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International Journal of Aerospace and Lightweight Structures
Vol. 1, No. 2 (2011) 221–238
c Research Publishing Services
DOI: 10.3850/S2010428611000171
An Experimental Study of Stall Hysteresis of
a Low-Reynolds-Number Airfoil
Hui Hua , Zifeng Yang, Hirofumi Igarashi and Matthew Martin
Department of Aerospace Engineering, Iowa State University, 2271 Howe Hall,
Room 1200, Ames, Iowa, 50011-2271, USA.
a huhui@iastate.edu
Accepted 9 September 2011
An experimental study was conducted to investigate static stall hysteresis of a NASA
GA(W)-1 airfoil at the chord Reynolds number of Re = 162,000. In addition to mapping
the surface pressure distribution around the airfoil, a digital PIV system was used to
make detailed flowfield measurements to quantify the occurrence and behavior of laminar boundary layer separation and transition on the airfoil when static stall hysteresis
occurs. The measurement results revealed clearly that, for a same angle of attack in
the hysteresis loop, incoming flow streams were found to be able to attach to the airfoil
upper surface in general with a thin separation bubble formed near the airfoil leading
edge when the angle is at the increasing branch of the hysteresis loop. The attached
flow pattern resulted in higher lift and lower drag acting on the airfoil as well as a lower
Reynolds stress level and smaller unsteadiness in the wake of the airfoil. When the angle
of attack is at the decreasing branch of the hysteresis loop, the laminar boundary layer
was found to separate from the airfoil upper surface for good at a location very near
to the airfoil leading edge. The turbulence transition of the separated laminar boundary layer was found to take place rapidly accompanied by periodical shedding of strong
Kelvin-Helmholtz vortex structures in the wake of the airfoil. Large-scale flow separation
was found to take place on almost the entire upper surface of the airfoil. As a result, the
lower lift and higher drag acting on the airfoil were found with Reynolds stress and turbulence kinetic energy levels in the wake of the airfoil increased significantly. The present
study elucidates quantitatively that static stall hysteresis of a low-Reynolds number airfoil is closely related to the behavior of laminar boundary layer separation and transition
on the airfoil. The ability of the flow to remember its past history is responsible for the
stall hysteretic behavior.
1. Introduction
A number of military and civilian applications require efficient operation of airfoils
in low chord Reynolds numbers. The applications include propellers, sailplanes,
ultra-light man-carrying/man-powered aircraft, high-altitude vehicles, wind turbines, Unmanned Aerial Vehicles (UAVs) and Micro-Air-Vehicles (MAVs). It is well
known that many significant aerodynamic problems occur for low-Reynolds number airfoils (Carmichael, 1981). Stall hysteresis, a phenomenon where stall inception
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and stall recovery do not occur at the same angle of attack, has been found to be
relatively common in low-Reynolds-number airfoils.
When stall hysteresis occurs, aerodynamic characteristics of an airfoil become
history dependent, i.e., dependent on the sense of change of the angle of attack.
The coefficients of lift, drag, and moment of the airfoil are found to be multiplevalued rather than single-valued functions of the angle of attack. Stall hysteresis is
of practical importance because it produces widely different values of lift coefficient
and lift-to-drag ratio for a given airfoil at a given angle of attack. It could also
affect the recovery from stall and/or spin flight conditions. Whereas stall hysteresis
associated with the pitching motion of airfoils (also known as dynamic stall) has
been investigated extensively as summarized in the review article of McCorskey
(1982), the stall hysteresis phenomena observed for static stall of an airfoil have
received much less attention.
A good physical understanding is essential in order to provide guidance to minimize the detrimental effects of stall hysteresis for improved aerodynamic performance of low-Reynolds-number airfoils. This requires a detailed knowledge about
stall hysteresis and associated flow behavior around the airfoil. Pohlen & Mueller
(1984) and Mueller (1985) investigated the aerodynamic characteristics of Miley
M06-13-128 and Lissaman 7769 airfoils at low Reynolds numbers, and found both
airfoils produced stall hysteresis loops in the profiles of measured lift and drag
forces when they operated below chord Reynolds numbers of 300,000. Based on
qualitative flow visualization with smoke, Mueller (1985) suggested that airfoil hysteresis is related to laminar boundary layer transition and separation on the airfoils.
Marchman (1987) conducted a systematic study of the aerodynamic characteristics
of a Wortmaim FX63-137 airfoil at Reynolds numbers between 50,000 and 500,000,
and found that stall hysteresis behavior is very dependent on wind tunnel flow
quality and acoustic properties. Hoffmann (1991) studied the aerodynamic characteristics of a NACA 0015 airfoil at a chord Reynolds number of 250,000, whereby
the stall hysteresis loop was observed in the measured coefficients of lift and drag.
Hoffmann (1991) also revealed that stall hysteresis could be observed for low free
stream turbulence cases (up to ∼2% turbulence intensity) but disappeared for high
free stream turbulence cases. Biber & Zumwal (1993) and Biber (2005) reported
that stall hysteresis phenomena occur for not only single-element airfoils but also
multi-element airfoil configurations such as a GA(W)-2 airfoil equipped with a 25%
slotted flap. Landman & Britcher (2001) reported similar results in wind-tunnel tests
of a three-element airfoil. Mittal & Saxena (2002) conducted a numerical study to
predict the aerodynamic hysteresis near the static stall angle of a NACA 0012 airfoil
in comparison with the experimental data of Thibert et al. (1979).
Although much useful information has already been uncovered by those studies,
the majority of the previous experimental studies were conducted based mainly on
measuring overall aerodynamic forces and/or moments acting on airfoils, detailed
flow field measurements have never been carried out to quantify the occurrence
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and behavior of laminar boundary layer separation and transition on the airfoil
when stall hysteresis occurs. Very little can be found in literature to bring to light
the relation between the static stall hysteresis phenomena observed in the measured aerodynamic (lift, drag and moment) coefficients with the flow pattern and
behavior of vortex and turbulent flow structures around the airfoils. In the present
study, we conducted a detailed experimental study to investigate stall hysteresis of
a GA(W)-1 airfoil at the Reynolds number of Re = 162,000. In addition to mapping surface pressure distribution around the airfoil with pressure sensors, a digital
particle image velocimetry (PIV) system was used to make detailed flow field measurements to quantify the occurrence and behavior of laminar boundary layer separation and transition on the airfoil when stall hysteresis occurs. The detailed flow
field measurements were correlated with the airfoil surface pressure measurements
to demonstrate underlying fundamental physics associated with the stall hysteresis observed in the measured aerodynamic (lift and drag) coefficient profiles. To
the best knowledge of the authors, this is the first effort of its nature. The primary
objective of the present study is to gain further insight into the fundamental physics
of stall hysteresis of low-Reynolds-number airfoils through detailed flow field measurements. In addition, the quantitative measurement results will be used as the
database for the validation of computational fluid dynamics (CFD) simulations of
such complicated flow phenomena for the optimum design of low-Reynolds-number
airfoils.
2. Studied Airfoils and Experimental Setup
Y/C
The experiments were performed in a closed-circuit low-speed wind tunnel located
in the Aerospace Engineering Department of Iowa State University. The tunnel has
a test section with a 1.0 ft × 1.0 ft (30 cm × 30 cm) cross section and optically transparent walls. The tunnel has a contraction section upstream of the test section with
honeycomb, screen structures, and cooling system installed ahead of the contraction
section to provide uniform low turbulent incoming flow to enter the test section.
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Fig. 1.
GA(W)-1 airfoil geometry and pressure tap locations.
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Figure 1 shows the schematic of the airfoil used in the present study: a GA
(W)-1 airfoil (also labeled as NASA LS(1)-0417). The GA (W)-1 has a maximum
thickness of 17% of the chord length. Compared with standard NACA airfoils, the
GA (W)-1 airfoil was specially designed for low-speed general aviation applications
with a large leading-edge radius in order to flatten the peak in pressure coefficient
near the airfoil nose to discourage flow separation (McGee & Beasley, 1973). The
chord length of the airfoil model is 101 mm, i. e., C = 101 mm, for the present
study. The flow velocity at the inlet of the test section was U∞ = 24.3 m/s, which
corresponds to a chord Reynolds number of Re = 162, 000. The turbulence intensity
of the incoming stream was found to be within 1.0%, measured by using a hot-wire
anemometer.
The airfoil model is equipped with 43 pressure taps at its median span with the
spanwise length of the airfoil being 1.0 ft. The locations of the pressure taps are
indicated in Fig. 2. The 43 pressure taps were connected by plastic tubing to 43
channels of a pressure acquisition system (model DSA3217, Scanivalve Corp). The
DSA3217 digital sensor arrays incorporate temperature compensated piezoresistive
pressure sensors with a pneumatic calibration valve, RAM, 16 bit A/D converter,
and a microprocessor in a compact self-contained module. The precision of the
pressure acquisition system is ±0.2% of the full scale (±10 inch H2 O). During the
experiment, each pressure transducer input was scanned at 400 Hz for 20 seconds.
2
), around the airfoil
The pressure coefficient distributions, Cp = (P − P∞ )/( 21 ρU∞
at various angles of attack were measured by using the pressure acquisition sys2
2
tem. The lift and drag coefficients, Cl = l/( 21 ρU∞
· C) and Cd = d/( 21 ρU∞
· C),
of the 2-D airfoil were determined by numerically integrating the measured pressure distribution around the airfoil. It should be noted that the drag coefficient
of an airfoil is composed of two parts, the pressure drag component (which comes
from the fore and aft unbalance in the pressure distribution around the airfoil) and
the skin friction component (which comes from the viscous surface stresses around
the airfoil). At low angles of attack skin friction dominates the total drag while
the pressure drag component is minor. At high angles of attack the reverse is true.
Since skin friction drag component was ignored in the present study, as a result,
the drag coefficient of the airfoil was underestimated. However, since stall hysteresis
of an airfoil is usually found to occur at high angles of attack, the pressure drag
component is significant and skin friction drag is negligible when stall hysteresis
occurs.
Figure 2 shows the schematic of the experimental setup used for the PIV measurement. The test airfoil was installed in the middle of the test section. A PIV
system was used to make flow velocity field measurements along the chord at the
middle span of the airfoil. The flow was seeded with ∼1 µm oil droplets. Illumination
was provided by a double-pulsed Nd:YAG laser (NewWave Gemini 200) adjusted
to the second harmonic and emitting two laser pulses of 200 mJ at a wavelength of
532 nm with a repetition rate of 10 Hz. The laser beam was shaped into a sheet by a
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Fig. 2.
225
Schematic of the experimental setup for the PIV measurements.
set of mirrors, spherical and cylindrical lenses. The thickness of the laser sheet in the
measurement region was about 0.5 mm. A 12-bit (1376 × 1040 pixel) CCD camera
was used for PIV image acquisition with the axis of the camera perpendicular to the
laser sheet. The CCD camera and the double-pulsed Nd:YAG lasers were connected
to a workstation (host computer) via a Digital Delay Generator (Berkeley Nucleonics, Model 565), which controlled the timing of the laser illumination and the
image acquisition. In the present study, a careful pre-test, which included testing
different seeding methods, applying different paints to the airfoil model, adjusting
laser excitation energy levels, camera positions and optic lens arrangements, was
conducted in order to minimize the reflection from the airfoil surface for the near
wall PIV measurements.
In the present study, PIV measurements were conducted at two spatial resolution levels: a coarse level to visualize the global features of the flow pattern around
the airfoil with the measurement window size being about 150 mm × 120 mm; and
a refined level to reveal further details about the transient behavior of the laminar boundary layer separation and transition near the leading edge of the airfoil
with a measurement window size of about 40 mm × 30 mm. The time interval
between the double-pulsed laser illumination for the PIV measurements was set
as ∆t = 20.0 µs, and 4.0 µs. Instantaneous PIV velocity vectors were obtained by a
frame to frame cross-correlation technique involving successive frames of patterns
of particle images in an interrogation window of 32 × 32 pixels. An effective overlap
of 50% was employed for PIV image processing. The effective resolutions of the PIV
measurements (i.e., grid sizes) at two resolution levels were ∆/C = 0.018 and 0.0045
respectively. After the instantaneous velocity vectors (ui , vi ) were determined, the
distributions of spanwise vorticity (̟z ) were derived as suggested by Abrahamson
& Lonnes (1995). The time-averaged quantities such as mean velocity (U, V ), turbu2
) and
lent velocity fluctuations (u′ , v ′ ), normalized Reynolds stress (τ = −u′ v ′ /U∞
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2
2
normalized turbulent kinetic energy (T.K.E. = 0.5 ∗ (u′ + v ′ )/U∞
) were obtained
from a cinema sequence of 200 frames of instantaneous velocity fields.
3. Experimental Results and Discussions
3.1. Measured lift, drag and surface pressure coefficients
During the experiments, in order to eliminate the effect of the flow disturbances
due to the change of airfoil angle of attack (AOA), measurement data were taken at
about 5.0 minutes later after the airfoil was set to a pre-determined angle of attack.
Figure 3 shows the profiles of the measured lift and drag coefficients versus angle
of attack. Static stall hysteresis in the aerodynamic coefficients can be observed
clearly for angles of attack lying between 12.0 and 16.0 degrees. With increasing
angle of attack, airfoil stall was found to occur at AOA = 15.0 deg, while for the
decreasing angle of attack it occurs at AOA = 12.0 deg. The hysteresis loop was
found to be clockwise in the lift coefficient profiles, and counter-clockwise in the
drag coefficient profiles. The stall hysteresis resulted in significant variations of lift
coefficient, Cl , and lift-to-drag ratio, l/d, for the airfoil at a given angle of attack.
For example, the lift coefficient and lift-to-drag ratio at AOA = 14.0 degrees were
found to be Cl = 1.33 and l/d = 23.5 when the angle was at the increasing branch
of the hysteresis loop. The values were found to become Cl = 0.8 and l/d = 3.66
for the same 14.0 degrees angle of attack when it was at the deceasing angle branch
of the hysteresis loop.
Figure 4 shows the measured surface pressure coefficient distributions around
the airfoil as the angle of attack of the airfoil changed from 12.0 to 17.0 degrees along
both the increasing and decreasing branches of the hysteresis loop. When the angles
of attack are out of the hysteresis loop (i.e., AOA ≤ 12.0 degrees or AOA ≥ 16.0
degrees), the measured surface pressure coefficient distributions around the airfoil
for the same angles of attack were found to be single-valued and almost invariant in
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Lift Coefficient, Cl
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Fig. 3.
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Angle of Attack (degree)
(b). drag coefficient
Measured lift and drag coefficients versus the angle of attack.
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Fig. 4.
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(f). AOA= 17.0 degrees
Measured surface pressure distributions around the airfoil.
spite of the angles that were reached along increasing or decreasing branches of the
hysteresis loop. However, when the angles of attack are inside the hysteresis loop
(i.e., 12.0 < AOA < 16.0 degrees), the surface pressure distributions on the airfoil
lower surface do not change very much, but the surface pressure distributions on the
airfoil upper surface were found to vary significantly for the same angles of attack
with the angles being reached along the increasing branch of the hysteresis loop
compared with those along the decreasing branch of the hysteresis loop. When the
AOA = 13.0, 14.0 and 15.0 degrees are at the increasing branch of the hysteresis
loop, the surface pressure coefficient profiles along the airfoil upper surface were
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found to reach a negative peak rapidly at a location near the airfoil leading edge. The
surface pressure then recovered over the airfoil upper surface, which is similar to the
case with AOA = 12.0 degrees. A region of nearly constant pressure (i.e., “plateau”
region) was found at the locations of X/C ≈ 0.05 with a sudden increase in surface
pressure following the “plateau” region. Further downstream when X/C > 0.15,
surface pressure was found to recover gradually and smoothly. Such a feature of the
surface pressure coefficient profiles is actually closely related to laminar boundary
layer separation and transition, and formation of laminar separation bubbles on
low-Reynolds-number airfoils.
Based on the original ideas proposed by Horton (1969), Russell (1979) developed a theoretical model to characterize laminar separation bubbles formed on
low-Reynolds-number airfoils, which is illustrated schematically in Fig. 5. Russell
(1979) suggested that the starting point of the pressure plateau indicates the location where the laminar boundary layer would separate from the airfoil upper surface
(i.e., separation point). Since the transition of the separated laminar boundary layer
to turbulence will result in a rapid pressure rise brought about by fluid entrainment,
the termination of the pressure plateau could be used to locate the transition point
(i.e., where the transition of the separated laminar boundary layer to turbulence
would begin to occur). The pressure rise due to the turbulence transition often overshoots the invisicid pressure that exists at the reattachment location. Therefore, the
location of the point of equality between the actual and inviscid surface pressure
marks the location of reattachment (i.e., reattachment point).
Fig. 5.
Typical surface pressure distribution when a laminar separation bubble is formed.
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Following the work of Russell (1979), the locations of critical points (separation,
transition, and reattachment points) at different angles of attack can be estimated
based on the measured airfoil surface pressure profiles. Based on the measured surface pressure distribution given in Fig. 4, the separation, transition, and reattachment points at AOA = 14.0 degrees along the increasing branch of the hysteresis
loop were estimated to be located at X/C ≈ 0.05, X/C ≈ 0.10, and X/C ≈ 0.15
respectively. The length of the laminar separation bubble (i.e., the distance between
the separation and reattachment points) was found to be about 10% of the airfoil
chord length.
When the airfoil angles of attack of AOA = 13.0, 14.0 and 15.0 degrees are at the
decreasing branch of the hysteresis loop, the negative pressure coefficient peak near
the airfoil leading edge was found to decrease significantly, which is very similar to
the cases with AOA = 16.0 and 17.0 degrees. The surface pressure over the airfoil
upper surface was found to be nearly constant. Such surface pressure distribution
indicates that large-scale flow separation has occurred over almost the entire upper
surface of the airfoil, i.e., the airfoil is in stall state (O’Meara & Muller, 1987, Lin,
et al., 1996 and Yaruseych et al., 2006), which was visualized quantitatively by the
PIV measurement results given in Fig. 7.
3.2. PIV measurement results
While the measurements of the surface pressure distributions and the lift and drag
coefficients can be used to reveal global characteristics of static stall hysteresis of the
low-Reynolds-number airfoil, quantitative flow field measurements taken by using
the digital PIV system can reveal many more details about the significant differences
in flow pattern and behavior of vortex and turbulent flow structures around the
airfoil when stall hysteresis occurs. As aforementioned, PIV measurements were
conducted at two spatial resolution levels for the present study: a coarse level to
visualize the global features of the flow pattern around the airfoil; and a refined
level to reveal further details about the transient behavior of the laminar boundary
layer separation and transition near the leading edge of the airfoil.
Figure 6 shows the PIV measurement results of the flow field around the lowReynolds-number airfoil at AOA = 14.0 degrees in terms of instantaneous velocity field, instantaneous vorticity distribution, ensemble-averaged velocity field, and
streamlines of the mean flow field when the angle is at the increasing branch of the
hysteresis loop. As visualized clearly from the PIV measurement results, incoming
flow streams were found to be able to attach to the airfoil upper surface in general
when the 14.0 degrees angle of attack was at the increasing branch of the hysteresis
loop. The measured surface pressure distributions shown in Fig. 4 revealed that a
separation bubble would be generated on the airfoil upper surface in the region of
X/C ≈ 0.05∼0.15. However, since the thickness of separation bubbles generated on
low-Reynolds-number airfoils is usually very small, i.e., <1% of the chord length
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(d). Streamlines of mean flow field
Fig. 6. PIV measurement results with AOA = 14.0 degrees at the increasing branch of the
hysteresis loop.
(see Fig. 8), the separation bubble could not be revealed clearly from the PIV measurement results given in Fig. 6 due to the limited spatial resolution of the PIV
measurements (i.e., ∆/C = 0.018). However, the existence of the separation bubble
in the region of X/C ≈ 0.05∼0.15 can still be seen vaguely from the distributions
of the mean velocity vectors and corresponding streamlines. Since the incoming
flow streams could attach to the airfoil upper surface in general, the wake region
downstream of the airfoil is reasonably small. The small wake region indicates a
relatively small aerodynamic drag force acting on the airfoil, which is consistent
with the measured airfoil drag coefficient data given in Fig. 3.
Figure 7 shows the PIV measurement results when the 14.0 degrees angle of
attack was at the decreasing branch of the hysteresis loop. The flow pattern around
the airfoil was found to be completely different from that with the 14.0 degrees angle
of attack at the increasing branch of the hysteresis loop. As visualized clearly from
the instantaneous PIV measurement results given in Fig. 7(a) and Fig. 7(b), the
laminar boundary layer (i.e., the thin vortex layer) affixing to the airfoil upper surface at the airfoil leading edge was found to separate from the airfoil upper surface
for good at a location quite near the airfoil leading edge. Strong unsteady vortex
and turbulent structures were found to shed periodically in the wake of the airfoil
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Spanwise
vorticity
1/s * 1000
-40
-4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5
0
20
40
60
80
100
-20
120
-0-1.
.5 5
1.5
2.5
20
40
60
80
100
120
X/C *100
(b). Instantaneous vorticity distribution
60
40
40
20
20
Y /C *100
60
0
GA(W)-1 airfoil
25 m/s
0.5
-4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5
0
X/C *100
(a). Instantaneous velocity field
-20
-0.5
shadow region
-40
-20
-0
.5
0.5
-20
shadow region
-2.5
0.5
-1.5
.5
-0.5
GA(W)-1 airfoil
GA(W)-1 airfoil
25 m/s
.5
-2 -1
.5
-2
0.5
Y/C *100
-0.5
-3.5
-1.5
-0.5
-1.5
0
-20
Y /C *100
-0.5
20
20
0
GA(W)-1 airfoil
-20
shadow region
shadow region
-40
-40
U m/s:
-20
0
5.0 10.0 15.0 20.0 25.0 30.0 35.0
20
40
60
80
100
120
X/C *100
(c). Ensemble-averaged velocity field
-20
0
20
40
60
80
100
120
X/C *100
(d). Streamlines of mean flow field
Fig. 7. PIV measurement results with AOA = 14.0 degrees at the decreasing branch of the
hysteresis loop.
after the separation of the laminar boundary layer. Both the mean velocity vectors
and the corresponding streamlines reveal clearly that large-scale flow separation
occurred on almost the entire upper surface of the airfoil, i.e., the airfoil is in a
state of stall, when the 14.0 degrees angle of attack is at the decreasing branch of
the hysteresis loop. Another interesting feature that can be identified from the distribution of the streamlines of the mean flow field is that the boundary layer, which
separated from the airfoil upper surface near the airfoil leading edge, seems to try
to reattach to the airfoil upper surface in the neighborhood of X/C ≈ 0.35. However, the strong reversing flow from the airfoil trailing edge prevented the separated
boundary layer from reattaching to the airfoil upper surface and kept the airfoil in
stall state. Since the airfoil was in stall state before it was changed to AOA = 14.0
degrees along the decreasing branch of the aerodynamic hysteresis loop, the flowfield
around the airfoil seems to be able to “remember” its past history (i.e., stall state)
when the angle of attack was changed inside the hysteresis loop. The large-scale
flow separation on the airfoil upper surface caused the generation of a very large
circulation region in the wake of the airfoil, indicating a significant aerodynamic
drag force acting on the airfoil. This was confirmed again from the measured drag
coefficient data given in Fig. 3.
While the PIV measurement results given in Figs. 6 and 7 revealed clearly that
the flow pattern and behavior of the vortex and turbulent flow structures around
the airfoil with AOA = 14.0 degrees at the decreasing branch of the hysteresis loop
July 5, 2007 8:52 RPS/INSTRUCTION FILE
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Hui Hu, Zifeng Yang, Hirofumi Igarashi and Matthew Martin
25
25
20
20
15
15
Y /C *100
Y /C *100
were significantly different from those with the same angle of attack of 14.0 degrees
at the increasing branch of the hysteresis loop, further details about the occurrence
and transient behavior of the laminar boundary layer separation and transition near
the leading edge of the airfoil could not be uncovered successfully due to the limited
spatial resolution of the PIV measurements. Refined PIV measurements near the
leading edge of the airfoil with much higher spatial resolution (∆/C = 0.0046)
10
5
shadow region
0
spanwise vorticity
(1/s)*1000
-27.0 -21.0 -15.0 -9.0
3.0
9.0
10
5
0
25 m/s
GA(W)-1 airfoil
reattachment
separation
-5
-5
-22.0 -18.0 -14.0 -10.0 -6.0
-2.0
2.0
GA(W)-1 airfoil
6.0
-10
-10
-10
-5
0
5
10
15
20
25
30
35
-5
0
5
10
20
25
30
35
(b). Instantaneous vorticity distribution
25
20
20
15
15
Y /C *100
25
10
5
0
15
X/C *100
X/C *100
(a). Instantaneous velocity field
Y /C *100
-3.0
5
0
25 m/s
GA(W)-1 airfoil
10
separation bubble
-5
GA(W)-1 airfoil
-5
U m/s: 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
-10
-10
-5
0
5
10
15
20
25
30
35
-5
0
5
10
X/C *100
-u'v'/U
20
2
35
T.K.E.
0.005 0.015 0.025 0.035 0.045 0.055 0.065 0.075 0.085
Y /C *100
10
0.0
5
05
0.005
0.
02
0.02
5
0.001
2
2
0.010
0.0
1
0.035
00
5
0.
5
4
0.
00
10
0.015
0 .01
5
0.00
Y /C *100
30
15
15
0
1
GA(W)-1 airfoil
GA(W)-1 airfoil
-5
-5
-10
-10
25
25
0.001 0.004 0.007 0.010 0.013 0.016 0.019 0.022 0.025
0
20
(d). Streamlines of mean flow field
25
20
15
X/C *100
(c). Ensemble-averaged velocity field
-5
0
5
10
15
20
25
30
35
-10
-10
X/C *100
(e). Normalized Reynolds stress distribution
-5
0
5
10
15
20
25
30
35
X/C *100
(f).Turbulent kinetic energy distribution
Fig. 8. Refined PIV measurement results with AOA = 14.0 degrees at the increasing branch of
the hysteresis loop.
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25
20
20
15
15
5
shadow region
0
-3.0
3.0
9.0
10
5
.0
-3
0
1.
-2
0
GA(W)-1 airfoil
-27.0 -21.0 -15.0 -9.0
-9
-1
.0
.0
-3
-3
.0
10
spanwise vorticity
(1/s)*1000
0
5. -9.0
-3.0
-3.0
-2
1.0
-2
7.
0
Y /C *100
25
-15.0
Y /C *100
were carried out in order to provide further insights into the underlying physics
associated with stall hysteresis of the low-Reynolds-number airfoil. The refined PIV
measurement results are shown in Fig. 8 and Fig. 9 with the same angle of attack
of 14.0 degrees at the decreasing and increasing branches of the hysteresis loop,
respectively.
When the 14.0 degrees angle of attack is at the increasing branch of the hysteresis loop, the laminar boundary layer was revealed clearly as a thin vortex layer
25 m/s
GA(W)-1 airfoil
-5
-5
-22.0 -18.0 -14.0 -10.0 -6.0
-2.0
2.0
6.0
-10
-10
-10
-5
0
5
10
15
20
25
30
35
-5
0
5
10
20
25
30
35
(b). Instantaneous vorticity distribution
25
20
20
15
15
Y /C *100
Y /C *100
(a). Instantaneous velocity field
25
10
5
0
15
X/C *100
X/C *100
5
0
25 m/s
GA(W)-1 airfoil
10
flow separation
-5
-5
GA(W)-1 airfoil
U m/s: 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
-10
-10
-5
0
5
10
15
20
25
30
35
-5
0
5
10
X/C *100
25
30
35
25
-u'v'/U
2
20
0.001 0.004 0.007 0.010 0.013 0.016 0.019 0.022 0.025
T.K.E.
0.005 0.015 0.025 0.035 0.045 0.055 0.065 0.075 0.085
15
15
5
01
7
00
0.
0.004
7
0.0
0.004
Y /C *100
0.0
10
10
0.00
0.0
Y /C *100
20
(d). Streamlines of mean flow field
25
20
15
X/C *100
(c). Ensemble-averaged velocity field
22
0.0130.019
0.015
10
0.02
0.005 0.035
5
0.005
0.016
0.001
5
0.075
0.055
0.065
0.045
0.015
5
03
0.
0
0
GA(W)-1 airfoil
GA(W)-1 airfoil
-5
-5
0.001
-10
-10
-5
0
5
10
15
X/C *100
20
25
30
35
-10
-10
-5
0
5
10
15
20
25
30
35
X/C *100
(e). Normalized Reynolds stress distribution (f). Turbulent kinetic energy distribution
Fig. 9. Refined PIV measurement results with AOA = 14.0 degrees at the decreasing branch of
the hysteresis loop.
July 5, 2007 8:52 RPS/INSTRUCTION FILE
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Hui Hu, Zifeng Yang, Hirofumi Igarashi and Matthew Martin
affixed to the airfoil upper surface from the instantaneous PIV measurement results
shown in Fig. 8(a) and Fig. 8(b). The laminar boundary layer was found to attach
to the airfoil upper surface near the airfoil leading edge, as it is expected. Because
of the severe adverse pressure gradient on the airfoil upper surface at AOA = 14.0
degrees, as revealed from the surface pressure measurements given in Fig. 3, the
laminar boundary layer (i.e., the thin vortex layer) was found to separate slightly
from the airfoil upper surface, at first, then reattach to the airfoil upper surface at a
downstream location, which results in the formation of a separation bubble between
the separation point and the reattachment point. Time sequencing of instantaneous
PIV measurements reveals clearly that, while the locations of the separation points
and reattachment points varied dynamically from one frame to another, most of the
separation points were found to be located at X/C ≈ 0.05 and reattachment points
at X/C ≈ 0.15. The formation of the separation bubble can be seen more clearly
from the ensemble-averaged velocity field and the streamlines of the mean flow
field shown in Fig. 8(c) and Fig. 8(d). Based on the PIV measurement results, the
ensemble-averaged location of the separation point (i.e., from where the streamlines
of the mean flow separates from the airfoil upper surface) was found to be in the
neighborhood of X/C ≈ 0.05, which agrees reasonably well with the starting point
of the pressure plateau in the measured airfoil surface pressure profile when the
14.0 degrees angle of attack is at the increasing branch of the hysteresis loop. The
ensemble-averaged PIV measurement results also revealed that the reattachment
point (i.e., where the separated streamline would reattach to the airfoil upper surface) was in the neighborhood of X/C ≈ 0.15, which also agrees with the estimated
location of the reattachment point based on the airfoil surface pressure measurements. While the total length of the separation bubble was found to be about 10%
of the airfoil chord length, the separation bubble was found to be very thin, with
its height only about ∼1% of the chord length.
Figure 8(e) shows the distribution of the measured normalized Reynolds stress
2
). It should be noted that only the contour lines of the normalized
(−u′ v ′ /U∞
Reynolds stress above a critical value of 0.001 are shown in the Fig. 8(e). This
critical value has been chosen in the literature to locate the onset of the turbulent
transition in separated shear layers (Ol et al., 2005, and Burgmann et al., 2006 and
2007). Following the work of Ol et al., (2005) and Burgmann et al., (2007), the
transition onset position was estimated as the streamwise location where the normalized Reynolds stress first reaches a value of 0.001. Therefore, the transition onset
position was found to be in the neighborhood of X/C ≈ 0.10 based on the measured
Reynolds stress distribution, which also agrees well with the estimated location of
the transition point based on the surface pressure measurements described above.
Since the incoming flow streams could attach to the airfoil upper surface in
general with a very thin separation bubble formed near the airfoil leading edge, no
apparent large-scale flow separation can be found in the flowfield around the airfoil.
′2
′2)
) level of the
As shown in Fig. 8(f), the turbulent kinetic energy (T.K.E. = (u 2U+v
2
∞
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235
flow field around the airfoil was found to be relatively low. As it is expected, the
regions with relatively high T.K.E. values were found to be concentrated in a thin
layer close to the airfoil upper surface when the 14.0 degrees angle of attack is at
the increasing branch of the hysteresis loop.
The flow structures around the airfoil leading edge were found to change significantly when the 14.0 degrees angle of attack was at the decreasing branch of the
hysteresis loop. As visualized clearly from the PIV measurement results given in
Fig. 9, the laminar boundary layer on the airfoil upper surface was found to separate from the airfoil upper surface for good at a location near to the airfoil leading
edge. The instantaneous velocity vectors and corresponding vorticity distribution
show clearly that the separated laminar boundary layer would transit to turbulence
rapidly accompanied by generating strong unsteady vortex structures due to the
Kelvin-Helmholtz instabilities. Compared to the case with the AOA = 14.0 degrees
at the increasing branch of the hysteresis loop (Fig. 8), the separated boundary layer
was found to be “lifted” up far away from the upper surface of the airfoil, which
could not reattach to the airfoil upper surface anymore. Flow separation close to
the airfoil leading edge can be seen very clearly from the ensemble-averaged velocity field and corresponding streamlines of the mean flow, which reveals again that
large-scale flow separation occurs almost on the entire upper surface of the airfoil,
i.e., the airfoil is in stall state, when the 14.0 degrees angle of attack is at the
decreasing branch of the hysteresis loop. The streamline distribution of the mean
flow field shown in Fig. 9(d) elucidate again that the separated boundary layer seems
to try to reattach to the airfoil upper surface near X/C ≈ 0.35. However, the strong
reversing flow from the airfoil trailing edge prevented the separated boundary layer
from reattaching to the airfoil upper surface and kept the airfoil in stall state. The
PIV measurement results suggest that flowfield around the airfoil seemed to be able
to “remember” its past history when the angle of attack was changed inside the
hysteresis loop.
Compared to the case with the AOA = 14.0 degrees at the increasing branch
of the hysteresis loop, the measured normalized Reynolds stress distribution shown
in Fig. 9(e) revealed that turbulent transition of the separated shear layer would
take place earlier when the 14.0 degrees angle of attack is at the decreasing branch
of the hysteresis loop. For example, the streamwise location where the normalized
Reynolds stress first reaches a value of 0.001 was found to move to upstream location
of X/C ≈ 0.03. The size of the regions with high values of normalized Reynolds
stress was found to increase tremendously. The measured turbulent kinetic energy
(T.K.E.) distribution given in Fig. 9(f) revealed that the T.K.E. level of the flowfield
around the airfoil became significantly higher when the AOA = 14.0 degrees was at
the decreasing branch of the hysteresis loop. The regions with higher T.K.E. values
were found to be along the shedding path of the strong unsteady Kelvin-Helmholtz
vortex structures.
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Hui Hu, Zifeng Yang, Hirofumi Igarashi and Matthew Martin
4. Concluding Remarks
An experimental study was conducted to investigate static stall hysteresis of a lowReynolds-number airfoil. The experimental investigation was conducted in a closedcircuit, low-speed wind tunnel with the chord Reynolds number of Re = 162,000.
In addition to mapping surface pressure distribution around the airfoil with pressure sensors, a digital particle image velocimetry (PIV) system was used to make
detailed flow field measurements to quantify the occurrence and behavior of laminar boundary layer separation and transition on the airfoil when stall hysteresis
occurs. The flow field measurements were correlated with the airfoil surface pressure
measurements to elucidate underlying fundamental physics associated with the stall
hysteresis phenomena of low-Reynolds-number airfoils.
The measurement results revealed clearly that, for the same angle of attack in the
hysteresis loop, flow pattern and behavior of the vortex and turbulent flow structures
around the airfoil would be completely different for the cases with the angle at the
increasing branch of the hysteresis loop and those at the same angle of attack but
at the decreasing branch of the hysteresis loop. Incoming flow streams were found
to be able to attach to the airfoil upper surface in general when the angles are at
the increasing branch of the hysteresis loop. A thin separation bubble was found
to form on the upper surface of the airfoil with its length about 10% of the airfoil
chord length and height only about 1% of the chord length. The critical points (i.e.,
separation, transition, and reattachment points) of the separation bubble identified
from the PIV measurements were found to agree well with those estimated based
on the surface pressure measurements. The attached flow pattern resulted in higher
lift and lower drag acting on the airfoil as well as lower Reynolds stress level and
less unsteadiness in the wake of the airfoil.
When the angles of attack are at the decreasing branch of the hysteresis loop,
incoming flow streams were found to separate from the airfoil upper surface for good
at a location quite near to the airfoil leading edge. The turbulence transition of the
separated laminar boundary layer was found to take place much earlier at a further
upstream location accompanied by periodical shedding of strong Kelvin-Helmholtz
vortex structures in the wake of the airfoil. While the separated boundary layer was
found to try to reattach to the airfoil upper surface, the strong reversing flow from
the airfoil trailing edge prevented the separated boundary layer from reattaching
to the airfoil upper surface, thus keeping the airfoil in stall state. As a result, the
lower lift and higher drag acting on the airfoil were found with Reynolds stress and
turbulence kinetic energy levels in the wake of the airfoil increased significantly.
The present study revealed quantitatively that stall hysteresis of low-Reynolds
number airfoils is closely related to the behavior of the laminar boundary layer
separation and transition on the airfoils. The ability of the flow to remember its
past history is suggested to be responsible for the stall hysteretic behavior.
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Acknowledgments
The authors want to thank Mr. Bill Rickard of Iowa State University for his help in
conducting the experiments. The support of National Science Foundation CAREER
program is gratefully acknowledged.
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