layer reattaches which suggests that the

theory inaccurately accounts for the effect of vorticity distri-

bution in the wake on the lift.

4.2 Deep-stall kinematics

Figure 9 shows flow visualization and normalized vorticity

contours for the SD7003 and the flat plate airfoils and deep-

stall kinematics at Re = 60,000. Flow visualizations were

taken at Re = 10,000 and 30,000, and it revealed no signifi-

cant change in flow development and flow topology. The

deep-stall kinematics have an effective angle of attack range

between -6� and 22�, and a large LEV and TEV formed

during the cycle. The leading edge separation and the sub-

sequent formation of a LEV occur at an earlier stage of the

cycle for the flat plate airfoil compared to the SD7003 airfoil.

This delay in the flow development between for the SD7003

and flat plate airfoil is approximately t/T = 0.08. Figure 10

illustrates this effect; it shows a comparison of u-component

velocity profiles on the leeward side of the airfoils for the SD

7003 airfoil at t/T = 0.33 and for the flat plate airfoil at

t/T = 0.25. Additional comparisons between the flat plate and

SD7003 airfoils can be found in the experimental results

reported by Baik et al. (2009), Baik (2011) and computational

results by Kang et al. (2012).

Analogous to the flat plate shallow-stall case, formation

of the LEV causes strong curvature of streamlines that

Fig. 9 Flow visualization and

normalized vorticity contours of

SD7003 and flat plate airfoils

undergoing deep-stall

kinematics at Re = 60,000

(refer Supplementary material

for high resolution figures)

1988 Exp Fluids (2012) 53:1979–1992

123

attach and terminate on the leeward side of the airfoil

upstream of the trailing edge. The LEV convects down-

stream past the trailing edge and it induces the formation of

a TEV as shown by the vorticity contours at t/T = 0.33 for

the flat plate airfoil. The size of the TEV is approximately

1/6 of the chord length and it dissipates much faster than

the LEV. Similar flow topology is observed for the SD7003

airfoil but with a delay of approximately t/T = 0.08. The

flow topology of deep-stall kinematics is independent of

Re, and it is preserved as long as the reduced frequency is

unchanged (Baik et al. 2012).

Turbulence statistics computed from PIV data are shown

in Fig. 11. As expected, significant Reynolds stresses are

found in the LEV and TEV vortices, and the separated flow

region. The difference between u02=U21 and v02=U2

1 con-

tours suggests anisotropic turbulence. High values of

u02=U21 are concentrated in the leading edge shear layer,

similar to the shallow-stall case. The shear layer is better

defined for the flat plate due to smaller radius of curvature

of the leading edge. A laminar flow is observed to be

trapped between the LEV and the airfoil surface at

t/T = 0.42 for the SD7003 and t/T = 0.33 for the flat plate.

Fig. 10 An x-component

velocity comparison between

flat plate and SD7003 to

illustrate the delay in flow

development present during the

down stroke motion (x/c = 0.00

denotes the leading edge)

Fig. 11 Contours of normalized turbulence statistics of SD7003 and flat plate airfoils undergoing deep-stall kinematics at Re = 60,000

Exp Fluids (2012) 53:1979–1992 1989

123

Streamlines indicate a reverse flow at this region, and the

turbulence statistics suggest that this reverse flow is lami-

nar. The reverse flow is created by the formation of TEV,

and the vortex exhibits an isotropic turbulence as shown by

u02=U2

1 and v02=U2

1 contours. The u02=U2

1 and v02=U2

1values exceed 0.4 which is amplified by the phase-to-phase

variation on the location of TEV formation. The SD7003

airfoil shows larger region of high concentration of tur-

bulence statistics compared to the flat plate, and the leading

cause of this is due to a sharper trailing edge of the SD7003

airfoil compared to the rounded flat plate. The TEV introduces

u0v0=U21 values that are similar in magnitude but having

opposite signs within the vortex. The u0v0=U21 values are

mostly negative in the flow field except within the TEV.

The deep-stall case produces a large LEV that is com-

parable to the chord length of 152 mm. Since the tunnel

walls are only 608 mm apart, the presence of LEV may

introduce a significant blockage. In order to test the pres-

ence of blockage, the measurements were repeated for

smaller chord lengths models for the shallow-stall and the

deep-stall cases. A 76-mm chord length flat plate model

was used for both kinematics, and a 51-mm chord was used

for the deep-stall kinematics to further probe the blockage

effect on the 76-mm model.

The lift coefficient measured from the shallow-stall

kinematics is shown in Fig. 12a. The results show that

there is no evidence that there exists a blockage effect for

the 152-mm flat plate model for the shallow-stall kine-

matics. Since the SD7003 airfoil have the same chord

length and less separated flow compared to the flat plate

model, this would imply that the blockage effect for the

SD7003 airfoil undergoing shallow-stall kinematics is also

blockage free.

A blockage effect was present for deep-stall kinematics

with chord length of 152 mm. The lift coefficients mea-

sured from the deep-stall kinematics is shown in Fig. 12b.

The 152-mm chord flat plate model introduces blockage

that increases the peak lift coefficient by approximately

20 % compared to the smaller chord models. The increase

in the peak lift coefficient is a well-known characteristic of

the blockage effect. A significant increase in lift coefficient

is only observed during the down stroke motion where the

LEV is present. No blockage effect was present for the

76- and 51-mm chord models.

The blockage study finds that there is a high chance of

blockage effect present in the 152-mm chord force mea-

surement. However, the qualitative features found in the

force measurement still provide insight along with the PIV

measurement obtained for the deep-stall kinematics. Fig-

ure 13 plots the lift coefficient of 152-mm flat plate and

SD7003 airfoil undergoing deep-stall kinematics at

Re = 10,000 and 30,000. The location of the peak is not

identical between models, and the peak occurs earlier in the

motion for the flat plate. This observation is consistent with

the documented flow delay that is approximately t/

T = 0.08 between the airfoils. The difference in airfoil

shape results in approximately 25 % greater lift force for

the flat plate compared to the SD7003 airfoil. The point is

that the different evolution of the LEV for the SD7003 and

flat plate airfoil produce different force history, and these

effects are more significant than Reynolds number effects.

Compared to the shallow-stall kinematics, the peak lift

coefficient is approximately 50 % greater for the deep-stall

kinematics.

The Re effect is clearly present independent of airfoil

shape as evidenced by a higher peak lift coefficient during

the mid-down stroke and less lift during the up stroke

motion at Re = 10,000 compared to Re = 30,000. This

observation is similar to the shallow-stall case. It should be

noted that the flow topology is the same for all Re, so the

difference in forces should be due to circulation. Flat plate

undergoing shallow-stall kinematics showed Re effect on

lift due to pitch rate even though flow topology remained

the same across all Re studied. Although the pitch rate is

not a factor in deep-stall kinematics, the LEV circulation

value will be different for different Re as the shear layer

Fig. 12 Measured lift

coefficients for (a) shallow-stall

kinematics and (b) deep-stall

kinematics using different chord

length flat plate models (refer

Supplementary material for high

resolution figures)

1990 Exp Fluids (2012) 53:1979–1992

123

characteristic is different at Re = 10,000 compared to

Re = 30,000. The difference in LEV circulation leads to

difference in force generated, although this effect is not as

prominent as the airfoil shape effect or changing St (Baik

et al. 2012).

5 Conclusions

The current study documents unsteady flow field and

force generation produced by pitching and plunging air-

foils at Re = 1 9 104, 3 9 104, and 6 9 104. The

SD7003 airfoil and flat plates were pitched and plunged

using two different effective angle of attack profiles with

range of 2.4� to 13.6� (shallow-stall) and -6� to 22�(deep-stall). The flow fields resulting from both kine-

matics were quantified using PIV and direct force mea-

surements were performed to compare with existing linear

potential flow theory.

The shallow-stall kinematics presented laminar-to-tur-

bulent transition for the SD7003 airfoil where increase in

drag and lift was documented at Re = 10,000; the onset of

laminar-to-turbulent transition caused formation of vortices

on the leeward side of the airfoil that produced a closed

streamline at the trailing edge which acted as an effective

camber effect. The flat plate airfoil resulted in laminar

separation and reattachment at low effective angles of

attack, but the leading edge separation was observed during

the down stroke motion where the effective angle of attack

exceeded the static-stall limit. The effective camber effect

was also present for the flat plate as observed from curved

streamlines that terminated at the trailing edge. While the

Re effects were negligible in flow topology, measured

forces showed signs of Re effects for the flat plate. The

linear theory proposed by Theodorsen was in a good

agreement with the SD7003 at high Re where the for-

mation of turbulent boundary layer during the down

stroke motion resulted in attached flow field. For the other

cases with a leading edge separation, Theodorsen theory

with C(k) = 1 resulted in better agreement with the

experimental data; however, the measured peak lift

coefficient was still higher for the flat plate models

compared to the theory. The turbulence statistics showed

highly anisotropic turbulence for the leading edge sepa-

rated flows on both airfoils. The shear layer at the leading

edge of the airfoil was concentrated with high values of

turbulence statistics from cycle-to-cycle variation on the

precise shear location. The concentration of turbulence

statistics in the flow field varied as Re was changed while

maintaining similar flow topology.

The deep-stall kinematics was highlighted by the for-

mation of a large LEV. The measured peak lift coefficient

was approximately 50 % higher than the shallow-stall

kinematics. Similar to the shallow-stall kinematics, curved

streamlines due to LEV terminated at the trailing edge of

the airfoil during down stroke motion, which attributed to

the camber effect. The SD7003 airfoil experienced a delay

of LEV formation by approximately t/T = 0.08 compared

to the flat plate due to leading edge curvature, and this

delay was identified using PIV and force measurement. The

lift force generated by the flat plate was approximately

25 % greater than the SD7003 airfoil, which was greater

than the apparent Re effect on force generation. The tur-

bulence statistics revealed anisotropic turbulence in the

LEV during the down stroke motion with concentrated

high values of turbulence statistics in the shear layer

formed by the leading edge. On the other hand, TEV

showed signs of isotropic turbulence with the u0v0=U21

distribution of TEV displaying mixture of positive and

negative values.

The key findings of the present study are the following:

(1) Re effects can cause laminar-to-turbulent transition that

increases lift by forming a closed curved streamlines, (2)

flow topology is almost independent of Re, but the force

generation has a small Re effect, (3) the formation of LEV

caused by the increase in effective angle of attack signifi-

cantly increases the peak lift coefficient due to effective

camber effect, (4) anisotropic turbulence is observed dur-

ing the down stroke with emphasis near the shear location,

(5) isotropic turbulence is present with mixture of positive

and negative values of u0v0=U21 inside the TEV, (6) The-

odorsen theory works well for attached flow fields (SD7003

at high Re flows), but setting C(k) = 1 performs better for

leading edge–separated flows, and (7) airfoil shape effects

is stronger than the Re effects on lift generation.

Fig. 13 Lift coefficients for deep-stall kinematics with flat plate and

SD7003 airfoils (refer Supplementary material for high resolution

figures)

Exp Fluids (2012) 53:1979–1992 1991

123

Acknowledgments This work has been supported in part by the Air

Force Office of Scientific Research’s Multidisciplinary University

Research Initiative (MURI) and by the Michigan/AFRL (Air Force

Research Laboratory)/Boeing Collaborative Center in Aeronautical

Sciences.

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