Full text of DOI:10.2514/2.2091

AIAA JOURNAL
Vol. 41, No. 7, July 2003
Bubble Bursting and Stall Hysteresis on Single-Slotted
Flap High-Lift ConŽ guration
M. Baragona,¤ L. M. M. Boermans,† M. J. L. van Tooren,‡ H. Bijl,§ and A. Beukers‡
Delft University of Technology, 2629 HS Delft, The Netherlands
Slotted multi-element conŽ gurations are widely used because they are very effective in increasing the maximum
lift of airfoils during takeoff and landing. However, when stall occurs in the leading-edge region of one of the
elements, the outcomeis a sudden anddangerousdrop in performance of the whole conŽ guration.The results of the
experimental veriŽ cation of a computer-designed single-slotted  ap are presented. Many realistic conŽ gurations,
including the computed optimum, were tested and compared to the numerical predictions. For a number of these
conŽ gurations, sudden leading-edgestall due to the bursting of a laminarbubblewas detected on the  ap, followed
by severe stall hysteresis. Present numerical design codes do nothelp the designermuch in predicting thisimportant
phenomenon, and wind-tunnel testing remains necessary. Therefore, there is a need for better bubble bursting
prediction methods. A possible direction for improvement is discussed, focusing on the unsteadiness of the  ow.
Nomenclature
drag coefŽcient
lift coefŽ cient
maximum lift coefŽcient
pressure coefŽcient
in poststall behavior. On the other hand, existing bubble bursting
predictors perform badly, especially in the low-Reynolds-number
Cd
Cl
Cl
Cpmax
c
Rk
Tu
U
=
=
=
=
=
=
=
=
=
=
=
=
=
Re
range, unless an accurate and dedicatedtuning againstavailable
(if any) experiments is performed.1 The most widespread numeri-
cal design codes for single and multi-element airfoils, for example,
XFOIL,2 MSES3 and the Eppler code,4 lack the required accuracy
to predict stall behavior and do not include any of these bursting
predictors. The designer currently relies heavily on experimental
analysis, much more than for cruise conditions.
aerodynamic chord with  ap nested
p
reŽ nement ratio
freestream turbulence level,
uncertainty
velocity
u02
V
=
In this paper, the two-dimensional physics and airfoil design is-
sues in relation to bubble bursting, will be addressed. The two-
dimensional case permits a much deeper and detailed investigation
of the driving  ow phenomena5 than does the three-dimensional
approach and for ordinary unswept wings, three-dimensional ef-
fects are usually limited to a small region near the tip. (A deŽ ni-
tion of the global characteristics of three-dimensional separation
and of its topology is still a matter of discussion.6;7) In addition,
transition at low Reynolds numbers develops mainly as a two-
dimensional process. All evidence suggests that the ampliŽ cation
of three-dimensional disturbances by secondary instabilities is in
fact less rapid in this case, being somehow “locked” on a dominant
V
x y
;
coordinates
angle of attack
displacement thickness
momentum thickness
®
±
µ
Introduction
HE main focus of high-lift design is to maximize the
whereaslessattentionis devotedto poststall ow development.
C
,
l
max
T
This practicecan leadto a dangerousoptimumdesign,especiallyfor
Reynolds numbers up to an order of 106 when laminar separation
bubbles are involved. The bursting of a laminar bubble causes a
8
two-dimensionalwave frequency.
C
hysteresisloop in the curve l – ® thatcan turnout to be ratherlarge.
First, a review of the present theoretical knowledge on laminar
bubbles will be given. Also, a parallel will be drawn between the
multi-element and the single-element case. In the following sec-
tions, the experimental and numerical results obtained during and
after the design process of a multi-element single-slotted  ap con-
Ž guration will be presented. Finally, a number of physical aspects
will be addressed that are not included in the classical model of a
laminarbubbleand, hence,not accountedfor in the existingbursting
predictionmethods,indicatingapossibledirectionforimprovement.
The experimental and numerical results show that the bubble
presentin the noseregionof the  ap of thisslottedconŽ gurationwas
extremely important in determining the performance of the whole
multi-element conŽ guration. When this bubble burst and the  ap
stalled, a sudden loss of lift and a large hysteresis loop followed, a
behavior similar to that observed in the single-element case. This
is an important and rather new Ž nding9;10 because the possibilityof
bursting and stall hysteresisis usually ignored in the process of de-
signinga new  ap. The Reynoldsnumber range where this bursting
may happen is found to be higher than for single-element airfoils.
The result is a very dangeroussituationbecause of the combination
of the sudden lift loss and the large 1® reduction that is needed to
resume prestall conditions. This is particularlyrelevant for the  ap
of a multi-element conŽ guration where the possible occurrence of
such a situation has only recently been discovered.
The formationof laminarbubbleson the leadingedge of a single-
element airfoil and their possible bursting are known to affect
stronglythe stall behaviorof single-elementairfoils.The possibility
of burstingand stall hysteresis,however,is oftendisregardedduring
the design process. When experiments are done, it is not uncom-
mon that tests are stopped just after stall occurs, with no interest
Received 22 March 2002; revision received 3 February 2003; accepted
°c
for publication 4 February 2003. Copyright
2003 by the authors. Pub-
lished by the American Institute of Aeronautics and Astronautics, Inc., with
permission. Copies of this paper may be made for personal or internal use,
on condition that the copier pay the $10.00 per-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.
¤Research Fellow, Department of Aerospace Engineering,Kluyverweg 1.
†Associate Professor, Department of Aerospace Engineering, Kluyver-
weg 1.
The experimentsshown in this paper were carriedout at a Reynolds
6
£
number of about 2 10 , as required by the speciŽcations of the
Eaglet two-seater training motor plane for which the  ap had been
designed. This value of 2 10 is a typical value for general avia-
tion airplanesin landing conditions.Hence, it may be expectedthat
the Ž ndingsfor the current setup should have a more generalsignif-
icance and that the possibility of bursting should be regarded as a
6
£
‡Professor, Department of Aerospace Engineering, Kluyverweg 1.
§Assistant Professor, Department of Aerospace Engineering, Kluyver-
weg 1.
1230

BARAGONA ET AL.
1231
major danger during the design of a  ap for low-Reynolds-number
applications.
the hysteresis is not detected because in the experiments the angle
of attack was not reduced after bubble bursting.
Theoretical Background
Slotted Multi-Element ConŽ guration
A laminar boundary layer may reach the separation point before
transitionto a turbulentlayer is achieved. For each airfoil shape and
thickness, this will happen at a certain combination of Reynolds
The idea to split an airfoil in more elements dates back to the
end of the Ž rst World War when a German engineer pilot, G. V.
–
(
Lachmann who had just survived a crash following a stall during
Tu
number, freestream turbulence level , and angle of attack ®. For
)
its early training  ights , Ž rst proposed it to Prandtl. The results of
any airfoil at a relatively low turbulence level and a given ®, there
exists a value of the Reynolds number below which laminar separa-
tionoccurs.The ow developmentaftertheseparationpointdepends
strongly on the behavior of the separated laminar shear layer. It is
thought that, due to its high instability, transition to turbulence oc-
curs shortly after the separation point, increasing the entrainment
with the external ow, and, thus,causingreattachmentto the surface
and the formationof a regionof relativelystagnant ow, a shortbub-
the ensuing experimental tests were indeed encouraging, in some
cases with spectacular lift increase beyond 30% of the basic value,
demonstrating the validity of the proposal. However, the principle
on which it works has beenmisinterpretedfor many yearsafterthese
early applications.It has become clearer that the slot does not work
asa boundary-layercontroldevice,but,asSmith12 pointedout, owes
its remarkable performancemainly to the change it produces in the
characteristicsof the external inviscid  ow. The pressure rise over
the whole conŽ gurationis splitintoa numberof lessseverepressure
rises,thus,leadingtothelargeoverallliftincreaseobservedintheex-
periments.Both the circulationaroundthe main airfoilandtheeffect
of its wake act in the direction of reducing the pressure peak in the
nose region of the  ap, which can then delay separation and in turn
raise the circulation and the lift contribution of the main element.
Another importantfeatureis that each element has a new boundary-
layer development.However, when large separatedregions, usually
on the  ap surface,are present,viscouseffectsbecome decisiveand
they place an upper limit to the achievable lift increase.
(
)
ble Fig. 1 . However, at high angles of attack or at low Reynolds
numbers, the  ow may become unable to overcome the adverse
pressure gradient and fail to reattach. The  ow pattern will then
change into a so-called long bubble or into a completely separated
(
)
 ow leading-edgestall .
In this view, bubble bursting can, therefore, be seen as either the
(
)
momentarybreakdown in case of long bubbleformation or deŽ ni-
(
)
tive breakdown in case of leading-edgestall of the turbulentshear
layer reattachment process. No physical difference exists between
the long and the short bubble in this model. The differencelies only
in the effect of the bubble on the pressure distribution: local and
limited in the case of a short bubble, more in uential in the case of
a long bubble.
Stall Hysteresis on a Slotted Multi-Element ConŽ guration
Although it is a well known and identiŽ ed  ow feature in the
case of single-element airfoils, the possibility of stall hysteresis
over multi-element conŽ gurations seems to be poorly known, and
there is little in the literature about the subject.
Stall Hysteresis on a Single-Element Airfoil
–
C
Once bubble bursting occurs, a hysteresisloop in the
® curve
l
is observed. When it is present, this loop represents a real danger
for pilots. The main reason why uncoveringthe physics behind the
bursting of a laminar bubble is such an important issue is to be able
to prevent stall hysteresis occurrence.
Like for the single-element case, bubble bursting and stall hys-
teresis are readilyconnected.The  ow on the  ap behaves in a very
similar way, displaying after bursting a typical leading-edge stall
pattern. In the slotted multi-element case, the main element wake
and the directionand the strengthof the slot ow are very important
additional factors that are absent in the single-element case. They
strongly affect the  ow development on the  ap and the eventual
burst of the bubble in its nose region. Because of the reduced pres-
sure gradient, the boundarylayer over the  ap tends to stay laminar
longer,providedthatturbulencecontaminationfromthe main airfoil
wake is avoided. In addition, the chord of the  ap is much shorter
A review of hysteresis can be found in Ref. 9 both for Ž xed
and rotary wings. Here the concern is particularly with Ž xed-wing
aircraft, where the phenomenon is usually referred to as stall hys-
teresis.A shortdescriptionof a typicalhysteresisloop may be given
as follows. By raising ®, the laminar bubble Ž rst moves toward the
leadingedge,diminishingits length.Suddenlyit bursts,turninginto
a completely separated ow or into a long bubble,which widens to-
ward the trailing edge of the proŽ le until, ultimately, the  ow is
completely separated. If at this stage ® is decreased, the  ow will
remain separated for a while before the bubble is reformed, thus,
–
than the main airfoil, so that a scale effect on the Reynolds num-
6
Re
Re D
Re D
£
ber
a
is present. In our case, an upstream
2
10 becomes
5
£
c
4:36 10 when based on the 21:8% chord of the  ap,
clearly falling in the range where stall hysteresis is more likely to
C
giving rise to the observed loop in the
Re
® curve. Notice that at
l
low Reynoldsnumber
almost every airfoil experiencesthis kind
occur on single-elementairfoils. This effect is much stronger once
of hysteresis loop, even if sometimes at such a high ® value that
it is not captured during usual experimental tests. Also, as shown
by Gault,11 bubble bursting can happen also at high Reynolds num-
bers if the curvature of the nose is high enough. In many cases, in-
cluding the NASA experiments on which Gault’s work was based,
(
)
the gap Fig. 2 is made wider because the  ow around the  ap
Fig. 1 Classical structure of a short laminar bubble.16
Fig. 2 Gap and overlap deŽ nition.

1232
BARAGONA ET AL.
becomes less dependent on the  ow over the main element. When
bubble bursting occurs on the  ap, the pressure distribution over
the  ap surface suddenly collapses. The reduced circulation of the
 ap in turn reduces the circulationof the main element, leading to a
global effect on the  ow over the entire airfoil system. Here again,
the angle of attack must be lowered considerably before the  ap
again reaches prestall conditions, giving rise to the observed hys-
teresis loop. Hence, the bursting on the  ap controls the hysteresis
on a multi-element airfoil.
designed for a maximum speed in the test section of 120 m/s. The
turbulencelevelvariesfrom 0.018%at 10 m/s up to 0.1%at 100m/s.
To prevent separation at wing wall junctions, suction boxes were
–
attachedtothetestsectionwallduringthisinvestigation.Theamount
of suction was chosen according to Foster and Lawford,21 and the
resulting  ow behavior was checked through tufts applied near the
trailing edge of the  ap and main element surfaces.
Thecompositewind-tunnelmodelhasa  apnestedchordof0.6m
and a span of 1.25 m. The  ap chord is 21.8% of the  ap nested
chord. The model was installed vertically in the test section and
equipped with a total of 59 pressure oriŽ ces on the main wing and
DifŽ culties in Current High-Lift Design Practice
Numerical Modeling DifŽ culties
(
)
23 on the  ap 0.4-mm diam locatedin diagonalrows between 0.45
and 0.55 m from the top of the test section.The surfaceof the model
consists of polyestergelcoat, which has been polished to ensure an
aerodynamicallysmooth Ž nish.
Both stall and poststall behavior should be taken into account to
achieve an optimum high-lift design. For a prediction of poststall
–
evolution, a Navier Stokes code or at least a dedicated treatment
A total and static pressure wake rake, mounted on a cross beam,
was positioned behind the model, with the tips of the total pres-
of the separated region would be required.13 The use of a Navier
–
Stokes code, however, is usually not an option for high-lift design
purposes. There are two main reasons for this. The Ž rst one is more
generaland also is validwhen laminarbubblesare absent,thatis, the
largecomputationaltimeinvolvedand the highnumberofparameter
combinations that should be tested. The second is that the physics
of bursting and the mechanism of transition, especially close to
or after bursting, are not clear yet and, thus, no reliable model is
available. An unsteady direct numerical simulation solver would
then be required. This option is currently not viable, not only for
design purposes.
As a numerical tool for two-dimensional high-lift design,
boundary-layercodesare atpresenttheusualchoice,forbothsingle-
element airfoils and for multi-element high-lift conŽ gurations. Al-
though some of these codes can deal even with large separated re-
gions, the results are not as satisfactory as for attached  ows,14
ultimately leading to the breakdown of the code when the separated
region becomes too extensive. Hence, for the problem analyzed
here, not more than a warning on bubbleburstingoccurrencecan be
expected.An accuratepredictionof the onset of burstingis very im-
c
sure tubes at 57% of the chord downstream of the  ap trailing
edge. A pitot static tube was mounted on the side wall in front
of the model, at about two chord lengths from the leading edge.
All pressure taps were connected to a multitube liquid manometer
200tubes equippedwith an automaticinfraredreadingdevice.The
measuredpressurecoefŽ cients were numericallyintegrated trapez-
(
)
(
)
ium rule to obtain the main element and  ap normal force and
pitching moment coefŽ cients. The section proŽ le drag coefŽ cient
was computed from the wake rake total and static pressures using
the Jones method.22 Standardlow-speedwind-tunnelboundarycor-
rections have been applied to the data according to the method of
Allen and Vincenti.23
Experimental Accuracy
The automatic reading devicereads the manometertubes with an
accuracy of 0.1 mm, that is, 1 Pa. Because of the need of a refer-
ence run, the accuracy in the measured pressure values is 2 Pa. A
speciallydevelopedspeedcontrolsystemisinstalledinthewindtun-
nel, accurate within 0.02% of the set speed. When these values are
C
portantbecauseparameterchangesleadingto max improvementare
l
U
C
can be
p
taken into account, the uncertainty
of the measured
C
p
also driving bubble bursting occurrence and because of the strong
link between bursting and the hysteresisphenomenon.
estimated.24 Focusing on the 3.0% gap/1.0% overlap arrangement,
U
D §
we estimate a value of
0:00179513at 0 deg and a value of
0:00430969 at 10 deg. These are roughly the largest and
smallest uncertaintiesfor the 3.0% gap/1.0% overlap arrangement.
The uncertaintiesare the same order of magnitude for the other ar-
rangements as well. The uncertainty
C
p
Manysemi-empiricalmethodstopredictburstingonsethavebeen
proposedin thepast for instance,Crabtree,15 Horton,16 van Ingen,17
(
UC D §
p
1
Dini and Maughmer,18 and Shum . None of them, however, suc-
)
cessfully predict bubble bursting in all  ow conditions, especially
U
in the angle of attack is
®
Re
in the low-Reynolds-number
range, where they require a very
U D §
0:01 deg. The uncertaintyin the gap and overlap measure-
®
accuratetuningto work well. This tuningis time consumingand ex-
tremely difŽ cult when no previous experimental data are available.
For thisreason,these methodsare not practical,and most boundary-
layer codes for design purposes do not include them. In addition,
these codes usually show no sign of breakdown when close to the
conditions when bursting occurs in the experiments. As a result
of these modeling difŽ culties, experimental tests are necessary to
verify the numerical design.
U
ments, g;o, is estimated to be about 0.1 mm, hence, 0.02% of the
)
U
chord.
D §
0:02% . The uncertaintyin the integratedquantities
g;o
is more difŽ cult to estimate. It depends on the spacing between the
oriŽ ces,and itishigherintheregionsofhigh-pressuregradients,that
is, close to the nose. Errors due to three dimensionality of the  ow
–
were minimized by the suction applied at the wing wall junctions.
Experimental Results
All pressure distributions presented in this section are measured
Flap of the Eaglet
c
with a gap of 3% and an overlap of 1% of the chord . However, lift
In the present investigation, one of the most widespread and ef-
Ž cient boundary-layerdesign codes, the MSES code developed by
Drela,3 was used for the design of a single slotted  ap for the Euro-
ENAER Eagletutilityaircraft19 startingfroma NACA 63-415airfoil
section.TheoptimumgeometrywascheckedintheLow SpeedWind
and drag curves from other  ap settings are also presented to show
–
the trends resultingfrom changes in gap overlap. All results shown
(
)
are relative to the  ap in landing conŽ guration 30-deg de ection .
–
A scheme relating the gap overlap settings to the occurrenceof the
hysteresis loop is shown in Fig. 3. The effect of a change in gap
dimension was particularly investigated. For the overlap, only two
different setups were checked, 1 and 2%. As can be seen in Fig. 3,
a rise in the gap increases the possibility of a hysteresis loop. For a
gap value of 1.5%, no hysteresis was observed. On the other hand,
for a gap value of 4%, the  ow over the  ap was always separatedat
all measured angles of attack. Changes in the overlap value around
the computed optimum position seemed to be less relevant to the
occurrence of hysteresis than a change in the gap. However, for
2.0% gap, hysteresis was observed for an overlap value of 1%, but
not for an overlap of 2%. For a 1% overlap and 2.5 and 3.0% gap
values, the  ap was separatedat the beginningof the measurements
Tunnel LTT of the Delft University of Technology.20 The analysis
(
)
for the cruise conŽ gurationwas found satisfactory,but when testing
the landingconŽ guration 30-deg ap de ectionand
large discrepancies with the numerical predictions were found. In
the next sections, Ž rst the experimental results will be shown and
then the numerical calculations.
6
(
)
Re D
£
2
10 ,
Experimental Investigation
Experimental Setup
The LTT of the Delft Universityof Technologyis a closed-return-
type wind tunnel with a contractionratio of 17.9 Ref. 20 . The test
section is 1.8 m wide, 1.25 m high, and 2.6 m long. The tunnel is
(
)
(
)
0 , and ® had to be lowered Ž rst, before obtaining an attached
D
®

BARAGONA ET AL.
1233
a) Cl–Cd curve
Fig. 3 Observed relationship between gap–overlap and hysteresis
¡
occurrence in the measured range from ® » 6 to ® » 16 deg,
Re = 2 £ 106, NACA 63-415 airfoil with slotted  ap.
b) Cl–® curve
Fig. 5 Experimental drag and lift coefŽ cient for gap 3.5, 4, and
3.0% (overlap 2.0%) showing the hysteresis loop for the 3.5% case,
Re = 2 £ 106, NACA 63-415 airfoil with slotted  ap.
a) Cl–Cd curve
a) Cl–Cd curve
b) Cl–® curve
Fig. 4 Effect of gap variation before bursting occurrence (overlap
2.0%), Re = 2 £ 106, NACA 63-415 airfoil with slotted  ap.
 ow on the  ap surface.This effect is rather peculiarand is reported
also by Biber.9
When bubble bursting does not occur, a wider gap enhances the
performance of the conŽ guration in terms of lift coefŽ cient. This
–
C
Cd
polar and the
effect can be seen clearly in Fig. 4, where the
l
lift curve for 1.5, 2.0, and 2.5% gap, with 2.0% overlap, are shown.
C
The maximum
increases by increasing the gap, ranging from
l
Cl
D
C
D
C
D
2:4 to
2:5 upto
2:52,respectively.However,a
l
l
max
wimdaex r gap also increasesthe danmgaex r of bubble bursting over the  ap
b) Cl–® curve
–
C
Cd
polar and the
surface, as can be seen in Fig. 5, where the
Fig. 6 Gap 3% overlap 1%: experimental results and computational
predictions (see also Fig. 7), Re = 2 £ 106, NACA 63-415 airfoil with
slotted  ap.
l
The corresponding pressure distributions are shown in Fig. 7 for
some representative angles of attack covering the entire hystere-
(
D
sis loop. At the beginning of this test ® 0/, right after turning
on the wind tunnel, the  ow over the  ap was completely sepa-
¡
rated. The  ow attached only after ® had been lowered to 6 deg
(
)
Fig. 7a . From this starting value, the pressure distributionson the
¡
 ap and main airfoil were recorded.Raising ® from 6 up to 11 deg
–
(
)
Figs. 7a 7f , the  ow on the  ap stayed attached. The main airfoil

1234
BARAGONA ET AL.
g) ®= 11.5 deg, rising; bursting on the  ap
¡
a) ® = 6 deg, start of measurement
h) ® = 15 deg, maximum ® reached in experiment
¡
b) ® = 2 deg, rising
i) ® = 10 deg, decreasing
c) ® = 2 deg, rising
d) ® = 4 deg, rising
e) ® = 8 deg, rising
f) ® = 11 deg, rising
j) ® = 6 deg, decreasing
k) ® = 2 deg, decreasing
l) ® = ¡6 deg, decreasing; pressure recovery on the  ap
Fig. 7 Hysteresis loop for gap 3% overlap 1%: pressure distribution, Re = 2 £ 106, NACA 63-415 airfoil with slotted  ap.

BARAGONA ET AL.
1235
kept on gaining lift, while the pressure peak on the  ap nose was
slightly reduced as ® was increased. From Fig. 6b it can be seen
Numerical Results
For the prediction of the transition point in the present analysis,
C
that the
n
an factor equalto 7 was chosenbased on previousexperiencewith
l
C
about
the designand wind-tunneltestingof the wing airfoilfor the general
l
max
sure distribution over the  ap suddenly leveled, as can be seen in
(
)
(
aviation aircraft EXTRA 400 Ref. 19 . The grid used was the most
C
C
D
Fig. 7g. As a result, the
dropped to a value of about
1:9
)
£
reŽ ned used in the accuracy analysis 197 40 points .
The 3.0% gap/1.0% overlap case will be especially compared
l
l
max
(
)
(
C
Fig. 6b while the
increased to almost twice its value before
bursting Fig. 6a . The angle of attack was still raised up to 15 deg
d
)
with the experimental Ž ndings. From Fig. 8 it can be noticed that
(
)
Fig. 7h . The trailing-edgeseparation on the main element, which
could hardly be noticed in Figs. 7f and 7g, is now covering most
C
C
in-
d
of the main element surface, resulting in further loss and
l
(
)
crease Fig. 6 . When the angle of attack was lowered, the  ow on
D
the  ap stayedseparatedfar beyondthe valueof ® 11:5 deg where
bursting Ž rst occurred Figs. 7i 7k , causing the hysteresis loop of
–
(
)
¡
Fig. 6b. The angle of attack had to be lowered to 6 deg to obtain
again an attached  ow on the  ap Fig. 7l .
(
)
In this case, the reason for the hysteresis occurrence is readily
identiŽ ed with the  ap  ow behavior. The pressure distributions
show that the  ow over the  ap separatedsuddenlywith the charac-
teristics of a leading-edge-typestall due to bubble bursting. Mean-
while, no major trailing-edgeseparation on the main wing was de-
(
)
tectedat thisburstingonset Figs. 7fand 7g . Such trailing-edgesep-
aration on the main airfoil has been reportedon other multi-element
9
conŽ gurations and appears after bursting also in the presentanaly-
sis, as can be seen from the pressuredistributionat 15 deg. However,
(
)
at bursting for ® between 11 and 11.5 deg , while the pressureover
the  ap is leveled, only the effect due to the loss of circulation is
evidenton the main wing. The  ow appearsto be separatedclose to
the trailingedgeof the main elementbut in this case this seems to be
the consequencerather than the cause of the separation on the  ap.
Computational Investigation
The MSES code solves the Euler equationsstrongly coupled to a
two-equationsintegralboundary-layerformulation.Two-pointcen-
tral differencing is generally used to discretize the boundary-layer
en
equations.Atransitionpredictionmethodofthe type25 isincluded
in the viscous formulation. The complete set of equations is then
–
solved by a global Newton method so that strong viscous inviscid
a) Lower branch of the hysteresis loop  ap
interactions can be taken into account.3 MSES has proven to be a
very useful tool for multicomponent airfoil design purposes. It is
currently widely used for the design of many successful airfoils.
Large separationregions can, in principle, be handled, although, as
for all other boundary-layer codes,14 the results are less accurate.
The codeis a steadysolver,and thus,no unsteadyeffectscan be cap-
tured. As for all other codes for design purposes, MSES does not
includeany burstingcriterion,and no warning regardingits possible
onset is given to the designer.
Numerical Accuracy
A convergencestudyin spacewas performedusingthreedifferent
p
C
grids with a reŽ nement ratio of 2 comparing the values of the
l
(
C
and d of the whole conŽ guration. The grids had about2000,4000,
and 8000 points, with 64 points on the  ap surface and 94 on the
)
main element, 92 and 132, 136 and 188, respectively . Following
Stern, et al.26 it is then possible to check under which convergence
conditionthe calculationsare performed.This can be done by look-
–
R
ing at the ratio
between the solution changes for medium Ž ne
k
–
R D
and coarse medium solutions. In this case, a value of
0:1546
k
was found, which means a monotonic convergence condition that
allows an estimate for the order of accuracy and the leading-order
term of the space discretizationerror of the solution. For this, gen-
(
)
eralized Richardson-extrapolation is used see Ref. 26 giving an
order of accuracy of 5.4 against an expected theoretical value of 2.
This result for the order of accuracymeans that the solutionsare not
in the asymptotic range and that the leading-orderterm of the series
expansion estimating the error underpredicts the error. The uncer-
value, thus, will be estimated.26
C
l
U
tainty
When a clorrection factor accounting for the higher-orderterms26 is
D §
, not the error on the
C
b) Upper branch of the hysteresis loop
U
used,a value of
performedfor the
is found for the drag coefŽ cient.
0:0198 is found.When a similaranalysis¡i5s
C
Fig. 8 Pressure distribution on the  ap for ® = 8 deg, gap 3%/overlap
1%; experimental results vs computational predictions, Re = 2 £ 106,
NACA 63-415 airfoil with slotted  ap: ——, calculated.
l
C
U
D §
£
values,an uncertaintyof
5:25 10
d
C
d

1236
BARAGONA ET AL.
the pressure distribution over the  ap as computed appears to be
physically different from the experimental results. The computed
model predicts a small laminar bubble at about 20% of the  ap
chord followed by a turbulent separation that approaches the reat-
tachment point of the bubble when ® is increased. This result is
very different from the sudden leading-edge stall observed in the
experiments. No relevant turbulent separation previous to bursting
is evident from the experimental pressure plots on the  ap. Figures
9 and 10 show a typicalskin-frictioncoefŽ cient and boundary-layer
Bursting Prediction and Unsteadiness of
Low-Reynolds-Number Laminar Separation
The  aw found in the numerical predictions of bursting onset
suggests that the modeling, if not the understandingof the physics
involved, is still lacking. In this section, an attempt is made to indi-
cate what seems to be missing in the classical model of a laminar
separation bubble.
The region where the  ow reattaches to the surface has always
been described as turbulent and steady in the mean  ow. This is
(
)
parameters ± and µ distributionas given by MSES in thissituation.
On the upper surface, the skin friction becomes zero at the location
x c D
Re
probably true at higher Reynolds numbers
, where transition
is more readily connected with viscous primary instabilities, that
of laminar separation
=
0:857, and it stays negative over the
–
is, Tollmien Schlichtingwaves ampliŽ cation without necessarily a
length of the bubble before being zero again at turbulent reattach-
vorticitymaximumawayfromthewall.At lowerReynoldsnumbers,
however, availableexperimentalevidenceshows that a differentbe-
havior may be expected.
x c D
ment,
again at about
=
0:868. After turbulent reattachment, it becomes zero
x c D
=
0:92, being the location of the predicted tur-
bulent separation.When Fig. 10 is examined, both µ and ± display
a large increase after turbulent separation before decreasing in the
wake. The stall behavior on the  ap is controlled by the turbulent
separation proceedingfrom the trailing edge, with transitiontaking
place in the bubble just before the reattachment point. The experi-
ments show, however, that stall suddenly takes place on the  ap as
a result of bursting of the laminar bubble,with no previous relevant
separation taking place on the  ap surface. Consequently, MSES
underpredicts the lift and overpredicts the drag. To show this, the
Gaster27 Ž rst observedin his experimentsthat low-frequencyos-
Re
cillationsseemed to be a characteristicof low Reynoldsnumber
bubbles. These oscillationswere especially strong in long bubbles;
a patch of high-frequency turbulence formed intermittently in the
earlystagesof transition,delayingtheformationofa continuoustur-
bulentsignalto a positionmuch more downstreamthanin the higher
28
Re
Reynolds number , short bubbles he tested. Gleyzes et al. ex-
perimentally analyzed the transitional  ow over the surface of an
ONERA LC-100-D airfoil at Reynolds numbers equal to 0:5 10
and higher. They focusedon the long bubbleobtainedafterbursting.
Flow visualizations showed the formation of well-deŽ ned vortical
structuresin the rearregionofthislongbubbledueto theappearance
of an in ection point, that is, a vorticity maximum, in the separated
6
£
–
–
C
Cd
C
polar and
l
computed
® curves for gap 3.0% overlap 1%
l
are compared with the measuredones in Fig. 6. The large separated
regionafterturbulentseparationpredictedby the codeis responsible
for these discrepancies. The presence of unsteady structures in the
 ow, which is, of course, not modeled in the code, may well be one
of the reasons for this result.
(
laminar shear layer velocity proŽ le a so-called inviscid primary
instability .
)
These structureswere seento characterizestronglythe Ž rst stages
of turbulent boundary layer development and to be quite persistent
in the ensuing turbulent  ow as well. In both investigations, how-
ever, no additionaleffortswere made to better understandwhat was
going on, nor to identify the parameters involved. No more recent
experiments on the topic are known to the authors.
More recently, Ripley and Pauley29 reproduced numerically
27
–
Gaster’s experiments, using an unsteady laminar Navier Stokes
solver. They identiŽ ed the aforementioned structures with the oc-
currence of vortex shedding in the rear region of the bubble. A
large-scale laminar vortex shedding resulted for the long bubble.
The shedding was indeed found also for the short bubbles tested in
Gaster’s work. In this case, however, the frequencywas higher, and
the strength of the disturbance signiŽ cantly lower. Time averaging
the unsteadyresults, Ripley and Pauley found that the surface pres-
suredistributionsmatchedGaster’s Ž ndingsand thatthe streamlines
(
)
showed the classical steady closed bubble pattern Fig. 1 . Similar
numerical Ž ndings were reported for an Eppler 387 airfoil.29 The
same vortexsheddingoccurrencewas later conŽ rmed by the numer-
ical resultsobtainedby Tatineniand Zhongover the APEX airfoil.30
Fig. 9 Friction coefŽ cient Cf over the  ap showing laminar bubble
(negativeCf ) and turbulent separation, Re = 2 £ 106, NACA 63-415air-
foil with slotted  ap: – – –, ®= 10 and ——, ® = 11.5.
Fig. 10 Displacement ± and momentum µ thickness on the  ap, Re = 2 £ 106, NACA 63-415 airfoil with slotted  ap: – – –, ® = 10 and ——, ® = 11.5.

BARAGONA ET AL.
1237
The analyses of Ripley and Pauley29 and Tatineni and Zhong 30
were two dimensional and neglected completely any small-scale
turbulenceeffect. Their results clearly show, however, that the lam-
inar part of the bubble is not a region of stagnant  ow but rather a
region where shedding of well-deŽ ned vortical structures periodi-
callyoccurs.These structuresand theireffecton the mean  ow grow
Flows,” Proceedings of the Seminar in Boundary-Layer Separation in Air-
craft Aerodynamics, Delft Univ. of Technology, Delft, The Netherlands,
–
1997, pp. 109 126.
7Wu, J. Z., Tramel, R. W., Zhu, F. L., and Yin, X. Y., “A Vorticity Dy-
namics Theory of Fully Three-Dimensional Flow Separation near a Generic
Separation Line,” AIAA paper 99-3695, 1999.
8Rist, U., Maucher, U., and Wagner, S., “Direct Numerical Simulation of
Some Fundamental Problems Related to Transition in Laminar Separation
Bubbles,” Computational Fluid Dynamics’96, edited by J.-A. De´side´ri, C.
Re
stronger when the Reynolds number
drops. Moreover, in the
Re
Reynolds number
range where they are present,these structures
–
seem to grow stronger when the short bubble approaches bursting
conditions and Ž nally turns into a long one. In the short bubble far
frombursting,the reattachmentregioncould indeedbe substantially
steady or weakly unsteadyin the mean  ow, as well as, most likely,
fully turbulent: The laminar structures are weaker in this case, and
they are likelyto dissipaterapidlyafterreattachment.Close to burst-
ing and in the long bubble, the reattachment region would instead
be characterized by a strong shedding of laminar structures, long
persisting in the turbulent  ow developing behind the bubble. This
differencein the local stability characteristicsof the laminar bubble
may well be a signal for determining the onset of bubble burst-
ing conditions. All bursting predictors developed so far assume a
substantially steady, stagnant  ow in the laminar part of the bub-
ble. This assumption appears to be incorrect, especially at lower
Reynolds numbers and may explain their poor performance in this
range. This difŽ culty of an accurate prediction of transition onset
position stems also readily from the precedingdiscussion:The cus-
tomary assumption that transition occurs at the laminar separation
point31 is found to be inadequate, especially for the low-Reynolds-
Hirsch, P. Le Tallec, M. PandolŽ , and J. Pe´riaux, Wiley, 1996, pp. 319 325.
9Biber,K., “PhysicalAspectsofStall-Hysteresis on an AirfoilwithSlotted
Flap,” AIAA Paper 95-0440, Jan. 1995.
10Biber, K., and Zumwalt, G. W., “Hysteresis Effects on Wind-Tunnel
Measurements of a Two-Element Airfoil,” AIAA Journal, Vol. 31, No. 2,
–
1993, pp. 326 330.
11Gault, D. E., “A Correlation of Low-Speed Airfoil Section Stalling
Characteristics with Reynolds Number and Airfoil Geometry,” NACA TN
3963, March 1957.
12Smith, A. M. O., “Aerodynamics of High-Lift Airfoil Systems,” Fluid
–
Dynamics of Aircraft Stalling, CP-102, AGARD, 1972, pp. 10-1 10-26.
13
–
Chow, R. R., and Chu, K. W., “Navier Stokes Solution for High-Lift
Multi-Element Airfoil System with Flap Separation,” AIAA Paper 91-1623,
1991.
14Balleur, J. C. L., and Ne´ron, M., “Une Me´thode d’Interaction Visqueux
Non-Visqueux pour Ecoulements Incompressibles Hypersustentes sur Pro-
Ž ls Multi-Corps en Re´gime de De´collement Profond,” High-Lift Systems
Aerodynamics, CP-515, AGARD, 1993.
15Crabtree, L. F., “Effects of Leading-Edge Separation on Thin Wings in
Two-Dimensional Incompressible Flow,” Journal of the Aeronautical Sci-
–
ences, Vol. 24, No. 8, 1957, pp. 597 604.
16Horton, H. P., “A Semi-Empirical Theory for the Growth and Bursting
of Laminar Separation Bubbles,” Aeronautical Research Council, CP-1073,
London, 1969.
Re
number range.Whenthe laminarboundarylayeris stableenough
to avoid this early breakdown, the prediction of transition onset is
indeed a big challengedue to the number of parameters involved.32
17van Ingen, J. L., “On the Calculation of Laminar Separation Bubbles in
Two-Dimensional Incompressible Flow,” Conference Proceedings on Flow
–
Separation, CP-168, AGARD, 1975, pp. 11-1 11-16.
Conclusions
18Dini, P., and Maughmer, M. D., “A ComputationallyEfŽ cient Modeling
of Laminar Separation Bubbles,” Proceedings of the Conference in Low
Reynolds Number Aerodynamics, Univ. of Notre Dame, Notre Dame, IN,
June 1989.
The problem of bubble bursting and stall hysteresis has been
presented and discussed. The relevance and the danger of bursting
at high lift has been pointed out, and the importance of an accurate
predictionof thisphenomenonhasbeenstressed,notonlyfor single-
19Tromp, E., “Design of Single Slotted Flaps for the EAGLET,” M.S.
Thesis, Dept. of Aerospace Engineering, Delft Univ. of Technology, Delft,
The Netherlands, June 1997.
Re
element airfoils at low Reynolds number
, but also for multi-
element slottedconŽ gurations,where the possibilityof burstinghas
been only recently discovered.
20Dushin, A. B., “Aerodynamic Design and Tests of Wing Airfoils for
Low-Speed Application,” M.S. Thesis, Dept. of Aerospace Engineering,
Delft Univ. of Technology, Delft, The Netherlands, Nov. 1998.
21Foster, D. N., and Lawford, J. A., “Experimental Attempts to Obtain
Uniform Loading over Two-Dimensional High-Lift Wings,” Royal Aircraft
Establishment, Rept. RAE-TR68283, Farnborough, England, U.K., 1968.
22Jones, B. M., “Measurement of ProŽ le Drag by the Pitot-Traverse
Method,” Aeronautical Research Council, R&M No. 1688, London, 1936.
23Allen, H. J., and Vincenti, W. G., “Wall Interference in a Two-
Dimensional Flow Wind Tunnel with Consideration of the Effect of Com-
pressibility,” NACA Rept. 782, 1944.
The experimental and numerical results obtained on a single-
slotted ap conŽ gurationdesignedfor the wing of a generalaviation
aircraftwere presented.The resultsclearlyshowthatcurrentnumer-
ical design codes are incapable of predicting bursting occurrence.
This is indeed a major cause for concern: Once bursting occurs, it
–
C
can give rise to a large hysteresisloop in the
® curve. The angle
l
of attack has to be lowered appreciablyto regainprestallconditions.
Aliteraturereviewwascarriedoutshowingthatthecurrentunder-
standingof the physicsunderlyingthe bubbleburstingphenomenon
isstilllackingofmanyissues,mostofthemrelatedtothe structureof
the transitionalregion.A numberof crucialpoints,especiallyrelated
to the unsteadiness of the laminar separation, have been identiŽed
as currently missing for an effective bursting prediction.
24Kline, S. J., and McClintock,F. A., “Describing Uncertainties in Single-
–
Sample Experiments,”MechanicalEngineering, Vol. 75, Feb. 1953,pp. 3 8.
25van Ingen, J. L., “Teaching and Research in Boundary-Layer Flows,”
Proceedings of the Seminar in Boundary-Layer Separation in Aircraft
Aerodynamics, Delft Univ. of Technology, Delft, The Netherlands, 1997,
–
pp. 139 162.
Further research will focus on the importance of the laminar un-
26Stern, F., Wilson, R. V., Coleman, H. W., and Paterson, E. G., “Com-
prehensive Approach to VeriŽ cation and Validation of CFD Simulations—
Part 1: Methodology and Procedures,” Journal of Fluids Engineering,
steadinessforthestructureofthebubble,especiallyclosetoandafter
–
bursting conditions. Unsteady experiments and unsteady Navier
Stokes calculationswill be performedto improve the existingburst-
ing prediction methods.
–
Vol. 123, Dec. 2001, pp. 793 810.
27Gaster, M., “The Structure and Behaviour of Laminar Separation Bub-
bles,” CP-4, AGARD, May 1966.
28Gleyzes, C., Cousteix, J., and Bonnet, J. L., “Bulbe de De´collement
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(
)
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A. Plotkin
Associate Editor