Full text of DOI:10.2514/2.2098

AIAA JOURNAL
Vol. 41, No. 8, August 2003
Airfoil Flow Visualization and Pressure Measurements
in High-Reynolds-Number Transonic Flow
Herbert Olivier,¤ Thomas Reichel,† and Mitja Zechner‡
RWTH Aachen University, 52056 Aachen, Germany
Today most wind tunnels operated for aerodynamic testing are not able to reproduce  ight Reynolds numbers.
To overcome this problem, a shock tube  ow is used to generate a high-Reynolds-numbertransonic  ow. With this
technique,Reynoldsnumbers up to 40 £ 106 based on modelchord length are attainablein the Mach numberrange
between 0.6 and 0.9. Time-resolved surface pressure measurements, as well as  ow visualizations, are performed
for the airfoil BAC3-11/RES/30/21. Two models of different chord lengths, 80 and 100 mm, have been used. The
maximum Reynolds number achieved to date is 38 £ 106 for a freestream Mach number of 0.8. The results show
that by calibrating the test-section  ow carefully, this wind-tunnel technique can generate high-Reynolds-number
 ows, allowingaerodynamictesting at low cost. The techniqueavoidsthe complexcryogenic wind tunnel and model
technique, at the expense of relatively short running times and relatively small test-section cross size. The testing
–
time is on the order of 10 15 ms, which is sufŽ ciently long for  ow establishment and development of a useful
measuring phase with stationary or at least quasi-stationary  ow.
Introduction
ODERN civil transport aircraft cruise in the high transonic
velocity region with  ight Mach numbers in the range of
but which is long enough for  ow establishment and to perform
reliablemeasurementsduringa stationary ow period.13 The facility
described offers the possibility to perform high-Reynolds-number
testingatlowcostand to avoidthe cryogenicwind-tunneltechnique,
but at the expense of short running time and relatively small test-
section cross size.
M
0.85 and Reynolds numbers based on wing chord length extending
up to 50 10 or beyond. Wind-tunnel testing, still necessary for
6
£
development, mostly suffer from low-Reynolds-number capabili-
ties that make the extrapolation of wind-tunnel data to  ight con-
ditions difŽ cult and/or questionable. Cryogenic wind tunnels have
been developed to increase the Reynolds number to  ight condi-
tions. However, these facilities are extremely costly and require a
complex wind-tunnel model and measuring techniques. Therefore,
these facilities are not affordable, for example, for universities for
the study of high-Reynolds-numbertransonic  ows.
The idea to use the shock tube ow for aerodynamictesting is not
new. Geigeret al.1 describedexperimentsperformedin a shock tube
to study transonic and supersonic  ow patterns in 1949. Attempts
to overcome the problem of relatively small test section sizes were
made by area enlargementbetween driver and driven section2 but at
the cost of lower Reynolds numbers. In the past, a lot of work has
been performedto study the in uence of the test sectionwalls on the
model  ow and how to minimize their effect.3¡8 This work showed
that with suitable slotted test section walls in a shock tube it is pos-
sible to achieve the same  ow as in a continuously working wind
tunnel. More recently, this work was extended in Japan9¡12; how-
ever, note that in all of these experiments the maximum Reynolds
number based on model chord length did not exceed 2 10 .
At the shock wave laboratory of RWTH Aachen University, a
shock tube has been modiŽ ed to perform airfoil testing at transonic
Mach numbers and relatively high Reynolds numbers extending
up to 38 10 . The  ow behind the incident shock wave provides
the testing  ow. Overall testing time is on the order of 10–15 ms,
which is very short compared to that of conventionalwind tunnels,
Description of the Facility
In Fig. 1 (top), the working principle of the tube is schemati-
cally shown. The shock tube is divided into a high-pressure and a
low-pressure section by metal diaphragms. In this case, the high-
pressure section is Ž lled with compressed air up to an initial Ž lling
p
T
pressure 4 attemperature 4. The low-pressuresectionisŽ lledwith
p
the test gas, typicallynitrogen or air of pressure 1 and temperature
T
T
1
T
and of the test and driver
4
1. In our case, the temperatures
gas, respectively,match ambient temperature. Because of the pres-
p
p
1 after ruptureof the main diaphragm,a planar
sure difference
–
4
u
shock wave develops that propagates with velocity downstream
s
into the low-pressure section compressing and acceleratingthe test
gas at the same time. The strength of the incident wave is such
that the desired transonic ow establishesbehind it. Here, the main
differencecompared to the conventionalwind-tunneltechniquebe-
comesobvious,where usuallythe desired ow conditionis achieved
by a nozzle expansion. In a shock tube, the  ow is accelerated by
the gasdynamicprocesstakingplace acrossa shock wave and, at the
same time, is compressedto higherpressuresand densities,offering
the possibility to achieve a high-Reynolds-number ow. The total
lengthof the shock tube used in this study is to 35.5 m, and its inner
diameter is 300 mm. The maximum working pressure of the tube is
limited to 25 MPa. The overall length of the facility consisting of
shock tube, test section,and dump tank as shown in Fig. 1 (bottom)
is 46 m.
6
£
6
£
Shortly after the bursting of the main diaphragm between the
high- and low-pressure sections, the incident shock wave enters the
test section, followed by the transonic  ow. The test section is lo-
cated at the downstream end of the low-pressuresection. It consists
of modular plates and forms a rectangular  ow cross section. It is
possible to install slotted or perforated inserts into the upper and
lower wall to decrease wall interference effects. The inner cross
sectionaccommodatingthe model stationhas a Ž xed width of 0.2 m
and a variable height of 0.2–0.28 m. Figure 2 shows a longitudinal
view of the test sectionwith a calibrationrake installedat one of the
two possible model positions. Entry and exit of the 2.2-m-long test
section are formed as boundary-layercookie cutters. These cookie
cutters are designed as sharp-wedged leading edges of the upper
Presented as Paper 2002-0301 at the 40th Aerospace Sciences Meeting,
Reno, NV, 14–17 January 2002;received 7 March 2002;revisionreceived 11
°c
February 2003; accepted for publication 4 April 2003. Copyright
2003
by the authors. Published by the American Institute of Aeronautics and
Astronautics, Inc., with permission. Copies of this paper may be made for
personal or internal use, on conditionthat the copier pay the $10.00per-copy
fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers,
MA 01923; include the code 0001-1452/03 $10.00 in correspondence with
the CCC.
¤Head of Shock Wave Laboratory, Templergraben 55; olivier@swl.rwth-
aachen.de. Member AIAA.
†Research Engineer, ShockWave Laboratory,Templergraben55.Member
AIAA.
‡Research Engineer, Shock Wave Laboratory, Templergraben 55.
1405

1406
OLIVIER, REICHEL, AND ZECHNER
and lower walls, as well as of the side walls of the test section. The
wedge with a wedge angle of 12 deg is located toward the bypass
channel, whereas there is a plane surface oriented toward the inner
part of the test section (Fig. 2). The test  ow that is generated in
the circular shock tube enters the rectangulartest section,where the
sharp edges of the cookie cutters cut out a homogeneouscore  ow
and divert most of the shock tube boundary layer into separate by-
passesaroundthetestsection.In thisway duringthequasi-stationary
measuring phase, for the test section an almost fresh wall boundary
layer develops with a running length for the upstream test position
of only 556 mm and for the downstreamposition of 1300 mm. This
holds for the nearest position of 200 mm of the upper and lower
test section wall, respectively.The boundary-layerthickness of the
shock tube  ow at the test section has been estimated according to
the theory of Mirels.14 It grows from 0 up to 60 mm within 20 ms.
make use of a slightly convergent–divergent two-dimensionalnoz-
zle at the downstreamend of the test section, which is not shown in
Fig. 2. In the divergent part of the nozzle, the  ow is acceleratedto
low supersonic speed. In this case, the expansion wave mentioned
beforeas wellasotherdisturbancesarekeptfromtravelingupstream
into the test section.
Calibration Experiments
The relativelysmall dimensionsof the airfoilmodels with a max-
imum chord length of 100 mm and a maximum thicknessof 11 mm
prevent the direct installation of a high number of pressure trans-
ducers into the models. Furthermore, for high-Reynolds-number
experiments, the aerodynamic loads lead to stresses in the model
that are on the order of the strength of the model material. In this
case, model or mounting failure should not lead to the loss of all
transducers.Therefore, the pressure transducers, one for each pres-
sure tap, are mountedin the inner sidewalls of the test section.They
are connected to the surface pressure taps by thin pressure tubings
about150 mm long.The dynamic behaviorof the completepressure
measurement system was investigated thoroughly, including pres-
sure tap, tubing, pressure transducer, and data acquisition system.
Length and inner diameter of the tubings were varied over a wide
range. Figure 3 shows the response of Ž ve different pressure tub-
ings to the pressure jump generated in a shock tube. All pressure
taps were located in the same cross section. It is observed that the
shorter is the tubing, the higher is the overshootof the pressure sig-
nal, which is caused by oscillationsof the gas column in the tubing.
When the inner diameter of the tubing is reduced, damping caused
by wall friction becomes more important. This leads to a reduction
of the oscillation phenomenon but at the expense of a longer rise
time. These counteractingeffects necessitate the choise of an opti-
mum inner tubing diameter for the pressure range considered. It is
seen in Fig. 3 that, after nearly 5 ms, all tubings result in the same
This holds for a typical test  ow condition of Mach number 0.7
6
£
and maximum Reynolds number of 40 10 , based on a reference
length of 0.1 m.
For a larger height of the test section, during the measuring time
partoftheshocktubeboundarylayerentersthetestsectionand  ows
along the upper and lower walls. The maximum possible distance
between these walls is to 280 mm. Increasing the height of the
test section results in smaller blockage ratios, with the advantage
of reduced wall interference effects and increased Mach number
capability. Experiments performed so far with different heights of
the test section show, however, that the in uence of the shock tube
boundary layer inside of the test section is negligible on the  ow
around the model. The test section side walls are Ž xed at a position
of 200 mm, which correspondsto the smallest possible distance of
the lower and upper wall, that is, most of the shock tube boundary
layer is peeled off at the side walls.
The test section is designed for a maximum static pressure of
4 MPa, which is necessary to achieve high Reynolds numbers on
6
£
the order of 40 10 based on a model chord length of 100 mm.
Between the test section and dump tank, another diaphragmmay be
installedto allow evacuationofthe dump tankbeforetesting.During
the run, the gas expands into the dump tank. This leads to an expan-
sion wave traveling upstream into the test section, which reduces
the maximum achievabletheoreticaltest time. Current experiments
Fig. 3 In uence of diameter and length of pressure tubings on tempo-
ral signal behavior for a steplike pressure pulse.
Fig. 1 Transonic shock tube and wave plan.
Fig. 2 Longitudinal section of the test section.

OLIVIER, REICHEL, AND ZECHNER
1407
stationary pressure value within the experimental uncertainty. The
remaining scatter of the signals during the stationary phase may be
regardedas typicaluncertaintyof the pressure measurement,which
§
is determined from Fig. 3 to be 3%. These preliminaryinvestiga-
tions gave evidencethat, with a suitable pressure tubing of 150 mm
length,pressuremeasurementsat leastfor quasi-stationary ows are
possible,providedthe overallmeasuringtime exceeds3–5 ms. This
is the case for the facility described in this paper.
The homogeneityof the test section ow was checkedwith a pitot
rake, schematically shown in Fig. 2. The pitot rake, consisting of
15 pressure measuring locations, made use of the pressure tubings
investigatedin Fig. 3. The static wall pressurewas measuredin par-
allel, so that the freestream Mach number can be deduced from the
pitot and static pressure.Figure 4 shows a typicalexample of a pitot
and static pressure history. It is seen that during the useful running
Fig. 6 Pitot surveys in the horizontal plane of the test section for
different  ow Mach numbers.
Fig. 4 Example of pitot and static wall pressure histories measured in
the test section of the transonic shock tube.
–
Fig. 7 Mach Reynoldsnumber envelope; reference length l = 100mm.
time from 5 to 15 ms the pitot pressure as well as the static pressure
rise slightly. Because the pitot pressure increases a little more than
the static pressure, the freestream Mach number increases slightly
with time. This effect is caused by the shock tube boundary layer,
which results in a slight attenuation of the incident shock. Because
of this, during the running time, at a Ž xed position the freestream
Mach number increases by about 2–5%. Fortunately, before the
Mach number starts to rise, in general a short period of testing time
with constant Mach number can be identiŽed. At present, this time
window is used for Ž nal data evaluation.An example of this is given
in Fig. 5, which shows the Mach number history and the historiesof
pressure coefŽ cients for different positions along the upper side of
an airfoil model described in the following section. In this case, the
Mach number starts to rise at about 9 ms. Further researchis related
to shock tube methods, which results in an even more stationary
 ow behavior, as shown in Fig. 5. Furthermore, numerical studies
have to be performed to prove the quasi-stationary  ow behavior
for time periods taking place after that indicated in Fig. 5. In this
case, data reduction can be extended to longer running times than
those given in Fig. 5. The pitot rake measurements revealed a spa-
tially homogeneous  ow in the test section. Figure 6 shows pitot
surveys for the horizontal plane of the test section for various  ow
Mach numbers. The largest spatial deviation is 5%, which repre-
sents a typical value for shock tube facilities.Further effort devoted
to an optimized design of the test section and to the measurement
techniquewould lead to a reducedscatter and a more homogeneous
 ow. In Fig. 7, the Reynolds–Mach number envelope of the facil-
ity is shown together with calibrated conditions and experiments
performed so far indicated by the cross symbols.
)
a
Results
)
b
A time-resolvedshadowgraphsystemis set up for  ow visualiza-
tion, which allows 24 single frames per shot. In the following, only
one representativeframe for each experiment is shown. The airfoil
model is Ž xed by two thin side plates with a thickness of 4.5 mm
Fig. 5 TypicaltimehistoriesofMach numberandpressure coefŽ cients
along the upper side of an airfoil model; Re = 38 £106, reference length
0.1 m.

1408
OLIVIER, REICHEL, AND ZECHNER
)
)
c M = 0.73
1
a M = 0.67
1
)
)
d M = 0.77
1
b M = 0.71
1
Fig. 8 Flow on the upper side of the airfoil BAC3-11; ® = 2 deg and Rec = 3.2 £106.
for  ow visualization. These plates are Ž xed at the two tunnel side
walls. Therefore, either the upper or lower part of the airfoil and the
corresponding owŽ eld is visible. Because of the high mechanical
loadingcausedby the high-Reynolds-number ow, theairfoilmodel
cannot be Ž xed by clamping between the tunnel windows.
152 mm. The pressure taps are located in the midspan area of the
model. Commercial piezoresistivepressure gauges have been used
as pressure transducers.
In Fig. 9, some of the measured pressure histories are given for
6
£
an experiment with a medium Reynolds number of 7:2 10 and
In Fig. 8, the in uence of the freestream Mach number is exem-
plarily shown for an angle of attack of 2 deg. For the low-Mach-
number case (Fig. 8a), a weak two-shocksystem develops.Because
of the off-axis arrangement of the 24 sparks and receiving optics, a
small vertical shift of the picture occurs, which is especiallyvisible
along the upper surface of the airfoil in Figs. 8a and 8d. With in-
creasingMach number,the two-shocksystemvanishes,and a single
shock develops (Fig. 8b). The Mach lines in the supersonic region
between the nose and shock are clearly visible, as well as the ex-
pansionregion aroundthe nose. The shock is still too weak to cause
boundary-layer separation. For the slightly increased Mach num-
ber of 0.73, the shock becomes a little stronger, and as expected,
its location is a little farther downstream. For this Mach number, a
weak boundary-layerseparation behind the shock takes place. For
the highestMach numberconsidered(Fig. 8d),a strongseparationis
visiblebehindtheshock.Furthermore,a lambdashockconŽ guration
develops, and the whole shock system moves farther downstream.
In Fig. 8d, the Mach lines in the supersonicregion are not as clearly
visible as in the earlier case because of reduced sensitivity of the
optical setup.
In addition to  ow visualization, measurements of the pressure
distributionaroundtheairfoilhavebeenperformed.For this,a model
of 200-mm span and 100-mm chord length has been built, with 24
pressure taps located on the upper side and 19 on the lower side
of the model. As already mentioned, the relatively short running
times of the facility do not allow for very small inner diameters of
the pressure taps and very long connecting tubes to the pressure
transducers. Based on the experimental results already discussed,
the inner diameterof the pressuretaps was chosen to be 0.6 mm and
the typical length of the pressure tubing of each pressure tap to be
a freestream Mach number of 0.74. In this case, a strong shock
develops, especially on the upper side, which is visible in the shad-
owgraphs, as well as in the pressure distributionand time-resolved
pressure histories. Along the upper side of the airfoil from the nose
x c D
up to the position of
=
52:3%, the pressure histories exhibit
steadybehaviorafterthe owestablishment(Fig.9).Downstreamof
thisposition,a shockdevelopsduringthe  ow establishment,which
x c D
thenmovesdownstreamto stabilizeits positionat about =
67%.
This development and the downstream movement are clearly vis-
x c D
ible for the pressure history at
=
65:5%. After the shock has
passed this position, the pressure becomes steady at a lower level.
At its Ž nal position, the shock oscillates with small spatial ampli-
x c D
tude, which causes the pressure  uctuations at
=
68:5%. Far-
ther downstream of the shock position, the pressure histories be-
come more steady. A much weaker shock is generatedon the lower
surface, which causes slight pressure  uctuations at the position
x c D
=
43%.
For this  ow condition, shadowgraphs were taken separately for
the upper and lower sides of the airfoil in two shots. They were
put together to visualize the whole  owŽ eld (Fig. 10). At the lower
side, downstream of the nose, a Ž rst shock is generated at about
x c D
=
5–8%. This shock of small lateral extent is visible at the end
of the dark region at the nose (Fig. 10). Behind this shock, the  ow
is subsonic, and consequently,no Mach lines are visible. However,
the  ow accelerates again to supersonic speed. In a high-quality
copy, the supersonicregionis clearlyvisible by the Mach lines. The
end of this region is determined by the second shock at the lower
surface.
The most interesting feature of the facility is the achievement
of high-Reynolds-number  ow. To now, the maximum Reynolds

OLIVIER, REICHEL, AND ZECHNER
1409
Fig. 9 Pressure histories for M = 0.74, Rec = 7.2 £106, and ® = 0 deg.
1
In the transonic shock tunnel, high Reynolds numbers are achieved
by high static pressures. Therefore, in the pressure plots shown in
Fig. 11, the maximum pressure on the airfoil model reaches up to
2.1 MPa, which represents a remarkably high value.
D
At ® 0 deg for the low- and high-Reynolds-numbercases, no
signiŽ cantdifferencecanbe detectedon theshadowgraphs(Fig.12).
For the high-Reynolds-number  ow, the expansion region around
the nose is resolved in more detail, and the generation of a weak
shock on the upper side becomes apparent. This weak shock or
strong compression waves are responsiblefor the pressure  uctua-
tions observed on the upper side of the airfoil in Fig. 11.
The Reynolds number in uence becomes more pronounced for
higher angles of attack, where a stronger shock develops.The inter-
action of the turbulentboundarylayer with the shock for this special
airfoil leads to a shock oscillation.The high temporal resolutionca-
pability of the measuring techniqueemployed in these experiments
allowed the study of these effects. Figure 13 gives the distributions
of the pressure coefŽ cient for 0- and 2-deg angles of attack for a
low- (square symbols) and a high-Reynolds-number ow (circles)
for three different times during the running time.15
D
The experimentsat ® 0 deg reveal an interestingphenomenon.
If the  ow approachesor slightlyexceedsthe criticalstate, that is, if
the  ow becomes sonic, it tends to exhibit unsteady behavior. This
is visible for the pressure distributions on the upper side between
Fig. 10 Shadowgraph from two experiments, lower and upper sides;
M
= 0.74 and Rec = 7.2 £106.
1
x c D
=
c¤
in Fig. 13 gives the pressure co-
p
35 and 60%. The value
6
£
number based on the model chord length has been 38 10 for a
Mach number of 0.8. Figure 11 shows pressure histories obtained
efŽ cient for which sonic velocity is reached. The developmentof a
local unsteady owŽ eld is more pronouncedfor the high-Reynolds-
number  ow than for the lower Reynolds number. Upstream and
downstream of this region the pressure coefŽ cient shows a much
more steady behavior. The situation changes if there is a strong
shock imbedded in the  owŽ eld, as in the case in Fig. 13b for 2-deg
angle of attack. For the low-Reynolds-number ow during the time
periodbetween 7.5 and 9.5 ms, the shock moves a little downstream
for the upper and lower sides of the airfoil at an angle of attack
6
£
of 0 deg for a medium Reynolds number of 20:5 10 and a Mach
x c D
numberof 0.7. On the uppersidefrom =
47 up to 65%, pressure
 uctuationsare visiblein the signals causedby compressionwaves,
which steepen to form a weak shock. For other positionsduring the
measuringtime, the pressurehistoriesexhibitquite steadybehavior.

1410
OLIVIER, REICHEL, AND ZECHNER
Fig. 11 Pressure histories for airfoil BAC3-11, M = 0.7, ® = 0 deg, and Rec = 20.5 £106.
1
6
6
)
)
a Rec = 3.1 £10
b Rec = 20.7 £10
Fig. 12 In uence of Reynolds number on airfoil  ow; M = 0.71 and ®= 0 deg.
1
very slowly. The velocity of this shock movement amounts to only
2 m/s, which is a relatively small value compared to the freestream
velocity of 290 m/s, that is, there should be enough time to estab-
lish a quasi-steady  ow during the shock movement. For the high-
Reynolds-numbercase, the shock moves Ž rst upstream from about
x c D
show that, despite the different distributionsfor this Mach number,
the overall lift is practically not affected by the Reynolds number.
In Fig. 14, the pressure coefŽcient distributions are compared
6
Re D
£
for an experiment with Reynolds number
experiment yielding a Reynolds number of
20 10 with an
6
Re D
£
36 10 and for
=
60 to 56%. Then it moves downstream, and during the re-
0-deg angle of attack. The latter represents a test for almost maxi-
mum operatingperformanceof the facility.In both cases, the Mach
number of the freestream was 0.73, and as in all tests, there was
no boundary-layertripping. Furthermore,the pressure distributions
are not corrected with regard to wall interferenceeffects. This may
also be of in uence on the slightly higher pressure coefŽcients for
mainingmeasuringtime, it becomesstationaryat a positionof about
60%. In this case, the shock position is located more upstream than
for the low-Reynolds-number ow. Also the high Reynoldsnumber
leads to a lower suction pressure on the upper side but to a higher
pressure on the lower side. Integration of the pressure distributions

OLIVIER, REICHEL, AND ZECHNER
1411
that is located at the downstream end of the low-pressure section.
The span of the models installed between the two tunnel side walls
is 200 mm, whereas the height of the test section can be varied
from 200 to 280 mm. The upper and lower test section walls can be
equippedwith slottedinsertsto reducewall interferenceeffects.Ex-
perimentshave been performedso far with airfoilmodelsof 80- and
100-mmchordlength.Time-resolvedshadowgraphsshowdetailsof
the  owŽ eld, such as Mach lines, shocks, separation,etc. For pres-
sure measurements,one model was equippedwith 43 piezoresistive
pressure transducers.The highestReynolds number achievedso far
6
Re D
£
is
38 10 based on 100-mm model chord length. The typi-
c
cal running time is on the order of 10–15 ms. Experimental results
show that this time is sufŽ cient for  ow establishmentand a quasi-
steady ow periodduringwhich representativepressurecoefŽcients
and other data are determined. As is typical for transonic  ow, the
 ow behaviorstrongly depends on the Mach number, which, there-
fore, needs a careful technique for determination. In this work, the
Mach number has been determined from time-resolved pitot and
static pressure measurements.These revealed that, due to the shock
tube boundary-layerin uence, the Mach number rises slightly with
time. Up to now, representative quantitative data have only been
taken during a short period of time during the running time, for
which the Mach number is constant within the experimental uncer-
tainty. Future work will be related to the study of different shock
tube techniques that allow the time period of steady-state condi-
tions to be prolonged. The pressure histories measured around the
airfoil exhibit no unusual behavior. The fast measuring technique
allows the detectionof highlytransient ow processes,such as pres-
sure oscillationscaused by shock oscillations,etc., which cannotbe
resolved with standard wind-tunnel measuring techniques. The re-
sults achieved so far show that with this type of facility very high
Reynolds numbers that approach  ight Reynolds numbers can be
achieved easily and cost effectively.
)
a
)
b
)
Fig. 13 Distribution of pressure coefŽ cient, M = 0.7: a ® = 0 deg:
1
6
6
, Rec = 2.7 £ 10 and J , Rec = 20.5 £ 10 ; and b ® = 2 deg: , Rec =
Acknowledgments
)
¤
¤
7.5 £ 106 andJ , Rec = 20.3 £ 106.
This work has been funded by the Deutsche Forschungsgemein-
schaft as part of the CollaborativeResearch Center SFB 401 “Flow
Modulation and Fluid–Structure Interaction at Airplane Wings” at
the RWTH Aachen University, Germany.
References
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Univ., Kyoto, Japan, 1975, pp. 472–479.
Fig. 14 Comparison of pressure coefŽ cient distributions for airfoil
BAC3-11 for two different Reynoldsnumbers; angleof attack ® = 0 deg.
4Cook, W. J., “A Study of Test Section ConŽ guration for Shock Tube
Testing of Transonic Airfoils,” NASA Ames Research Center, Final Rept.,
Grant NSG-2152, 1978.
the high-Reynolds-numbercase. Because in this case the boundary
layer on the tunnel walls, as well as on the model, is thinner than
for the lower Reynolds number, there is less of a blockageeffect. In
this case, the effective  ow Mach number is lower than the nomi-
nal one, which yields slightly larger pressure coefŽ cients, as for the
smaller Reynolds number. On the upper surface of the airfoil, com-
pression waves occur, which cause the pressure rise in the region
x c D
5Cook, W. J., Chaney, M. J., Presley, L. L., and Chapman, G. T., “Ap-
plication of Shock Tubes to Transonic Airfoil Testing at High Reynolds
Numbers,” NASA TP 1268, 1978.
6Cook,W. J., Presley, L. L., and Chapman, G. T., “Shock Tubeas a Device
for Testing Transonic Airfoils at High Reynolds Numbers,” AIAA Journal,
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7Cook, W. J., Presley, L. L., and Chapman, G. T., “Use of Shock Tubes
in High Reynolds Number Transonic Testing,” Shock Tubes and Waves,
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Symposium on Shock Tubes and Waves, Hebrew Univ., Jerusalem, 1980,
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from
=
0:6 to 0.7. These pressure waves are also visible on the
shadowgraphsof Fig. 12. Obviously, the in uence of the Reynolds
number on the pressure coefŽ cient is much less intensive for the
recompression zone of the airfoil than for the accelerating part of
the  ow.
8Cook, W. J., and Heidegger, N. J., “Dense Gas Aerodynamic Studiesin a
Shock Tube,” NASA Ames Research Center, Progress Rept., Contract NAG
2-175, 1993.
Conclusions
9Yamaguchi, Y., “Performance of a Slotted Wall Test Section for Aero-
dynamic Testing in a Shock Tube,” Theoretical and Applied Mechanics,
Vol. 37, 1989, pp. 39–47.
A shock tube has been rebuilt and used for airfoil testing in the
transonicregime. The  ow behind the incident shock is used as test
 ow. The airfoil models are installed in a rectangular test section

1412
OLIVIER, REICHEL, AND ZECHNER
10Yamaguchi, Y., and Amemiya, T., “A Preliminary Study on the Fixed
13Reichel, T., Zechner, M., and Olivier, H., “Der Stoßrohr-
Transschallkanal der RWTH Aachen, ein 2-D Windkanal zur gleichzeitigen
Einhaltung von Mach- und Reynoldszahla¨hnlichkeit,” DGLR Jahrestagung,
Paper DGLR-JT2000-017 [CD-ROM], Sept. 2000.
Transition Technique for a Shock Tube Transonic Airfoil Flow,” Transac-
tions of the Japan Society for Aeronautical and Space Sciences, Vol. 37,
No. 118, 1995, pp. 311–318.
11Yamaguchi, Y., Amemiya, T., and Wada, S., “Application to Trip Strips
of Shock Tube Airfoil Flows,” Shock Waves, edited by R. R. Boyce, P. M.
Danehy, M. Hannemann, J. J. Kurtz, T. J. Mclntyre, S. J. McMahan,
D. J. Mee, R. J. Sandeman, and H. Tanno, Panther Publishing and Print-
ing, Canberra, Australia, 1997, pp. 529–534.
14Mirels, H., “Shock Tube Test Time Limitation due to Turbulent-Wall
Boundary Layer,” AIAA Journal, Vol. 2, No. 1, 1964, pp. 84–93.
15Zechner, M., “Transsonische ProŽ lumstro¨mungen im Stoßrohr-
Transschallkanal,” Ph.D. Dissertation, Shock Wave Lab., Aachen Univ.,
Aachen, Germany, April 2002.
12Yamaguchi, Y., Kaibara, K., and Saito, T., “Application of Wall Inter-
ference Corrections to a Low Aspect Ratio Airfoil Model,” AIAA Paper
97-0916, Jan. 1997.
G. V. Candler
Associate Editor