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J O U R N A L O F A I R C R A F T
Vol.
31, No. 2,March-April 1994
Quantitative Low-Speed Wake Surveys
G. W.
Brune*
Boeing Comm ercial Airplane
Group, Seattle,
Washington
98124
Theoreticaland practical aspectsof conducting three-dimensional
wake
measurements in large
wind
tunnels
are reviewed
with
em phasison applicationsin low-speed aerodynamics. Such quantitative wake surveys furnish
separatevalues
for thecomponentsof drag
such
as
profile
drag and
induced drag,
b utalso
m easure li t
without
the use of abalance. In addition toglobal
data,
details of the wake flowfield aswell as
spanwise
distributions
of
l i t
and
drag
are
obtained. This article demonstrates
the value of
this measurement technique using
data
from wakemeasurements conducted on a variety of
low-speed
configurations including the
complex high-lift
system of a transport aircraft.
Nom enclature
b = model span
C
D
-
total drag
coefficient
C
D
. =
induced drag coefficient
C
D
- profile drag coefficient
C
L
= total lift coefficient
c = local
wing
chord
c
d
. = wing section induced drag coefficient
c
d)
=
wing section profile drag coefficient
c, =
wing
section lift coefficient
M = Mach number
p
= static pressure
p, =
total pressure
q = dyna mic pressure
Re = Reynolds number
5 = tu nn el cross-sectional area
U
=
axial velocity
component
V, W =
crossflow
velocity components
y,z Cartesian coordinates
in
measuring plane
a = angleofattack
AC
D
= upsweep drag
= axial compon ent of vorticity, Eq. (8)
p = density
a =
source,
Eq. (9)
< I>
= velocity potential,
Eq.
(11)
^
=
stream
function, Eq.
(10)
Subscripts
f t = value pe r
foot
MA C
= meanaerodynamicchord
ref
= reference condition
00
= freestream values
Introduction
Q
UALITATIVErwake surveys employing wake imaging
have verified that most aerodynamic
flows of
interest
are stable.
1
Moreover, theycan be surveyed economicallyin
large
windtunne ls using mechanicaltraversersandpneumatic
probes* Qualitative wake surveys are conducted to visualize
theflowfield, whichis aprerequisiteto abetterunderstanding
of aerodynamic performance.
Quantitative
three-dimensional wake surveys
are a
natura l
extension of wake imaging; They allow separate measure-
ments ofprofile drag, induced drag, an d
lift,
including span-
wise
distributions. How ever, there
are significant
differenc
indata acquisition
and
processing betw een w ake imaging
an
quantitative wake surveys.
The
latter
requires
the use of
pneumatic
probe with multiple holes instead
of
asingle tot
pressure probeto record pressures and velocities whichca
then be
converted into aerodynamic forces. Furthermore
quantitative
wake surveys require very accurate probe pos
tion
m easurem ents since spatial derivativesof flow velociti
mustbe computed duringdatareduction.
Quantitativew ake surveys are ofmu ch value to the aer
dynamicdesign
of
airplanes
for the
following
reasons:
1) Theycan be used as a diagnostic tool during airplan
development to
study
the effect of
configuration changes
o
the
components
of
drag.
2)
Separate measurements of induced drag and profile dra
facilitate
the
prediction
of
flight drag based
on
measuremen
at low
Reyno lds num ber w ind-tunnel test con di tions. This
because induced drag
and
profile drag
are
associated
wi
different
flow
pheno mena w hich must
be
scaled
differently
account for
changing Reynolds num ber.
3)
Separate measurements of the components of drag a
also
ofvalueto thedeveloperof CFDc odes since profile dra
an d induced drag
ar e
usually predicted
with different
aer
dynamic
flow models which must be validated separately.
Thisarticle describes the wake survey technique in use
the
Boeing Aerodynamics Laboratory which
is
based
on th
work
of Maskell
2
an d
Betz.
4
The underlying theory for th
measurement of
induced drag
and
lift
ha d
been published
b
Maskell whoalso conducted an exploratory w ind-tun nel te
confirming the validity of his method. The theory for th
measurement ofprofile drag is that of
Betz.
3
'
4
.
Th ew ake survey methodology also includes certain f eatur
of
the work ofothers. Among them are Wu
5
an dHackett
6
whocontributed to the theoretical fou ndatio n and develope
apractical w ake survey method with emphasiso napplicatio
in automotive engineering.
Severalother experimentalistsreported quanti tative wak
surveys.
Onorato
et
al.
8
conducted w ake measurements b
hind
models of automobiles, but their drag analysis
does
n
utilize
the
simplifications introduce d
by
Maskell
an d
Bet
Chometon and
Laurent
9
performed wake measurements
o
asimple win gtoinvestigatethe relation between induced dra
and
vortexdrag,Weston
10
ofNA SA Langley conducted qua
titativew ake surveys behind w ing half-mode ls based on th
theory
of
Maskell
and Betz. In his
data analysis, Westo
focused on the
role
of
vortex cores,
an d
modified
the
def
nitions
of
profile
drag an d induced drag implementing
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Wakes of two-dimensional airfoils have been routinely
measured
f ormanyyearswiththe primary objec tive of getting
accurate profile
drag
data which cannot be obtained
from
balances. Wake
surveys
of three-dimensional
configurations
haveocc asionally
been
conducted
but are not
widelyaccepted
by
design aerodynamicists.
The main
reason
for this is a le-
gitimate
concern about thecost of such wake measurements
which require the measurement of a large number of
data
points.
This ca n indeed be a time consuming and, hence,
expensive process if methods that work so well in
two-di-
mensional wake surveys are
applied
wi thout further refine-
ments.
I n
addit ion,three-dimensionalw a ke
surveys
were
sus-
pected to be inaccurate since the
desired
drag and lift values
are the
com posites
of a large
numbe r
of individual measure-
ments.
This articleaddresses these an d other issues and re-
ports on theprogressmade sinceMaskellconducted the
first
wind-tunnel test
of this kind at the Royal Aircraft Establish-
ment
in the UK some20 yrago.
Theory
Assum ptions
Aerodynamicforcesa recalculated
from
th emeasuredwake
flow data assuming the following:
1)
Wake
flow data
are
measured
in a single
plane
down-
streamof themodel .
This plan e,
locatedat theso-calledwake
survey station
(Fig. 1), is
assumed
to be
perpendicular
to the
wind-tunnel
axis. In
mostwind tunne ls ,
the wake survey
sta-
t ion must be moved veryclose to the model because of
test
section and hardware limitations.
2)
The flow at the
wake survey
station is steady and in-
compressible
w hich limitsthe freestream Machnum ber in the
wind
tunnel
to about0.5.This
does
not
turn
out to be a serious
l imitation,
as
will
be
discussed later.
3) The flow in the empty wind tunne l is a
uniform
free-
stream
parallel to the tunnel axis. Any deviations from
this
ideal wind
tunne l ,
as
well
as instrumentation misalignments,
ar e
assumed
to beaccountedfor bym easurementsat the wake
survey
station with
the
model
and its
support
apparatus re -
moved.
4) The effective
ceiling, floor,
an d side walls of the empty
wind
tunnel , defined
as the geometric
walls modified
by the
displacement
thickness
of the
wallbo undary layers developing
in th e empty
tunne l ,
ar e
such
that the tunnel
freestream
ve-
locity
is everywhere tangent to
these
surfaces.
Note
that the
presence of a
model ,
particularly a
model that
is
large
com-
pared to the
test section
size, will disturb this displacement
surface. Also
notice that
thischoice neglects
the possible ef-
fect of an axialpressure gradient in the empty tunne l
(buoy-
ancy).
5) Viscous
shear stresses at
the wake
survey
station are
neglected.
6)A sw ri t ten , th e equationsdo not account fo rblowingor
suction through the model surface, but could
easily
be mod-
ified.
Com ponents
of Drag
With these assumptions,
an
application
of the
momentum
integral
theorem,employing thecontrolvolume shown in
Fig.
1,
provides
the following equation fo r model drag:
Pt
,-
ds
u
p
c
-T 1
s
Control volume j
^ / lltlliii
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2
Th eeliminationof theu'
termfrom
the induceddrag
equa-
tionis the
most
questionable
aspect
of
Maskell'stheory
since
the distinction between
vortex
drag
and induced
drag disap-
pears.
In princ ipal, theu'termshould remain
part
of induced
drag even
thoug h it is proba blysmallcomparedto vortex
drag
in
many applications.
16
Induced
Drag
According to Maskell, the
remainder
of the induced drag
equation can be
approximated
by
7)
where
the
symbol f
represents the component of wake vor-
ticity
in the direction of the tunnel axis, a is the
crossflow
divergence
o rsource.They are calculated
from
the
measured
V, Wusing
their
definitions
,
is
calculated
from
(U)
dy
2
dz
2
and thefollowing
boundary
condition of no flow
through
the
tunnel
walls:
dn
Notice
that the
first integral
in Eq. (7) is
limited
to the
viscous w akesince vorticity
vanishes
outside.The second term
would stillrequire m easurements throughout the test
section
area, butwakemeasurementsbehind m odels of airplanecon-
figurations have shown that the sourcea is negligibly small
outside the viscous wake. Hence, induced drag can be ap-
proximated
by
0 ,
ds
(12)
Lift
The
momentumintegral
theorem
togetherwith
the control
volume of
Fig.
1 yields the following
equation
fo r
lift:
L
=
p ds - p
ds-
p
WU ds (13)
S3
from the downwash
behind
th e model . The
equation
fo r l
can be cast into the
following form (e.g.,
Refs. 2 and16):
L =
y
ds
+
p
- U )W ds (1
in whichthefirstintegralisexpressedintermsofaxial vortici
which vanishes
outside
the viscous wake
and, hence,
on
requires measurem ents in the
wake .
In most
cases
the secon
integral is
expected
to be small so
thatlift
can be
approximate
by
L~pU^
Instrum entation
(15
Most three-dimensional w akesurveysconductedby
Boein
employ
pneumaticprobes
with
multiple
orifices
mounted o
mechanicaltraversers.A l l wake
surveytestsdescribed
in
th
article
used a single
five-hole
conicalprobe 0.25 in. in dia
(Fig.2), in a nonnulling
mode
f or
fast
data
acquisition. Pneu
maticprobeshave thefollowingadva ntages for testing in larg
low-speed
wind tunnels:
1)
They can accurately and simultan eouslymeasureallthre
components of wake velocity an d total pressure.
2)They provide timeaverageso fdata, therebylimitingth
data
volume
an d data processing time.
3)They
are rugged and not easily
contaminated
by
dirt
the tunnel
circuit.
Data
Reduction
Inthe usualprocedure,the
five-hole
probemeasures tot
pressure
deficit and all
three components
of wake
velocity
alargenumber ofpoints,usuallyinexcessof
10,000.
Handli
thisdatavolume in a
timelyfashion
is themost
difficult
aspe
of the data reduction procedure. Basically, the procedu
consistsof two steps, a review of the data fo rerroneous an
duplicate datasets, and thecalculation of lift an ddrag fro
the final data
set.
Th e
calculation
of
profile drag
using Eq.
(4)
is
straightfo
wardandonlyrequires
integration.
Thecalculationof induc
drag
an d
lift
using
Eqs. (12)
an d
(15)
is
more difficult sin
vorticity
an dsource strength must be computed as interm
diate
results.
Thesecalculations require numerical differe
tiation ofmeasuredcomponents
V
an d W, which ca n easi
lead
to
erroneousvalues
of
induced drag
an d
lift
if not
o
properly. Numericalexperimentation with various schem
showed that accurate vorticity andsource data could be ca
culated by
fitting
cubic
splines
to the measured
crossflow
v
locities.
In
order
to
obtain M
and
< i> from Eqs. (10)
and (11), th
computational domain isextended with uniform
grid
spaci
from thewakesurvey
region
to the
walls
of the windtunne
Wherenecessary,fillets in thecornersof thetest section a
neglected. Values of axial vorticity and source strength a
prescribed
throughout the computationaldomain,w hicha
in generalnonzeroin the wakesurveyregion andzerooutsid
A fast Poisson solver of the FISHPAK library
17
provides s
lutions
fo r
P
and
< I > . Since
the
total num be r
of
grid poin
necessary for the calculation frequentlyexceeds200,000, th
use of asupercomputer isrequired for thisphase of the da
40deg
0.25
in 0
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reduction. Software for this
purpose
has
been developed
at
Boeing.
Standard
correction methods
18
ar e applied to lift and drag
obtained
from wake surveys
to
account
for the
effects
of
wind-
tunnel walls. Th e effect of
model
support strutsis
accounted
fo r
byincluding
part
of the
modelsupport
wakeduring wake
surveys.
Wake
Survey
Test
Results
Threetestsar e described
ranging
incomplexity from mea-
surements
behinda simplewing to a wing-body-nacellecom-
bination inhigh-lift configuration. All
tests
usedbasically the
same data acquisition system an d data reduction procedure,
bu t
different hardware .
High-Lift Test of TransportAircraft
A
large
half-model of a
twin
engine transport w as
tested
at Mach 0.22 and 1.4 million
chord
Reynolds number in the
Boeing
Transonic
Wind
Tunne l .
The tunnel features an 8- by
12-ft test sectionwithslotted
walls. The
wing
was in
high-lift
configuration with
takeoff
flaps
deployed. The model had a
half-span
of 52 in. and wasinstalled vertically above a hori-
zontal
splitter
plate.
Tw o different
engine
simulations were
employed including
a
flow-through
nacelle and a turbopow-
ered
simulator
(TPS).Thepurposeofthisex periment was to
determine the
feasibility
of
makingqu anti tativewake
surveys
using models of realistichigh-lift configurations.
Wake surveys
were
conducted in a plane two mean aero-
dynamic
chord
lengths (2 4
in.) downstream
of the
inboard
wingtrailingedgewhich
w as as far
down stream
a s
testsection
an d data acquisition hardwarepermitted. Th e boundaries of
the
wake
survey
region
(Fig. 3)werechosen to
capture
wing
an d
nacelle wakes, but did not include the wake behind the
fuselage.
Wake surveys are timeconsuming
since
a
large
number of
data points must
be taken to adequatelydescribe the wake.
In
this
case measurements had to be performed at about15,000
wake points. In
order
to
complete
a wake survey within a
reasonable
time of about 2 h, data
were
recorded while the
probe traversed at a fixed speed.
Preliminary investigations
in which the traversing speed w as varied showed that this
mode
of testingproduced accuratedata up to aprobe speed
of
1
in./s.
Measured
velocities
of the
crossflow
perpendicular to the
tunnel
axis
were converted into
axial vorticity as
described
above.
Such
vorticity
data together with the measured total
pressure deficit
provides much
insight
into
the
structure
of
wing
wakes
(Fig.
4). The wake flows are shown in airplane
view with
the wingtip vortex of the right wing on the right
sideof the plots. The n acelle region of the TPS pow ered mo del
is
visible
on the
left
side of
each
plot.
The
vorticity
data in the wake were used to calculatewing
spanload
as
described
in Ref. 19. The result is
shown
in
Fig.
5 together with inviscid
theoretical predictions
of the panel
code P AN A I R .
20
These
theoreticaldata representa
span wise
l i f t distribution,
scaled
by the
local wing chord
an d
nondi-
mensionalized by the sum of all lift an d side
forces
in the
P
f~
P
foo
0 8
a Total Pressure Contours 0.025
Testsection
Wake survey region
-0.8
- 0.025
-0.1
Fig . 4 Wake
flow
data of transport
high-lift
model with turbo-po
ered
simulator (TPS)
nacelles.
Wake surveytestTPSnacelle
1.6
1.2
C
L
REF
C
REF
0.8
0.4
PANAIR
predictions
Nacelle
region
0 0.2 0.4
0.6
0.8 1.0 1.2
2y/b
Fig . 5 Spanwise wing
loads
of transport
high-lift model
from wa
survey
and
PAN AI Rcode predictions.
outboard
wing
an d nacelle
region. Good
agreement is de
onstrated outboard of the nacelle. The large
differences
the nacelle region are
mainly
due to sideforces,
which
in t
wake
survey
data, could
not be
distinguished from
lift.
Simple Wing Study
The main objectiveof thistestw as to learnmore
about
t
accuracy
a nd
measurement
repeatabilityo f quantitativewa
surveys.
21
I n
this
test,
the
wake
w as
mapped
behind a simp
rectangular wing
model
which
had a span of
6
ft and an u
twisted
NACA 0016 airfoil section. The test was conduct
at the University of Washington
Aeronautical
Laboratory
an 8- by12-ft
low-speed
windtunne l .A ll
m easurements
we
taken at0.18Mach
numbe r
an d
1.27
million
chord
Reynol
number . The model was installed horizontally at the
cent
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M =
0.18 Re
ft
=1.18x10
Upswept
aftbody
7.2 deg
Symmetric
|---
aftbody
-2 2 4
a~deg
Fig .
Drag componentso f symm etric and upswept
aft-body
config-
urations.
30
AC
D
x10
H
-2
-10
737-300Aftbody
M
=
0.18
Re
ft
= 1.18x10
6
Force
data
Uncertainty o f
force
data
Wake survey
Fig .
10 Upsweep
drag
from balance and wake
surveys.
crements
o f
profile drag
a nd
induceddragassociatedwith
the
addition of vortex
gen erators.
Spanwise distributions of profile drag and induced drag
measured in the wake of
this simple rectangular
wing ar e
shown
in
Fig.
8. Here the
span
wise value of induced drag is
the integrand of the induced drag
integral
of Eq. (12). Notice
that this
quant i ty
differs from
the usualdefinition ofspanwise
induceddrag calculated as the
product
o fwingsection lift an d
induced
angle
of attack.
Aft-Body Drag Tests
Wake
surveyswere conductedwithvar iousfuselage models
of
transport
airplanes
in
order
to improve our
understanding
of
aft-body
flowfields
and the
drag
associated
withthem.Con-
traryto
mostmilitary
transports ,civiltransports
feature mod-
erate
aft-body
upsweep
with
a correspondingly smaller con-
tribution
todrag.The vortices shed
from
such aft-bodies
ar e
relatively
w e a k ,
bu t
their
associated
drag must nevertheless
be understood wh en seeking opportunit ies
fo r
airplane drag
reduct ion.
Aft-body dragexperiments
were carr ied
out in the Boeing
Research Wind
Tunnel inSeattle at
0.18
Mach
n u m b e r an d
1.18 million
Reynolds number
per foot. In all tests, the fu-
selage was supported by wing stubs extending through the
tunnel side walls.
The
wingt ips,
in tu rn ,
were
mounted on an
externalbalance, situated below the
test
section. Thisallowed
acomparison ofwakesurveydrag measurementswithbalance
drag.
Parametric studies
investigating the effect of
aft-body length
an d upsweep
angle
on
fuselage drag provided quantitative
data forvortex
drag
and profile drag as
functions
of angle of
attack.
22
As shown in the example of Fig. 9, vortex drag of
Thiskind of drag is defined as the difference indrag betwe
symmetrican d
upswept aft-bodies
at the sametest
condit io
A s seen,
wake drag
iswel l
within
th e
uncertaintyband
of t
force
measurements
providing further
demonstration
for t
accuracy
of
three-dimensional wake
m easurements.
Conclusions
This article describes the wake
survey
methodology deve
opedatBoeingfor thepurposeof measuring the componen
of
drag of lowspeed, high-lift configurat ions. Impor tan t e
men ts of thistechnique
including
mechanical
probe
travers
an d
pneumat ic probe design, re f inemen t
of the
underlyi
theory,
an d data reduction procedures ar e still
under deve
opment at the
present
time.
However ,
the technique has a
ready been successfully applied inseveral
wind-tunnel
te
as shown in
this article.
The fol lowing valuable
features
this measur ing technique should be noted:
1)
The
wake
survey technique providesseparate measu
ments
of
induced
drag, profile drag, an d
lift.
2) Measurement accuracy and data
repeatability
are com
parable
to balance
measurements ,
even though
lift
and dr
data are the
composites
o f a largenumber of
individual
me
surements.
3)
Small increments
in
individual
components of
drag
d
to minor configurat ion changes can be measured accuratel
4) Spanwise distributions of lift can be
obta ined.This
is
value
in
high-lift
aerodynamics since the small
flap
sizes
most high-lift models make it
extremely
difficult to measu
spanlift data using surface pressure taps. However,
all spa
wise
wing
data measured
in wake surveys should be
inte
preted
with caution
since
they
ar e
usually
distorted to som
degreeby wake roll-up, and
hence
ar einfluenced by practic
limitations
on the location of the plane in which th e surv
is conducted.
5) Wake surveys provide spanwise distributions of prof
drag
and induced
drag, which
are of value in diagnosing t
effects
of local changes to the
configuration
geometry.
6 )
Dur ingeach
w ake survey a
large
num ber of velocity a
pressure data arerecordedwhichcan serve as
validation
da
fo r CFD codes in addition to providing lift an d dragdata.
Acknowledgments
I would like to ackno wledge the technical contr ibutions
mypresent an dformer colleagues at Boeing,in part icular ,
Bogataj,
J. Crowder ,T.
Hallstaff,
M. Hudgins, D. Kotk
R. Stoner, and E. Tinoco. I wou ld also like to thank
McMasters,
M. Mack, and K.
Moschetti
for their review an
comments on the draft of this article.
References
Crowder, J . P . , Quick an d
Easy Flow Field Surveys, Astro
nautics an dAeronautics,Vol. 45 ,
Oct.
1980, pp. 38, 39.
2
Maskell , E. C.,
Progress
Towards a Method for the Measur
ment of the Components of the Drag of a Wing of Finite Span
Royal Aircraft Establishment, TR 72232, UK,Dec. 1972.
3
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