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NASA Technical Paper 3591
Effect of Full-Chord Porosity on AerodynamicCharacteristics of the NACA 0012 Airfoil
Raymond E. Mineck and Peter M. Hartwich
April 1996
NASA Technical Paper 3591
Effect of Full-Chord Porosity on AerodynamicCharacteristics of the NACA 0012 Airfoil
Raymond E. Mineck
Langley Research Center • Hampton, Virginia
Peter M. Hartwich
ViGYAN Inc. • Hampton, Virginia
National Aeronautics and Space AdministrationLangley Research Center • Hampton, Virginia 23681-0001
April 1996
Available electronically at the following URL address: http://techreports.larc.pasa.gov/ltrs/ltrs.html
Printed copies available from the following:
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Summary
A wind tunnel test was conducted on a two-
dimensional model of the NACA 0012 airfoil section
with either a conventional solid upper surface or a porous
upper surface with a cavity beneath for passive venting.
The purposes of the test were to investigate the aero-
dynamic characteristics of an airfoil with full-chord
porosity and to assess the ability of porosity to provide a
multipoint or self-adaptive design. The tests were con-ducted in the Langley 8-Foot Transonic Pressure Tunnel
over a Mach number range from 0.50 to 0.82 at chordReynolds numbers of 2 x 106, 4 x 106, and 6 x 106. The
angle of attack was varied from -1 ° to 6° in 1° incre-
ments. The porous surface nominally extended over the
entire upper surface. The porosity was zero at the leading
and the trailing edges and was distributed by using a
square-root-sine function with a maximum value of
2.44 percent at the model midchord. The average poros-
ity (ratio of total hole area to total porous surface area) of
the upper surface was 1.08 percent.
In general, full-chord porosity reduces the lift curve
slope and increases the drag at a given section normalforce coefficient. At lower Mach numbers, porosity leads
to a dependence of the drag on the normal force. At sub-
critical conditions, porosity tends to flatten the pressuredistribution, which reduces the suction peak near the
leading edge and increases the suction over the middle ofthe chord. At supercritical conditions, the compression
region on the porous upper surface is spread over a
longer portion of the chord. In all cases, the pressure
coefficient in the cavity beneath the porous surface is
fairly constant with a very small increase over the rear
portion. For the porous upper surface, the trailing edge
pressure coefficients exhibit a creep at the lower section
normal force coefficients, which suggests that the bound-
ary layer on the rear of the airfoil is significantly thicken-ing with increasing normal force coefficient. Porous
airfoils exhibit an adaptive characteristic in that the
thickness and the leading edge radius of an equivalent
solid airfoil decrease with increasing Mach number, thus
making the porous NACA 0012 airfoil perform more like
a high-speed airfoil.
Introduction
For supercritical flow over a solid surface airfoil,
the supersonic zone may be terminated by a strong nor-mal shock. In addition to causing wave drag, the pressure
rise across the shock may lead to boundary layer separa-
tion, which further increases the total drag. Narrow
porous surface strips with cavities beneath the surface of
transonic airfoils have been proposed to delay the drag
rise that is associated with the energy losses due to
shocks and shock-induced boundary layer separation
(refs. 1 to 6). The principle underlying this passive drag
reduction technique, often referred to as shock venting, is
presented in figure 1(a).
By placing a porous strip on the surface over a cavity
beneath the foot of the shock, a secondary flow is
induced into and out of the cavity. The velocities through
the surface and the velocities in the cavity are relatively
small by design. Since the velocity of the flow in the cav-
ity is small, the pressure gradient in the cavity is also
small. The pressure level in the cavity can be considered
nearly constant with a value between the minimum andthe maximum pressures on the porous surface. The pres-
sure rise associated with the shock above the porous sur-
face creates a chordwise pressure gradient. Aft of the
shock, the pressure on the porous surface is greater than
the pressure in the cavity, so the secondary flow goesinto the cavity. The secondary flow travels upstream in
the cavity and exits through the porous surface upstream
of the shock, where the pressure on the porous surface is
less than that in the cavity. This secondary flow proceeds
downstream over the porous surface. The resulting bub-
ble of recirculating flow acts like a bump on the airfoilsurface, which leads to an oblique compression wave
(which can be isentropic) that forms the upstream edge ofa lambda shock. To be effective, the porous strip must be
located beneath the shock for the operating Mach numberand lift coefficient.
Flow visualization studies (refs. 1 and 2) show that a
porous strip placed beneath a shock does lead to a weaker
lambda shock system. Data from exploratory experi-ments (refs. 1 to 3) indicate that, at supercritical condi-
tions with a strong shock, a narrow porous strip reduces
the drag, may increase the lift, and increases the buffetboundary. At subcritical conditions, the porous strip
increases the drag (ref. 1).
Computational studies of solutions to the full poten-tial flow, the Euler, and even the Navier-Stokes equa-tions have simulated the flow over an airfoil with a
porous strip (refs. 4 to 7). Calculated results agree with
the experimental data in that a porous strip can increase
the lift and reduce the wave drag. The results also show
the formation of the lambda shock system over the
porous strip. Calculations with viscous effects show that
a porous strip can suppress transonic shock-induced
oscillations causing buffet (ref. 7). When the addition of
a porous strip leads to more negative pressure coeffi-cients on surfaces with downstream-directed, outward
normal vectors, the calculated pressure drag will
increase. Viscous calculations indicate that porosity can
lead to a separated flow region downstream of the porous
strip and to an increase in the viscous drag. Increases in
the pressure and the viscous drag offset to some degreethe reduction of the wave drag. As a result, the net drag
increaseswhenthereiseitheraweakshockor noshockandthenetdragdecreaseswhenthereisastrongshock.
A pressuregradientalongthelengthof aporoussur-facecreatesasecondaryflowfieldthatactslikeabumporalocalincreaseinthickness.Bylocatingaporousstripontheforwardportionof theairfoil,theincreasein localthicknesscanincreasetheeffectiveleadingedgeradiusandcanimprovetheperformanceof theairfoilathighincidenceangles,whichproducesa self-adaptiveairfoil(ref. 8).ResultsfromanEulerstudy(ref.9) showthatporositythatcoversalmosttheentirechord(fig.1(b))notonlydelaysthedragdivergence,butalsoproducessur-facepressuredistributions,whichsuggestthatfull-chordporositymightprovideameansforachievingmultipointdesignfortransonicairfoils.
Thepurposeof thisreportis topresentexperimentalsurfacestaticpressureandwaketotalpressuredistribu-tionssothattheeffectof full-chordporosityonairfoilaerodynamiccharacteristicsis betterunderstood.Theresultsarealsousedto determinewhetherthedelayindragdivergenceandthemultipointdesigncapabilitypre-dictedin theEulerstudyreportedin reference9 canbeachieved.Theexperimentalstudypresentedhereinwasconductedin the Langley8-FootTransonicPressureTunnel(ref. 10) with a two-dimensionalmodelthatincorporatedtheNACA0012airfoilsection.
Twouppersurfacesweretested:onewithfull-chordporosityandtheotherwithnoporosity(solidsurface).Thelowersurfaceof themodelwassolid.Measurementswereobtainedovera Machnumberrangefrom0.50to0.82,anangle-of-attackrangefrom-1° to 6°, andchordReynoldsnumbersof2x 106,4x 106,and6x 106.Chordwisestaticpressuredistributionsweremeasuredontheupperandthelowerexteriorsurfacesof theairfoilandalongthebottomof thecavity.Totalpressuredistri-butionsweremeasuredacrosstheairfoilwake.Thesepressuredata,aswellastheintegratedforceandmomentcoefficients,areusedto studytheeffectof porosityontheairfoilaerodynamiccharacteristics.Equivalentsolidairfoilsweredefinedbyan inversedesignmethodandtheporousuppersurfacepressuredistributionsto assessanymultipointdesigncharacteristicsin theporousairfoilresults.
Symbols
Theresultsarepresentedincoefficientformwiththemomentreferencecenteratthequarter-chord.All experi-mentalmeasurementsandcalculationsweremadeinU.S.customaryunits.
b model span, 83.9 in.
Cp pressure coefficient
Cp, le
C
Cd
Cm
c n
M**
Pt
Pt,*_
Rc
rl e
tmax
x
(X
Ay
rl
o
Subscript:
max
pressure coefficient near the trailing edge(x/c = 0.99)
pressure coefficient at local sonic conditions
model chord, 25.00 in.
section drag coefficient
section pitching moment coefficient resolved
about the quarter-chord
section normal force coefficient
free-stream Mach number
local total pressure in wake, psi
free-stream total pressure, psi
Reynolds number based on model chord andfree-stream conditions
airfoil leading edge radius, in.
airfoil maximum thickness, in.
chordwise distance from the leading edge,positive downstream, in.
normal distance from the chord line or rake
tube location, positive up, in.
spanwise distance, positive out the rightwing, in.
angle of attack, positive leading edge up, deg
measured normal distance - design normaldistance from the chord line, in.
znondimensional spanwise location, _-_
surface permeability parameter
maximum value
Wind Tunnel
The investigation was conducted in the Langley
8-Foot Transonic Pressure Tunnel (8-ft TPT). Informa-
tion about the wind tunnel may be found in reference 10.The tunnel is a single-return, fan-driven, continuous-
operation pressure tunnel. The top and the bottom wallsare slotted and the sidewalls are solid. The test section is
160 in. long with an 85.5-in-square cross section at the
beginning of the slots. The cross-sectional area of the test
section is equivalent to the cross-sectional area of an 8-ft-
diameter circle. A photograph of an airfoil model
installed in the test section is presented in figure 2(a).
The empty test section Mach number is continuously
variable from about 0.20 to 1.30. Stagnation pressure can
be varied from 0.25 atm to 2.00 atm. Air dryers are used
to control the dew point. A heat exchanger located
upstream of the settling chamber controls the stagnationtemperature. Five turbulence reduction screens are
2
locatedjust downstreamof the heatexchanger.Anarc-sectormodelsupportsystemwith ananglerangefrom-12.5° to 12.5° is locatedin thehigh-speeddif-fuser.For this test,a wakerakewasinstalledon themodelsupportsystem.Thewholearcsectorwastrans-latedlongitudinallyto positionthe wakerakeat thedesiredtestsectionstation.
Model
An unswept,two-dimensionalairfoil modelwas
used for this investigation. Photographs of the model are
presented in figure 2 and sketches are presented infigure 3. The model spanned the width of the tunnel at avertical station 1.4 in. above the tunnel centerline. The
model chord was 25.00 in., which yields an aspect ratio
of 3.36 and a ratio of tunnel height to model chord
of 3.42. The angle of attack was set manually by rotating
the model about pivots in the angle-of-attack
plates mounted on the tunnel sidewalls. (See figs. 2(a)
and 3(a).) Fixed pivot settings provided an angle-of-
attack range from -1.00 ° to 6.00 ° in increments of 0.25°:
however, only 1o increments were used.
The model was fabricated in two parts: a main spar
and an interchangeable center insert. (See figs. 3(a)
and 3(b).) The upper and the lower surfaces of the outer
portions of the main spar were solid and followed thecontour of the NACA 0012 airfoil section. The center
portion of the main spar was also solid and the lower sur-face followed the contour of the NACA 0012 airfoil. The
interchangeable insert, installed over the center portion
of the main spar, defined the leading and the trailing
edges of the lower surface, as well as the entire upper
surface of the center portion of the wing. (See fig. 3(b).)
The upper surface of the interchangeable insert was
porous and the lower surface was solid. The model shapewas measured at three spanwise stations and the devia-
tion of the measured airfoil shape from the desired shape
is presented in figure 4. The solid lower surface was very
close to the desired contour, with the maximum deviation
less than 0.0002c. The porous upper surface, with a max-
imum deviation of 0.0009c, did not follow the desired
contour as closely as the lower surface.
The interchangeable center insert was machined with
46 chordwise cavities, each 0.94 in. wide and spaced at
1.00 in. intervals. (See figs. 3(b) and 3(c).) The remain-
ing 0.06 in. between the cavities formed ribs to support
the porous surface. The maximum cavity depth of0.75 in. was maintained from near the nose to the 0.5c
location. The depth decreased linearly from that location
to zero at the trailing edge.
The porous surface was a perforated titanium sheet,
0.020 in. thick. (See figs. 2(b) and 3(c).) The poroussheet had 368 chordwise rows with 440 holes in each
row. The holes were laser drilled with a diameter of
0.010 + .001 in. The porous sheet was bonded to the ribs
with epoxy resin. Near the trailing edge, where the cavity
was shallow, the perforated plate was bonded to the solid
lower surface, which eliminated the porosity there. The
chordwise rows were spaced 0.125 in. apart so that there
were 8 rows over each cavity. The chordwise distribution
of the porosity is defined by
O = Omax,,/sin(/t x/c) (1)
This distribution and the value Ornax= 0.6 were
selected to be consistent with the Euler study of ref-
erence 9. This distribution was implemented by varying
the spacing of the holes along the length of the chord.
Determination of the chordwise spacing of the holes is
presented in the appendix. The average porosity (ratio of
total hole area to total porous surface area) was 1.08 per-
cent and the peak porosity was 2.44 percent.
A single chordwise row of pressure orifices was
installed on the upper surface and the lower surface near
the model centerline. Two spanwise rows of pressure ori-
rices were installed on the upper surface and the lower
surface. A single chordwise row was installed on the bot-
tom of the cavity just to the right of the model centerline.
A sketch of the locations of the pressure orifices is pre-
sented in figure 3(a) and a listing is presented in table 1.The orifices were installed normal to the local surface
and had a diameter of 0.020 in. For the chordwise row,
the upper surface orifices were located on the centerline
(except for the two orifices at x/c = 0 and x/c = 0.0029).The lower surface orifices were located 1.5 in. to the
right of the centerline. There were 49 orifices on the
upper surface that extended from the leading edge backto 0.99c and 47 orifices on the lower surface that
extended from 0.0068c back to 0.99c. The orifices were
concentrated near the leading edge. In the cavity, the ori-rices were located along the center of the cavity bottom,
0.5 in. from the model centerline. (See fig. 3(c).) There
were 13 cavity orifices that extended from 0.033c to
0.923c and spaced at approximately 0.07c intervals. The
two spanwise rows on each surface were located at 0.80cand 0.90c.
Wake Rake
A wake rake was mounted vertically on the model
support system to survey the total and the static pressuredistributions in the model wake on the tunnel centerline.
The rake was pitched on the model support system to
align the maximum total pressure loss with the rake
centerline. Except where noted otherwise, the wake rakestreamwise location was fixed at 37.50 in. downstream of
the model trailing edge. A sketch of the wake rake is pre-
sented in figure 5 and a photograph is presented in
figure 6. The rake tube locations are listed in table 2. The
wake rake had 61 total pressure tubes located between17.685 in. above and 17.685 in. below the rake center-
line. The inside of each total pressure tube was flattened
into an oval shape 0.02 in. high and 0.07 in. wide. Thetubes were concentrated near the center of the rake where
the total pressure gradient was expected to be the largest.
In addition, there were 7 static pressure probes installedbetween 10.015 in. above and 10.015 in. below the rake
centerline in a vertical plane 0.50 in. from the plane ofthe rake total pressure tubes.
Instrumentation
The test section total and static pressures were mea-
sured with quartz Bourdon tube differential pressuretransducers referenced to a vacuum. Each transducer had
a range from +30 psid and a quoted accuracy from the
manufacturer of +0.003 psid. The test section stagnation
temperature was measured with a thermocouple mountedin the settling chamber. The wing static pressures and the
wake rake static and total pressures were measured with
an electronically scanned pressure measurement systemwith a transducer dedicated to each orifice. Each trans-
ducer had a range of +5 psid and a quoted accuracy from
the manufacturer of +0.005 psid. The model angle of
attack was determined by a pinhole selected to fix the
model attitude on the angle-of-attack plates.
Tests and Procedures
The model angle of attack was set manually. Theangles used for this test ranged from -1 o to 6 ° in 1°
increments. At each angle of attack, the free-stream
Mach number was varied from 0.50 to 0.82 at Reynoldsnumbers of 2 x 106, 4 x 106, and 6 x 106 based on a
model chord of 25.00 in. The nominal test conditions are
presented in table 3. All tests were conducted at a stagna-tion temperature of 100°F. At each test condition, the
model support system (and consequently the wake rake)angle was adjusted so that the location of the maximum
loss in total pressure coincided with the center tube of the
wake rake. This ensured that the portion of the wake with
the largest total pressure gradient was measured by that
portion of the rake with the closest total pressure tubespacing. Normally, the total pressure tubes on the wake
rake were positioned 1.5c (37.5 in.) downstream of the
model trailing edge at an angle of attack of 0% A limitednumber of measurements were obtained with the wake
rake positioned 1.0c (25.0 in.) downstream of the model.
A comparison of the results obtained with the wake rake
at these two locations, presented in figure 7, shows nosignificant effects from the wake rake location on the
integrated force and moment coefficients.
Boundary layer transition was fixed for all tests with
a 0.1-in.-wide strip of number 80 carborundum grit onboth the upper and the lower surfaces. The strip on each
surface began 1.25 in. back (x/c = 0.05) from the leading
edge. The grit size was determined by using the tech-nique described in reference 11.
The section normal force and pitching moment coef-
ficients were obtained by numerically integrating (with
the trapezoidal method) the local pressure coefficient at
each orifice multiplied by an area weighting function.
(The area weighting function is determined by the loca-
tion of the surface pressure orifices.) The section drag
coefficient was obtained by numerically integrating (withthe trapezoidal method) the point drag coefficient calcu-
lated at each rake total pressure tube by using the proce-dure of Baals and Mourhess (ref. 12).
No corrections were applied to the model angle ofattack or to the free-stream Mach number for the effects
of top and bottom wall interference or to the Mach num-
ber for sidewall interference. Corrections to the porousairfoil results should be similar to the corrections to the
solid airfoil results at similar test conditions. Therefore,
comparisons of porous and solid airfoil results at similar
test conditions should provide reasonable values for theeffects of porosity.
A single porous insert with 0.75-in-deep cavities wastested. The solid surface results were obtained from the
model with the porous insert covered with an impervioustape. The tape, which was 0.002 in. thick, covered the
exterior of the model from the location of the transition
strip on the lower surface, extending around the leading
edge, and continuing back to the upper surface trailing
edge. By using the same upper surface shape for both the
solid and the porous surface tests, the effect of changes inthe shape between the solid and the porous surface testsshould be minimized.
Data Quality
As noted previously, the upper surface shape devi-
ated slightly from the design shape. To evaluate theeffect of the difference, the results from the current test
are compared in figure 8 with results obtained previouslyon an NACA 0012 airfoil section in the 8-ft TPT
(ref. 13). For the tests reported in reference 13, the
Reynolds number was smaller and the grit size (number
54 carborundum grit) used to fix transition was largerthan that used in the current test.
The comparison shows good agreement at a Mach
number of 0.50 except for the angle of zero normal force
coefficient and some small scatter in the drag data for the
current test. These results suggest a model misalignment
of-0.10° in thecurrenttestthatcouldbedueto flowangularity and/or the actual model attitude at _ = 0 °. Thedifference between the section normal force coefficients
is larger at a Mach number of 0.70, but the drag coeffi-
cients are in good agreement at normal force coefficients
below the break in the drag polar. At a Mach number of0.80, there is a sizable difference of 0.0020 in the drag
coefficients at zero normal force.
Although there are differences between the resultsfrom the current test and those from the test reported inreference 13 because of the difference in the transition
grit, Reynolds number, and surface shape, the current testis consistent (i.e., same transition grit, Reynolds number,
and surface shape were used for the solid and the porous
surface tests).
The porous upper surface extended from a non-
dimensional spanwise location, 11= z/(b/2), of about q =
-0.6 to 1] = 0.6. Since the flow over the central poroussurface will be different from that over the outer solid
surface, the spanwise extent of two-dimensional flow
will be smaller for the porous surface than for the solid
surface. The spanwise rows of pressure orifices wereused to assess the extent of the two-dimensional flow.
The spanwise pressure distributions at x/c = 0.8 on the
upper surface are presented in figure 9 at the lowest, anintermediate, and the highest test Mach numbers for both
the solid and the porous upper surfaces. For the solid sur-
face, there is no significant spanwise variation in the
pressure coefficient at these three Mach numbers. For the
porous surface, there is no significant spanwise variationat the lowest Mach number. At the intermediate and the
highest Mach numbers, spanwise gradients develop at
stations outboard of 1] = 0.12 and "q = -0.34, which indi-
cates the presence of three-dimensional flow for those
test conditions. However, there is still a region with little
spanwise pressure gradient around the model centerline
so that there is a region of two-dimensional flow about
the model centerline from the lowest to the highest testMach numbers. Thus, the flow at the model centerlinecan be assumed to be two-dimensional for the conditions
encountered in this test.
The model with the porous upper surface was
retested at an angle of attack of 0 ° during the test and the
results are presented in figure 10. Although there are
only a limited number of repeat points, the data repeat-
ability is excellent.
Presentation of Results
The results from this investigation are presented with transition fixed on both surfaces at x/c = 0.05. The moment
reference center was 0.25c. The results are presented in the following figures:
Figure
Chordwise pressure coefficient distributions for solid and porous surfaces at:
Constant angle of attack .................................................................................................................................... 11 to 19
c. -- 0.3 ....................................................................................................................................................................... 20
Effect of porosity on pressure coefficient near trailing edge ............................................................................................ 2 l
Effect of porosity on total pressure profiles at constant angle of attack ........................................................................... 22
Effect of Mach number on integrated force and moment coefficients .............................................................................. 23
Effect of Reynolds number on integrated force and moment coefficients:
Solid upper surface ..................................................................................................................................................... 24
Porous upper surface .................................................................................................................................................. 25
Effect of porosity on integrated force and moment coefficients ....................................................................................... 26
Variation of section drag coefficient with Mach number .................................................................................................. 27
Equivalent upper surface shape obtained from solid upper surface Cp distributions ........................................................ 28
Equivalent upper surface shape obtained from porous upper surface Cp distributions ........................................ 29 and 30
5
Discussionof Results
Airfoil SurfacePressureDistributions
Comparisons of the chordwise pressure coefficient
distributions for the solid and the porous airfoils at the
same angle of attack are presented in figures 11 to 19 for
Mach numbers from 0.50 to 0.82 at a chord Reynolds
number of 4 x 106 over the angle-of-attack range. It
should be noted that, although the comparisons are pre-
sented at the same angle of attack, the section normalforce and the drag coefficients are different. Thus, there
may be small differences in the wall interference for the
two points compared in each plot. For those cases withsupersonic flow, the pressure coefficient for sonic flow is
noted on the plot by Cp*. No data were obtained for the
solid upper surface airfoil model at an angle of attack of-1 o. Assuming that the model is symmetric and that the
tunnel upwash can be neglected, results from the lower
surface of the solid airfoil at an angle of attack of 1° can
be compared to the results from the upper surface of theporous airfoil at-1% Therefore, results from the model
with the solid surface at an angle of attack of 1o are plot-
ted with the results from the porous surface at an angle ofattack of- 1o.
The pressure coefficient along the length of the cav-
ity is, in general, fairly constant with a small positive
gradient toward the rear part of the cavity for some cases.The constant pressure level indicates that the flow in the
cavity is small, which validates the assumption of con-
stant cavity pressure used in reference 9. The pressurecoefficient in the cavity is about the same as the pressure
coefficient on the upper surface just aft of the midchordlocation.
If the addition of porosity to the upper surface does
not significantly change the pressure coefficient at the
trailing edge, the flow along the lower surface should not
be changed by the addition of porosity. This is indeed the
case as shown by the measured chordwise pressure distri-
butions. The lower surface pressure distribution is the
same with and without upper surface porosity when there
is no change in the trailing edge pressure coefficient.
(See oc = 2 ° in fig. 14.) However, if the addition of poros-
ity reduces the pressure coefficient at the trailing edge,
the change will be felt upstream on the lower surfacesince the pressure reduction will hinder the flow from
approaching stagnation conditions at the trailing edge.The pressure coefficients on the lower surface are indeed
reduced when porosity reduces the trailing edge pressure
coefficient, which is an indication of a significantly
thickened upper surface boundary layer and possible sep-
aration. (See ct = 4 ° in fig. 14.)
For the solid airfoil at subcritical conditions, the
flow accelerates over the forward portion of the upper
surface, which creates a leading edge suction peak athigher angles of attack. Aft of the initial acceleration, the
pressure coefficient increases. Over the forward portionof the porous airfoil, where the surface static pressure
coefficient is less than the cavity pressure, flow will be
drawn out of the cavity. Over the rear portion of the
porous airfoil, where the surface pressure coefficient is
greater, flow will be drawn into the cavity. This second-
ary flow through the porous surface tends to flatten (or
reduce the gradient in) the upper surface chordwise pres-
sure distribution over the midchord region. The leading
edge suction peak (when present) is reduced, the suctionover the forward portion of the airfoil is reduced, and the
suction over the central portion of the airfoil is increased(e.g., compare pressure distributions with and without
porosity for tx = 5 ° in fig. 12).
For the solid airfoil at supercritical conditions, the
accelerated flow region on the upper surface is termi-
nated by a shock. For the porous airfoil, flow is drawn
out of the cavity on the forward portion of the upper sur-
face and forced into the cavity on the aft portion. The
flow induced through the porous surface spreads the
compression region over a longer portion of the chord,
which replaces the sharp compression associated with a
shock on the solid upper surface (e.g., see pressure distri-
butions for t_ = 0 ° in fig. 18). The compression on the
porous upper surface becomes steeper, suggesting the
formation of a weak shock, as the angle of attack (and
section normal force coefficient) increases (e.g., comparepressure gradients near x/c = 0.20 for tx = 2 ° and ct = 4 °
in fig. 18). However, this steepening is reduced when
compared with that experienced by the shock on the solidsurface airfoil, which results in a reduction of the wave
drag portion of the total drag.
The effects of porosity on the chordwise surfacepressure distributions at a nominal section normal force
coefficient of 0.3 are presented in figure 20. For the sub-
critical case, the results are presented at the same angle
of attack. Porosity reduces the leading edge suction peakon the upper surface, reduces the suction over the front of
the upper surface, and increases the suction over the mid-
dle of the upper surface, which results in a redistribution
of the pressure loading on the forward portion of the air-
foil. There is only a little change in the lower surface
pressure distributions. For the supercritical cases, the
angle of attack for the model with the porous upper sur-face must be increased to match the section normal force
coefficient. As the Mach number increases, the accelera-
tion over the forward portion of the porous upper surface
increases, sometimes exceeding the suction pressure
coefficients for the solid upper surface. The compression
region on the porous upper surface is spread over alonger portion of the chord. The compression does
become steeper as the Mach number increases. For these
cases,thetrailingedgepressuredoesnotrecoverto thesamelevelfoundforthesoliduppersurface.Thelowersurfacepressurecoefficientdistributionsoverthefor-wardportionofthechorddifferbecauseofthedifferencein theanglesof attackandthechangein thetrailingedgepressurecoefficientduetoporosity.
Aspreviouslyindicated,porosityaffectsthegrowthof theuppersurfaceboundarylayer,andconsequently,affectsthepressurecoefficientnearthetrailingedge.A comparisonofthepressurecoefficientsneartheuppersurfacetrailingedge(x/c = 0.99) is presentedinfigure21.FortheMachnumberspresented,thetrailingedgepressurecoefficientfor thesoliduppersurfaceisrelativelyconstantuntil trailingedgeseparationbegins.With separation,thetrailingedgepressurecoefficientbecomeslesspositive(morenegative).Fortheporousuppersurface,the trailingedgepressurecoefficientsexhibitacreepatthelowersectionnormalforcecoeffi-cientssuggestingthattheboundarylayerontherearpor-tion of the airfoil is significantlythickeningwithincreasingnormalforcecoefficient.Thetrailingedgepressurecoefficientfortheporoussurfacealsoexhibitsarapiddecreaseatthehighernormalforcecoefficients.
Wake Pressure Distributions
The shape of the total pressure profile in the airfoil
wake can be used to assess the viscous and the wave drag
contributions to the total drag. Comparisons of the wake
total pressure ratio distributions for three angles of attack
are presented in figure 22 for selected Mach numbersfrom 0.50 to 0.80 at a chord Reynolds number of 4 × 106.
The profile below the peak total pressure loss is nearlythe same for the solid and the porous surfaces. This pro-file is consistent with the similar lower surface chordwise
pressure distributions found for the solid and the porous
surfaces. At subcritical conditions, the peak total pres-
sure loss and the thickness of the wake are larger for the
porous surface. This difference indicates greater losses
for the porous upper surface, probably due to increasedviscous losses (increased skin friction) and losses associ-
ated with decelerating the flow into the cavity and accel-
erating the flow out of the cavity. Measurements at a
Reynolds number of about 3 x l06 on a smooth solid and
a smooth porous cylinder indicate that the skin friction
for the porous wall is about 30 percent larger than that
for the smooth wall (ref. 14). Thus, porosity significantly
increases the viscous contribution to the total drag. At
supercritical conditions, the wake profiles for the solid
surface show an additional triangular region of total pres-
sure loss from the upper surface associated with the wave
drag due to the presence of shocks. Most of the wake
profiles for the porous surface do not show the additional
triangular region (e.g., see t_ = 2° in fig. 22(d)). Exami-
nation of the associated chordwise pressure distributions
(ix = 2 ° in fig. 16) show a shock on the solid upper sur-
face, but no shock on the porous upper surface. The
chordwise pressure distributions and wake profiles asso-
ciated with the porous surface for more extreme cases
(higher angles of attack and Mach numbers) show that
porosity does not always eliminate the shock or wave
drag. (See t_ = 4° in figs. 18 and 22(e).) Porosity reduces
the contribution of wave drag to the total drag.
Integrated Force and Moment Coefficients
Effect of Mach number. The effect of Mach number
on the integrated force and moment coefficients for the
airfoil with the solid upper surface and the porous upper
surface is presented in figure 23. Results for the model
with the solid upper surface (fig. 23(a)) follow the
expected trends. For the lower Mach numbers, the drag
coefficient is independent of the section normal forcecoefficient over the linear portion of the normal force
curves. At transonic Mach numbers, increasing shock
strength and wave drag with increasing normal force
coefficient leads to increasing drag. The positive slope of
the pitching moment coefficient curve indicates that the
aerodynamic center is slightly forward of the moment
reference center (0.25c). The slope of the section normal
force curves increases with increasing Mach number. Asthe Mach number increases, the normal force curve
becomes nonlinear at progressively smaller angles ofattack.
Results for the model with the porous upper surface
(fig. 23(b)) do not follow all of the same trends. As wasfound for the solid surface, at subcritical conditions, the
normal force curve slope at zero normal force increases
with increasing Mach number. Unlike the results for the
solid surface, at the lower Mach numbers the drag coeffi-cient for the porous surface increases with increasing
normal force coefficient and increasing Mach number,
which is a direct result of losses through the porous sur-
face. At supercritical conditions, the normal force coeffi-
cient at an angle of attack of 0 ° becomes more negative
with increasing Mach number.
Effect of Reynolds number. The effect of Reynolds
number on the integrated force and moment coefficients
for the model with the solid upper surface is presented in
figure 24 and for the model with the porous upper surfacein figure 25. The effect of Reynolds number on the
porous surface is similar to that for the solid surface.
Increasing the Reynolds number generally reduces the
turbulent skin friction, and therefore, reduces the dragcoefficient at a given normal force coefficient. It has lit-
tle effect on the linear portion of the normal force or on
the pitching moment curves.
Effect of porosity. The effect of porosity on the inte-
grated force and moment coefficients is presented in fig-
ure 26. In general, upper surface porosity reduces the
normal force curve slope and increases the drag at agiven section normal force coefficient. The loss in nor-
mal force at a given angle of attack arises from the reduc-
tion in the pressure over the forward portion of the airfoil
discussed previously. The increased drag arises from the
increased viscous drag noted in the wake pressure distri-
butions. At the lower Mach numbers, porosity leads to a
dependence of the drag on the normal force. As the angleof attack and the normal force increase, the difference
between the cavity pressure and the airfoil surface pres-
sure increases and the flow through the porous surface
increases. The chordwise component of this flow must bedecelerated to zero and turned as the flow enters the cav-
ity and accelerated and turned as the flow exits the cav-
ity. The force required to decelerate and accelerate the
flow increases the drag. Since the flow increases with
normal force, the drag also increases with normal force.
At supercritical conditions, the normal force curves for
the airfoil with the porous upper surface develop a sec-ond, nearly linear segment (e.g., see oc > 3° in fig. 26(e)).
The start of this second segment appears to correlate with
the formation of the localized steeper pressure gradient
associated with the presence of a weak shock and wave
drag noted in the discussion of the pressure distributions.
The effect of porosity on the variation of the sectiondrag coefficient with the free-stream Mach number at
two section normal force coefficients is presented in fig-ure 27. For this study, drag divergence is defined as thepoint on the drag coefficient versus Mach number curve
where dcdldM** = 0.1. The solid surface exhibits a small
amount of drag creep at subcritical Mach numbers with adramatic increase at the transonic Mach numbers. The
porous surface exhibits a higher level of drag, a higher
drag creep, and a reduced drag divergence Mach number.
For example at cn = 0 and M** = 0.5, the drag coefficient
on the solid surface was 0.0085 and the drag coefficienton the porous surface was 0.0121. The Mach number
associated with drag divergence decreased fromabout 0.78 for the solid surface to about 0.77 for the
porous surface. Similarly at c n = 0.3 and M** = 0.5, thedrag coefficient on the solid surface was 0.0086 and the
drag coefficient on the porous surface was 0.0156. The
Mach number associated with drag divergence decreasedfrom about 0.74 for the solid surface to about 0.70 for the
porous surface. For these conditions, the increased vis-
cous losses, pressure drag, and momentum losses associ-
ated with the secondary flow into and out of the cavityarising from the porous surface are larger than the wave
drag reduction from the porous surface.
Effective Airfoil Shape
The pressure distribution obtained from the airfoil
with the porous upper surface could also be obtained
from an equivalent solid airfoil with a different upper
surface shape. The measured porous airfoil upper surfacepressure distribution was used as input to the Direct Iter-
ative Surface Curvature (DISC) method described in ref-
erence 15 coupled to the Euler solver described inreference 16 to obtain the new solid surface. Viscous
effects were modeled with the boundary layer displace-ment thickness by using a modified theory of Stratford
and Beavers (ref. 17). This particular combination of a
design algorithm and a flow solver was experimentallyverified in reference 18.
The airfoil design program should calculate the
actual upper surface shape from the measured solid uppersurface pressure distribution. A comparison of the base-
line NACA 0012 airfoil upper surface shape with the re-
sulting equivalent solid upper surface shape is presentedin figure 28. The equivalent solid shapes are in goodagreement with each other and with the NACA 0012
upper surface shape, thus validating the design process.
Next, the design program was used to generate
equivalent solid upper surface shapes that correspond to
the measured pressure distributions from the porous
upper surface. Equivalent upper surface shapes with aclosed trailing edge could not be generated for test condi-
tions in which the upper surface trailing edge pressure
coefficients indicated significant separation. These sepa-
rated flows were beyond the capability of the flow solverwith the attached-boundary-layer model.
A comparison of the equivalent solid upper surface
shapes generated from the porous upper surface pressuredistributions at constant angles of attack is presented infigure 29 for several Mach numbers. At the lowest Mach
number, the addition of porosity at tx = 0° leads to an air-foil that is thicker than the NACA 0012 airfoil section
across the midchord region but has a reduced leadingedge radius. The maximum airfoil thickness and the lead-
ing edge radius decrease as the Mach number increases at
both of the angles of attack presented. The equivalentupper surface shape falls below that of the NACA 0012
over the forward portion of the chord at the higher Mach
numbers. Porosity leads to a desirable self-adaptive fea-
ture of decreasing effective thickness with increasing
Mach number. A comparison of the equivalent solid
upper surface shapes generated from the porous uppersurface pressure distributions at constant Mach numbers
is presented in figure 30 for several angles of attack. Atboth Mach numbers presented, the maximum thickness
and the leading edge radius decrease as the angle of
8
attackincreases.Thus,porositybestowsa self-adaptivequalityto the airfoil, albeit at a penalty of increased drag
due to the venting losses.
Conclusions
A wind tunnel investigation was conducted on a two-dimensional airfoil model of an NACA 0012 airfoil sec-
tion with a conventional solid upper surface and a porous
upper surface. The purpose of the investigation was to
study the effects of porosity on aerodynamic characteris-
tics and to assess the ability of porosity to provide a
multipoint or self-adaptive design. The tests were con-
ducted in the Langley 8-Foot Transonic Pressure Tunnel
over a Mach number range from 0.50 to 0.82 at chordReynolds numbers of 2 x 106, 4 x 106, and 6 x 106. The
angle of attack was varied from -1 o to 6°. The porous
surface nominally extended over the entire upper surface.
When compared to the solid surface airfoil, the conclu-
sions from this investigation are
1. At subcritical conditions, porosity tends to flatten
the pressure distribution, which reduces the suction peak
near the leading edge and increases the suction over the
middle portion of the chord.
2. At supercriticai conditions, the compression
region on the porous upper surface is spread over a
longer portion of the chord.
3. At supercritical conditions, for the porous uppersurface, the trailing edge pressure coefficients exhibit a
creep at the lower section normal force coefficients,
which suggests that the boundary layer on the rear por-tion of the airfoil is significantly thickening with increas-
ing normal force coefficient.
4. The pressure coefficient in the cavity is fairly
constant with a very small increase over the rear portion,which indicates that the flow in the cavity is small.
5. Porosity reduces the lift curve slope and increases
the drag at a given section normal force coefficient.
6. At the lower Mach numbers, porosity leads to a
dependence of the drag on the normal force and the Machnumber.
7. Porous airfoils exhibit an adaptive characteristic
in that the thickness and the leading edge radius of an
equivalent solid airfoil decrease with increasing Machnumber, albeit at a penalty of increased drag.
NASA Langley Research CenterHampton, VA 23681-0001February 2, 1996
Appendix A
Determination of Chordwise Spacing of Holes
on Porous Surface
Symbols
b width of porous patch
D hole diameter
l length of porous patch
vh mass flow rate
N number of holes through porous patch
R unit Reynolds number based on free-streamconditions
v n equivalent normal transpiration velocity
9 average velocity through hole in poroussurface
V** free-stream velocity
Ap pressure difference across porous surface
kt_ free-stream viscosity
p_ free-stream density
p local density
c permeability parameter
Gmax maximum value of permeability parameter
x thickness of porous surface
Determination of Spacing
The porous upper surface of the model was drilledwith 368 chordwise rows of holes. The effect of the dis-
crete regions of flow into and out of the cavity through
this surface is modeled by an equivalent normal transpi-
ration velocity. Darcy's law is used to relate the equiva-
lent normal transpiration velocity to the pressuredifference across the porous surface:
ov n = -- • Ap (Al)
P_oVoo
The flow through an individual hole can be esti-
mated with the Hagen-Poiseuille solution for fully devel-
oped, viscous flow through a circular pipe:
D 2 Ap- (A2)
321aoo x
If a porous patch of length l, width b, and N holes is
selected, the mass flow through the N individual holes
must equal the mass flow from the equivalent transpira-tion velocity over the patch of area 1- b. Assuming that
the selected porous patch is small enough that the pres-
sure difference can be assumed constant, the equivalence
of the mass flow rates through the surface for the two
representations can be expressed as
_reD 2 .
Cn = pv--_---lv = pvnlb (A3)
Upon substituting the expressions for vn from equa-tion (A1) and the expression for 9 from equation (A2)into equation (A3), an expression is obtained that relates
the geometric characteristics of the porous surface to the
permeability:
gD 4 N o- lb (A4)
128_,_x p V.,
Substituting for the unit Reynolds number produces
_D4RN- t_lb (A5)
128 x
For this study, the porous surface parameters were
x = 0.020 in. and D = 0.010 in. The design was done at aunit Reynolds number R of 2 x 106/ft. A modified sine
distribution was chosen for the surface permeabilitydistribution:
t_ = t_max_Sin(nx/c ) (A6)
For this study, Omax = 0.6. The modified sine distri-
bution and the value of Omax were selected to be consis-
tent with the computational study in reference 9.
The chordwise spacing of the holes can be deter-
mined by selecting a section of the porous surface that
contains one hole (N = 1). Since there are 8 longitudinal
rows per inch, the width of the section b would be
0.125 in. The length of the section 1 would be the
unknown chordwise spacing. Solving equation (A5) for 1
and substituting the value of the surface permeability ofrom equation (A6) for the desired chordwise location
will yield the chordwise spacing at the selected chord-wise location:
N_D4Rl - (A7)
128xbt_
10
References
1. Bahi, L.; Ross, J. M.; and Nagamatsu, H. T.: Passive Shock
Wave/Boundary Layer Control for Transonic Airfoil Drag
Reduction. AIAA-83-0137, Jan. 1983.
2. Nagamatsu, H. T.; Trilling, T. W.; and Bossard, J. A.: Passive
Drag Reduction on a Complete NACA 0012 Airfoil at Tran-
sonic Mach Numbers. AIAA-87-1263, June 1987.
3. Thiede, E; Krogmann, P.; and Stanewsky, E.: Active and Pas-
sive Shock/Boundary Layer Interaction Control on Super-
critical Airfoils. Improvement of Aerodynamic Performance
Through Boundary Layer Control and High Lift Systems,
AGARD CP-365, Aug 1984. (Available from DTIC as
AD A147 396.)
4. Chen, C.-L.; Chow, C.-Y.; Hoist, T. L.; and Van Dalsem,
W. R.: Numerical Simulation of Transonic Flow Over Porous
Airfoils. AIAA-85-5022, Oct. 1985.
5. Hsieh, Sheng-Jii; and Lee, Lung-Cheng: Numerical Simula-
tion of Transonic Porous Airfoil Flows. Proceedings of the
Fifth International Symposium on Numerical Methods in Engi-
neering-Volume 1, R. Gruber, J. Periaux, R. E Shaw, eds.,
1990, pp. 601-608.
6. Chen, Chung-Lung; Chow, Chuen-Yen; Van Dalsem,
William R.; and Holst, Terry L.: Computation of Viscous
Transonic Flow Over Porous Airfoils. AIAA-87-0359, Jan.
1987.
7. Gillian, Mark A.: Computational Analysis of Drag Reductionand Buffet Alleviation in Viscous Transonic Flow Over Porous
Airfoils. AIAA-93-3419, Aug. 1993.
8. Musat, Virgil M.: Permeable Airfoils in Incompressible Flow.
J. Aircr., vol. 30, no. 3, May 1992, pp. 419-421.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Hartwich, Peter M.: Euler Study on Porous Transonic Airfoils
With a View Toward Multipoint Design. AIAA-91-3286,
Sept. 1991.
Brooks, Cuyler W., Jr.; Harris, Charles D.; and Reagon,
Patricia G.: The NASA Langley 8-Foot Transonic Pressure
Tunnel Calibration. NASA TP-3437, 1994.
Braslow, A. L.; and Knox, E. C.: Simplified Method for Deter-
mination of Critical Height of Distributed Roughness Particles
for Boundary-Layer Transition at Mach Numbers From 0 to 5.
NACA TN-4363, 1958.
Baals, Donald D.; and Mourhess, Mary J.: Numerical Evalua-
tion of the Wake-Survey Equations for Subsonic Flow Includ-
ing the Effect of Energy Addition. NACA WR L-5 H27, 1945.
Harris, Charles D.: Two-Dimensional Aerodynamic Character-
istics of the NACA 0012 Airfoil in the Langley 8-Foot Tran-
sonic Pressure Tunnel. NASA TM-81927, 1981.
Kong, Fred Y.; Schetz, Joseph A.; and Collier, Fayette: Turbu-
lent Boundary Layer Over Solid and Porous Surfaces With
Small Roughness. NASA CR-3612, 1982.
Campbell, Richard L.: An Approach to Constrained Aero-
dynamic Design With Application to Airfoils. NASA TP-3260,
1992.
Hartwich, Peter M.: Fresh Look at Floating Shock Fitting.
AIAA J., vol. 29, no. 7, July 1991, pp. 1084-1091.
Stratford, B. S.; and Beavers, G. S.: The Calculation of the
Compressible Turbulent Boundary Layer in an Arbitrary Pres-
sure A Correlation of Certain Previous Methods. R. & M.
No. 3207, British Aeronautical Research Council, 1961.
Mineck, Raymond E.; Campbell, Richard L.; and Allison,
Dennis O.: Application of Two Procedures for Dual-Point
Design of Transonic Airfoils. NASA TP-3466, 1994.
11
Table 1. Pressure Orifice Locations
(a) Chordwise rows
0.0001
0.0029
0.0062
0.0133
0.0212
0.0305
0.0404
0.0604
0.0804
0.1004
0.1252
0.1504
0.1803
0.2153
0.2502
0,2853
0.3202
Upper surface xlc Lower surface x/c Cavity x/c
0.3503
0.3802
0,4102
0.4352
0.4601
0.4801
0.5002
0.5202
0.5400
0.5602
0.5802
0.6001
0.6201
0.6401
0.6601
0.6801
0.6999
0.7200
0.7401
0.7601
0.7801
0.8001
0.8200
0.8400
0.8600
0.8800
0.8998
0.9201
0.9399
0.9598
0.9746
0.9899
0.0068
0.0136
0.0216
0.0306
0.0398
0.0599
0.0799
0.1000
0.1249
0.1500
0.1799
0.2150
0.2500
0.2850
0.3200
0.3500
0.3799
0.4099
0.4349
0.4600
0.4800
0.5000
0.5199
0.5399
0.5600
0.5801
0.6000
0.6200
0.6400
0.6600
0.6800
0.7000
0.7200
0,7400
0.7599
0.7799
0.8000
0.8200
0.8401
0.8601
0.8795
0.9007
0.9209
0.9408
0.9609
0.9759
0.9908
0.033
0.105
0.176
0.246
0.315
0.384
0.452
0.520
0.587
0.654
0.721
0,789
0.856
0,923
(b) Spanwise rows
Upper surface 1] at-- Lower surface r I at--
x/c = 0.8 x/c = 0.9 x,/c = 0.8 x/c = 0.9
-0.468
-0.350
-0.234
-0,116
-0.456
-0.340
-0,222
-0,106
-0.456
-0.340
-0.222
-0,106
-0.456
-0.340
-0.222
-0.106
0.116
0.234
0.350
0.468
0.106
0.222
0.340
0.456
0.106
0.222
0.340
0.456
0.106
0.222
0.340
0.456
12
17.685
15.885
14.085
12.285
10.485
8.685
6.885
5.445
4.365
3.285
2.655
2.475
Table2. WakeRakePressureTubeLocations
(a)Totalpressuretubes
z, in.
2.295
2.475
1.935
1.755
1.575
1.395
1.215
1.035
0.900
0.810
0.720
0.630
0.540
0.450
0.360
0.270
0.180
0.090
0.000
-0.090
-0.180
-0.270
-0.360
-0.450
-0.540
-0.630
-0.720
-0.810
-0.900
-1.035
-1.215
-1.395
-1.575
-1.755
-1.935
-2.115
-2.295
-2.475
-2.655
-3.285
-4.365
-5.445
-6.885
-8.685
-10.485
-12.285
-14.085
-15.885
-17.685
(b) Static pressure tubes
z, in.
10.015
4.015
1.665
0.000
- 1.665
-4.015
-10.015
Table 3. Nominal Test Conditions
R(?
M,_ 2 × 106 4 × 106 6 x 106
0.50 X X X
0.60 X X
0.65 X X
0.70 X X
0.74 X
0.76 X
0.78 X
0.80 X
0.82 X
X
X
X
X
X
X
X
X
13
Y
_.shock wave
(a) Narrow porous strip for shock venting.
v ×
Y
__. /-- Poroussu,ace
Cavity
(b) Full chord porous upper surface.
Figure 1. Airfoil with porous surface in transonic flow.
v
14
c_
r--
"_ "0_ o
._ o
L_
15
16
C_
a_
/
//
///
/
//
//
/
//
//
//
//
t
x
M
Spanwise tunnel width --'-
,( 50 _ . •
40 --}.- " ,r_i
"', -Solid NACA 0012 airfoil-" ",/
, /
Angle-of-attack plates_"
(a) Top view of model.
Interchangeable
J center/ insert/..
/
,/
/
/
/
/
/
/
/
/
/
/
/
/
/,
Detail
0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0
0 0 0 0 0
0.125
Chordwisespacing
Interchangeable
Holediameter
0.010
Maximumthickness
3
Chord 25.00
Spanwisespacing
0.125
depth
Skin thickness 0.020
Main spar },-
(b) Cross section of model.
Figure 3. Details of model. All dimensions are in inches.
17
Modelcentedine
Surface holes _ 0.94
0.010 diameter---, Spanwise
-_ _ 006 _ I___s_.c_i_.g _- Skinv. =_'_ thickness
ooo*°.4'-"-1_- ,v,t,,,,ressoreo,,,ceO
(c) Cross section of cavities.
Figure 3. Concluded.
18
.001
Ay/c 0
-.001 I
0
Su rface
Lower
Upper
I I I I I i.2 .4 .6
x/c
fJ
Jf/
fJ
ff
rl = -0.35
I i.8
I1.0
.001
F-.001 I
0
Jf
/
.2 .4 .6
x/c
Jf
JJ/.1- 11=0
I I i.8
I1.0
.001
_y/c 0
-.001
f\ t
= 0.35
i I i I J I i I J0 .2 .4 .6 .8
_C
Figure 4. Deviation of model shape from design NACA 0012 shape.
I1.0
19
6.00
36.03
Total
p ressu re
tube -_
Static
pressure //7=====tube --"
13.11
11
T' i _static Dretsaisl°f tu be
u_ Static
orifices (7)
+y
I
y=O_='t 1'00
Detail oftotal pressure tube
,_ Model support-- centerline
Figure 5. Details of wake rake. All dimensions in inches.
2O
21
.05
C n
c d
0
-.05
-.10
.035
.030h
.025
.020
.015
.010
.3
l:)
Rake position
IIII
O 25.0
[] 37.5
I I I I
t3
I I I I I I I I I I I I I I I I
.4 .5 .6 .7 .8 .9
aco
.O4
.02
0
-.02
C m
(a) R c = 4 x 106.
Figure 7. Effect of rake position on integrated force and moment coefficients of baseline porous airfoil, t_ = 0 °.
22
C n
cd
.05
0
-.05
-.10
.035
.030
.025
.020
.015
.010
.3
IIII
©
[]
IIII
.4
C
Rake position
25.0
37.5
I I I I
.5
IIII IIII
.6 .7 .8
Moo
(b) R c = 6 x 106.
Figure 7. Concluded.
!
illl
.04
.02
0
m
-.02
.9
C m
23
If)
0
0
0
m
(D0
-- xo
rr
(
on"
0 rl
[] L)--- ------@L
\
"------o
\\
\\
[]c
coo
o
o
o
o
o
to
o
o
LOoo
o
-oo
Q
c5
c5II
_J
m
=
o
EoE
c_
o_
o=
r_Eo_J
c_
o
E(j_
Illl
r,,.o
|
IIII IIII IIII IIII Ittl
r-_j
Illl IIII
oi
2.4
{3
E)
0
(D0,r.=
XU
rr
F-
['3
"_ C'_
_rr
0 [] \
U
0
Q
O
Lr}
0
0(XlO
{3
0
(3
LrJ00
E)
l.r)
"0
CXl
0
"0(3
II
g
_J
=
L_
?
IIII IIII IIII
I
Eo
till till IIII lill tlil IIII I I I I
"T,u
25
mm
o
m YU
o
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REPORT DOCUMENTATION PAGE FormAppro_OMB No. 0704-0188
Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this:ollection of information, including suggestions for reducing this burden, to Washington HeaOquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson
Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Managemenl and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.
1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED
April 1996 Technical Paper
4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
Effect of Full-Chord Porosity on Aerodynamic Characteristics of theNACA 0012 Airfoil WU 505-59-10-30
6. AUTHOR(S)Raymond E. Mineck and Peter M. Hartwich
7. PERFORMINGORGANIZATIONNAME(S)ANDADDRESS(ES)
NASA Langley Research CenterHampton, VA 23681-0001
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
National Aeronautics and Space AdministrationWashington, DC 20546-0001
8. PERFORMING ORGANIZATIONREPORT NUMBER
L-17492
10. SPONSORING/MONITORING
AGENCY REPORT NUMBER
NASA TP-3591
11. SUPPLEMENTARY NOTES
Mineck: Langley Research Center, Hampton, VA; Hartwich: ViGYAN Inc., Hampton, VA.
12a. DISTRIBUTION*AVAILABILITY STATEMENT
Unclassified-Unlimited
Subject Category 02Availability: NASA CASI (301) 621-0390
12b. DISTRIBUTION CODE
13. AB_IHACT (Maximum 200 words)
A test was conducted on a model of the NACA 0012 airfoil section with a solid upper surface or a porous uppersurface with a cavity beneath for passive venting. The purposes of the test were to investigate the aerodynamiccharacteristics of an airfoil with full-chord porosity and to assess the ability of porosity to provide a multipoint orself-adaptive design. The tests were conducted in the Langley 8-Foot Transonic Pressure Tunnel over a Mach num-ber range from 0.50 to 0.82 at chord Reynolds numbers of 2 x 106, 4 x 106, and 6 x 106. The angle of attack wasvaried from -1 o to 6°. At the lower Mach numbers, porosity leads to a dependence of the drag on the normal force.At subcritical conditions, porosity tends to flatten the pressure distribution, which reduces the suction peak near theleading edge and increases the suction over the middle of the chord. At supercritical conditions, the compressionregion on the porous upper surface is spread over a longer portion of the chord. In all cases, the pressure coefficientin the cavity beneath the porous surface is fairly constant with a very small increase over the rear portion. For theporous upper surface, the trailing edge pressure coefficients exhibit a creep at the lower section normal force coef-ficients, which suggests that the boundary layer on the rear portion of the airfoil is significantly thickening withincreasing normal force coefficient.
14.SUBJECTTERMSPorous airfoils
17. SECURITY CLASSIFICATION
OF REPORT
Unclassified
NSN 7540-01-280-5500
18. SECURITY CLASSIFICATION
OF THIS PAGE
Unclassified
19. SECURITY CLASSIFICATION
OF ABSTRACT
Unclassified
15. NUMBER OF PAGES
8916. PRICE CODE
A05
20. LIMITATION
OF ABSTRACT
Standard Form 298 (Rev. 2-89)
Prescribed by ANSI Std. Z39-18298-102
