Computational Simulations of a Three-Dimensional High-Lift Wing

10 Pages·2002·2.3 MB·English

by  Khorrami, M. R.

/
..../.12,
AIAA-2002-2804
Computational Simulations of a Three-
Dimensional High-Lift Wing
M. R. Khorrami
NASA Langley Research Center
Hampton, VA
M. E. Berkman, F. Li
High Technology Corporation
Hampton, VA
B. A. Singer
NASA Langley Research Center
Hampton, VA
20th AIAA Applied Aerodynamics Conference
24-26 June 2002
St. Louis, Missouri
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Computational SimulationsofaThree-DimensionalHigh-Lift Wing
Mehdi R. Khorrami 1
NASA Langley Research Center
MS 128, Hampton VA
Mert E. Berkman 2
and
Fei Li3
High Technology Corporation
28 Research Drive, Hampton VA
Bart A. Singer 4
NASA Langley Research Center
MS 128, Hampton VA
producing fluid dynamical processes at a flap side edge.
Abstract The deeper insight gained through this work will guide
the development of simplified physics-based models
Highly resolved computational simulations of a three- that mimic flow unsteadiness (and thus noise generation
dimensional high-lift wing are presented. The steady mechanisms) at the edge. Ultimately, such physics-
Reynolds Averaged Navier-Stokes computations are based models will allow efficient design of quiet
geared towards understanding the flow intricacies airplanes.
associated with inboard and outboard flap side edges.
Both moderate and high flap deflections are simulated. In a parallel effort to several companion experiments,
Computed surface pressure fields accurately capture the our previous research focused on steady Reynolds
footprint of vortices at flap side edges and are in Averaged Navier-Stokes (RANS) simulations of
excellent agreement with pressure sensitive paint unswept and untapered high-lift configurations. 3-6 The
measurements. The computations reveal that the configurations were generic two-or three-element high-
outboard vortex possesses higher rotational velocities lift models that consisted of a two-dimensional (2D)
and lower core pressure than the inboard vortex and main element with or without a 2D slat and a part span
therefore is susceptible to severe vortex breakdown. flap. These early studies captured the complex nature
of the flap side-edge flow field and revealed the
Introduction intricacies of shear layer roll-up, multiple vortex
formation, vortex merging, and vortex breakdown
Projected future growth in air travel and significant processes. Two important aspects of a high-lift
quieting of modern jet engines has brought renewed configuration left for future exploration were the effects
attention to the non-propulsive (airframe) component of of sweep and taper on a flap side-edge flow field.
aircraft noise. Past studies that focused on airframe
noise have identified high-lift devices along with the These aspects were addressed in a series of tests
landing gears as dominant noise producing conducted at NASA Langley Research Center (LaRC)
components. 1'2 Those studies have established flap- in the 14x22 foot wind tunnel during 1998-1999. The
side-edges as a potent noise source that deserves tested model is a trapezoidal (trap) wing design that
focused attention. The present paper continues our provides a 3D high-lift flow environment. Extensive
effort towards uncovering prominent flow structures at acoustic and limited aerodynamic measurements were
a flap side edge in high-lift settings. These efforts are obtained. Using a microphone array technique,
motivated by our lack of understanding of noise acoustic measurements were obtained by a team from
the Boeing Company. Sample ground-ward flap
acoustic spectra at moderate and high flap deflections
1Research Scientist, Computational Modeling and are shown in Fig. 1. At a flap deflection angle of 20
Simulation Branch, Associate Fellow AIAA.
degrees, the emitted noise from the inboard and
2Research Scientist: currently with ArvinMeritor outboard side-edges are nearly similar both in
Exhaust Systems.
3Senior Scientist, Member AIAA.
4Assistant Branch Head, Computational Modeling
and Simulation Branch, Senior Member AIAA.
amplitudaendfrequenccyontent.At30degreefslap in similar studies of high-lift configurations by
deflectionw, hilethe inboardedgeshowsonlya Khorrami et al.4and Berkman et al.5.
moderatreiseinnoiselevelsrelativetothelowerflap
angle,thereis a markedincrease(8-10dB)in the Table 1. Geometrical settings
amplitudoeftheradiatendoisefromtheoutboareddge.
Clearly,the measuremenptsoint to significant Parameters Setting
differencebsetweetnheestablishefldowfieldsatthe Slat angle, deg 25
twosideedgebsecausoefsweeapndtaper. Flap angle, deg 20, 30
Slat gap, % 1.5
Thecurrentcomputationsatludysimulatetshetrap Flap gap, % 1.5
wingflowfield.Emphasiissplacedonhighresolution Slat overlap, % 1.5
oftheflap'sside-edgeOs.urgoalsherearetocapture Flap overlap, % 0.5
thedifferencetshatmayexistbetweenthetwoflow
fieldsaswellastohighlighttheprominencht angetos Two different configurations, corresponding to the
thenoiseproducinfglowfeaturetshatmayoccurwith acoustic measurements displayed in Fig. 1, are
increasinflgapdeflection. computed. In both cases, the slat deflection angle is 25
degrees and the main element angle of attack is 10
Model Geometry and Computational Grid degrees. The flap deflection angle is 20 degrees in one
configuration and 30 degrees in the second
The trap wing is a high-lift model consisting of a configuration, representing aircraft approach and
constant chord leading edge slat, a main element, and a landing conditions, respectively.
part span flap. Figure 2a displays the tested trap wing
model which had a simple center body. To ease the A multi-block structured grid is used to simulate the
gridding task, for our computational model the center flow past the trap wing. Limited use of patching
body was removed and the wing was extended all the strategy is made to reduce the total number of points.
way to the tunnel floor. As will be shown later, this High concentrations of grid points occur adjacent to the
model alteration has no significant effect on local or model solid surfaces, slat cove, main element leading
global aerodynamic characteristics of the trap wing. edge, and flap edges. The surface grid distribution is
Figure 2b shows the trap wing geometry as simulated. shown in Fig. 3. Near the flap side-edges, the grids are
Both main element and flap are swept and tapered. In clustered in the spanwise direction to resolve edge
the stowed position, the leading edge and trailing edge vortices. Chordwise resolution is also high over the
sweep are 33.89 and 16.24 degrees respectively. The flap. Grid concentration in the vicinity of the outboard
simulated model has a root chord of 53.473 inches flap edge is displayed in Fig. 4 with a similar mesh
(1.358m), a tip chord of 21.12 inches (0.536m), a mean clustering occurring at the inboard edge. The total grid
aerodynamic chord of 37.3 inches (0.947m), and a span is comprised of 51 blocks with nearly 17.5 million
of 85 inches (2.16m). The flap has an inboard chord of nodes. Typically, more than 20 grid points are
13.56 inches (0.344m), an outboard chord of 8.97 clustered in the boundary layers adjacent to the model
inches (0.228m), and a span of 42.19 inches (1.07m). surface, with the first point less than 5x10 -6 wing-root-
chords off the model surfaces.
The relative positions of the slat and the flap with
respect to the wing (i.e., the gaps and the overlaps)
Flow Solver
were fixed to match an experimental setting of interest.
The settings for the simulated configurations are
presented in Table 1. The tabulated gaps and overlaps As in our previous studies, the CFL3D code 7is used to
are normalized with respect to the local stowed chord. perform the computations. CFL3D offers a wide
All of the trailing edges of the tested model are blunt. selection of turbulence models, ranging from zero- to
To ease the computational task and reduce the number two-equation models. For the present effort, the one-
of grid points required, the surfaces of respective equation Spalart-Allmaras (SA) turbulence model s is
elements were shaved smoothly (while maintaining the used with a solid-body rotation modification. 9 Because
cambers) to produce sharp trailing edges. For a realistic of the strong centrifugal force field, the cores of
comparison with the measured quantities, the entire test streamwise vortices displaying solid body rotation
section of the 14x22 foot tunnel is modeled to simulate usually exhibit rather weak turbulent fluctuations and
the experiment. The wind tunnel walls are treated as behave in a laminar-like manner. The present alteration
inviscid surfaces to avoid the additional computational dampens the turbulent viscosity in regions
cost of resolving the wall boundary layers. This demonstrating solid-body-rotation and has no effects on
assumption had previously been shown to be adequate other regions of the flow field. In previous studies
(Dacles-Mariani et al.9 and Khorrami et al._°), the
modifiedSAmodewl asshowtnoproducbeetterresults Table 2 Grid-resolution studies
forvortexdominatefldowss,uchasthepresenctase.
Lift Coefficient
Results and Discussion Flap Mid-level Fine-level Difference,
deflection mesh mesh %
Computations and postprocessing of the results are 20 degree 1.10 1.144 3.8
performed in a non-dimensional fashion. The scales
used in our normalizations are the free stream speed of 30 degree 1.24 1.312 5.5
sound, density, kinematic viscosity, and the wing root
chord. For the present case, reference flow variables
are set to match conditions at the 14x22 test section Table 3Computed and measured lift coefficients
entrance. All simulations are obtained for a free stream Lift Coefficient
Mach number of 0.2 and the root chord Reynolds
number of 5.65 million. Computations are done in a Flap Computed Measured Difference,
deflection %
fully turbulent mode using the one-equation SA model
with the solid-body-rotation modification. 20 degree 1.144 1.125 1.69
30 degree 1.312 1.31 0.15
Because of the large grid, the computations were
performed on the SGI clusters of National
Aerodynamic Simulation facility at NASA Ames. Each We begin the discussion with a brief presentation of the
individual run utilized 52 CPUs and slightly less than
global flow before directing our attention to the details
12 GB of memory. A typical run, producing 100 of the flap side-edge flow fields. Figure 5 shows the
iterations on the finest level, took nearly 6 hrs of
pressure distribution over the entire model for the 30
physical time or approximately 300 hrs of CPU time. degree case. Note that regions of significant pressure
To achieve a faster and more efficient convergence rate, suction occur near the wing and flap leading edges and
mesh sequencing was employed with two coarser level both flap side edges. Figure 6 illustrates a comparison
meshes (where successive removal of every other node of the computed chordwise pressure variation with that
provides the lower level meshes). For both 20 and 30 measured over the main wing at the 50 percent span
degree flap deflections, in a steady mode, convergence location. Except for the two bad ports near x=0.5, the
was assumed when the calculations had no changes in measured Cp are in remarkable agreement with the
the lift coefficients to 3-4 significant digits with computed pressure. The small discrepancies near the
subsequent iterations. At this stage, the overall global trailing edge may be attributed to the sharpening of the
residual displayed 5 orders of magnitude drop before edge in the simulation. The Mach number contours at
leveling off. Although the residual remained flat for the the mid-span location for 30 degree flap deflection are
20 degree case, the residual for the higher flap angle presented in Fig. 7. The contour plot shows significant
showed a somewhat low amplitude oscillatory acceleration of the flow through the slat and flap gaps
behavior, suggesting the onset of an unsteady event. causing the Mach numbers in the vicinity of the main
The probable cause of residual oscillation will be element and flap leading edges to approach a value
discussed in the following sections. Nevertheless, the nearly twice the freestream Mach number of 0.2. The
lift coefficient for the 30 degree case never displayed an recirculating zones and the corresponding low Mach
oscillatory pattern and it converged to a finite value numbers in the slat and main element coves are also
very smoothly. An estimate (in a global sense) on the vividly visible in Fig. 7. The simulation for 20 degree
grid dependency of the computed solutions is obtained flap shows similar global features.
via comparison of the lift coefficients. Tabulated in
Table 2 are the computed lift coefficients from the mid- As mentioned in the introduction, surface pressure
and fine-level grids. More importantly, in Table 3 we distributions near flap edges were obtained using the
present a comparison between the fine-level computed Pressure Sensitive Paint (PSP) technique. The
and experimentally measured lift coefficients. Good measured pressure distributions for the 20 degree flap
agreement is achieved between the two sets of lift deflection are shown in Fig. 8a. The middle section of
coefficient. This close agreement suggests that the the flap was not treated with PSP and therefore is
removal of the center body from the simulated assigned a value of Cp=0.0. The flap leading edge
configuration has had minimal impact on the experiences a higher suction peak towards the outboard
aerodynamic characteristics of the wing. segment. In addition, both edges display a pear-shape
low-pressure region that is the footprint of the main
vortex after the vortex has moved on the top surface.
These region of intense low pressures are quite similar
tothefootprinotfvorticesforunswepatnduntapered First,vortexlift ismoreprominenatttheinboardedge
flapsr,eporteidnreferenc4e-s6.Thecomputepdressure (z=0.39)and its contributionis increasedwith
fieldontheflapisplottedinFigure8b.Thesimulated increasinfglapdeflection.Second,vortexlift is
fieldisingoodagreemewnitthPSPresultandshows severeldyiminisheadttheoutboareddgeatthehigh
thattheprominenflot wfeatureasssociatwediththeflap flapdeflectionG. iventhefactthattheoutboarvdortex
arewellresolvedT.hecorrespondiCngpdistributions experiencleoswerpressureinsitscorethantheinboard
forthe30degreeflapdeflectioanreplottedinFig.9. vortex,thelift distributiopnlotreinforceosurearlier
Onceagainexcellenatgreemebnettweetnhemeasuredassertionthsat,theoutboarvdortexpathremaincsloser
andcomputepdressuriessshownM. uchhighesruction to the edgethanthe inboardpath,and vortex
peaksattheflapleadingedgeandinthefootprintosf breakdowfnirstoccursattheoutboareddgeandat
the edgevorticesareobserved.Theshapeand lowerflapdeflections.
orientatioonfthevortex-inducseudctionpeakisndicate
that,onceontop,theinboardvortexmovesinwardof Thepresencoef a vortexbreakdowbnecomemsore
theedgewhiletheoutboarvdortexremaincslosetothe evidenwthenthestreamwisveelocitydistributioinnthe
edge.Fromthepointofviewofnoisegeneratioannd coreof vorticesis viewed.A sampleplotof the
scatterinagtsharpedgesth,esesubtledifferencehsave streamwisveelocityforthe20degreceaseisshownin
strongramifications. Fig.15.Thetwoplanesshownareslightlyinwardof
theflapedges.Recaltlhatthefreestreamvelocityis
Baseodntheacoustiacrraymeasuremetnhteso,utboard u=0.2. Duetoextremelowpressurebso,thvortices
flapedgewasfoundtobeamorepotenntoisesource attainajet-likeaxialvelocityintheircores.Forthe
thantheinboardedgethussuggestinthgattheremay inboardvortex,themaximumvelocitieasretypically
existsomefundamentdailfferencebsetweetnhetwo 60-70percenhtighetrhanthefreestreavmelocity.The
flowfields.Fortunateltyh,evolumetriCcFDdatabase outboarvdortexcoreshowanadditiona1l0-20percent
can be analyzedthoroughlyto highlightthese higheraxialvelocitierselativetotheinboardvortex.
differencesT.hepressurceontouraslongtheinboard- Noticethattheinboardvortexmaintaintshejet-like
edgechordfor20degrefelapareplottedinFig.10and behavioinrtoregionwsellbeyondtheflaptrailingedge.
thecorrespondincogntourfsortheoutboareddgein Ontheotherhandt,heexcesvselocityinthecoreofthe
Fig.11. Thecontouprlotsshowtheformationofa outboarvdortexdisappeasrslightlydownstreaomfthe
strongvortexnearthebottomsharpedgeandamuch trailingedge.Thecorrespondainxgialvelocityplotfor
weakevrortexatthetopsharpcorner.Themerginogf the30degreecaseis displayeidnFig.16. At the
thetwovorticesoccursatastationpasttheflapmid- inboardedge,startingatthemid-chordregion,the
chordwhenthestrongevrortexhasmovedontotheflap vortexexperiencaesjet-likeaxialvelocityinitscore.
top surface.Theoutboardvortexattainsa lower Atthisflapsettingth, emaximumcorevelocityis70-80
pressurien itscore,asit is evidenftromthemore percenhtigherthanthefreestream.Asthetrailing
severesaturatioonfthepressurceontour(shollowed edgeoftheflapis approachetdh,eadversperessure
regionsinsidethecores).Becausoefthecentrifugal gradienctauseasrapiddeceleratioonfthevortexcore
forcebalanceth,elowerthecorepressurderopst,he velocity.Beyondthetrailingedget,hevortexbreaks
highetrhevortexrotationavlelocitiebsecomeS.imilar downandthereisaregionofaxialflowreversal.In
pressurceontouprlotsforthe30degreeflapdeflection contrastth,eoutboardvortexexperienctehseadverse
are displayedin Fig. 12 (inboard)andFig. 13 pressurgeradienmt uchearlierandthereforebreaks
(outboardA).ttheinboardedget,hevortexcoreattains downimmediatealyssoonasit movesonthetop
alowersuctionpeakrelativetothe20degrecease(Fig. surfacein the mid-chordregion. Themaximum
10)andmaintaintshelowpressurbeeyondtheflap magnitudoef thereverseflow experiencebdy the
trailingedge.Attheoutboareddgein, itially,thevortex vorticesis ontheorderof 5-10percenotfthefree
showsextremellyowpressureinsitscore.However, streamvelocity.MonitoringoftheCFDdatabasaet
oncethevortexmovesonflaptopsurfacew,ithina differingiteratiocnyclesrevealetdheonseotflowlevel
veryshordtistanceit,experiencaesseverperessurriese flowunsteadineinssthebreakdowrengion.Giventhe
in itscore. Typically,suchrapidpressurreiseis finespatiarlesolutioantthesideedgesit,wouldnotbe
associatewdith thecoreexpansiona,ppearancoef surprisingif theunsteadiynternalstructureof the
stagnatiopnointinsidethecorea,ndtheonseotfvortex vortexbreakdowins partiallybeingresolved.It is
breakdown. believedthattheobservedoscillationin theglobal
residuaislrelatetdothistime-dependaecntitvity.
Tohelpunderstanthdedifferenceasssociatwediththe
twoflapsettingsth,espanwislieft distributioonnthe Thepresencoefvortexbreakdowantaflapsideedge
flapforbothdeflectionanglesisplottedinFig.14. wasfirstreporteidnreference[4s,5]andsubsequently
Two featuresimmediatelydistinguishthemselves.byBerkmaental6. forunswepatnduntaperefdlaps.
Thepresensttudyindicatetshatvortexbreakdowins References
notuniquetothosesimplegenericconfiguratioannsdin
realityoccurastanyflapsideedgeinahigh-lifstetting. Crighton, D., "Airframe Noise," Aeroacoustics of
Thedetectioonfvortexbreakdowanttheoutboareddge Flight Vehicles: Theory and Practice, NASA
raisesseveraiml portanqtuestionsIs.vortexbreakdown Reference Publications 1258, Vol.l, edited by H.
solelyresponsibfloertheincreasendoiselevelsatthe H. Hubbard, WRDC TR 90-3052, Aug. 1991.
flapoutboardedge?Isthecausalitbyetweevnortex
breakdowanndincreasendoisedirecotrindirectS?ince
. Macaraeg, M. G., "Fundamental Investigations of
theinternasltructuroefvortexbreakdowonscillateast
Airframe Noise," AIAA Paper 98-2224, June 1998.
lowfrequencieosn,emayruleoutthedirecet ffecat nd
assumtehatthenoisesourceasremodifiedindirectly Khorrami, M.R., Singer, B.A., and Takallu, M.A.,
viaincreaseRdeynoldsstresasctivitieasndotherlocal "Analysis of Flap Side-edge Flow Field for
flowalterations.Of coursef,urtherexperimenitns
Identification and Modeling of Possible Noise
conjunctiownithaccuratuensteadfylowsimulations Sources," SAE paper No. 971917. Presented at the
areneededto addresssomeof theseimportant 1997 SAE Noise and Vibration Conference and
questions. Exposition, Ground Traverse, Michigan, May
1997.
Conclusions
. Khorrami, M.R., Singer, B.A., and Radeztsky,
Steady Reynolds Averaged Navier-Stokes (RANS) R.H.J., "Reynolds Averaged Navier-Stokes
simulations of a complex three-dimensional high-lift Computations of Flap-Side-Edge Flowfield," AIAA
wing were conducted in an effort to understand the J., Vol. 37, No. 1,January, pp. 14-22, 1999.
effect of sweep and taper on the flap-side-edge flow
field. Flap deflection of 20 and 30 degrees, . Radeztsky, R. H., Singer, B. A., and Khorrami, M.
representing aircraft approach and landing R., "Detailed Measurements of a Flap Side-Edge
configurations, were computed. Emphasis was placed Flow Field," AIAA Paper 98-0700, Jan. 1998.
on fine resolution of the inboard and outboard flap side
edges to highlight the prominent differences between . Berkman, M., Khorrami, M.R., Choudhari, M., and
the established flow fields at the two edges. Sadowski, S., "Investigation of High-Lift Flow
Comparison between measured and computed lift Field of an Energy Efficient Transport Wing," J.
coefficients showed very good agreement. Excellent Aircraft, Vol. 37, No.l, Jan.-Feb., pp. 45-52, 2000.
comparison between PSP measurements of flap surface
pressure and simulations were obtained both . Thomas, J., Krist, S., and Anderson, W., "Navier-
qualitatively and quantitatively. Careful analysis of Stokes Computations of Vortical Flows over Low
RANS database revealed the outboard edge vortex to be Aspect-Ratio Wings," AIAA J., Vol. 28, No.2, pp.
the stronger vortex, attaining lower pressures and thus 205-212, 1990.
higher rotational velocities in its core. Moreover, the
outboard vortex path remains closer to the side edge Spalart, P.R. and Allmaras, S.R., "A One-Equation
while that of the inboard vortex is more inward of the Turbulence Model for Aerodynamics Flows,"
edge. The higher suction peaks in the core of the AIAA Paper 92-0439, 1992.
outboard vortex make it susceptible to undergo vortex
breakdown at lower flap deflections relative to the . Dacles-Mariani, J., Rogers, S., Kwak, D., Zilliac,
inboard vortex. G., and Chow, J., "A Computational Study of
Wingtip Vortex Flowfield," AIAA Paper 93-3010,
Acknowledgements July 1993.
The work of the second and third authors was 10. Khorrami, M. R., Li, F., and Choudhari, M., "A
sponsored by NASA contract NAS1-00088 (Lockheed Novel Approach for Reducing Rotor Tip-Clearance
Martin Corporation subcontract RT46324). The Induced Noise in Turbofan Engines, " AIAA Paper
computations were performed on the SGI computer 2001-2148 (also to appear in July 2002 issue of
clusters provided by the National Aerodynamic AIAA J.), May 2001.
Simulation (NAS) Facility. The authors would like to
thank Mr. Michael Wiese formerly of Computer
Sciences Corporation for constructing the
computational grids.
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Ix
65
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_ 55
-_ 50
Ix 45
4O • d
35 I I I I { I I I I
10 20 30 4050
Frequency (kHz)
Figure 1. Effect of flap angle on radiated sound from
side edges. Figure 3. Surface grid distribution.
l
Figure 4. Grid distribution in vicinity of flap inboard
edge.
a) Tested
b) Simulated Figure 5. Computed surface pressure distribution for
Figure 2. Trapezoidal wing geometry. 30 de_ee flap.
-3
-2
0 [] []
1 a) Experiment
0 0.2 0.4 0.6 0.8
X
Leading Eclgo
Figure 6. Chordwise pressure distribution on main
element at 50 percent span.
b) Computation
Figure 7. Mach contours at mid-span location for 30 Figure 8. Comparison between PSP and computed
de_ee flap. surface pressure on flap suction surface for 20 de_ee
deflection. Inboard edge is on right and outboard edge
on left and flow direction is from top to bottom.
Pressure Sensitive Paint ....... ._¢_{_iiiii._ii_,.a.:;,_iiiiiiiiiii_i_iiii.,._i_i_i_i{_i_i_i_
_N_i_iIgi_i#iiiiiii_iIiiiiiiiiliiiiiiliii_
i.l....._.{.i_.,._..'.;.._.._.._..._;_._.;.._:_
_;_i{!i_iliiiiil_i_iililiiii!!iii!illiii!i!iililiiiiilii_ii'_ii_{i_ii_i_!
a) Experiment
Figure 11. Pressure contours along outboard edge for
20 degee flap deflection.
Computational Simulation ........_.;.._,#:._m"
•"..e_%._
.......... : :: :.......... : ::+ ::.
......:.._.. .......... J_ -0-.5i!{
b) Computation
Figure 9. Comparison between PSP and computed
surface pressure on flap suction surface for 30 degee Figure 12. Pressure contours along inboard edge for 30
deflection. Inboard edge is on right and outboard edge degee flap deflection.
on left and flow direction is from top to bottom.
0 66
Figure 10. Pressure contours along inboard edge for 20
Figure 13. Pressure contours along outboard edge for
degree flap deflection. 30 degree flap deflection.
0.3
0.25
0.2
"6o.15
=_
0 0.1
(,,)
,1=0.05
=,__1
0 ........ flap20 degree
....................f.la.p 30 degree
-0.1 I , , L , I , i , , I i , L : I , : , ,
0.4 0.6 0.8 1
Flap Span
Figure 14. Spanwise lift distribution on flap. Inboard
edge is at z=0.39 and outboard edge at z= 1.116.
iiiiiiiiiiiiiiiii y i .
Figure 15. Streamwise velocity field in planes adjacent Figure 16. Streamwise velocity field in planes adjacent
to side edges for 20 degree flap deflection. to side edges for 30 degree flap deflection.