AIAA-2001-0911 Reynolds Number Effects on a Supersonic Transport at Subsonic High-Lift...

AIAA-2001-0911Reynolds Number Effects on a SupersonicTransport at Subsonic High-Lift Conditions(Invited)

L. R. Owens, and R. A. WahlsNASA Langley Research CenterHampton, Virginia

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39th AIAA Aerospace Sciences Meeting & Exhibit8-11 January 2001

Reno, Nevada

AIAA-2001-0911

1American Institute of Aeronautics and Astronautics

REYNOLDS NUMBER EFFECTS ON ASUPERSONIC TRANSPORT AT

SUBSONIC HIGH-LIFT CONDITIONS

L. R. Owens*, and R. A. Wahls †

Aerodynamics, Aerothermodynamics, and Acoustics CompetencyNASA Langley Research Center

Hampton, Virginia

ABSTRACTA High Speed Civil Transport configuration

was tested in the National Transonic Facility at theNASA Langley Research Center as part ofNASA’s High Speed Research Program. Theprimary purposes of the tests were to assessReynolds number scale effects and high Reynoldsnumber aerodynamic characteristics of a realistic,second generation supersonic transport whileproviding data for the assessment ofcomputational methods. The tests includedlongitudinal and lateral/directional studies attransonic and low-speed, high-lift conditionsacross a range of Reynolds numbers from thatavailable in conventional wind tunnels to nearflight conditions. Results are presented whichfocus on Reynolds number and static aeroelasticsensitivities of longitudinal characteristics at Mach0.30 for a configuration without an empennage. Afundamental change in flow-state occurredbetween Reynolds numbers of 30 to 40 million,which is characterized by significantly earlierinboard leading-edge separation at the highReynolds numbers. Force and moment levelschange but Reynolds number trends areconsistent between the two states.

INTRODUCTIONGround to flight scaling remains one of

many challenges facing today’s designers ofaerospace vehicles. The goal of ground to flightscaling is the preflight prediction of multiple keyaerodynamic characteristics with sufficientaccuracy to meet both performance guaranteesand certification requirements. In other words, thedesigner and his company strive to know theperformance of their vehicle with high confidenceprior to flight, thus enabling optimal design tradesprior to flight and elimination of costly fixes to theaircraft after the first flight. Specific challenges,experiences, and suggested approaches toground to flight scaling have been documentedextensively over the years for a variety of vehicleclasses (refs. 1, 2, among many others).Reynolds number effects are foremost amongmany factors affecting successful ground to flightscaling (refs. 3 - 5). The Reynolds number is theratio of inertial to viscous forces, and is theprimary aerodynamic scaling parameter used torelate sub-scale wind tunnel models to full-scaleaircraft in flight. The challenge of Reynoldsnumber scaling increases with the size of a full-scale aircraft as the Reynolds number incrementbetween that obtainable in conventional windtunnels and fl ight conditions expands.Additionally, the challenge for both wind tunneland computational approaches increases as flowfeatures become dominated by viscous-sensitivephenomena such as boundary-layer transition,shock/boundary-layer interaction, and separationonset and progression.

The present investigation was conductedin support of NASA’s High Speed Research (HSR)Program, Phase II, which was conducted from1993-1999 (ref. 6). The objective of this program,which was NASA sponsored and jointly executedwith US industry, was to develop critical high-risk

*Aerospace Engineer, Subsonic Aerodynamics Branch, Senior

Member, AIAA†Assistant Head, Configuration Aerodynamics Branch,

Associate Fellow, AIAA

Copyright © 2001 by the American Institute of Aeronautics andAstronautics, Inc. No copyright is asserted in the United Statesunder Title 17, U. S. Code. The U. S. Government has aroyalty-free license to exercise all rights under the copyrightclaimed herein for Governmental Purposes. All other rights arereserved by the copyright owner.

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airframe and propulsion technologies to enableindustry development of an economically viableand environmentally acceptable secondgeneration, high speed civil transport (HSCT).Aerodynamic performance, one of several broadairframe technology areas, included tasks toaddress Configuration Aerodynamics for high-speed conditions and High-Lift Technology fortake-off and landing. These elementsencompassed not only the challenge of efficientsupersonic cruise flight, but also the off-designchallenges (ref. 7) of efficient transonic cruise andacceleration and quiet high-performance take-offand landing. The objective of the High-LiftTechnology task was the development of practicallow-speed high-lift concepts and design andanalysis methods to allow the HSCT to operatesafely and efficiently and reduce terminal areanoise. Towards this goal, a scaling effort wasdefined to reduce the risk in the design process byidentifying those physical features of an actualflight vehicle that would contribute to theaerodynamic differences between it and wind-tunnel models of various scale. Figure 1 showsthe nominal mission profile for the baselinereference configuration used in the HSR program,and comparison to the capability of several windtunnels. The baseline reference configuration,known as Reference H, was provided by Boeingand represented a Mach 2.4, 300 passengeraircraft with a 5000 nautical mile range.

A series of wind tunnel tests was executedin the National Transonic Facility (NTF) at NASALangley Research Center (LaRC) across a widerange of Reynolds numbers from that available inconventional wind tunnels to near flight conditionat subsonic and transonic Mach numbers. Thetests included longitudinal and lateral/directionalstudies with and without an empennage attransonic and low-speed, high-lift conditions. Thispaper presents results focused on the Reynoldsnumber sensitivities of longitudinal characteristicsat low-speed, high-lift conditions representative oftake-off and landing for the configuration withoutthe empennage; reference 8 provides similarresults for transonic cruise conditions.

0

50

100

150

200

250

300

350

0.0 0.4 0.8 1.2 1.6 2.0 2.4

MachR

n, m

illio

ns

ETW (-250°F), 1.94%

LaRC 16-ft, 3.80%

ARC 12-ft, 2.81%

NTF (-250°F), 2.20%q,max

NTF (-250°F), 2.20%q = 2700 psf

HSCT flight envelopefull scale

ARC 11-ft, 2.96%

Figure 1. Nominal HSCT mission profile and wind tunnelcapabilities (model scale adjusted to test section size,

2.2% scale in the NTF is the baseline size).

TERMS, ABBREVIATIONS, & ACRONYMSARC NASA Ames Reseach CenterBL butt-line, model coordinatesCI95 95% confidence intervalc local chord lengthCD drag coefficientCL lift coefficientCM pitching-moment coefficient referenced to

0.50macCp pressure coefficientETW European Transonic WindtunnelFS fuselage station, model coordinatesHSCT High Speed Civil TransportHSR High Speed ResearchLaRC Langley Research CenterM Mach numbermac mean aerodynamic chordNTF National Transonic FacilityPT total pressureq dynamic pressureRn Reynolds number based on macr local leading-edge radiusTT total temperaturetmax local maximum airfoil thicknessWL waterline, model coordinatesα angle of attackη nondimensional semispan stationθ sectional wing twist change, relative to

wind-off twist

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EXPERIMENTAL APPROACHFacility Description

The NTF (ref. 9) is a unique nationalfacility (fig. 2) that enables tests of aircraftconfigurations at conditions ranging from subsonicto low supersonic speeds at Reynolds numbers upto full-scale flight values, depending on the aircrafttype and size. The facility (fig. 3) is a fan-driven,closed-circuit, continuous-flow, pressurized windtunnel capable of operating in either dry air atwarm temperatures or nitrogen from warm tocryogenic temperatures. The test section is 8.2 ftby 8.2 ft in cross section and 25 ft in length. Thetest section floor and ceiling are slotted (6 percentopen), and the sidewalls are solid. Freestreamturbulence is damped by four screens and a14.95:1 contraction ratio from the settling chamberto the test section. Fan-noise effects areminimized by an acoustic treatment both upstreamand downstream of the fan. A detailedassessment of the dynamic flow quality in the NTFis reported in reference 10, and reconfirmed withmore recent measurements shown in reference11. The NTF is capable of an absolute pressurerange from 15 psi to 125 psi, a temperature rangefrom –320°F to 150°F, a Mach number range from0.2 to 1.2, and a maximum Reynolds number of146×106 per ft at Mach 1. Typical tests use atemperature range from -250°F to 120°F. Furtherfacility details can be found in reference 12.

Model DescriptionThe wind-tunnel model is a 2.2% scale

representation of the HSR baseline configurationknown as Reference H. Although the full modelwith empennage was tested during the HSRprogram, the present paper focuses on resultsobtained for the wing/body configuration with thebody truncated slightly aft of the wing trailing edge.Figure 4 shows a planform drawing of the modelwith wing pressure taps and reference locationsnoted. The model has a cranked-delta wingplanform with an aspect ratio of 2.367, a span of34.23 inches, and a mean aerodynamic chord of22.71 inches. The inboard wing (η ≤ 0.522) has ablunt (r/c ~ 0.0025 to 0.0030) subsonic leading-edge with a sweep change from 76 to 68.5 deg atη = 0.226, a twist varying from approximately 1deg near η = 0.10 to –2 deg near η = 0.50, andvariable thickness ratio (tmax/c) from 0.043 to0.024. The outboard, supersonic leading edge issharp, swept 48 deg, has a constant twist of –1.6deg for η ≥ 0.65, and a constant thickness ratio of

FS 58.396 BL 17.113WL 5.098

BL 8.928

FS 0.000BL 0.000

FS 9.35 FS 26.10

FS 34.245

FS 37.98 FS 41.45

FS 46.50 FS 49.55

FS 60.815

50% mac = FS 46.445

forebody pressure rings

upper surface wing pressures, starboard side

model part lines = solid lines

lower surface wing pressures, port side

flap hingelines/edges = dashed lines

WL 5.104 WL 5.462

FS 60.410

FS 59.807

Figure 4. Model drawing with pressure locations(linear dimensions in inches).

Figure 2. External view of the NTF.

200

48.6

25 dia

Turn 3 Turn 2

Turn 1

16.8 dia

27-dia plenumHigh-speed diffuser2.6° half-angle

19.7-dia fan

Turn 4

Wide-angle diffuserCooling coil

Screens

14.95:1 contraction

Slotted test section8.2 by 8.2

Low-speed diffuser

Figure 3. NTF clrcuit diagram (linear dimensions in ft).

Figure 5. 2.2% Reference H model in the NTF.

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ref. area / NTF cross sectional area 0.0515

model span / NTF width 0.3478

solid blockage ratio, α = 0 deg 0.0022

Table 1. Model size relative to the NTF test section.

0.024. The reference area for the model is 3.436ft2. Table 1 provides several key ratios relating themodel size to the NTF test section.

The model was designed and constructedspecifically for testing in the cryogenic,pressurized conditions of the NTF, where dynamicpressures reached approximately 2700 psf duringthese tests at transonic conditions; the model jigshape was that of the Mach 2.4 cruise designpoint. The model was built of maraging steel witha surface finish of 8-16µ-inches (root meansquare) and a contour tolerance of ±0.005 inches.The model is shown in figure 5 mounted in theNTF test section on a straight sting; the stingmounts to a 6-deg offset stub sting which in turnmounts to the facility arcsector resulting in a modelangle-of-attack range from –4 to 24 degrees.

The model has multiple inboard leadingand trailing edge parts, multiple outboard wingpanels each with different leading and trailingedge deflections, and four detachable, 8.43 inchlong, constant internal diameter (1.236 inches),circular flow-through nacelles with boundary-layerdiverters located between the wing and nacelle.The inboard nacelles are rigged with toe-in andpitch (nose down) angles of 1 and 4.17 deg,respectively; the outboard nacelles are rigged withtoe-in and pitch angles of 2.4 and 2.84 deg,respectively. The multiple leading and trailingedge parts in combination with the multipleoutboard panels enabled testing of a variety ofconfigurations including the baseline (supersoniccruise), take-off, landing, stall recovery, andtransonic cruise configurations as defined in table2. Results for the baseline and take-offconfigurations (with the nacelle/diverters) areincluded herein.

The model was instrumented with 48forebody pressures distributed circumferentially attwo fuselage stations and 146 wing pressuresdistributed in both spanwise and chordwise rowson the starboard upper and port lower surfaces ofthe wing, as shown in figure 4. Additionally, oneinboard and one outboard nacelle wereinstrumented with an internal Preston tube, and 6nacelle base pressure taps enabling correction fornacelle internal and base drag effects.

InstrumentationAerodynamic force and moment data were

obtained with an internal, unheated, six-component, strain gauge balance. The balanceused was one of the NTF-113-class balanceshaving the load capacity and accuracy shown intable 3. An internal, heated accelerometerpackage was used to measure the onboard angle

Designation LE Deflection, degInboard/Outboard

TE Deflection, degInboard/Outboard

Baseline 0/0 0/0

Take-Off 30/30 10/10

Landing 30/30 20/20

Stall Recovery 50/50 30/30

Transonic Cruise 0/10 0/3

Table 2. Available Wing Configurations.

Component Full-ScaleLoad

Nominal Accuracy95% confidence

Normal, lbs ±6500 ±0.09% full-scale

Axial, lbs ±400 ±0.30% full-scale

Side, lbs ±4000 ±0.18% full-scale

Pitch, in-lbs ±13000 ±0.09% full-scale

Yaw, in-lbs ±6500 ±0.18% full-scale

Roll, in-lbs ±9000 ±0.29% full-scale

Table 3. NTF-113 balance capacity and accuracy.

of attack; quoted accuracy of the package undersmooth operating wind tunnel conditions is ±0.01deg (ref. 13). Model pressure measurementswere obtained using three 48-port, 30-psid,onboard, heated, electronically scanned pressure(ESP) transducers with a quoted accuracy of±0.2% of full-scale (worst case) throughout therange. The body cavity pressure was measuredwith a heated, 5-psid ESP module located in thef a c i l i t y a r c s e c t o r . Wing deformationmeasurements were made at 3 spanwise stations,η = 0.635, 0.778, and 0.922, using a video modeldeformation system (ref. 14). The systemprovided sectional twist change data relative to thewind-off shape with a quoted accuracy of ±0.10deg.

The primary measured flow variablesinclude both the total and static pressures and thetotal temperature. Mach number, Reynoldsnumber, and dynamic pressure are calculatedfrom these measured parameters. A complete

AIAA-2001-0911


description of these measurements andsubsequent calculations is given in reference 15.

Data Reduction and CorrectionsInformation on the various instrumentation

devices, the data acquisition and controlcomputers, and the data reduction algorithms forthe different measurement systems is provided inreference 15. Standard balance, angle-of-attack,and tunnel parameter corrections have beenapplied. Note that the use of unheated balancesin the cryogenic environment requires additionalattention towards temperature compensation. Thetemperature compensation methods are designedto correct balance output due to thermal loads(refs. 15,16). Body cavity pressure and nacelleinternal drag and base pressure corrections wereapplied based on the measurements describedpreviously. The angle of attack was corrected forflow angularity (upflow) by measurement of bothupright and inverted model force data for a givenconfiguration and flow condition. Wall and modelsupport interference effects have not beenaccounted for in the data; these effects wereminimized through model sizing (table 1).

Test ConditionsThe NTF allows testing across a wide

range of Reynolds numbers from that available inconventional wind tunnels to near flight conditionsat subsonic and transonic Mach numbers. Testsof the 2.2% Reference H model spanned Machnumbers from 0.30 to 1.10, and Reynoldsnumbers from 4 to 120 million based on the meanaerodynamic chord. The present paper focuseson the low-speed regime representative of take-offand landing, and specifically at Mach 0.30 for aReynolds number range from 8.5 to 90 million.Figure 1 indicates the relationship of the NTF testconditions to flight, and figure 6 provides the NTFoperational envelope for Mach 0.30 with specifictest points identified. Full-scale flight Reynoldsnumbers were not obtainable due to the large sizeof the full-scale aircraft and model size and loadlimitations (q = 2700 psf boundary in figure 1) atleast in part driven by the requirement of testingthe same model at transonic conditions.

The goals of assessing Reynolds numberscale effects and extrapolation to flight conditionsrequired a series of intermediate conditions tobetter identify trends. As seen in figure 6, thedesired Reynolds number range could not becovered at a constant total pressure level, and

thus dynamic pressure level. However, theindependent control of total pressure, totaltemperature, and fan speed in the NTF allow theisolation of pure Reynolds effects, pure staticaeroelastic (dynamic pressure) effects, and purecompressibility (Mach) effects. Several conditionsare used to isolate static aeroelastic effects fromthe Reynolds number effects for Mach 0.30 asshown in figure 6. During Reynolds numbersweeps, it is actually the ratio of dynamic pressure(q) to the model material modulus of elasticity (E)that is held constant to maintain a constant staticaeroelastic state (q/E) due to the variability of themodulus of elasticity over the temperature rangeof the NTF. Note that constant q/E was notmaintained for the two lowest Reynolds number

conditions due to the use of air rather thannitrogen to conserve resources. However, theaeroelastic adjustment methodology (explained inResults & Discussion section) is sufficient toprovide pure Reynolds number effects at thislower dynamic pressure level.

Boundary-Layer TransitionA basic strategy used in the NTF includes

testing at high Reynolds number conditions withfree transition. The high Reynolds number testcondition typically corresponds to a design flightcondition. To anchor the NTF data to lowReynolds number data obtained in a conventionalwind tunnel, the NTF model is usually tested at amatching low Reynolds number condition with theboundary-layer tripping (forced transition) strategy

15

0F

75

F

0F

-50

F

-10

0F

-15

0F

-20

0F

-22

5F

-24

0F

-26

0F

Rn (millions)

PT(p

sia)

0 10 20 30 40 50 60 70 80 90 10020

30

40

50

60

70

80

90

100

110NTFENVELOPE--MACH= 0.300

Chord=1.8925ftREYNOLDSNUMBER, MILLIONS

TOTALPRE

SSURE,

PSIA

Figure 6. NTF operational envelope, Mach =0.30.

AIAA-2001-0911


used in that facility. The majority of the data forthe 2.2% Reference H model was not acquiredwith fixed transition on the wing, primarily due tothe potential at the time for a one-third-scale flighttest (which never occurred) anticipated to fly atconditions susceptible to transitional flow. No datawith fixed transition on the wing is available forconfigurations presented herein. Transition wasconsistently fixed on the forebody with a ring ofcarborundum grit located 1.5 inches from thenose, and on the nacelle internal surface tofacilitate the internal nacelle drag correction.These trips were sized and located based ontraditional criteria (ref. 17).

RESULTS & DISCUSSIONThe purpose of this paper is to document

the Reynolds number sensitivities of longitudinalaerodynamic characteristics for a relevant,supersonic transport configuration at conditionsrepresentative of take-off and landing, Mach 0.30.Though the configuration was tested with anempennage, the present results are limited to thewing/body configuration with installed nacelles.Figure 7 presents representative data for thebaseline and take-off configurations at Reynoldsnumbers of 8.5 and 90 million, and is provided toindicate the basic, longitudinal aerodynamiccharacteristics of the configuration. The data asacquired, and presented in figure 7, include thecombined effects of static aeroelastic deformationand Reynolds number effects; this fact ishighlighted in figure 7 by the distinctly differentdynamic pressure levels for the two Reynoldsnumbers. The discussion will address staticaeroelastic effects as a means to isolate and moreproperly address Reynolds number effects.

RepeatabilityData presented herein were acquired

within a single wind-tunnel test of the model. Thissection provides examples of short-termrepeatability (within test / Mach series), as definedin reference 18, quantified in terms of a 95%confidence interval for each configuration. The95% confidence interval is interpreted as thebounds about an estimated mean (average ofmultiple, repeat polars) that encompasses the truemean value with a chance of 95%. Examples ofshort-term repeatabi l i ty of longitudinalaerodynamic data are shown in figure 8 for thebaseline and take-off configurations at a Reynoldsnumber of 90 million. The figure shows the

0 .04

.08

.12

.16

.20

.24

.28

.32

.36

.40

CD

-.2

0

.2

.4

.6

.8

1.0

1.2

CL

-4 0 4 8 12 16 20 24

α, deg

-.045

-.030

-.015

0

.015

.030

.045

.060

.075

.090

.105

CM

Rn (millions)

8.51

90.00

8.52

89.95

q, psf

318.

839.

318.

842.

config

Baseline + nac

Baseline + nac

Take-off + nac

Take-off + nac

Figure 7. Representative longitudinal force and momentdata, M = 0.30.

residuals of the longitudinal coefficients defined asthe difference in the individual measured datapoints from the estimated mean of the group ofrepeated polars; the estimated mean was theaverage of the grouped data based on piecewise,2nd order polynomial fits of the individual polars.The figure also indicates, with a solid line, the

AIAA-2001-0911


bounds of the 95% confidence interval as afunction of angle of attack; the average confidenceinterval over the range of angle of attack is noted.

Results shown in figure 8 are typical ofother test conditions. In general, the coefficientresiduals are small up to angles-of-attack ofapproximately 12 deg. Beyond this angle of attackrange, larger-scale separations begin to dominatethe wing flow field as indicated by the morenonlinear behavior exhibited in the pitchingmoment coefficient data and the increasingvariations in the drag residual data. For reference,the average 95% confidence interval values foreach coefficient at each test condition are includedin table 4. These values were used to determinethe significance of the differences observed in thedata.

Rn q, psf ∆CD ∆CL ∆CM

8.5 318 0.00011 0.00050 0.00007

10.2 381 0.00010 0.00047 0.00007

21.6 267 0.00028 0.00092 0.00015

21.6 430 0.00027 0.00096 0.00019

21.6 587 0.00007 0.00037 0.00006

21.6 803 0.00012 0.00065 0.00008

30.0 817 0.00011 0.00076 0.00011

40.0 825 0.00047 0.00136 0.00190

50.0 834 0.00027 0.00113 0.00140

90.0 839 0.00023 0.00122 0.00140

a) Baseline configuration.

Rn q, psf ∆CD ∆CL ∆CM

8.5 318 0.00012 0.00059 0.00009

10.2 381 0.00013 0.00051 0.00010

21.6 267 0.00019 0.00064 0.00013

21.6 430 0.00040 0.00134 0.00029

21.6 587 0.00010 0.00037 0.00005

21.6 803 0.00018 0.00100 0.00014

30.0 817 0.00018 0.00074 0.00008

40.0 825 0.00029 0.00062 0.00015

50.0 834 0.00022 0.00066 0.00009

90.0 839 0.00030 0.00133 0.00017

b) Take-Off configuration.Table 4. Repeatability data (95% confidence intervals

averaged over α range).

-20 -16

-12

-8

-4

0

4

8

12

16

20 × 10 -4

∆CD

CI95 = 0.00023

-.004 -.003

-.002

-.002

-.001

0

.001

.002

.002

.003

.004

∆CL

CI95 = 0.00122

-4 0 4 8 12 16 20 24

α, deg

-10 -8

-6

-4

-2

0

2

4

6

8

10 × 10 -4

∆Cm

CI95 = 0.00014

Rn (millions) PT, psi TT, °F q, psf

90.05 99.41 -247.5 839.2 90.02 99.41 -247.4 839.6 89.99 99.41 -247.4 839.1 89.95 99.40 -247.3 839.5

a) Baseline configuration with nacelles.

Figure 8. Short-term repeatability, M = 0.30.

AIAA-2001-0911


-20 -16

-12

-8

-4

0

4

8

12

16

20 × 10 -4

∆CD

CI95 = 0.00030

-.004 -.003

-.002

-.002

-.001

0

.001

.002

.002

.003

.004

∆CL

CI95 = 0.00133

-4 0 4 8 12 16 20 24

α, deg

-10 -8

-6

-4

-2

0

2

4

6

8

10 × 10 -4

∆Cm

CI95 = 0.00030

Rn (millions) PT, psi TT, °F q, psf

90.06 99.40 -247.2 842.2 89.80 99.40 -247.0 840.2 89.92 99.40 -247.2 840.5 90.03 99.40 -247.1 843.1

b) Take-off configuration with nacelles.

Figure 8. Concluded.

The wing pressure data presented in thisreport did not have repeat run sets available toevaluate the repeatability of this data. However,the consistency of the pressure coefficients at thelower angles of attack as well as the repeatabilityduring the aeroelastic sweeps provided someconfidence that differences of the order of 0.1were distinguishable.

Static Aeroelastic EffectsAchieving high Reynolds numbers

approaching those characteristic of flight requiresthe manipulation of both the total temperature andpressure, as seen in figure 6. As a result, thestatic aeroelastic deformation of the model, inparticular the wing, under load must be consideredwhen attempting to isolate Reynolds numbereffects. Previous reports for high aspect ratiosubsonic transport configurations have shown thestatic aeroelastic effects to be on the order ofReynolds number effects, and often opposite insense to that of Reynolds number trends, thusmasking the Reynolds number effects (ref. 19, 20).Like the subsonic transport configurations, thecurrent low aspect ratio HSCT model is flexibleunder load, most notably on the thin outboard wingpanel.

Video model deformation measurementsof the wing under load were concentrated on theoutboard wing panel. These measurementsindicated that as the aerodynamic load on thewing increased, the outboard wing panel wouldtend to washout, similar to that observed on thehigher aspect ratio subsonic transports. This typeof wing bending occurs because the local liftingcenter of pressure is located behind the elasticaxis of the wing, which produces a local nose-down torsional moment at each outboard wingsection. Figure 9 shows representative wing twistdata at η = 0.922, relative to the wind-off twist, asa function of dynamic pressure and angle ofattack. At the higher dynamic pressures and/orhigher angles of attack, the local twist changeincreases (more nose-down) on the order of 1deg. The relationship between local wing twistchange and dynamic pressure is linear, at leastover the range of dynamic pressure shown here.One would expect that extrapolation to the wind-off condition (q = 0 psf) would indicate no twistchange; the data at α = 9 deg does approach thisresult for the baseline wing configuration.

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-4 0 4 8 12 16 20 24

α, deg

-2.5

-2.0

-1.5

-1.0

-.5

0

.5

θ, d

eg (

η=0.

922)

Rn, (millions)

21.62

21.59

21.59

21.54

q,psf

267.

426.

588.

804.

0 500 1000 1500 2000

q,psf

-1.5

-1.0

-.5

0

.5

1.0

1.5

θ, d

eg (

η=0.

922)

α = 9 deg

Figure 9. Outboard wing twist change under load, baselineconfiguration with nacelles, M = 0.30.

The effects of static aeroelastic wingbending on the longitudinal aerodynamic dataobtained are presented in figure 10. These datawere obtained with a constant Reynolds number of21.6 million for several total pressure (dynamicpressure) conditions, as shown in figure 6. Thedata for the dynamic pressure level of about 430psf is significantly different from the other threedynamic pressure levels surrounding it, especiallythe drag increments for both configurations. Thisdifference was also observed in the wing pressuredata for the baseline configuration. An example oftwo pressures near the wing leading edge as afunction of angle of attack is shown in figure 11.The inboard wing pressure (η = 0.405) data for thedynamic pressure level of about 430 psf show amuch earlier leading-edge separation than that ofthe other three dynamic pressures that surround it.This suggests that it is likely there was somethingother than model deformation affecting the 430 psfdata. The outboard wing pressure (η =0.619) also

-.0080 -.0070 -.0060 -.0050 -.0040 -.0030 -.0020 -.0010

0 .0010 .0020 .0030 .0040 .0050 .0060 .0070 .0080

∆CD

-.020 -.016 -.012 -.008 -.004

0 .004 .008 .012 .016 .020

∆CL

-4 0 4 8 12 16 20 24

α, deg

-.002 -.001

0 .001 .002 .003 .004 .005 .006 .007 .008

∆CM

Rn (millions)

21.64 21.58 21.51

PT, psi

50.01 68.69 93.80

TT, °F

-99.75 -4.106 120.5

q, psf

430. 587. 803.


Figure 10. Static aeroelastic effects on longitudinalcoefficients, reference to q = 267 psf, M = 0.30.

show a slight difference in the 430 psf data fromthat of the other three dynamic pressure levels.The cause for this difference was not clear (andremains unclear) from the available data. Onepossible explanation for the difference at the 430psf test conditions is that unobservable frost mayhave developed on the wing leading edge

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-.0080 -.0070 -.0060 -.0050 -.0040 -.0030 -.0020 -.0010

0 .0010 .0020 .0030 .0040 .0050 .0060 .0070 .0080

∆CD

-.020 -.016 -.012 -.008 -.004

0 .004 .008 .012 .016 .020

∆CL

-4 0 4 8 12 16 20 24

α, deg

-.002 -.001

0 .001 .002 .003 .004 .005 .006 .007 .008

∆CM

Rn (millions)

21.60 21.59 21.55

PT, psi

50.01 68.71 93.82

TT, °F

-100.2 -3.991 120.5

q, psf

427. 588. 806.



and influenced the separation characteristics.Recent testing of a subsonic transport semi-spanmodel, documented in reference 21, indicates thattunnel test conditions below the dewpoint for thetest gas sometimes produced frost on the model,especially in regions of highly accelerated flow.However, there were no reports of frost observedon the model during the HSR test. Also,measurements of losses in the tunnel circuit (i.e.,

1

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-9

CP

η = 0.405

-4 0 4 8 12 16 20 24

α, deg

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9

CP

Rn (millions)

21.62 21.59 21.59 21.55

q, psf

267. 426. 588. 804.

TT, °F

-201.9 -100.1 -4.028 120.0

η = 0.619

Figure 11. Wing leading-edge pressure characteristics,baseline configuration with nacelles, M = 0.30.

at the cooling coil), which tend to increase as frostaccumulates, were not consistent enough toconclude that frost was a factor for this data.Another possible cause is that the flow field is verysensitive to transitional flow at this intermediateReynolds number, and causes changes inboundary-layer state.

When the anomalous 430 psf data runsare ignored in figure 10, the force and moment

AIAA-2001-0911


increments tend to behave in a consistent manneras dynamic pressure and angle of attack increasefor both configurations shown. The drag changefor both configurations tends to decrease withincreasing dynamic pressure at the higher anglesof attack. The sensitivity to dynamic pressurechange increased up to a certain angle of attack,about 8 deg for the baseline and about 12 deg forthe take-off configuration, and then became nearlyconstant. This behavior suggested that theoutboard wing loads increased the washout up tothese angles of attack and then did not produceany further twisting as the model attitudeincreased. The washout tendency is alsosupported by the twist data for the baselineconfiguration, which generally showed that thetwist changed less as the angle of attackincreased beyond an angle of attack of about 8deg (see figure 9). No wing twist measurementswere made for the take-off configuration, but thecharacter of the drag changes is consistent with awashout tendency similar to that observed for thebaseline configuration.

The lift change for the baselineconfiguration was relatively insensitive to dynamicpressure changes up to an angle of attack ofabout 8 deg. Beyond this angle of attack, the liftincreased with increasing dynamic pressure. Thislift increase occurred in the same angle of attackregion where the wing washout was relativelyconstant. The lift change for the take-offconfiguration was more sensitive to dynamicpressure changes than for the baselineconfiguration because the outboard wing panel ismore highly loaded with the deflected flaps. Up toan angle of attack of about 12 deg, the liftdecreased with increasing dynamic pressure forthe take-off configuration, which was consistentwith the expected increase in washout withincreased dynamic pressure. Above this angle ofattack, the lift increased with increasing dynamicpressure in the angle of attack region where it isexpected that the washout has become constant.This behavior is similar to that observed for thebaseline configuration.

The pitching moment change for thebaseline configuration showed an increasedsensitivity to dynamic pressure as the angle ofattack increased. As the dynamic pressureincreased, the baseline configuration generated anose up moment change over the entire angle-of-attack range. The take-off configuration alsogenerated a nose-up moment increment over the

angle-of-attack range with increased dynamicpressure. However, the sensitivity to dynamicpressure was relatively constant over most of theangle-of-attack range.

At this point in the analysis, the differencein the data at the 430 psf (nominal) dynamicpressure level was deemed due to somethingother than static aeroelastic effects. As a result,static aeroelastic adjustments to the longitudinalforce and moment coefficients were based on thesensitivities derived from the three nominal levelsof 270, 590 and 800 psf for each configuration.These adjustments are applied to essentiallyaccount for static aeroelastic effects whenisolating pure Reynolds number effects; ingeneral, data was translated to the 270 psfdynamic pressure level when isolating Reynoldsnumber effects.

Reynolds Number EffectsThe primary Reynolds number effects

observed in the data were a drag reduction anddelay of leading-edge flow separation. Afundamental change of flow-state occurs betweenReynolds numbers of 30 and 40 million, which ischaracterized by significantly earlier inboardleading--edge separation at the high Reynoldsnumbers. The following discussion will examinethe Reynolds number trends for the longitudinalforce and moment coefficients (adjusted for staticaeroelastic effects) at two angles of attack. Theseangles of attack are characterized as follows: 1)near minimum drag (α = 1 deg), and 2) near thetake-off design condition (α = 9 deg). Force andmoment data for the baseline and take-offconfigurations, both with nacelles installed, arepresented for each of these angles of attack.

The Reynolds number effects forconditions near minimum drag are presented infigure 12 for each configuration. Drag decreasesas the Reynolds number increases, and is mostlyaccounted for by the established trend of skinfriction with Reynolds number. Theoretical skinfriction drag for the configuration was calculatedusing equivalent flat plate theory, plus formfactors, using the Blasius and Karman-Schoenherrincompressible skin friction correlations for laminarand turbulent boundary layers, respectively, withcompressibility effects accounted for with thereference temperature method (ref. 22). Asapplied herein, the flat-plate theory assumed thatthe same extent of laminar flow was present onboth the upper and lower outboard wing surfaces

AIAA-2001-0911


.0060

.0065

.0070

.0075

.0080

.0085

.0090

.0095

.0100

.0105

.0110 CD

.0060

.0065

.0070

.0075

.0080

.0085

.0090

.0095

.0100

.0105

.0110

Theory

Fully turbulent 10% local chord 30% local chord 70% local chord

.005

.010

.015

.020

.025

.030

CL

100 1 5

101 1 5

102 1

Rn (millions)

.0090

.0095

.0100

.0105

.0110

.0115

.0120

.0125

.0130

.0135

.0140

CM

α, deg

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Rn (millions)

8.51 10.20 21.55 21.64 21.58 21.51 29.91 40.00 49.97 90.00

q, psf

318. 381. 267. 430. 587. 803. 817. 825. 834. 839.

PT, psi

37.12 44.52 31.32 50.01 68.69 93.80 95.30 96.41 97.20 99.41

TT, °F

120.6 120.3 -201.5 -99.75 -4.106 120.5 -4.090 -90.38 -143.5 -247.4

Outboard Laminar Run


Figure 12. Longitudinal coefficient trends with Reynoldsnumber, near minimum drag, M = 0.30.

.0165

.0170

.0175

.0180

.0185

.0190

.0195

.0200

.0205

.0210

.0215

CD

.0165

.0170

.0175

.0180

.0185

.0190

.0195

.0200

.0205

.0210

.0215

Theory

Fully turbulent 10% local chord 30% local chord 70% local chord

.135

.140

.145

.150

.155

.160

CL

100 1 5

101 1 5

102 1

Rn (millions)

-.0370 -.0365

-.0360

-.0355

-.0350

-.0345

-.0340

-.0335

-.0330

-.0325

-.0320

CM

α, deg

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Rn (millions)

8.52 10.23 21.51 21.60 21.59 21.55 29.92 40.04 49.91 89.95

q, psf

318. 383. 267. 427. 588. 806. 818. 828. 834. 842.

PT, psi

37.11 44.53 31.33 50.01 68.71 93.82 95.31 96.39 97.22 99.40

TT, °F

120.4 120.3 -201.1 -100.2 -3.991 120.5 -3.984 -90.18 -143.1 -247.1

Outboard Laminar Run


Figure 12 . Concluded.

AIAA-2001-0911


and that fully turbulent flow existed on both upperand lower surfaces of the inboard wing. Severaltheoretical curves are included where the variableis the extent of laminar flow on the outboard wing.All theoretical data was adjusted by a constantincrement such that the fully turbulent theoreticalcurve was anchored to the experimental data forthe 90 million Reynolds number conditions. Thetheoretical curves indicate the sensitivity of drag tothe transition location on the outboard wing.

The fully turbulent theoretical skin frictiondrag trend aligned well with the experimental dragdata obtained for 21.6 and 30 million Reynoldsnumbers for the baseline configuration. The dragbehavior at this angle of attack suggests that thechanges are due primarily to skin friction. Theextent of laminar flow inferred from figure 12compares favorably with temperature sensitivepaint measurements of the transition location onthe outboard wing for the baseline configuration.The character of the drag for the take-offconfiguration with changing Reynolds numbersimilarly suggests that skin friction drag reductionis the dominant flow phenomenon. However,there were two distinct groupings of the take-offdrag data. One of the groups of data includesReynolds numbers of 30 million and below (exceptfor the anomalous 430 psf data at Rn = 21.6million). The second grouping contained all thehigher Reynolds number data and the 430 psfdata at Rn = 21.6 million. Note also that thehigher Reynolds number group closely follows thefully turbulent theoretical skin friction trend.

The lift trend with Reynolds numberpresented in figure 12 for the baselineconfiguration shows that the lift is essentiallyconstant over the range of Reynolds numberstested at this angle of attack. The lift for the take-off configuration increases slightly over the rangeof Reynolds numbers tested. The two distinct datagroupings are not apparent in the lift data at thisangle of attack.

The pitching moment trends with Reynoldsnumber are presented in figure 12. For reference,the pitching-moment coefficients can be related tothe effects of stabilizer deflection. The stabilizereffectiveness for the full configuration withempennage (when closed aftbody and horizontaltails are present) is approximately 0.005 change inpitching-moment coefficient for one degree ofstabilizer deflection; one major division representsroughly 0.10 deg of stabilizer to regain trim. Forthe baseline configuration, the data is essentially

constant. For the take-off configuration, theReynolds number effect is on the order a 0.4 degstabilizer change to balance the nose-downpitching moment that develops with the Reynoldsnumber increase. As with lift, the two distinct datagroupings were not apparent in the pitchingmoment data at this angle of attack.

The Reynolds number effects forconditions near the take-off design condition areshown in figure 13. In general, the coefficienttrends exhibit the same behavior as that observedat the minimum drag condition. However, the twodistinct groups noted in the take-off configurationdrag data only (fig. 12) now appear in both thedrag and pitching moment data for eachconfiguration.

Since the force and moment data for bothconfigurations show a fundamental shift in dragand pitching moment levels above Reynoldsnumbers of about 30 million, wing pressures wereexamined to determine if there was anyconsistency in this pattern. It is important to notethat the pressure data was obtained early in thetest and then the pressure tubing was removed toconduct the force and moment testing at the sametest conditions. However, the different behaviorfor the data taken at Reynolds numbers greaterthan 30 million was consistent between both thepressure and force/moment testing. Typicalpressures at or near the wing leading edge as afunction of angle of attack are shown in figure 14for each configuration. In general, the inboardpressures (η = 0.405) were more sensitive toReynolds number changes than the pressures onthe outboard wing panel (η = 0.619). Theinsensitivity of the outboard wing pressures toReynolds number is due to the sharp, outboardwing leading-edge radius. For the blunt inboardwing pressures, a distinct grouping of the dataexists. For each configuration, the data forReynolds numbers 30 million and below show thatthe leading-edge flow stays attached to greaterangles of attack than for higher Reynoldsnumbers. There was one exception to thisobserved trend for each configuration. For thebaseline configuration, the leading edge pressuredata indicated separation at a lower angle ofattack for a Reynolds number of 21.6 million and adynamic pressure of 426 psf, as discussedpreviously (see Static Aeroelastic Effects). For thetake-off configuration, the different behavior alsooccurs at a Reynolds number of 21.6 million, butat a dynamic pressure of 268 psf. However, the

AIAA-2001-0911


.0480

.0485

.0490

.0495

.0500

.0505

.0510

.0515

.0520

.0525

.0530

CD

.375

.380

.385

.390

.395

.400

CL

100 1 5

101 1 5

102 1

Rn (millions)

.0160

.0165

.0170

.0175

.0180

.0185

.0190

.0195

.0200

.0205

.0210

CM

α, deg

9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0

Rn (millions)

8.51 10.20 21.55 21.64 21.58 21.51 29.91 40.00 49.97 90.00

q, psf

318. 381. 267. 430. 587. 803. 817. 825. 834. 839.

PT, psi

37.12 44.52 31.32 50.01 68.69 93.80 95.30 96.41 97.20 99.41

TT, °F

120.6 120.3 -201.5 -99.75 -4.106 120.5 -4.090 -90.38 -143.5 -247.4


Figure 13. Longitudinal coefficient trends with Reynoldsnumber, near take-off design point, M = 0.30.

.0470

.0475

.0480

.0485

.0490

.0495

.0500

.0505

.0510

.0515

.0520

CD

.500 .505

.510

.515

.520

.525

CL

100 1 5

101 1 5

102 1

Rn (millions)

-.0310 -.0305

-.0300

-.0295

-.0290

-.0285

-.0280

-.0275

-.0270

-.0265

-.0260

CM

α, deg

9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0

Rn (millions)

8.52 10.23 21.51 21.60 21.59 21.55 29.92 40.04 49.91 89.95

q, psf

318. 383. 267. 427. 588. 806. 818. 828. 834. 842.

PT, psi

37.11 44.53 31.33 50.01 68.71 93.82 95.31 96.39 97.22 99.40

TT, °F

120.4 120.3 -201.1 -100.2 -3.991 120.5 -3.984 -90.18 -143.1 -247.1


Figure 13 . Concluded.

AIAA-2001-0911


1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9

CP

η = 0.405

-4 0 4 8 12 16 20 24

α, deg

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9

CP

Rn (millions)

8.53 10.24 21.62 21.59 21.59 21.55 29.91 40.06 49.93 89.94

q, psf

319. 383. 267. 426. 588. 804. 818. 827. 834. 838.

TT, °F

120.1 119.7 -201.9 -100.1 -4.028 120.0 -3.919 -90.42 -143.3 -247.4

η = 0.619


Figure 14. Wing leading-edge pressure characteristics,M = 0.30.

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9

CP

η = 0.405

-4 0 4 8 12 16 20 24

α, deg

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9

CP

Rn (millions)

8.50 10.20 21.57 21.52 29.92 39.92 49.94 90.00

q, psf

317. 381. 268. 803. 818. 825. 835. 841.

TT, °F

120.3 120.4 -201.5 119.8 -4.010 -89.96 -143.3 -247.2

η = 0.619



AIAA-2001-0911


force and moment data used to define the staticaeroelastic adjustments for the take-offconfiguration were acquired separately during thetest, and did not show signs of early leading-edgeseparation.

Both force and moment, and pressuredata indicate the wing leading edge separatesearlier for Reynolds numbers greater than 30million, as compared to the lower Reynoldsnumber data. This produced two Reynoldsnumber data groupings in both the drag andpitching moment trends. Note that similar dragand pitching moment trends with increasingReynolds number exist for both the low and highReynolds number groups, suggesting thepossibility of a flow-state change between the lowand high Reynolds number groups that did notsignificantly change the Reynolds numbersensitivity.

To further illustrate the differences inleading-edge separation for the low and highReynolds number groups, figures 15 and 16 showpitching moment coefficient incrementshighlighting the effect of Reynolds number. Infigure 15, the increments are referenced to thelowest Reynolds number condition, 8.5 million, atthe low dynamic pressure level. Increasing theReynolds number from 8.5 to 21.6 millionproduces the expected change in pitchingmoment, especially at the higher angles of attack.In figure 16, the increments are referenced to the

lowest Reynolds number condition, 21.6 million, atthe highest dynamic pressure level. Theincreased nose-up pitching moment relative to thedata for Reynolds numbers 30 million and below isclearly seen for both configurations at the higherangles of attack. Also note that within theincremental data for Reynolds numbers greaterthan 30 million, the nose-up pitching momentincrement decreases slightly as the Reynoldsnumber increases. This is consistent with thepreviously discussed similarity of the Reynoldsnumber trend between the low and high Reynoldsnumber groupings.

Although the cause for the earlier wingleading-edge separation for the higher Reynoldsnumber data is not understood, the Reynoldsnumber effects for both the low and high Reynoldsnumber data groupings appear to be consistent.As Reynolds number increases within eachgrouping, the drag decrease is consistent withtheoretical skin friction reductions. Also, aReynolds number increase tends to produce amore nose-down pitching moment that is usuallyassociated with a delay in the wing leading-edgeseparation.

-4 0 4 8 12 16 20 24

α, deg

-.008 -.006 -.004 -.002

0 .002 .004 .006 .008

∆CM

Rn (millions)

10.20 21.55

PT, psi

44.52 31.32

TT, °F

120.3 -201.5

q, psf

381. 267.

-4 0 4 8 12 16 20 24

α, deg

-.006 -.004 -.002

0 .002 .004 .006 .008 .010

∆CM

Rn (millions)

10.23 21.51

PT, psi

44.53 31.33

TT, °F

120.3 -201.1

q, psf

383. 267.

a) Baseline configuration with nacelles. b) Take-off configuration with nacelles.

Figure 15. Pitch-up delay with Reynolds number at low dynamic pressure, M = 0.30.

AIAA-2001-0911


CONCLUDING REMARKSA series of wind tunnel tests with a 2.2%

scale HSCT model was executed in the NTF atNASA LaRC across a wide range of Reynoldsnumbers from that available in conventional windtunnels to near flight condition at subsonic andtransonic Mach numbers. Results were presentedwhich focus on both the Reynolds number andstatic aeroelastic sensitivities of longitudinalcharacteristics at Mach 0.30 for the configurationwithout the empennage. General conclusions aresummarized as follows:1. Static aeroelastic effects were significant.

Increasing the dynamic pressure at constantMach and Reynolds numbers increases thewashout of the outboard wing, which in turncontributes to changes in longitudinalcoefficients. Adjustments for static aeroelasticeffects can be determined and applied toenable investigation of pure Reynolds numbereffects.

2. A fundamental change in flow-state occurredbetween Reynolds numbers of 30 to 40million, which is characterized by significantlyearlier inboard leading-edge separation at thehigh Reynolds numbers. Force and momentlevels change but Reynolds number trends areconsistent between the two states. Furtherstudies are necessary to understand the

cause for the changes between Reynoldsnumbers of 30 and 40 million.

3. Reynolds numbers effects are larger whenseparated flow dominates at angles of attackabove take-off conditions. Separation on theblunt inboard leading edge in particular issensitive, and significantly impacts the pitchingmoment characteristics.

ACKNOWLEDGEMENTSThe authors would like to thank our many

partners from industry and the staff of the NTF formaking these tests successful. In particular, wewould like to acknowledge Chet Nelson (Boeing),Marvine Hamner (Boeing/McDonnell Douglas),and Susan Williams (NASA-retired) who investedconsiderable effort over many years towards thedevelopment and testing of this model.

REFERENCES1. McKinney, L.W. and Baals, D.D. (editors):

“Wind-Tunnel/Flight Correlation – 1981,”NASA CP 2225, November 1981.

2. Haines, A.B.: “Scale Effects on Aircraft andWeapon Aerodynamics,” AGARD AG-323,1994.

3. Goldhammer, M.E. and Steinle, F.W. Jr.:“Design and Validation of Advanced TransonicWings Using CFD and Very High Reynolds

a) Baseline configuration with nacelles. b) Take-off configuration with nacelles.

Figure 16. Pitch-up delay with Reynolds number at high dynamic pressure, M = 0.30.

AIAA-2001-0911


Number Wind Tunnel Testing,” 17th ICASCongress, September 1990.

4. Lynch, F.T.: “Experimental Necessities forSubsonic Transport Configuration Develop-ment,” AIAA Paper 92-0158, January 1992.

5. Bushnell, D.M., Yip, L.P., Yao, C.S., Lin, J.C.,Lawing, P.L., Batina, J.T., Hardin, J.C.,Horvath, T.J., Fenbert, J.W., and Domack,C.S.: “Reynolds Number Influences inAeronautics,” NASA TM 107730, May 1993.

6. Wilhite, A. W., and Shaw, R. J.: “An Overviewof NASA’s High-Speed Research Program,”20th ICAS Congress, Paper 112, August 2000.

7. Nelson, C.P.: “Effects of Wing Planform onHSCT Off-Design Aerodynamics,” AIAA Paper92-2629, June 1992.

8. Wahls, R.A., Owens, L.R., and Rivers, S.M.B.:“Reynolds Number Effects on a SupersonicTransport at Transonic Conditions,” AIAAPaper 2001-0912, January 2001.

9. Gloss, B. B.: “Current Status and SomeFuture Test Directions for the US NationalTransonic Facility,” Wind Tunnels and WindTunnel Test Techniques, R. Aeronaut. Soc.,1992, pp. 3.1-3.7.

10. Igoe, W.B.: “Analysis of Fluctuating StaticPressure Measurements in the NationalTransonic Facility,” NASA TP-3475, March1996.

11. Bobbitt, C.W., Hemsch, M.J., and Everhart,J.L.: “NTF Characterization Status,” AIAAPaper 2001-755, January 2001.

12. Fuller, D.E.: “Guide for Users of the NationalTransonic Facility,” NASA TM-83124, 1981.

13. Finley, T.D. and Tcheng, P.: “Model AttitudeMeasurements at NASA Langley ResearchCenter,” AIAA Paper 92-0763, 1992.

14. Burner, A.W., Erickson, G.E., Goodman, W.L.,and Fleming, G.A.: “HSR Model DeformationMeasurements from Subsonic to SupersonicSpeeds,” 1998 NASA High-Speed ResearchProgram Aerodynamic PerformanceWorkshop, February 1998, NASA/CP-1999-209692, Vol. 1, p. 1569-1588.

15. Foster, J.M. and Adcock, J.B.: “User’s Guidefor the National Transonic Facility ResearchData System,” NASA TM-110242, April 1996.

16. Williams, M.S.: “Experience with Strain GageBalances for Cryogenic Wind Tunnels,”AGARD-R-774, 1989, pp. 18.1-18.14.

17. Braslow, A.L., and Knox, E.C.: “SimplifiedMethod for Determination of Critical Height ofDistributed Roughness Particles for Boundary-

Layer Transition at Mach Numbers from 0 to5,” NACA TN-4363, 1958.

18. Wahls, R.A., Adcock, J.B., Witkowski, D.P.,and Wright, F.L.: "A LongitudinalAerodynamic Data Repeatability Study for aCommercial Transport Model in the NationalTransonic Facility," NASA TP-3522, August1995.

19. Wahls, R.A., Gloss, B.B., Flechner, S.G.,Johnson, W.G.,Jr., Wright, F.L., Nelson, C.P.,Nelson, R.S., Elzey, M.B., and Hergert, D.W.:"A High Reynolds Number Investigation of aCommercial Transport Model in the NationalTransonic Facility,” NASA TM-4418, April1993.

20. Al-Saadi, J.A.: “Effect of Reynolds Number,Boundary-Layer Transition, and Aeroelasticityon Longitudinal Aerodynamic Characteristicsof a Subsonic Transport Wing,” NASA TP-3655, September 1997.

21. Payne, F.M., Wyatt, G.W., Bogue, D.R., andStoner, R.C.: "High Reynolds Number Studiesof a Boeing 777-200 High Lift Configuration inthe NASA ARC 12' Pressure Tunnel andNASA LaRC National Transonic Facility,"AIAA Paper 2000-4220, August 2000.

22. Sommer, S.C., and Short, B.J.: “Free-FlightMeasurements of Turbulent-Boundary-LayerSkin Friction in the Presence of SevereAerodynamic Heating at Mach Numbers from2.8 to 7.0,” NASA TN-3391, March 1955.

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AIAA-2001-0911 Reynolds Number Effects on a Supersonic Transport at Subsonic High-Lift...

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