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WIND TUNNEL AERODYNAMIC TESTS OF SIX AIRFOILSFOR USE ON SMALL
WIND TURBINES
Michael S. Selig∗and Bryan D. McGranahan†
Department of Aerospace EngineeringUniversity of Illinois at
Urbana–Champaign
Urbana, Illinois 61801
ABSTRACT
This paper presents detailed wind tunnel tests datataken on six
airfoils having application to small windturbines. In particular,
lift, drag and moment mea-surements were taken at Reynolds numbers
of 100,000,200,000, 350,000 and 500,000 for both clean and
roughconditions. In some cases, data was also taken at aReynolds
number of 150,000. The airfoils included theE387, FX 63-137, S822,
S834, SD2030, and SH3055.Prior to carrying out the tests, wind
tunnel flow qual-ity measurements were taken to document the
lowReynolds number test environment, and also oil flowvisualization
data and performance data were takenon the E387 for comparison with
measurements takenat NASA Langley in the Low Turbulence
PressureTunnel. The new results compare favorably with thebenchmark
NASA data. Highlights of the performancecharacteristics of the six
airfoils are then discussed.
INTRODUCTION
This paper documents the aerodynamic character-istics of six
airfoils, which were also examined in acompanion study dealing with
their aeroacoustic prop-erties.1 These projects together were
motivated by twointersecting factors. First, the U.S. Department of
En-ergy, National Renewable Energy Laboratory (NREL),has initiated
research into the aeroacoustics of windturbines, which is an
important design considerationwhen a potentially valuable wind
resource and a popu-lation center coincide. Such an event—the
confluenceof wind technology and people—is increasingly proba-ble
as wind turbines become more efficient and betterable to exploit
lower wind speed sites, which are oftenfound near U.S. load
centers. Improving our under-standing of the aeroacoustics will
help designers ex-ploit advances in noise mitagation design
strategies. It
∗Associate Professor, 306 Talbot Laboratory, 104 S. WrightSt.
email: [email protected]. Senior Member AIAA.
†Graduate Research Assistant, 306 Talbot Lab, 104 S. WrightSt.
email: [email protected]. Student Member AIAA.
Copyright c© 2004 by Michael S. Selig and Bryan D. McGrana-han.
Published by the American Institute of Aeronautics and
As-tronautics, Inc. or the American Society of Mechanical
Engineers,with permission.
is anticipated that having a reliable and self-consistentairfoil
performance dataset may be helpful in validat-ing aeroacoustics
prediction codes in support of suchdesign activities. Second, small
stand-alone wind tur-bines operating in close proximity to
residential areasposed a noise concern. Given that the
aerodynamicefficiency increases with the tip speed and hence
windturbine noise, advances in the development of smallwind
turbines can be envisioned using a suite of com-putational tools
capable of predicting both the aeroa-coustic characteristics and
aerodynamic performance.Thus, an aerodynamic dataset of
representative windturbines airfoils should help pave the way
toward thedevelopment of the necessary design methodologiesneeded
by the small wind turbine industry seeking toimprove efficiency as
well as acceptability.Prior to testing the airfoils for their
performance
data, an extensive study of the wind tunnel flow qual-ity was
carried out. This precursor study includedmeasurements of the
freestream turbulence as well asvariations in dynamic pressure and
freestream flow an-gle across the center region of the test
section. Theresults of these flow quality tests are presented.
Thispaper also includes validation data on the E387 air-foil as
compared with results from NASA Langley.Following this, the test
results on the six airfoils arediscussed.
WIND TUNNEL FACILITYAND MODELS
All experiments were conducted in the University ofIllinois at
Urbana–Champaign (UIUC) subsonic windtunnel (Fig. 1), which has a
nominal test section thatis 2.81-ft high and 4-ft wide. The test
set-up de-picted in Fig. 2 was used for this study.2,3 As seenin
Fig. 2, two 6-ft long Plexiglass splitter plates areinserted 2.8 ft
apart into the test section to isolate theairfoil models from both
the support hardware and thetunnel side wall boundary layers. The
1-ft chord airfoilmodels were inserted horizontally between the
splitterplates with nominal gaps of 0.040–0.080 in. betweenthe end
of the airfoil model and the splitter plates.Performance data were
taken at Reynolds numbers of
pmiglioreAIAA 2004-1188
pmiglioreWIND TUNNEL AERODYNAMIC TESTS OF SIX AIRFOILSFOR USE ON
SMALL WIND TURBINES
pmiglioreMichael S. Selig* and Bryan D. McGranahan**Department
of Aerospace EngineeringUniversity of Illinois at
Urbana--ChampaignUrbana, Illinois 61801
pmigliore**
pmigliore**
pmigliore*
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Fig. 1 UIUC low-speed subsonic wind tunnel.
Fig. 2 Experimental setup (Plexiglass splitterplates and
traverse enclosure box not shown forclarity).
100,000, 200,000, 350,000 and 500,000. In some cases,data was
also taken at a Reynolds number of 150,000.The lift was measured
using a strain gauge load cell,and the drag was determined using
the momentumdeficit method.2 To account for spanwise drag
varia-tions at low Reynolds numbers,4 the drag was obtainedfrom an
average of eight equidistant wake surveys overthe center of the
model so that a 10.5-in. wide spanwas covered. The overall
uncertainty in both the liftand drag measurements was estimated at
1.5%.2,3 Alllift and drag measurements were corrected for
windtunnel interference and validated with data from theNASA
Langley Low Turbulence Pressure Tunnel.2,4–6
The wind tunnel tests included a broad variety ofairfoils that
are summarized in Table 1. It should bementioned that later
suffixes are added to the airfoilnames (e.g. ‘(E)’) and used in the
captions to indicatethe wind-tunnel model versions of those
particular air-foils. For instance, the E387 (E) case is the 5th
modelof the E387 airfoil in the UIUC collection.
Table 1 Airfoils Tested
Airfoil Relevance/Usage
E387 Benchmark Eppler airfoil testedin NASA Langley LTPT
FX 63-137 Aeromag Lakota, SouthwestWindpower H-40, H-80
andcandidate for next-generationsmall wind turbine
S822 AOC/Windlite, Havatex 2000 andcandidate for next-generation
smallwind turbine, patented by DOE NREL
S834 New low-noise, low-Re airfoiland candidate for
next-generationsmall wind turbine, patent pendingby DOE NREL
SD2030 Southwest Windpower Air 403 andAir X turbines
SH3055 Bergey Windpower Excel turbine
The airfoil models were shaped in a computernumerically
controlled milling machine out of Ren-Shape high-density foam,
structurally reinforced,fiberglassed, then sanded and painted. A
coordinate-measuring machine was used to digitize the models.3
The differences between the nominal and measured co-ordinates
were calculated, allowing the computation ofan average accuracy for
each model (mean of the dif-ferences). For the airfoils used in the
current study,the differences between the nominal and measured
co-ordinates are indicated in Fig. 3 underneath the
airfoilnames.
TUNNEL FLOW QUALITYAND VALIDATION
As has been well documented, low Reynolds numberairfoil flows
are highly sensitive to the tunnel flow qual-ity. Consequently,
tunnel flow quality measurementswere taken and documented as
described below.
TURBULENCE INTENSITY MEASUREMENTSThe turbulence intensity was
measured using hot-
wire anemometry. In particular, the hot-wire systemwas a TSI
Incorporated IFA 100 anemometer in con-junction with a TSI Model
1210-T1.5 hot-wire probe.The probe makes use of a 1.5-micron
platinum-coated
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E387 (E)(0.0091 in.)
FX 63−137 (C)(0.0031 in.)
S822 (B)(0.0074 in.)
S834(0.0056 in.)
SD2030 (B)(0.0060 in.)
SH3055(0.0037 in.)
Fig. 3 Airfoils tested and their corresponding av-erage error in
inches for the 12-in. chord modelspresented in this study.
tungsten wire. The probe was mounted in the tun-nel end-flow
orientation with the wire perpendicularto the tunnel floor in order
to measure the axial turbu-lence intensity. A PC equipped with a
data acquisitioncard was used to log the signal from the
anemometer.A HP 35665A Dynamic Signal Analyzer, which per-formed a
FFT (Fast Fourier Transform) analysis, wasemployed to allow the
turbulence spectrum to be mon-itored over a broad range of
frequencies. More detailsof the method are given in Ref. 7.The
turbulence intensity was calculated from data
using a total of 50,000 samples with a sample frequencyof 10,000
Hz. Figure 4 shows the resulting turbulencelevels for both the
tunnel empty case and with thefull measurement apparatus installed.
In general theselevels are considered to be sufficiently low for
takinglow Reynolds number airfoil measurements.
DYNAMIC PRESSURE SURVEYS
The variation in the dynamic pressure in the testsection of the
UIUC low-speed subsonic wind tun-nel was obtained by comparing the
dynamic pressureat a pitot-static probe mounted near the entrance
ofthe splitter plates with that measured by a down-stream probe.
The upstream probe was located atthe centerline of the tunnel in
the spanwise direction
100,000 200,000 300,000 400,000 500,0000.05
0.1
0.15
0.2
0.25
Reynolds Number
Mea
n T
urbu
lenc
e In
tens
ity (
%)
Average Turbulence Intensity (Empty Test Section)
DC CoupledHPF = 0.1HzHPF = 3HzHPF = 10Hz
100,000 200,000 300,000 400,000 500,0000.05
0.1
0.15
0.2
0.25
Reynolds Number
Mea
n T
urbu
lenc
e In
tens
ity (
%)
Average Turbulence Intensity (Test Apparatus Installed)
DC CoupledHPF = 0.1HzHPF = 3HzHPF = 10Hz
Fig. 4 Turbulence intensity at tunnel centerline,empty test
section and with rig in place
(X = 0 in.), 0.97 ft below the centerline of the tun-nel in the
vertical direction (Y = −11.66 in.), and1.323 ft upstream of the
quarter-chord location of theairfoil model when mounted in the test
section. Thedownstream probe was traversed in the X-Y plane
per-pendicular to the freestream and coincident with thequarter
chord. Measurements were made both withthe test section empty and
with the test apparatusinstalled.The measurement plane extended
from 5.5 in. above
the tunnel centerline to 14.5 in. below in the verticaldirection
Y , and from 10.5 in. to the left of the tun-nel centerline to 10.5
in. to the right in the horizontaldirection X. A grid spacing of 1
in. was used for themeasurements, resulting in a total of 462
measurementpoints for each case tested.Figure 5 shows contours of
∆Q for various Reynolds
numbers plotted against its X and Y location for thecase with
the test rig installed. Several observationscan be made. There is a
slight increase in the flowspeed in going downstream. It is likely
that the ve-locity measured at the location of the model is
higherthan the upstream velocity because of the growth ofthe
boundary layer along the splitter plates, ceilingand floor as well
as the blockage that occurs betweenthe splitter plates and the
tunnel sidewalls. This per-centage increase in the flow speed grows
larger as theReynolds number is reduced, which is consistent
withthe thicker wall boundary layers at the lower Reynoldsnumbers.
This rise in the velocity is accounted forin the
airfoil-performance data-reduction procedure.Second, it is observed
that over the region where themodel is located, the net change in
flow speed is rela-tively small. For instance, Fig. 5 shows that at
Re/l =200,000/ft the increase in the flow speed ranges from
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−10 −5 0 5 10
−10
−5
0
5
X (in)
Y (
in)
∆Q (%), Re/l = 100,000/ft
1
1.4
1.4
1.6
1.6
1.6
1.6
1.6
1.6
1.8
1.8
1.8
1.8
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2
2
2
2
2
2
2
2
2.2
2.2
2.42.62.
8
−10 −5 0 5 10
−10
−5
0
5
X (in)
Y (
in)
∆Q (%), Re/l = 200,000/ft
1
1.4
1.4
1.6
1.6
1.6
1.6
1.6
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
2 22
2
2
2.2 2.4.6
−10 −5 0 5 10
−10
−5
0
5
X (in)
Y (
in)
∆Q (%), Re/l = 350,000/ft
0
1
1.2
1.21.2
1.2
1.2
1.4
1.4
1.4
1.4
1.4
1.4
1.6
1.6
1.6
1.6
1.6
1.6
1.8
1.8
1.8
22 2
2
2.2
−10 −5 0 5 10
−10
−5
0
5
X (in)
Y (
in)
∆Q (%), Re/l = 500,000/ft
0
0.2 0.4
0.4
0.40.4
0.4
0.4
0.4
0.6
0.6
0.6
0.6
0.6
0.6
0.8 0.8 0.8
0.80.8
0.8
0.8
1
1
1 1 1
1 1.2
1.4 1.4
Fig. 5 Dynamic pressure variation across test sec-tion with the
test rig installed.
approximately 1.4% to 1.8%, which is a relative differ-ence of
±0.2% in the working range of the test section.As stated in Ref. 8,
it is desirable to have the variationin dynamic pressure in the
working range of the testsection be less than 0.5% from the mean,
i.e. ±0.5%.The results show that the flow is well within the
“ruleof thumb.” A third observation, is the existence of aslight
asymmetry in the flow, noticeable mainly in the+X:−Y quadrant
(bottom right corner in Fig. 5). Theasymmetry is present with the
tunnel empty and withthe test rig in place, hence it is unrelated
to the test rig.Moreover, the lines of constant Q are parallel to
thetunnel floor at X = 0 (centerline), so the effect is neg-ligible
with respect to the performance-measurementquantities in the center
region of the test section.
FLOW ANGULARITY SURVEYSJust as it is important to have uniform
flow velocity
in the wind-tunnel test section, it is equally importantto have
the flow parallel to the axial direction.8 Forthe most part,
pitot-static probes are insensitive toflow angles in the range ±12
deg, so a large flow angleis required to introduce an error in the
dynamic pres-sure measurements. Similarly, large flow angles
arerequired to introduce errors into total head measure-ments.
Apart from pressure measurements, a smallchange in pitch angle,
however, contributes to a changein the effective angle of attack of
the airfoil model andthereby such an error can skew the lift and
drag mea-surements when they are plotted versus the angle
ofattack.The flow angularity in the test section of the UIUC
low-speed subsonic wind tunnel was measured using anAeroprobe
Corporation Model S7TC317 7-hole probeshown in Fig. 6. The probe
has a total-head port lo-
Fig. 6 Illustration of the 7-hole probe used forflow angle
measurements.
cated at the center, and six chamfered ports equallyspaced
circumferentially around the center. The probewas mounted in the
wind tunnel on a special two-beamsting attached to the
computer-controlled LinTech tra-verse. The flow measurements were
all taken with thetest rig installed in the wind-tunnel test
section, with-out the model. A more detailed description of the
useof the 7-hole probe is found in Ref. 9.The 7-hole probe was
traversed in a plane perpen-
dicular to the freestream flow over the range fromX = ±6.5 in.
to Y = ±10 in. The traverse wasnot extended to the edges of the
test section due toequipment limitations. Traversing this central
corewas acceptable because one would expect to find thelargest flow
angle variation in the center of the test sec-tion rather than
along the walls were at a minimumthe flow is parallel to the wall
(yaw or pitch is therebyzero). A grid spacing of 1 in. was used,
resulting ina grid of 252 sample locations for each case tested.The
7-hole probe tip was located approximately 1.5chord lengths behind
the quarter chord of the airfoilmodel. To set the tunnel speed, one
pitot-static probewas located at X = 0 in., Y = −11.66 in. For
redun-dancy an additional probe was located at X = 5 in.,Y = −11.66
in. Both pitot-static probes were mountedat the same streamwise
location, 1.323 ft upstream ofthe location of the quarter chord of
the airfoil model.The results shown in Fig. 7 indicate that the
total
flow angle (pitch and yaw combined) were smallest atRe =
500,000, becoming more pronounced at lowerReynolds numbers. The
pitch angle measurement (notshown) was generally between 0 and 0.2
deg (±0.1 deg)across the working region of the test section where
theairfoil model is located. According to Ref. 8, a flowangle
variation of ±0.2 deg is acceptable, but ±0.1 degor better is the
preferred. The current measurementsmeet this latter desired level
of flow quality.
AIRFOIL DATA VALIDATION
In this section, data taken on the E387 is com-pared with
results from NASA Langley in the Low-Turbulence Pressure Tunnel
(NASA LTPT).5,6 Fourtypes of data are compared: surface oil flow
visualiza-tion, lift data, moment data and drag polars. In this
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−5 0 5−10
−5
0
5
10
X (in)
Y (
in)
Combined Angle (deg), Re/l = 100,000/ft
0.1
0.1
.1
.2
0.2
0.2
0.2
.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3 0.3
0.30.
3
0.3
0.4
0.4
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0.4
0.4
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0.50.5
0.6
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0.6
0.6 0.70.80.
91
−5 0 5−10
−5
0
5
10
X (in)
Y (
in)
Combined Angle (deg), Re/l = 200,000/ft
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
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0.3
0.3
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0.4 0.4
0.40.4
0.4
.4
0.5
0.5
0.5
0.5
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0.6
0.7
0.7
0
0.8
0.91
1
−5 0 5−10
−5
0
5
10
X (in)
Y (
in)
Combined Angle (deg), Re/l = 350,000/ft
.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.3 0.3
0.3
0.3
0.4
0.4
0.4 0.4
0.5
0.5
0.6
0.6
0.7
0.8 0.90.9
1
1
−5 0 5−10
−5
0
5
10
X (in)
Y (
in)
Combined Angle (deg), Re/l = 500,000/ft
.1
0.1
0.1
0.1
0.20.2
0.2
0.2
0.2
0.2
.20.2
0.2
0.2
0.20.3
0.3
0.3
0.3
0.30.3
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.50.60.
70.8
0.8
0.9 1
Fig. 7 Combined pitch and yaw angle across testsection with the
rig installed.
order, these data are presented and discussed below.
SURFACE OIL FLOWVISUALIZATIONThe surface oil flow visualization
technique made
use of a fluorescent pigment (Kent-Moore 28431-1) sus-pended in
a light, household-grade mineral oil thatwas sprayed onto the
surface of the model using aPaasche Model VL double-action
airbrush. The modelwas then subjected to 20–45 min of continuous
wind-tunnel run time at a fixed Reynolds number and angleof attack.
During this period, the oil moved in thedirection of the local flow
velocity at a rate dependenton the balance of forces dictated by
the boundary-layer skin friction coefficient Cf and surface
tensionof the oil. As a result, regions of the flow could
beidentified and compared with the NASA Langley Low-Turbulence
Pressure Tunnel (LTPT) data.5,6
Figure 8 shows a photograph of the surface oil flowpattern made
visible under fluorescent light. Figure 9conceptually illustrates
the connection between thesalient surface oil flow features and the
skin frictiondistribution. Note that the skin friction
distribution,though conceptual, is consistent with the results
ofmany computational studies.10–15 The authors be-lieve that the
unique shape of the Cf distribution,in particular the strong
negative Cf spike, has yet tobe experimentally verified (as no
experimental datacould be found); however, the oil flow patterns
ob-served seem to confirm the validity of the negative Cfspike
concept.Several important flow features can be identified and
related to the underlying skin friction and surface ten-sion
forces. In Fig. 8, laminar flow is seen to existfrom the leading
edge to approximately 0.40c. The
Fig. 8 Representative upper-surface oil flow visu-alization on
the E387 (E), Re = 300,000, α = 5 deg.
oil streaks are characteristically smooth in this regionuntil
laminar separation occurs, which is identified inFig. 9 as the
point where Cf = 0. (Note again thatthe flow shown in Fig. 9 is
conceptual, and it is notintended to match Fig. 8 in detail.)
Downstream ofthe point of laminar separation, the original
airbrushed“orange-peel” texture that existed prior to running
thetunnel still exists, indicating that the flow is stagnantin this
region. This stagnant flow is consistent with theknown behavior of
flow in the interior leading-edge re-gion of a laminar separation
bubble. As sketched, theCf magnitude in this region is quite small
due to thelow flow speed and negative in sign due to reverse flowat
the surface.In the presence of a laminar separation bubble,
tran-
sition takes place in the free shear layer above thesurface of
the airfoil. Downstream of this point, reat-tachment occurs in a
process that is known to beunsteady as vortices are periodically
generated andimpinge on the airfoil surface.15,16 These
unsteadyvortices colliding with the surface lead to a
relativelyhigh shear stress that tends to scour away the oil atthe
mean reattachment point, pushing oil upstreamor downstream of the
reattachment point. As seen inFig. 9, the reattachment line is less
distinct becausethe bulk of the oil has been pushed away revealing
theunderlying black airfoil surface. In Fig. 8, the tunnelrun time
was long enough that the reattachment lineat 0.58c is even harder
to see than in Fig. 9. In theoriginal high-resolution color
photographs that werearchived, this feature is clear and easily
quantifiable.Downstream of reattachment the boundary layer is
turbulent. The high skin friction in this area relativeto the
laminar boundary layer upstream tends to clearaway more oil, again
making the black surface down-stream more visible than in the
upstream region.The remaining visible feature of the flow is a
line
where the oil tends to pool, termed here the “oil accu-mulation
line.” This intrinsic feature of the oil flow has
-
Fig. 9 Conceptual illustration of the relation-ship between the
surface oil flow features and skinfriction distribution in the
region of a laminar sep-aration bubble plotted against the airfoil
arc lengthcoordinate s/c.
no direct connection to laminar flow, reverse flow inthe bubble,
or the ensuing turbulent flow downstream.However, it does indicate
a relatively important fea-ture of the flow with regard to the
nature of the skinfriction in the vicinity of reattachment. The
negativeCf spike shown in predictions and sketched conceptu-ally in
Fig. 9 is most likely responsible for generatingthe oil
accumulation line. Assuming that this is thecase, the fluctuating
high skin friction that is gener-ated over the unsteady
reattachment zone will tend topush the oil upstream ahead of the
mean reattachmentpoint. At some location on the airfoil, however,
the oilmoving upstream will experience a balance of forcesbetween
the rapidly weakening skin friction force andthat of the surface
tension and oil adhesion that is re-tarding its motion. At the
location where these twoforces balance, the oil accumulates into a
line that be-comes the most distinguishable feature of the oil
flow.Consequently, it is speculated that this flow featureis
sometimes mislabeled as “reattachment” as will bediscussed
below.Figures 10 and 11 show the previously described flow
features compared with data obtained at the NASALangley LTPT. In
the low drag range between −2 degand 7 deg angle of attack, the
agreement in the laminarseparation line between the NASA LTPT and
UIUCdata sets is mostly within 0.01c to 0.02c, which isvery near
the uncertainty of the method. As previ-ously discussed, the next
feature to appear is the oilaccumulation line. The UIUC oil
accumulation lineagrees fairly well with the “reattachment” line
identi-
fied in the NASA experiment. It is believed, however,that based
on the previous reasoning this label givenin the original
reference6 is a misnomer. Had theUIUC tests been performed for a
longer duration, thereattachment zone would be scoured clean with
no dis-tinguishing feature, leaving only the oil accumulationline
to be labeled as the “reattachment line,” knowingthat one must
exist. Hence, it is speculated here andin prior UIUC work3 that
such a scenario took placein the NASA study, i.e. the
oil-accumulation line wasmisinterpreted as the reattachment
line.Guided by this working assumption, the two re-
sults again are in good agreement. It must be stated,however,
that the oil accumulation line might changeslightly from one
facility to the next since it is dic-tated by a force balance that
depends on the skinfriction forces of the boundary layer relative
to theadhesion forces of the particular oil used. The predic-tions,
however, show that the negative Cf region hasa sharp upstream edge,
which is most likely where theoil accumulates regardless of the
surface tension char-acteristics. Differences in the oil
accumulation line dueto differences in the type of oil used are
therefore be-lieved to be small. The good comparisons betweenUIUC
and Langley data tend to support this assump-tion.Moving further
downstream, the UIUC reattach-
ment data is plotted, but unfortunately no directcomparison can
be made because of the ambiguitywith respect to the reattachment
data reported in theNASA study. However, close inspection of the
datasuggests that at a Reynolds number of 300,000 andbetween 5 deg
and 7 deg angle of attack, the LTPTline merges with the UIUC
reattachment line. Per-haps in this case, the measurements at
Langley wereindeed the reattachment points.The conclusion to be
drawn from this comparison
of the oil flow visualization results is that the twofacilities
produce airfoil flows that are in close agree-ment. Moreover, if
the arguments regarding the oilaccumulation line are correct, then
the agreement canbe considered excellent and within the uncertainty
ofthe measurements.
LIFT DATA
Lift and moment data comparisons between theUIUC and LTPT data
are shown in Fig. 12. Discrep-ancies can be seen for a Reynolds
number of 100,000as well as in the stalled regime. For Re = 100,000
dif-ferences are most likely attributable to measurementaccuracy.
In stall for α > 12 deg, taking the Langleydata as the
benchmark, the UIUC data differs mostlikely as result of
three-dimensional end effects. Nev-ertheless, the results show good
agreement over the
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−2
0
2
4
6
8
10
12
14
16
18
x/c
α (deg)
E387UIUC
Re = 200,000
Laminar separationTransitionOil
accumulationReattachmentTurbulent separation
E387LTPT
Re = 200,000
Laminar separationTransitionOil
accumulationReattachmentTurbulent separation
Fig. 10 Comparison of major E387 (E) upper-surface flow features
between UIUC and LTPT forRe = 200,000.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−2
0
2
4
6
8
10
12
14
16
18
x/c
α (deg)
E387UIUC
Re = 300,000
Laminar separationTransitionOil accumulationReattachment
E387LTPT
Re = 300,000
Laminar separationTransitionOil accumulationReattachment
Fig. 11 Comparison of major E387 (E) upper-surface flow features
between UIUC and LTPT forRe = 300,000.
normal unstalled operating range, and this agreementimproves
with higher Reynolds number.
DRAG DATA
Figure 13 shows a comparison between UIUC andNASA LTPT drag data
for the Reynolds numbersof 100,000, 200,000, 300,000 and 460,000.
To beginthis discussion, data at a Reynolds number of 200,000and
300,000 are considered. For these cases, the oilflow results were
in close agreement as well as thelift data which taken together
suggest that the dragdata should likewise be in good agreement.
Indeed, forRe = 200,000, the agreement is quite acceptable.
How-ever, Re = 300,000 the agreement is not as good. Asfor the
other cases, for a Re = 460,000, the agreementimproves, while for
Re = 100,000, there is less agree-ment. When these cases are
studied in more detail, itis seen that the edges of the drag polar
are in quiteclose agreement for each case, with the Re =
100,000perhaps being the exception.There can be many reasons for
the observed dis-
crepancies, not the least of which is the fact thatat low
Reynolds numbers the drag data when deter-mined from downstream
wake measurements variesalong the span—the further downstream, the
morevariation. The current measurements were taken 1.25chord
lengths downstream of the trailing edge, whilethose in the NASA
study were taken 1.5 chord lengthsdownstream. Because of this
variation in spanwisedrag, ideally many wake profile measurements
shouldbe taken along the span and the resulting drag co-efficients
summed and averaged. This approach ofperforming multiple wake
surveys was taken in the cur-rent study (as mentioned previously
eight wake surveyswere taken), but in the NASA study wake rake
datawas taken at only one station for the purpose of acquir-ing the
full polar data that was reported. However,some limited spanwise
data was taken in the NASAstudy, and the degree of spanwise
variation observedis quite similar to that found in the current
study.7
Consequently, the discrepancies in part must be re-lated to the
variation in drag. In the NASA study,had data been taken at many
stations, it is likely thatbetter agreement would be observed.For
the Reynolds number of 100,000, which was not
critical to the current investigation, the discrepanciesare
larger. This result cannot be attributed solely tospanwise drag
variation. Figure 13 shows that at aCl = 0.7 and Re = 100,000, the
eight Cd data pointsobtained from the eight wake measurements fall
nearlyone on top of the other. Therefore, the spanwise vari-ation
in drag is small on a percentage basis, and asimilar variation in
Cd for this particular case was seenin the NASA data. Consequently,
for Re = 100,000
-
−10 0 10 20−0.5
0.0
0.5
1.0
1.5
α (deg)
Cl
E387 Re = 100,000
UIUC Lift
UIUC Moment
LTPT Lift
LTPT Moment
Cm
0.1
0.0
−0.1
−0.2
−0.3
−10 0 10 20−0.5
0.0
0.5
1.0
1.5
α (deg)
Cl
E387 Re = 200,000
UIUC Lift
UIUC Moment
LTPT Lift
LTPT Moment
Cm
0.1
0.0
−0.1
−0.2
−0.3
−10 0 10 20−0.5
0.0
0.5
1.0
1.5
α (deg)
Cl
E387 Re = 300,000
UIUC Lift
UIUC Moment
LTPT Lift
LTPT Moment
Cm
0.1
0.0
−0.1
−0.2
−0.3
−10 0 10 20−0.5
0.0
0.5
1.0
1.5
α (deg)
Cl
E387 Re = 460,000
UIUC Lift
UIUC Moment
LTPT Lift
LTPT Moment
Cm
0.1
0.0
−0.1
−0.2
−0.3
Fig. 12 Comparison between UIUC and LTPT E387 lift and moment
coefficient data for Re = 100,000,200,000, 300,000, and
460,000.
-
the cause for the bulk of the difference in the dragmeasurements
must be something other than spanwisedrag variation.When sources of
error were being considered to ex-
plain the discrepancies, several factors were ruled outin light
of the excellent agreement in surface oil flowvisualization and
also lift and moment data. Of thosethat remained, no sources of
uncertainty in the cur-rent data lingered after investigation.
Thus, the stateof the agreement for the Reynolds number of
100,000remains unexplained. It is recognized that the sourceof this
discrepancy might likely relate to some of thediscrepancies for the
higher Reynolds number cases aswell. Nevertheless, the agreement
overall is good, es-pecially in light of past historical
comparisons of lowReynolds number airfoil data, which vary
widely.2,17
Regarding the accuracy of the current data overall,this section
has made several important points thatshould instill confidence in
the data presented in thispaper. First, it was shown that surface
oil flow dataobtained on the E387 airfoil exhibited excellent
agree-ment with NASA LTPT data for Re = 200,000 and300,000. Second,
current lift data was shown to havegood agreement with LTPT data
for all Reynolds num-bers up to stall, after which point
three-dimensionalend effects and unsteady aerodynamics produced
slightdiscrepancies. Third, the pitching moment data wasshown to
agree well with LTPT data over a broadrange of angles of attack.
Lastly, in support of thethree previous conclusions, the drag data
showed goodagreement, with some discrepancies yet to be fully
ex-plained.
RESULTS AND DISCUSSION
In the remainder of this paper, the performancecharacteristics
of each of the airfoils are discussed indetail. Rather than
organizing this discussion by com-menting on broad categories of
various effects, insteadthe airfoils are discussed in the order
presented inFig. 3 (alphabetically).It should also be stated from
the outset that each
airfoil presented here was designed with unique anddifferent
constraints and desired performance charac-teristics in mind.
Consequently, the airfoils collectivelyrepresent a broad range of
performance characteristicsand geometric properties. Hence, to
compare directlythe performance of one airfoil to the next and
declareone airfoil better than another would be
misleading.Therefore, again, the focus will be on highlighting
in-teresting and important performance characteristicswhile leaving
design decisions and the establishmentof various figures of merit
to the wind turbine bladedesigner whose task goes beyond the scope
of topicsdiscussed here.
Fig. 14 Boundary layer trip geometry used to sim-ulate the
effects of leading edge debris and errosion(dimensions are in
inches).
Finally, to simulate the effects of roughness causedby
leading-edge debris and errosion, the airfoils weretested with
three-dimensional zigzag boundary-layertrips afixed to the upper
and lower surfaces near theleading edge. In particular, the
upper-surface andlower-surface trips were located at 2% and 5%
chord,respectively. These data are discussed along with the“clean”
airfoil data, that is, data taking on the air-foils without
boundary layer trips. Figure 14 shows adrawing of the
boundary-layer trip used in this study.It is denoted as “zigzag
trip type F” because it is the6th different zigzag trip geometry
tested at UIUC.
E387
The E387 airfoil was designed in the early 1960sby Richard
Eppler for model sailplanes where it wasquickly successful and is
still used. Beyond this, ithas taken on the additional role of
becoming a bench-mark section used to compare low Reynolds
numberairfoil measurements from one wind tunnel facilitywith
another. In fact, the E387 airfoil is likely themost widely tested
low Reynolds number section hav-ing been tested at Delft in the
Netherlands, Stuttgart,Princeton, NASA Langley and UIUC prior to
and in-cluding the current tests. Having already discussed
thecomparison between the UIUC data and that of NASALangley, the
focus in this chapter is on elucidating thelow Reynolds number
performance characteristics.Figures 15 and 16 show the drag polars
and the
lift and drag characteristics at Reynolds numbersof 100,000,
150,000, 200,000, 300,000, 460,000, and500,000. [The Re = 460,000
case was added for com-parison with Langley.] For the lowest
Reynolds num-ber of 100,000, the most prominent manifestation of
alaminar separation bubble is observed in the drag po-lar. Between
the limits of the low drag range, there isan increase in drag
associated principally with a lam-inar separation bubble. In the
vicinity of corners ofthe low drag range, the laminar separation
bubble isshort or nonexistent in which case the drag is not ashigh.
However, as the angle of attack is increased fromthe lower corner,
the adverse pressure gradient on theupper surface becomes stronger
and as a result thebubble drag grows until the drag is a maximum
neara lift coefficient of 0.7 (α ≈ 3 deg). Beyond this point,
-
0.00 0.01 0.02 0.03 0.04 0.05−0.5
0.0
0.5
1.0
1.5
Cd
Cl
LTPT
UIUC
E387 Re = 100,000
0.00 0.01 0.02 0.03 0.04 0.05−0.5
0.0
0.5
1.0
1.5
Cd
Cl
LTPT
UIUC
E387 Re = 200,000
0.00 0.01 0.02 0.03 0.04 0.05−0.5
0.0
0.5
1.0
1.5
Cd
Cl
LTPT
UIUC
E387 Re = 300,000
0.00 0.01 0.02 0.03 0.04 0.05−0.5
0.0
0.5
1.0
1.5
Cd
Cl
LTPT
UIUC
E387 Re = 460,000
Fig. 13 Comparison between UIUC and LTPT E387 drag coefficient
data for Re = 100,000, 200,000,300,000, and 460,000.
the size of the bubble begins to decrease (see Fig. 21of Ref.
12), which results in lower drag until the uppercorner of the polar
is reached where transition takesplace on the surface without a
drag producing bub-ble being present. As the Reynolds number
increases,the advantages of higher Reynolds number as well asa
reduction in the length of the bubble (due to earliertransition,
see Fig. 8) leads to correspondingly lowerdrag.
As mentioned, for this airfoil and all of the others, azigzag
boundary layer trip was added on the top andbottom surfaces near
the leading edge to simulate theeffects of roughness caused by
debris and errosion thatoccurs on wind turbine blades over time. In
general the
main effect of the trip is to promote transition
shortlydownstream of the trip. If a bubble is present in theclean
case, the trip has the effect of shortening thelaminar separation
bubble. When there is no bubble,transition is forced to occur
sooner than it otherwisewould.
In terms of performance, the beneficial effect ofshortening the
bubble and hence lowering the drag isto a some degree offset by the
increased length of tur-bulent flow. The net effect can be either
beneficialwhen the bubble is otherwise large or a hinderencewhen
the bubble is small or not present at all. As aresult, the
performance with boundary layer trips usedat low Reynolds numbers
is often complex.
-
For the E387, the effects of the trip are clearly seenin the
drag polars shown in Figs. 15 and 16. ForRe = 100,000, the drag is
overall reduced due to theshortened laminar separation bubble. In
the middleof the polar, the kink where the drag begins to
reducewith increasing angle of attack occurs at a lower lift
co-efficient (Cl ≈ 0.55) due to transition being promotedby the
boundary layer trip in addition to the pressuregradient effect that
is beneficial in both the clean andtripped cases.The effects of the
trip are also apparent in the lift
curves.7 For the clean case at Re = 100,000, the liftcurve is
offset slightly below the curves for the higherReynolds numbers.
This offset is caused by a decam-bering effect that results from
the added displacementthickness produced by the large bubble. When
thebubble is reduced in size by using a trip, this dis-placement
thickness effect is smaller, and the lift curvefor Re = 100,000
nearly coincides with the higherReynolds number cases that have
smaller bubbles.For Re = 200,000 with the boundary layer trip,
only
at a lift coefficient of ≈ 0.47 is the drag lower than theclean
case. Thus, for this condition, the tradeoff be-tween having lower
bubble drag and higher turbulentskin friction drag leads to lower
net drag, while forall other points the added turbulent skin
friction dragoutweighs the reduction in the bubble drag,
resultingin higher drag with the trip. This tradeoff leading
tohigher drag is particularly true for the higher Reynoldsnumber
cases.Finally, from the lift curves presented in Ref. 7, it
is interesting to note that there is a negligible drop inthe
maximum lift coefficient due to roughness effectsfor this airfoil.
This results from transition occurringvery near the leading edge
prior to reaching the airfoilmaximum lift coefficient. Thus, at
maximum lift theflow on the upper surface for the most part
behavesthe same whether or not there is a trip, and hence thestall
performance has little dependence on the pres-ence of the trip.
This general understanding of theconnection between the airfoil
maximum lift and tran-sition, which is discussed in Ref. 18, can be
used toprovide insight into the case when at stall there existsa
leading edge separation bubble, which is what hap-pens at low
Reynolds numbers. In such a case, theboundary layer trip can be
completely or partially im-mersed in the recirculating zone of the
bubble. Whenthis occurs, the airfoil stall can be quite insensitive
toa discrete roughness element such as the type testedin this
study.
FX 63-137
This airfoil was designed by F.X. Wortmann for theLiver Puffin
human-powered aircraft. It has since been
used for many low Reynolds number applications onaccount of its
high-lift, soft-stall characteristics in ad-dition to the overall
good performance. In particular,in the small wind turbine arena, it
has been used byAeromag (Lakota wind turbine) and Southwest
Wind-power (H-40 and H-80 wind turbines) and the nowdefunct
Worldpower Technologies.The original coordinates for this section
as well as
several other early Wortmann sections19 are not ana-lytically
smooth presumably due to a small numericalerror in the design
method. As described in Ref. 20,the original coordinates were
smoothed for use in com-putations, and those coordinates have been
used in thisstudy.As deduced from the high camber, this airfoil
should
be expected to produce considerably more lift thanthe E387.
Indeed, as shown in Fig. 17, the FX 63-137produces a Cl,max of
approximately 1.7. However, forRe = 100,000, the airfoil suffers
the consequences of alarge laminar separation bubble. In fact at
the lowerangles of attack, it is likely that the bubble does
notclose on the airfoil, but instead extends into the wake.Two
observations support this assumption. First, thelift curve at Re =
100,000 for low angles of attackfalls considerably below the curves
for higher Reynoldsnumbers. Second, for the same low Reynolds
numbercondition, the drag is quite high. At an angle of attackof
approximately 4 deg, the situation improves as thebubble begins to
attach to the airfoil. The lift increasesand the drag is
correspondingly reduced.This airfoil along with the S822 and S834
was tested
at an intermediate Reynolds number of 150,000 toobtain more
resolution in the low Reynolds numberrange where the drag changes
dramatically. As seenin Fig. 17, a large drag reduction is observed
for theRe = 150,000 case. Concurrent with this, the largeoffset in
the lift curve is absent. Both of these obser-vations indicate a
reduction in the size of the laminarseparation bubble vs. the Re =
100,000 case. Aswould be expected the performance continues to
im-prove with higher Reynolds number.When boundary layer trips are
applied, the perfor-
mance follows trends similar to those described for theE387.
First, for Re = 100,000, the effects of the bubbleare mitigated as
seen by the slight rise in the lift curveand by the reduction in
drag. For the higher Reynoldsnumbers, the polars tend to collapse
onto an envelope,which indicates that the flow on the upper surface
issimilar indicating early transition and the absence ofa laminar
separation bubble. For points that fall oneither side of this
envelope, a bubble still exists.In the polars, there is an
interesting trend reversal
where the drag first decreases and then increases asthe Reynolds
number is increased for a fixed angle of
-
attack. One instance of this is seen for an angle ofattack of 4
deg corresponding to a lift coefficient ofapproximately 0.7. This
same type of behavior wasseen for the E387 at an angle of attack of
1 deg (Cl ≈0.47). As previously described, there is first a
dragreduction due to a shortening of the bubble and thena drag rise
due to the added turbulent flow as theReynolds number is increased.
This same behavior canbe indentified in the performance of all of
the trippedairfoil polars.Other items to note include the
following. Unlike
the E387 airfoil, the maximum lift performance ofthe FX 63-137
suffers from the addition of simulatedroughness. Overall the drop
in Cl,max is 0.2. An-other difference is that while the E387 had a
highlyunsteady stall leading to a sharp break, the FX
63-137exhibited a soft stall with little unsteadiness. Finally,the
pitching moment curves7 unlike the E387 do notshow nearly constant
Cm,c/4 over the low drag range.Instead, the nose down moment is
gradually reducedwith increasing angle of attack. This behavior is
mostlikely produced by two phenomenon. First, a decam-bering effect
results from the displacement thicknessthat grows with increasing
angle of attack and thehigher drag that results. Second, and
probably moredominant, is the added aft load that results from
thepressure distribution produced by the laminar separa-tion
bubble. For this airfoil the bubble starts far aftand migrates
toward the leading edge with angle of at-tack; whereas, for the
E387 the upper surface bubblemoves over a shorter distance.
S822 AND S834
As described in Ref. 20, the S822 and S834 wereboth developed by
NREL for use on small wind tur-bines and are now available under
license. The S822airfoil has been used on the AOC/Windlite and
Hava-tex21 small wind turbines. Briefly, the S822 and S834were
designed for the outer blade span of rotors hav-ing diameters in
the range 3–10 meter and 1–3 meter,respectively. The newer S834 was
designed for low-noise, which was not a consideration in the design
ofthe S822 section.The performance of these airfoils is shown
in
Figs. 19, 20, 21, and 22. Many of the general char-acteristics
previously described are exhibited by thesetwo airfoils.
Differences in the details are of course dic-tated by the
associated design goals that collectivelylead to the resulting
performance discussed below.For both airfoils, an often
characteristic high-drag
knee in the drag polar due to the presence of a lam-inar
separation at the lower Reynolds numbers is ob-served. The
associated nonlinearities (offsets) in thelift curves are also
seen, except for these airfoils, as
compared with the Wortmann section, the offsets oc-cur for Re =
100,000 and 150,000 as well as 200,000 toa slight extent. This
behavior is also reflected in thedrag polars where the high-drag
knee is more exagger-ated than that for the FX 63-137.Adding the
zigzag boundary layer trips to both air-
foils yields lower drag at the lower Reynolds numbersas would be
expected from the past cases examined.Also, as would be expected,
the nonlinearities seen inthe lift curves are mitigated somewhat by
the bound-ary layer trips. However, the boundary layer trip onthe
upper surface is not large enough to completelyeliminate the bubble
for Re = 100,000 where over a2 deg range in the middle of the polar
the lift increasesnonlinearly (∆Cl ≈ 0.5) for both airfoils.
The S834, being designed for smaller rotors, wasdesigned for
lower Reynolds numbers. This trend isapparent in the drag polars
where it is observed thatthe S834 has better performance than the
S822 at lowReynolds numbers. The differences are mostly slightas
one might expect from the similarities in the geome-tries and
pressure distributions.7
For both airfoils, unsteadiness at stall prevented tak-ing high
angle of attack data for Re = 500,000. Thedegree of the
unsteadiness during the tests was ob-served to be somewhat less
than that for the E387.
SD2030This Selig/Donovan airfoil presented in Ref. 17 was
originally designed for model sailplanes. It has sincebeen used
on the Southwest Windpower Air 403 andAir X small wind turbines.
Figures 23 and 24 showthe performance characteristics.As compared
with the other airfoils discussed, this
airfoil has quite low drag at the expense of a nar-rower drag
polar. A high-drag knee is present forRe = 100,000; however, the
peak drag at the kink ismuch lower than that seen for the other
airfoils tested.This low drag is achieved by having a long
transitionramp, or “bubble ramp,”17 that leads to a thin
laminarseparation bubble. The causes for other general effectsseen
in the figures have been previously explained.Of the six airfoils
tested, this airfoil displayed the
most unsteadiness in stall, and this limited the angleof attack
range for the Re = 500,000 case.
SH3055The Selig/Hanley airfoil (see Figs. 25 and 26), de-
rived from prior SH/Bergey designs, is intended fora 7-meter
diameter variable-speed wind turbine to bemanufactured by Bergey
WindPower, Co. For the low-est Reynolds number case (Re = 100,000),
there is aconsiderable drop in lift as compared with the
higherReynolds number cases. This drop and associated highdrag is
likely caused by a laminar separation bubble
-
that does not reattach to the airfoil over the major-ity of the
lift range. Moreover, at the lowest angles ofattack tested, it is
speculated that the lower surfaceof the airfoil is stalled as well,
which further decam-bers the section. For the higher Reynolds
numbers,the performance improves as was seen with past ex-amples.
Boundary layer trips applied to the airfoillead to improved
performance for Re = 100,000, butat higher Reynolds numbers the
performance is mostlyhandicapped as has been observed with the
other sec-tions. Finally, for this airfoil, the stall behavior
wasquite gentle.
SUMMARY
An extensive database of performance characteris-tics on several
low Reynolds number airfoils applicableto small wind turbines has
been documented and dis-cussed. Prior to the collection of these
data, an exten-sive wind tunnel flow quality study was performed
tovalidate the test environment. Moreover, the data ac-quisition
and reduction procedures were validated bycomparing UIUC data on
the E387 airfoil with thattaken at NASA Langley. These data
compliment acompanion study that focused on the aeroacoustics
ofthese airfoils. Collectively the performance data pre-sented in
this paper and the related aeroacoustic datashould aid designers in
balancing the tradeoffs betweenrotor noise and performance.
ACKNOWLEDGEMENTS
The authors wish to thank Dr. Paul Migliore, tech-nical monitor,
of the National Renewable Energy Lab-oratory for his helpful input
and guidance during thecourse of this research. Also, Yvan Tinel,
Tinel Tech-nologies, is thanked for his skillful and meticulouswork
in making the six wind tunnel models presentedin the study.
Appreciation is extended to Dr. AndyP. Broeren and Biao Lu (UIUC)
for their assistance inhelping take the tunnel flow quality data.
Finally, adebt of gratitude is owed to Benjamin A. Broughton(UIUC)
for his dedication in helping to ensure thequality of the data
acquisition and reduction method-ology used to obtain the
performance data which formsthe central core of this work.
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-
0.00 0.01 0.02 0.03 0.04 0.05−0.5
0.0
0.5
1.0
1.5
Cd
Cl
Re = 100,000
Re = 200,000
Re = 300,000
Re = 350,000
Re = 460,000
Re = 500,000
E387 (E)
−10 0 10 20−0.5
0.0
0.5
1.0
1.5
2.0
α (deg)
Cl
Fig. 15 Drag polar for the E387 (E).
0.00 0.01 0.02 0.03 0.04 0.05−0.5
0.0
0.5
1.0
1.5
Cd
Cl
Re = 100,000
Re = 200,000
Re = 350,000
Re = 500,000
E387 (E)u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F (h/c =
0.11%)
−10 0 10 20−0.5
0.0
0.5
1.0
1.5
2.0
α (deg)
Cl
Fig. 16 Drag polar for the E387 (E) with trip type F.
-
0.00 0.01 0.02 0.03 0.04 0.05 0.0
0.5
1.0
1.5
2.0
Cd
Cl
Re = 100,000
Re = 150,000
Re = 200,000
Re = 350,000
Re = 500,000
FX 63−137 (C)
−10 0 10 20 0.0
0.5
1.0
1.5
2.0
2.5
α (deg)
Cl
Fig. 17 Drag polar for the FX 63-137 (C).
0.00 0.01 0.02 0.03 0.04 0.05 0.0
0.5
1.0
1.5
2.0
Cd
Cl
Re = 100,000
Re = 150,000
Re = 200,000
Re = 350,000
Re = 500,000
FX 63−137 (C)u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F
(h/c = 0.11%)
−10 0 10 20 0.0
0.5
1.0
1.5
2.0
2.5
α (deg)
Cl
Fig. 18 Drag polar for the FX 63-137 (C) with trip type F.
-
0.00 0.01 0.02 0.03 0.04 0.05−1.0
−0.5
0.0
0.5
1.0
1.5
Cd
Cl
Re = 100,000
Re = 150,000
Re = 200,000
Re = 350,000
Re = 500,000
S822 (B)
−10 0 10 20−1.0
−0.5
0.0
0.5
1.0
1.5
2.0
α (deg)
Cl
Fig. 19 Drag polar for the S822 (B).
0.00 0.01 0.02 0.03 0.04 0.05−1.0
−0.5
0.0
0.5
1.0
1.5
Cd
Cl
Re = 100,000
Re = 150,000
Re = 200,000
Re = 350,000
Re = 500,000
S822 (B)u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F (h/c =
0.11%)
−10 0 10 20−1.0
−0.5
0.0
0.5
1.0
1.5
2.0
α (deg)
Cl
Fig. 20 Drag polar for the S822 (B) with trip type F.
-
0.00 0.01 0.02 0.03 0.04 0.05−1.0
−0.5
0.0
0.5
1.0
1.5
Cd
Cl
Re = 100,000
Re = 150,000
Re = 200,000
Re = 350,000
Re = 500,000
S834
−10 0 10 20−1.0
−0.5
0.0
0.5
1.0
1.5
2.0
α (deg)
Cl
Fig. 21 Drag polar for the S834.
0.00 0.01 0.02 0.03 0.04 0.05−1.0
−0.5
0.0
0.5
1.0
1.5
Cd
Cl
Re = 100,000
Re = 150,000
Re = 200,000
Re = 350,000
Re = 500,000
S834u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F (h/c =
0.11%)
−10 0 10 20−1.0
−0.5
0.0
0.5
1.0
1.5
2.0
α (deg)
Cl
Fig. 22 Drag polar for the S834 with trip type F.
-
0.00 0.01 0.02 0.03 0.04 0.05−0.5
0.0
0.5
1.0
1.5
Cd
Cl
Re = 100,000
Re = 200,000
Re = 350,000
Re = 500,000
SD2030 (B)
−10 0 10 20−0.5
0.0
0.5
1.0
1.5
2.0
α (deg)
Cl
Fig. 23 Drag polar for the SD2030 (B).
0.00 0.01 0.02 0.03 0.04 0.05−0.5
0.0
0.5
1.0
1.5
Cd
Cl
Re = 100,000
Re = 200,000
Re = 350,000
Re = 500,000
SD2030 (B)u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F (h/c =
0.11%)
−10 0 10 20−0.5
0.0
0.5
1.0
1.5
2.0
α (deg)
Cl
Fig. 24 Drag polar for the SD2030 (B) with trip type F.
-
0.00 0.01 0.02 0.03 0.04 0.05−0.5
0.0
0.5
1.0
1.5
2.0
Cl
Re = 100,000
Re = 200,000
Re = 350,000
Re = 500,000
SH3055
−10 0 10 20−0.5
0.0
0.5
1.0
1.5
2.0
2.5
Cl
Fig. 25 Drag polar for the SH3055.
0.00 0.01 0.02 0.03 0.04 0.05−0.5
0.0
0.5
1.0
1.5
2.0
Cl
Re = 100,000
Re = 200,000
Re = 350,000
Re = 500,000
SH3055u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F (h/c =
0.11%)
−10 0 10 20−0.5
0.0
0.5
1.0
1.5
2.0
2.5
Cl
Fig. 26 Drag polar for the SH3055 with trip type F.