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NASA/TM-1999-206579

July 1999

Design and Predictions for a High-Altitude (Low-Reynolds-Number) Aerodynamic Flight Experiment

Donald Greer

and Phil HamoryDryden Flight Research CenterEdwards, California

Keith KrakeSparta Inc.Edwards, California

Mark DrelaMassachusetts Institute of TechnologyCambridge, Massachusetts

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NASA/TM-1999-206579

Design and Predictions for a High-Altitude (Low-Reynolds-Number) Aerodynamic Flight Experiment

Donald Greer

and Phil HamoryDryden Flight Research CenterEdwards, California

Keith KrakeSparta Inc.Edwards, California

Mark DrelaMassachusetts Institute of TechnologyCambridge, Massachusetts

July 1999

National Aeronautics andSpace Administration

Dryden Flight Research CenterEdwards, California 93523-0273

NOTICE

Use of trade names or names of manufacturers in this document does not constitute an official endorsementof such products or manufacturers, either expressed or implied, by the National Aeronautics andSpace Administration.

Available from the following:

NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS)7121 Standard Drive 5285 Port Royal RoadHanover, MD 21076-1320 Springfield, VA 22161-2171(301) 621-0390 (703) 487-4650

1

American Institute of Aeronautics and Astronautics

DESIGN AND PREDICTIONS FOR A HIGH-ALTITUDE (LOW-REYNOLDS-NUMBER) AERODYNAMIC FLIGHT EXPERIMENT

Donald Greer

*

and Phil Hamory

†

NASA Dryden Flight Research CenterEdwards, California

Keith Krake

‡

Sparta Inc.Edwards, California

Mark Drela

§

Massachusetts Institute of TechnologyCambridge, Massachusetts

*

Abstract

†

A

‡

sailplane

§

being developed at NASA DrydenFlight Research Center will support a high-altitude flightexperiment. The experiment will measure theperformance parameters of an airfoil at high altitudes(70,000 to 100,000 ft), low Reynolds numbers (200,000to 700,000), and high subsonic Mach numbers (0.5 and0.65). The airfoil section lift and drag are determinedfrom pitot and static pressure measurements. Thelocations of the separation bubble, Tollmien-Schlichtingboundary layer instability frequencies, and vortexshedding are measured from a hot-film strip. The detailsof the planned flight experiment are presented. Severalpredictions of the airfoil performance are also presented.Mark Drela from the Massachusetts Institute ofTechnology designed the APEX-16 airfoil, using theMSES code. Two-dimensional Navier-Stokes analyseswere performed by Mahidhar Tatineni and XiaolinZhong from the University of California, Los Angeles,and by the authors at NASA Dryden.

Nomenclature

A/D analog to digital

*

Research Engineer, Ph.D. Fluid Dynamics.

†

Flight Instrumentation Engineer.

‡

Flight Instrumentation Engineer, member AIAA.

§

Professor, Department of Aeronautics and Astronautics, memberAIAA.

Copyright

1999 by the American Institute of Aeronautics andAstronautics, Inc. No copyright is asserted in the United States underTitle 17, U.S. Code. The U.S. Government has a royalty-free license toexercise all rights under the copyright claimed herein forGovernmental purposes. All other rights are reserved by the copyrightowner.

chord, ft

section drag coefficient

section lift coefficient

section moment coefficient

pressure coefficient

derivative of velocity, ft/sec

derivative of length, ft

amplitude ratio

EMI electrical magnetic interference

force of gravity

gm gram

KEAS knots equivalent airspeed at sea level

Mach number

critical amplification parameter

pressure, lb/ft

2

PCM pulse code modulation

dimensionless pressure gradient

static pressure, lb/ft

2

total pressure, lb/ft

2

P.T. pressure transducer

dynamic pressure, lbm/ft/sec

Re Reynolds number

RFI radio frequency interference

RTD resistive temperature device

c

Cd

Cl

Cm

C p

du

dx

en

g

M

ncrit

P

Pmax

Ps

PT

q

2


separation

uncertainty of the variable

x

transition location

angle of attack, deg

ratio of specific heats

momentum thickness

kinematic viscosity, ft/sec

2

Introduction

¶

The need for cost-effective high-altitude vehicles toconduct atmospheric research has created interest inhigh-altitude (low-Reynolds-number) airfoils. Insupport of this need, NASA Dryden Flight ResearchCenter is developing a sailplane called APEX that willmeasure the parameters affecting the performance of theairfoil in actual high-altitude flight. The APEX sailplanewill be released from a high-altitude balloon fromapproximately 108,000 ft altitude and then remotelypiloted. Figure 1 shows a schematic of the flightmission.

Figure 1. APEX mission profile.

The first 30 sec after release from the balloon are themost critical for the APEX flight control system.Transition to horizontal flight occurs during this periodwith the assistance of four small rockets, which have acombined thrust of 784 lb. After the transition tohorizontal flight, the airfoil parameters affectingperformance are measured as the sailplane descendsfrom 100,000 to 70,000 ft. The sailplane is then broughtto a horizontal landing at the Rogers dry lakebed atEdwards Air Force Base, California.

Low-Reynolds-number airfoils typically exhibitlaminar separation bubbles as shown schematically infigure 2. These separation bubbles are known tosignificantly affect the performance of an airfoil. Thebubble is formed when the laminar flow separates as aresult of encountering the adverse pressure region of theairfoil. The separated free shear layer is unstable, whichamplifies the Tollmien-Schlichting instability waves.The free shear flow generally transitions rapidly fromlaminar flow to turbulent flow and then reattaches to theairfoil surface. The lambda shocks, which occur in thetransonic flight regime, are expected to increase theamplification of the Tollmien-Schlichting instabilitywaves.

The objectives of the APEX experiment are

•

To increase the understanding of airfoilperformance in the high-altitude, low-Reynolds-number, and high-subsonic-Mach-number flightregime.

•

To obtain flight test data of airfoil performanceparameters that can be used for validation of airfoildesign codes.

Figure 2. Laminar separation bubble.

¶

Use of trade names or names of manufacturers in this documentdoes not constitute an official endorsement of such products ormanufacturers, either expressed or implied, by the NationalAeronautics and Space Administration.

sep

Ux

xTR

α

γ

θ

υ

990000

Edwards AFB,California

Rogers Dry Lake

70K ft

100K to 102K ft

Balloonlaunch

Aircraft release108K ft

Transition to horizontal

flight

.5- to 1-hourflight

Two hoursascent

Testmaneuvers

Transonic lambda shock

Separation due to adverse pressure gradient

Separation bubble

Turbulent reattachment

Turbulentflow

Laminarflow

Free shearflow

990001

3


This paper presents a description of the APEXexperiment. The design details used to determine theperformance parameters of the airfoil will be discussed.A preliminary error analysis will also be presented.Various numerical models used to predict the airfoilperformance parameters will also be discussed.

Previous Research

Several studies investigating the performance andcharacteristics of low-Reynolds-number airfoils havebeen performed. Mueller

1

presents an excellentsummary of the research before 1985. One interestingaspect that Mueller discusses is the hysteresis that oftenoccurs in the drag polars. Mueller’s wind-tunnel studiesshow that the airfoil performance, including thehysteresis, could be significantly affected by free-streamturbulence and surface roughness. LeBlanc et al.

2

performed wind-tunnel measurements on a Liebeckairfoil at low Reynolds numbers. The boundary layervelocity fluctuations in the separation bubble weremeasured with hot-wire anemometry. The measuredvelocity spectra of peak instability frequencies agreedwith the predictions from linear stability theoryanalysis.

Howard and Kindelspire

3

performed a wind-tunnelstudy of the free-stream-turbulence effects on an airfoil.Their investigation shows that transition develops morerapidly by increased free-stream turbulence and alsothat boundary layer instability growth is greatest whenthe turbulence length scale is on the same order as theboundary layer thickness. Dovgal et al.

4

discuss severalaspects of the instability associated with laminarseparation bubbles including receptivity, linearinstability, and nonlinear interactions.

Recent investigations of Pauley et al.,

5

Ripley andPauley,

6

and Muti Lin and Pauley

7

show that theseparation bubble may become unstable under certainconditions, and experiences periodic vortex shedding.Their transient incompressible Navier-Stokes analyticalstudies characterized the unsteady vortex sheddingstructure. Tatineni and Zhong

8, 9

performed a two-dimensional, time-accurate Navier-Stokes analysis onthe APEX-16 airfoil flow field. Their analysis indicatesthat the airfoil separation bubble is unstable andperiodically sheds at the flight conditions of the APEXsailplane. A linear stability analysis also showed that themost dominant instability frequency matches thefrequency of the periodic vortex shedding.

Drela

10

investigated high-altitude, low-Reynolds-number airfoils in the transonic flight regime with the

ISES code. An interesting aspect of this investigation isthat airfoil performance in the high-altitude flightregime may depend largely upon the effectiveness oflambda shocks to increase the amplification ofinstability waves and increase the transition rate in theseparation bubble. A conclusion is that experimental testdata exploring laminar shock–boundary layerinteractions and its effect on Tollmien-Schlichtinginstability waves would significantly reduce theuncertainties in the analysis.

Turbulence is expected to be a major factor in theperformance of the APEX-16 airfoil. The length of theseparation bubble depends on the growth of theinstability waves within the free shear layer andtransition to fully developed turbulence. The process bywhich free-stream turbulence enters the boundary layerand becomes amplified is known as

receptivity

.Qualitatively, the concept is simple: Free-streamturbulence of various amplitudes and wavelengths entersthe boundary layer and either decays or grows. The mostunstable wavelengths grow at the greatest rates anddevelop into Tollmien-Schlichting instability waves andeventually cause transition to turbulence. Generally, thelarger the free-stream turbulence amplitudes, thequicker the boundary layer transitions to turbulence.Quantitatively, receptivity is a complicated subject thatis not well understood. Reshotko

11

summarizes thecurrent understanding of receptivity. Although thereceptivity process to transition is difficult toquantitatively predict, it is well known to be a strongfunction of free-stream turbulence as shown byDryden et al.

12, 13

in several experiments measuring thecritical Reynolds number of a sphere as a function offree-stream turbulent intensity. Fisher and Dougherty

14

performed a series of transition measurements on a conein wind tunnels and in flight. Their results show that thetransition location is a function of the free-streamturbulence. The atmospheric turbulence in flight is verylow and of large wavelength in relation to the thicknessof the boundary layer.

Presently, no existing wind tunnel can provide thehigh-altitude (70,000 to 100,000 ft), low-Reynolds-number (200,000 to 700,000), high-subsonic-Mach-number (0.5 to 0.65), and low-free-stream-turbulent-intensity (0.02 percent or less) environment necessary toaccurately measure the APEX-16 airfoil performance.Natural atmospheric turbulence is the rationale forconstructing the APEX research sailplane andmeasuring the in-flight airfoil performance parametersrather than performing a wind-tunnel study.

4


APEX Sailplane Description

Murray et al.

15

originally proposed the APEXsailplane as a modified Schweizer SGS 1-36 sailplane.As the APEX design proceeded, the sailplane evolvedinto the current configuration. Figure 3 shows the APEXsailplane geometry. The sailplane is 22.7 ft long with awingspan of 41.2 ft and has a wing aspect ratio of 13.6.The experimental test section, where the performanceparameters are measured, is at the midspan point of theright wing as shown in the figure. The sailplane isdesigned for a target gross weight of 600 lb with a 5-

g

maneuver load factor. The airframe has been designedand is currently being fabricated by Advanced SoaringConcepts (Camarillo, California) from graphite/epoxyand boron/epoxy composites.

Drela designed the APEX-16 airfoil using the coupledviscous/inviscid MSES code.

16, 17

The coordinates andairfoil shape are shown in table 1 and figure 4,respectively. The airfoil dimensional tolerances for thewing construction are specified at ±0.005 in. to reducethe effects of surface roughness and waviness. The wingis a rectangular planform of the APEX-16 airfoil, as wasshown in figure 3. The wing incorporates a 2-deg linearwashin to reduce three-dimensional (spanwise) effectsand to provide a more uniform section lift coefficient( ) distribution over the experimental area of the wing.

Figure 4. APEX-16 sectional (37.22-in. chord).

The forward undercut camber on the lower surface doesnot directly affect the separation bubble and wasincorporated into the design to increase the maximumlift coefficient and decrease the pitching moment. Theairfoil was designed to provide good performancethroughout the entire APEX flight envelope. Figure 5shows the predicted APEX flight envelope. Thechallenge of the design was to correctly predict thecharacteristics of the separation bubble withoutexperimental data for code verification in the high-subsonic-Mach-number and low-Reynolds-numberflight regime.

The experiment is limited by several designconstraints. Weight is a major design consideration forthe experiment. The gross vehicle flight weight for thesailplane is specified at 600 lb to provide an adequatestall margin for attaining a ceiling altitude of 100,000 ft.The experiment is limited to 10 percent of the grossvehicle weight or 60 lb. Packaging the experiment isalso another major design constraint. Much of theinstrumentation electronics, including pressuretransducers, accelerometers, and the hot-filmanemometry, signal conditioning, and analog-to-digital(A/D) conversion cards, are in the wing next to theexperiment. The electronic instrumentation is located

101.21 in.

494.35 in.

1.5°

6.0°

78.03 in.61.18 in.

77.70in.

322.78 in.

271.95 in.

74.40in.

APEX-16

Wing airfoil

Horizontal tailairfoil (inverted)

NACA 2412

Vertical tailairfoil

NACA 0012

75.40in.

Test section

40.56in.

7.22in.

990002

AreaWing Aileron Horizontal stabilizer Elevator Vertical fin Rudder

124.61 ft2

9.52 ft2

20.35 ft2

6.80 ft2

11.87 ft2

3.62 ft2

Figure 3. APEX three-dimensional view.

Cl

Table 1. Coordinates (

x, y

), inches.

Upper surface Lower surface

0.00 0.00 16.23 3.29 0.00 0.00 16.96 –1.41

0.09 0.25 18.80 3.22 0.11 –0.25 19.57 –1.22

0.51 0.64 21.35 3.05 0.56 –0.43 22.20 –0.99

1.72 1.30 23.90 2.80 1.94 –0.60 24.84 –0.74

3.81 2.00 26.44 2.45 4.47 –0.81 27.48 –0.49

6.17 2.52 28.98 2.01 6.99 –1.09 30.11 –0.27

8.63 2.89 31.50 1.50 9.45 –1.43 32.70 –0.08

11.14 3.13 34.00 0.90 11.87 –1.57 35.23 –0.02

13.69 3.26 37.22 0.00 14.38 –1.54 37.22 0.00

– 4– 2

0246

Distance,in.

403020100Distance, in.

990003

5


close to the experiment to minimize noise from radiofrequency interference (RFI) and electrical magneticinterference (EMI). The wing chord is 37.22 in. with amaximum interior thickness of 5 in., which makesinstrumentation packaging difficult. Another designconstraint is the high altitude. The available off-the-shelf instrumentation that can provide adequate rangeand accuracy at high altitude is limited. Someinstrumentation had to be specifically designed for theexperiment. The air density at 100,000 ft altitude isapproximately 1 percent of its value at sea level, whichsubstantially lowers the convective cooling rates of theelectronics to the air. Some electronics require aspecialized cooling design to avoid overheating.

APEX Experimental Description

The flight experiment to measure the performanceparameters of the APEX-16 airfoil consists of threeprimary measurements:

•

First, to measure section lift a series of staticpressure taps circle the airfoil at one spanwiselocation.

•

Second, to measure section drag a trailing rake sitsbehind the airfoil with a support sting.

•

Third, to measure the separation bubble location,Tollmien-Schlichting frequencies, and vortexshedding a hot-film strip sits on the top surface ofthe airfoil.

Figure 6 presents a schematic layout of the airfoilinstrumentation. In addition to the primarymeasurements, the instrumentation also includes a Kielprobe to measure free-stream total pressure, a trailing

static probe to measure free-stream static pressure, aboundary layer rake to determine the velocity profile, atotal temperature measurement, five integratingboundary layer rakes to determine the section dragdeveloping over the upper surface, two integratingtrailing rakes to determine total section drag, two vanesto measure angles of attack and sideslip, and threeaccelerometers to measure wing surface vibration.

Figure 6. APEX instrumentation layout on right-wingtest section.

Pressure Measurement System

Figure 7 presents a schematic of the pneumaticpressure measurement system. Fifty static pressure portsalong the chord (30 on the upper surface and 20 on thelower surface) measure the pressure distribution overthe airfoil. The ports have a 0.05-in. diameter and arestaggered at a 15-deg angle relative to the chord toprevent contamination from upstream ports. A trailingrake comprises 26 total pressure probes and 3 staticprobes to determine section drag ( ). The rake ismounted 0.3 chord length aft of the airfoil where thestatic pressure is expected to be fully recovered.

The airfoil section drag is calculated from the rakepressures based upon the Jones

18

method corrected forcompressibility effects. A Kiel probe, located mid-chord, 8 in. from the lower surface of the airfoil,measures a reference total pressure ( ). A trailing

120 x 103Launch and pullout corridor

Dynamic pressure limit

Stall limit

100

80

60

40

20

Altitude,ft

.7.6.5.4.3.2.10Mach number

990004

Figure 5. APEX flight envelope.

Flowdirection

APEX wingtest section

37.22 in.

74 in.

23 in. 14 in.23 in.71in.

Trailingstatic

Supportsting

Trailing rake Integrating trailing

rakes (qty 2)990005

Integrating boundary layer rakes (qty 5)

Static pressure ports (qty 50)

Accelerometers (qty 3)

Hot film strips (qty 54)

Boundary layer rake

Cd

PT

6


static probe, placed three chord lengths aft of the airfoil,measures a reference static pressure ( ). Aconventional boundary layer rake placed at 70-percentchord determines the boundary layer velocity profiledevelopment on the upper surface. Five integratingboundary layer rakes are located at 60-, 70-, 80-, 90-,and 100-percent chord, and two integrating trailingrakes are located at 0.3 chord lengths aft of the airfoil.The integrating rakes are multi-pitot probe rakes such asdeveloped by Silverstein and Katzoff

19

in which thepitot probes are plumbed into a common reservoir for asingle average total pressure measurement. The averagetotal pressure measurement has been shown by Drela

#

tobe a direct determination of the sum of momentumthickness and displacement thickness from which dragcan be calculated.

The pressure measurement system design uses fourelectronically scanned differential pressure transducersmanufactured by Pressure Systems Incorporated(Hampton, Virginia) to measure differential pressure.The transducers are silicon peizoresistive pressuresensors with a range of ±52 lb/ft

2

. This transducer was

chosen because it is flight proven, lightweight (3.7 oz),and small (1 by 4 by 1/2 in.). Each transducer has32 input pressure port channels. The input pressure isdifferentially measured against a reference pressure.The transducer may have only one reference pressure,either the static pressure from the trailing static probe orthe total pressure from the Kiel probe as was shown infigure 7.

The absolute pressure is measured by two Baratronstransducers manufactured by MKS InstrumentsIncorporated (Andover, Massachusetts). The transducersmeasure the static pressure in two ranges, 0 to 28 lb/ft

2

and 0 to 280 lb/ft

2

, and provide an absolute referencepressure measurement for the entire system. Both unitsare saturated below a 50,000-ft altitude, which isacceptable because the experiment is designed for highaltitude between 70,000 and 100,000 ft. The data fromall transducers are sampled and sent by telemetry to theground at a rate of 25 Hz. The pressure system mountedin and on the right wing including rakes, probes, andtransducers weighs less than 30 lb.

Uncertainty Analysis

A preliminary measurement uncertainty analysis wasperformed on the pressure system and is summarizedwith a discussion of the bias error for the calculation oflift. This analysis is based on the general uncertaintyanalysis of Coleman and Steele.

20

The pressurecoefficient ( ) can be defined in terms of measuredquantities as follows:

(1)

where is the port pressure, is the dynamic pressure, is the Mach number, and is the ratio of specific

heats.

Treating , , and as measuredquantities, the general uncertainty equation is

#

Drela, Mark, “Integrating Rake Design,” private communication,1995.

Ps

Static pressure ports

Boundaryrakes Trailing

rakes

Static ports and rakesReference staticReference total

Trailingstatic

Kielprobe

DifferentialP.T. 52 lb/ft2




AbsoluteP.T. 280 lb/ft2

AbsoluteP.T. 28 lb/ft2

990006

Figure 7. Pneumatic pressure measurement system forthe right-wing test section.

C p

C p

P Ps–

q---------------

P Ps–

0.7PsM2

---------------------= =

P Ps–

0.7Ps2

γ 1–-----------

PT

Ps------

γ 1–

γ-----------

1–

---------------------------------------------------------------=

P qM γ

P Ps– Ps PT Ps⁄

7


(2)

where is the uncertainty for the subscript variable.

For a and a flight condition of Mach 0.65and 100,000 ft altitude, the expected pressure quantitiesand their associated bias errors from the manufacturer’sspecifications are

(3)

Substituting these quantities into the uncertaintyequation (2) yields the pressure coefficient bias error of

(4)

For a , the result is

(5)

The bias error for the section lift coefficient,

(6)

is expected to be

(7)

where is the airfoil chord and the subscripts refer to the lower and upper surface, respectively.

A similar bias error analysis for the calculation of thesection drag coefficient for the flight condition ofMach 0.65 and 100,000-ft altitude yields

(8)

The percentage of bias error decreases as the sailplanedescends to lower altitudes because the measuredpressures become larger. For a and a flightcondition of Mach 0.65 and 70,000-ft altitude, theexpected bias errors are

(4a)

(7a)

(8a)

Marchman

21

states that “[d]rag has always been themost difficult aerodynamic force to measure and the lowdrag forces occurring in low Reynolds number flowsmake the problem even more difficult.” The APEXexperiment is not immune to these difficulties. Theaverage wake deficit pressure is estimated to be on theorder of 1 lb/ft

2

( = 0.65, altitude = 100,000 ft) and5 lb/ft

2

( = 0.65, altitude = 70,000 ft). The range ofthe differential pressure transducer used to measure thewake deficit pressure is ±52 lb/ft

2

and has an accuracyof ±0.1 percent full scale. A smaller range transducer tolower the bias percentage error was not available thatwould satisfy the APEX design constraints of size andweight. The transducer is capable of remote zero-pointcalibration by applying a single reference pressure toboth sides of the differential. This zero-point calibrationwill be performed before release from the balloon at100,000 ft altitude and just after the experimentalmeasurements are completed at 70,000 ft altitude.

A comparison was made by Marchman

21

of the dragcoefficient measurements on a Wortmann FX63-137airfoil performed by three different research facilities.The results show differences of more than 50 percent inthe measurement of drag coefficient for similar testconditions. Although the section drag coefficient biaserror range of ±20 to ±5 percent is large, it is notunreasonable given the difficulties of the measurement.The 5-percent error at 70,000 ft (Re = 700,000) is morerepresentative of measured in-flight drag errors at highReynolds numbers. For example Arnaiz

22

measured thein-flight drag on the XB-70 airplane accurate to±6.5 percent at Reynolds numbers ranging from1,000,000 to 3,000,000 per foot.

Other errors are associated with the accuracy of thepressure system measurements. The displacementeffects associated with the pitot probe disturbing thelocal flow field can affect the accuracy of the probe totalpressure measurement. Montoya et al.

23

discuss these

UC p

C p----------

2 UP Ps–

P Ps–-----------------

2 UPS

PS---------

2

+=

+

UPT PS⁄γ

γ 1–-------------

PT

Ps------

γ 1–

γ-----------

PT

Ps------

γ 1–

γ-----------

1–

-------------------------------------------------------

2

U

C p 1=

P Ps– 7.49 0.14 lb/ft2±=

Ps 22.7 0.072 lb/ft2±=

PT Ps⁄ 1.33 0.0012 lb/ft2±=

C p 1 0.02 (or 2%)±±=

C p 0.5–=

C p 0.5– 0.02 (or 4%)±±=

Cl1c--- C pl

C pu–( ) xd

0

c

∫=

Cl 0.9 0.028 (or 3%)±±=

c l and u

Cd 0.02 0.004 (or 20%)±±=

C p 1=

C p 1 0.005 (or 0.5%)±±=

Cl 0.9 0.006 (or 0.7%)±±=

Cd 0.01 0.0005 (or 0.5%)±±=

MM

8American Institute of Aeronautics and Astronautics

displacement effects in detail. Allen24 reports a surveyof pitot probe displacement corrections for free shearflows of approximately 18 percent of the probediameter. The APEX trailing rake pitot probes have a0.07-in. diameter and the airfoil wake height is expectedto be 3 to 5 in. depending on flight conditions. Thedisplacement effects of the pitot probe total pressuremeasurements are less than 0.2 percent.

Lag times in the pneumatic tubing between thepressure port and the transducer can also be a largesource of error under dynamic conditions. The low staticpressure at 100,000 ft altitude, 23 lb/ft2, can cause largepneumatic lag times. Laboratory tests and calculationsperformed at NASA Dryden show that the lag times areless than 1.5 sec. Lag times are reduced as the sailplanedescends in altitude because lag times are inverselyproportional to pressure. Lag times should not pose asignificant source of error as flight simulations showthat a flight condition of constant Mach number andconstant lift coefficient for the sailplane can bemaintained for 5 to 10 sec.

It is difficult to estimate how much pressuremeasurement uncertainty is a result of the three-dimensional effects of turbulence. Large-scale turbulentvortical structures and vortex shedding, if present, maysignificantly affect the accuracy of the static and pitotpressure measurements. The pneumatic tubing lagsdampen the dynamic response of the pressuremeasurements. Pressure variations caused by the largevortical structures moving across the airfoil flow fieldare not detected and their effects on a time averaged orlagged static and pitot pressure measurements areuncertain.

Large-scale vortical structures also presentuncertainties caused by changes in the local flowdirection. As shown by Mueller,1 the accuracy oftrailing rakes to determine drag is severelycompromised in flows with large-scale vorticalstructures resulting from the changing flow direction.The changing flow direction may also affect a staticpressure measurement in similar fashion as a vortexpasses over a static port on the surface of the airfoil. Thepresence of large-scale turbulent vortical structures andvortex shedding is detected from the hot-filmmeasurements.

The experiments of Batill and Mueller25 andGuglielmo and Selig26 suggest that spanwise variationsmay exist in the separation bubble dynamics caused bythe three-dimensional effects of turbulence. Bastedo andMueller27 measured a significant spanwise variation in a

laminar separation bubble due to wing tip vortices. TheAPEX wing incorporates a 2-deg linear washin toreduce spanwise effects of the wing tip vortex and toprovide a more uniform distribution over theexperimental area of the wing.

Random errors are often difficult to separate from thenatural in-flight pressure fluctuations. Random errorsare believed to be largely caused by RFI and EMI.Natural pressure fluctuations are caused by atmosphericturbulence, aircraft vibration, and changes to flightconditions such as angle of attack and angle of sideslip.Before releasing the sailplane from the high-altitudeballoon, a series of pressure data samples is taken andsent by telemetry to the ground. An assumption is that,while the sailplane is suspended under the balloon, theair relative to the sailplane is still and there are nonatural pressure fluctuations. All fluctuations in theprelaunch data samples, therefore, are assumed to berandom errors. Any additional random fluctuations thatoccur in flight are assumed to be natural pressurefluctuations occurring over the surface of the airfoil. Inaddition, the pneumatic tubing lags dampen all high-frequency natural pressure fluctuations.

The difficulty in obtaining accurate pressuremeasurements is realized when considering all thepossible errors (bias, nonlinear pitot effects, pneumaticlags, large-scale vortical structures, spanwise variations,and random). The presence of large-scale vorticalstructures severely compromises the measurementaccuracy. However, identifying flight regimes thatcontain large-scale vortical structures is an importantpart of the experiment. As will be discussed later, theseregimes are highly undesirable because of theirassociated large drag. The APEX experiment isexpected to significantly increase the understanding oflow-Reynolds-number airfoils at high altitude andprovide data for validation of airfoil design codes. Theuncertainties in the experimental data will be properlyaccounted for.

Hot-Film Measurement System

A multi-element hot-film strip is mounted over theAPEX-16 airfoil. The hot-film strip measures the stateof the boundary layer (i.e., laminar boundary layer,laminar separation, bubble region, turbulentreattachment, turbulent boundary layer, turbulentseparation, and vortex shedding) and the frequency ofthe Tollmien-Schlichting instability waves in theseparation bubble. The strip consists of 50 hot films onthe top surface in 2-percent chord increments starting at

Cl


zero-percent chord. The hot films are spacedapproximately 0.75 in. apart. In addition, four hot filmsare placed on the bottom surface at 10-, 30-, 60-, and90-percent chord. This hot-film-strip configuration isused for the initial flights. After the separation bubble islocated for the APEX flight regime, the strip is replacedwith a denser strip concentrated in the area of theseparation bubble (approximately 50 evenly spaced hotfilms on a 15-percent chord length).

The desire to obtain valid hot-film anemometry dataat frequencies up to 10 kHz combined with the weightand packaging limitations significantly influenced thedesign. The APEX telemetry system cannot handle thesehigh data transfer rates for the large number of channels.Therefore, the data are stored on board in random accessmemory and later, after the high-altitude tests arecompleted, sent by telemetry to the ground at lower datatransfer rates. The hot-film data are split into twocomponents: a DC component and an AC component.The DC component is sampled at 200 Hz and sent bytelemetry to the ground in real time. The AC componentis sampled in 1-sec data intervals at 20 to 25 kHz andstored in memory. The system is capable of storing up toten 1-sec data intervals during a flight. The system iscommanded from the ground uplink to begin storing a1-sec data interval of AC data. In summary, all 54 hotfilms are sampled for their DC component at 200 Hz asthe sailplane descends from 100,000 to 70,000 ft. The54 hot films are sampled for their AC component at 20to 25 kHz in 1-sec data intervals for up to 10 intervals asthe sailplane descends from 100,000 to 70,000 ft.

Figure 8 shows a schematic of the hot-filmanemometry and data acquisition system. Theanemometry is a temperature-compensated systemdeveloped by Chiles.28 The anemometry incorporates atemperature sensor located in proximity to the hot filmas part of the Wheatstone bridge. The temperaturesensor corrects the sensitivity of the anemometry circuitto changes in the average adiabatic wall temperaturecaused by changes in flight condition. The system alsoincorporates automatic gain ranging that automaticallyadjusts the AC signal gain so that the peak-to-peaksignal is approximately 50 percent of the total signalrange. Each hot film has an anemometry circuit, a signalconditioning circuit that includes the automatic gainranging, and a 10-kHz low-pass filter to prevent anti-aliasing.

The hot-film signals are multiplexed in groups of four,to a data logger and A/D converter (fig. 8). The data arethen transferred to the pulse code modulation (PCM)encoder at lower data rates to be sent by telemetry to the

ground after the high-altitude portion of the flight iscompleted. The hot-film system, excluding the PCM, isestimated to weigh 20 lb and sits in the right wing underthe hot-film sheet.

Spectral analysis is the primary means of datareduction of the hot-film data. Preliminary calculationsshow that a 1-sec interval of data sampled at 20 to25 kHz is adequate to resolve the spectral contentbetween 50 Hz and 10 kHz. This spectral content shouldbe adequate for determining the flow field on the uppersurface of the APEX airfoil. The detection of phasereversal and a significant change in power spectraldensity is expected to be the signature of laminarseparation and the beginning of the separation bubble.Phase reversal of low-frequency spectra has been shownby Mangalam et al.29 to be an effective method ofdetecting laminar separation.

Turbulent reattachment of the bubble is detected inthe same manner as laminar separation—by phasereversal and a significant change in power spectraldensity caused by turbulence. The presence of vortexshedding is detected by performing both auto and crosspower spectral density analysis on the hot films aft ofthe separation bubble. The detection of a significantincrease in spectra in a specific frequency range and aconsistent phase lag between the hot films is a signatureof vortex shedding.

990007

Hot films (qty 54)(50 on upper surface)

Anemometry andsignal conditioning

(qty 54)

Groups of four

Data loggerand A/D converter

(qty 14)

PCM encoderTelemetered to ground

Real time – DC componentDelayed time – AC component

Figure 8. Hot-film anemometry system for the right-wing test section.


The Tollmien-Schlichting instability wave frequenciesin the free shear layer of the bubble is detected byspectral analysis of hot films inside the separationbubble and possibly by hot films just upstream of theseparation bubble. The separated flow instabilityresearch of Dovgal et al.4 show that instability waves,which cause transition, can be generated either upstreamof the separation point or downstream of the separationpoint in the free shear layer. Their experiments show thatharmonic disturbances causing transition exist inside theseparation bubble. They discuss the concept of feedbackinteractions whereby instability waves are convectedforward to the separation point as the flow circulatesinside the bubble.

At present, hot films have not been used to detectTollmien-Schlichting instability frequencies and thebubble instabilities are assumed to be detected at thesurface of the airfoil. The computational fluid dynamicsanalysis and Orr-Sommerfeld analysis performed byTatineni and Zhong8, 9 suggest that the Tollmien-Schlichting instability waves occur at approximately1000 Hz. A significant increase in the spectral density inthis frequency range for hot films in the separationbubble is, therefore, a measure of the Tollmien-Schlichting instability frequencies.

Uncertainty Analysis

Before actual flight, any estimate of the data qualityfrom the hot-film system is difficult. The goal is asignal-to-noise ratio of 20 or greater. To reduce RFI andEMI noise, the hot-film strip comprises three laminatedsheets. The top and bottom sheets are ground planes toshield the hot-film leads in the middle sheet. Twistedand shielded cabling are used for connections. Theanemometry cards are packaged with ground planeprotection.

The aircraft power is filtered to ensure that theanemometry signals are not contaminated by powerfluctuations. Special preflight ground test equipment isbeing developed that selectively blows both laminar andturbulent air over each hot film, matching the Nusseltnumber expected in flight. This equipment allows theindividual hot-film signals to be compared and used toqualify, to first order, signal intensities between hotfilms. In addition, while the sailplane is suspendedunder the balloon, a 1-sec data interval is taken to assessnoise levels.

Vane, Total Temperature, and Accelerometer Measurements

A pair of identical vanes is being developed for APEXto measure the angle of attack and angle of sideslip. Thevanes will be calibrated to within ±0.25 deg to the localflow field angle of attack. The vanes will be mounted ona boom, located one-fuselage diameter in front of thenose of the aircraft. The position (upwash) error at thislocation, the difference between the local flow fieldangle of attack and the true angle of attack, can varysubstantially. This difference in angle of attack is causedby the upwash from the boom, wings, and fuselage. Theposition error is expected to be a function of liftcoefficient and Mach number. The error is estimatedfrom the results of Rogallo30 to be 0.3 deg at and 1.2 deg at for a Mach number of 0.6. Athree-dimensional potential flow calculation of theAPEX flow field provides a correction for the positionerror of angle of attack and angle of sideslip.

The vane is currently being designed and fabricatedand is expected to weigh approximately 10 gm to lowerthe moment of inertia and increase the vane responsetime. Preliminary near sea level wind-tunnel tests showthat the vane damping ratios are between 0.2 to 0.33 andthe natural frequencies are between 7 to 17.5 Hz as thedynamic pressure is varied between 18 and 50 KEAS.The in-flight time response of the vane is expected to beapproximately 1.5 sec and is calculated by extrapolatingthe near sea level data to a flight condition of 40 KEASat 100,000 ft by the method described in Barna andCrossman.31 The 1.5-sec time response is adequate forsteady-state measurements as flight simulations showthat a flight condition of constant Mach number andconstant lift coefficient for the sailplane can bemaintained for 5 to 10 sec.

The total temperature measurement is performed withan adaptation to a standard Rosemount (Burnsville,Minnesota) RTD total temperature probe. The RTDsensor is replaced with a Thermometrics (Edison,New Jersey) thermistor to increase the time response ofthe sensor. Friehe and Khelif32 developed thisadaptation. The in-flight response time is expected to beapproximately 1 sec and the accuracy is expected to be±0.5 °F. The sensor has been fabricated but has not beentested and calibrated.

Three Endevco (San Juan Capistrano, California)piezoelectric accelerometers are mounted inside thewing to the upper surface at chord locations of 20, 50,and 80 percent. The accelerometers are sampled at

Cl 0.3=Cl 1.2=


20,000 samples per second and have a frequency rangeof 1 to 10,000 Hz and an accuracy of ±0.05 . A spectralanalysis is performed on the accelerometer data andcompared with the hot-film spectral analysis to exploreany aeroelastic effects that may affect laminar-to-turbulent transition.

Predicted Airfoil Performance

The prediction of low-Reynolds-number airfoilperformance is a formidable task that involves correctlymodeling several flow phenomena as was shown infigure 2. Modeling the inviscid flow field including thepresence of shock waves is generally considered the firststep to determining the pressure distribution over thesurface of the airfoil. The viscous flow field is composedof the boundary layer, laminar separation, laminar freeshear layer, transition to turbulence in the free shearlayer, turbulent free shear layer, reattachment of theturbulent free shear layer, and turbulent boundary layer.In addition turbulent separation and laminar bubbleseparation, known as bubble bursting, are importantphysical characteristics to be modeled. The interactionbetween the inviscid and viscous flow fields can besignificant. The presence of the separation bubble altersthe effective shape of the inviscid airfoil. The classicassumption that pressure is constant across the boundarylayer may not be valid across the separation bubble. Inaddition, boundary layers become large at low Reynoldsnumbers increasing the boundary displacementthickness, which can have an appreciable effect on theinviscid pressure distribution.

The design and initial predictions of the APEX-16airfoil are performed with the MSES code. The MSESairfoil design code uses the Euler equations to solve theinviscid flow field coupled with a two-equationdissipation integral method to solve for the viscousboundary layer. The transition location is determined viathe amplitude ratio ( ) method, using growth rates thatare precomputed from solutions of the Orr-Sommerfeldequation and correlated to the local shape factorparameter and momentum thickness Reynolds number.No compressibility corrections are employed partlybecause of the large uncertainty in the appropriatecritical amplification parameter, , for this high-subsonic-Mach-number and low-Reynolds-numberflight regime. A value for of 12 was assumed fordesign of the APEX-16 airfoil. Liebeck33 uses an earlierversion of the MSES code, ISES, and finds that thepredictions for low-Reynolds-number airfoils arereliable and accurate for low Mach numbers. One goalof the APEX experiment is to determine whether MSESremains reliable in the high-subsonic-Mach-number and

low-Reynolds-number flight regime and what values are appropriate.

Figures 9 through 11 present the predicted drag polarsand lift curves for the APEX-16 airfoil for the chordReynolds numbers of 200,000, 300,000, and 500,000,respectively, from the MSES code. The first apparentcharacteristic in the figures is the decrease in maximumlift coefficient with increasing Mach number. Thisdecrease results from the separation of the turbulentboundary layer from the airfoil as the Mach numberincreases. The maximum lift coefficient decreases andthe drag coefficient increases as the Reynolds numbersdecrease. This result is expected as the separationbubbles become larger with lower Reynolds numbers,which decreases the overall performance of the airfoil.The lift curve slope is relatively unaffected by Machnumber and Reynolds number except near stall. Theslope of the pitching moment coefficients with angle ofattack is also relatively unaffected by Mach number andReynolds number. The predicted transition location,

, versus lift coefficient are also presented in thefigures. The transition location on the upper surfacemoves forward and the transition location on the lowersurface moves aft with increasing lift coefficient orangle of attack ( ).

Figure 12 presents the predicted drag polars and liftcurves for various chord Reynolds numbers between200,000 and 2,000,000 for a 0.6 Mach number. Thedecreasing airfoil performance with lower Reynoldsnumbers is again apparent. An interesting feature of thefigure is that the pitching moment increases with lowerReynolds numbers. Examining the data of McGheeet al.,34 the reverse would be expected. Their data showthat, with lower Reynolds numbers, bubble reattachmentoccurs farther aft on the airfoil, which delays thepressure recovery on the upper surface. This effectresults in decreasing the pitching moment. Figure 13shows the APEX-16 airfoil predicted pressuredistribution for a Reynolds number of 200,000 and300,000 at Mach 0.65. In the figure the bubblereattachment is predicted to move aft with lowerReynolds numbers and is in agreement with the data ofMcGhee et al.34 The reattachment point is shown in thefigure by the point of discontinuous change in slope ofthe pressure recovery on the upper surface. With lowerReynolds numbers, however, the separation point movesforward and the overall pressure on the upper surfaceincreases. The point of separation is just after the pointof minimum pressure on the upper surface as shown inthe figure. The overall gain in upper surface pressureresults in increasing the pitching moment with lowerReynolds numbers.

g

en

ncrit

ncrit

ncrit

xTR

α


Figure 9. MSES prediction for APEX-16 airfoil at Re = 200,000.


0

.5

1.0 –.3

–.2

–.1

1.5

.5

1.0

1.5Mach0.6000.6500.7000.750

Cl Cl

Cm

200 400 0 0 .5

Upper

MSES V 2.8

1.02 4 6 8

104 x CdXTR/Cα

990008

– 4 – 2

0

.5

1.0 –.3

–.2

–.1

1.5

.5

1.0

1.5Mach0.6000.6500.7000.750

Cl Cl

200 400 0 0 .5

Upper

MSES V 2.8

1.02 4 6 8

104 x Cdα

990009

– 4 – 2XTR/C

Cm



Figure 12. MSES prediction for APEX-16 airfoil at M = 0.6.

0

.5

1.0 –.3

–.2

–.1

1.5

.5

1.0

1.5Mach0.6000.6500.7000.750

Cl Cl

200 400 0 0 .5

Upper

MSES V 2.8

1.02 4 6 8

104 x Cdα

990010

– 4 – 2XTR/C

Cm

0

.5

1.0 –.3

–.2

–.1

1.5

.5

1.0

1.5

Cl Cl

200 400 0 .5

Upper

MSES V 2.8

1.02 4 6 8

104 x Cdα

990011

Re2,000,0001,000,000 500,000 300,000 200,000

– 4 – 2 0XTR/C

Cm


A time-accurate Navier-Stokes analysis wasperformed on the APEX-16 airfoil by Tatineni andZhong.8, 9 Their analysis predicts that the separationbubble on the upper surface of the airfoil is unstable.The separation bubble is predicted to periodically shedat about 950 Hz for the subsonic flight condition ofMach 0.5, Reynolds number 200,000, and an angle ofattack of 4 deg. The flow field over the upper surface is

predicted to become very erratic as the Mach number isincreased into the transonic range, as shown infigures 14 and 15.** The predicted interaction betweenthe shock waves and the shedding vortices, as seen inthe figures, has a profound effect on the flow field andthe airfoil section lift coefficient. The section drag alsoincreases substantially. A time-accurate Navier-Stokesanalysis was also performed at NASA Dryden on theAPEX-16 airfoil. Figure 16 shows the predictedunsteady separated vortex region on the aft uppersurface of the airfoil. The results are similar to those ofTatineni and Zhong.8, 9

The vortex shedding criterion suggested by Pauley etal.5 is

(9)

where is a dimensionless pressure gradientproposed by Gaster,35 is the boundary layermomentum thickness at separation, is the kinematicviscosity, and is the maximum velocity

Reattachment

Re = 300,000Re = 200,000

Separation– 2.0

– 1.5

– 1.0

– .5

0

.5

1.0

1.5

Cp

.4 .6 .80 .2 1.0Distance, percent chord

990012

**Tatineni, Mahidhar and Xiaolin Zhong, “Numerical Simulationof Unsteady Low-Reynolds-Number Transonic Separated Flows Overthe APEX Airfoil, APEX Critical Design Review,” NASA Dryden,1998, unpublished. Grant NCC 2-374, UCLA Flight Research Center.

Pmax

θsep2

υ---------- du

dx------

max

0.24–≈=

Pmaxθsep

υdu dx⁄( )max

Figure 13. MSES prediction of the pressuredistribution over the APEX-16 airfoil (M = 0.65;α = 3.5; Re = 200,000 and 300,000).

Figure 14. Unsteady variation of pressure contours for the transonic APEX-16 airfoil (M = 0.65; Re = 200,000;α = 4°). Time interval between frames is 0.0016 sec.

990013

Frame 1 Frame 2 Frame 3

Frame 4 Frame 5 Frame 6


gradient. The shedding criterion for the APEX-16 airfoilat a flight condition of Mach 0.65, Reynolds number200,000, and an angle of attack of 4 deg is

(10)

Therefore, unstable shedding vortices should beexpected on the APEX-16 airfoil according to thesuggested shedding criterion.

The stability of the separation bubble has a large effecton the airfoil predicted performance. The MSES code,based on stable bubble calculations, predicts a liftcoefficient of 0.96 at the flight condition of Mach 0.65,Reynolds number 200,000, and an angle of attack of4 deg. The Navier-Stokes code predicts an averagesection lift coefficient of 0.76 for the same flightcondition. The Navier-Stokes analysis assumed laminarflow. The effects of turbulence on the stability of theseparation bubble are uncertain. Gruber et al.36

performed a direct numerical simulation that showedthat an amplified Tollmien-Schlichting wave in the freeshear layer of a separation bubble develops into a largevortical structure. Whether the intensity of these vorticalstructures is large enough to maintain the structure astransition into turbulence occurs is unknown. Theselarge vortical structures may be analogous to large-scaleturbulent eddies that are quickly broken up in theturbulent flow field through vortex stretching and thethree-dimensional effects of turbulent flow.

.75

.85

.80

.70

Cl

.008 .010 .012 .014.004 .006Time, sec

990014

Pmax 1.47–=

Figure 15. Unsteady variations of average section liftcoefficient for the transonic APEX-16 airfoil (M = 0.65;Re = 200,000; α = 4°).

Figure 16. Unsteady variation of velocity vectors for the aft section of the APEX upper surface. Plot sequence timeinterval is 0.0015 sec (M = 0.65; Re = 200,000; α = 4°).

2

0

6

4

Distance,in.

2

0

6

4

Distance,in.

15 20 25 30 35 40Distance, in.

990015

15 20 25 30 35 40Distance, in.

Frame 1 Frame 2

Frame 3 Frame 4


Concluding Remarks

The purpose of the APEX experiment is to increasethe understanding of low-Reynolds-number airfoils in alow-turbulence flight environment. The APEXexperiment regime is for altitudes between 70,000 and100,000 ft, Mach numbers between 0.5 and 0.65, andReynolds numbers between 100,000 and 700,000. Thefollowing characteristics of the airfoil are to bedetermined:

1. Section lift.

2. Section drag.

3. Location of the separation bubble.

4. Vortex shedding characteristics.

5. Tollmien-Schlichting frequencies.

Acknowledgments

The authors express their gratitude to the APEXproject members developing the sailplane andexperiment. We gratefully acknowledge Albion Bowers(NASA Dryden Flight Research Center, Edwards,California) and Rick Howard (Naval PostgraduateSchool, Monterey, California) for their many helpfuldiscussions.

References

1Mueller, T. J., “Low Reynolds Number Vehicles,”AGARD-AG-288, 1985.

2LeBlanc, P., R. Blackwelder, and R. Liebeck, “AComparison Between Boundary Later Measurementsin a Laminar Separation Bubble Flow andLinear Stability Theory Calculations,” in Low ReynoldsNumber Aerodynamics Conference Proceedings, 1989,pp. 189–205.

3Howard, R. M. and D. W. Kindelspire, “FreestreamTurbulence Effects on Airfoil Boundary-Layer Behaviorat Low Reynolds Numbers,” J. Aircraft, vol. 27, no. 5,May 1990, pp. 468–470.

4Dovgal, A. V., V. V. Kozlov, and A. Michalke,“Laminar Boundary Layer Separation: Instability andAssociated Phenomena,” Prog. Aerospace Sci., vol. 30,1994, pp. 61–94.

5Pauley, Laura L., Parviz Moin, and William C.Reynolds, “The Structure of Two-Dimensional

Separation,” J. Fluid Mech., vol. 220, 1990, pp. 397–411.

6Ripley, Matthew D. and Laura L. Pauley, “TheUnsteady Structure of a Two-Dimensional SteadyLaminar Separation,” Phys. Fluids A., vol. 5, no. 12,Dec. 1993, pp. 3099–3106.

7Muti Lin, J. C. and Laura L. Pauley, “Low-Reynolds-Number Separation on an Airfoil,” AIAA Journal,vol. 34, no. 8, Aug. 1996, pp. 1570–1577.

8Tatineni, M. and X. Zhong, “Numerical Simulationof Unsteady Low-Reynolds-Number Separated FlowsOver Airfoils,” AIAA 97-1929, July 1997.

9Tatineni, Mahidhar and Xiaolin Zhong, “NumericalSimulations of Unsteady Low-Reynolds-Number FlowsOver the APEX Airfoil,” AIAA 98-0412, Jan. 1998.

10Drela, Mark, “Transonic Low-Reynolds NumberAirfoils,” J. Aircraft, vol. 29, no. 6, Nov.–Dec. 1992,pp. 1106–1113.

11Reshotko, E., “Environment and Receptivity,” inSpecial Course on Stability and Transition of LaminarFlow, AGARD-R-709, 1984, p. 4-1.

12Dryden, H. L. and A. M. Kuethe, Effect ofTurbulence in Wind Tunnel Measurements, NACAReport No. 342, 1929.

13Dryden, Hugh L., G. B. Schubauer, W. C. Mock, Jr.,and H. K. Skramstad, Measurements of Intensity andScale of Wind-Tunnel Turbulence and Their Relation tothe Critical Reynolds Number of Spheres, NACA ReportNo. 581, 1937.

14Fisher, David F. and N. Sam Dougherty, Jr., In-Flight Transition Measurement on a 10° Cone at MachNumbers From 0.5 to 2.0, NASA TP-1971, June 1982.

15Murray, James, Timothy Moes, Ken Norlin, JeffreyBauer, Robert Geenen, Bryan Moulton, and StephenHoang, Piloted Simulation Study of a Balloon-AssistedDeployment of an Aircraft at High Altitude, NASATM-104245, Jan. 1992.

16Giles, Michael B. and Mark Drela, “Two-Dimensional Transonic Aerodynamic Design Method,”AIAA Journal, vol. 25, no. 9, Sept. 1987, pp. 1199–1206.

17Drela, Mark and Michael B. Giles, “Viscous-Inviscid Analysis of Transonic and Low Reynolds


Number Airfoils,” AIAA Journal, vol. 25, no. 10, 1987,pp. 1347–1355.

18Jones, B. Melville, “The Measurement of ProfileDrag by Pitot Traverse Method,” Reports andMemoranda no. 1688, Brit. A.R.C., Jan. 1936.

19Silverstein, A. and S. Katzoff, “A SimplifiedMethod for Determining Wing Profile Drag in Flight,”J. Aeronautical Sci., vol. 7, 1940, pp. 195–301.

20Coleman, Hugh W. and W. Glenn Steele, Jr.,Experimentation and Uncertainty Analysis forEngineers, John Wiley & Sons, New York, 1989.

21Marchman, J. F., “Aerodynamic Testing at LowReynolds Numbers,” J. Aircraft, vol. 24, no. 2,Feb. 1987, pp. 107–114.

22Arnaiz, Henry H., Flight-Measured Lift and DragCharacteristics of a Large, Flexible, High SupersonicCruise Airplane, NASA TM X-3532, May 1977.

23Montoya, L. C., R. D. Banner, and P. F. Bikle,“Section Drag Coefficients From Pressure ProbeTrasverses of a Wing Wake at Low Speeds,”AIAA 78-1479, Aug. 1978.

24Allen, Jerry M., Pitot-Probe Displacement in aSupersonic Turbulent Boundary Layer, NASATN D-6759, Apr. 1972.

25Batill, Stephen M. and Thomas J. Mueller,“Visualization of Transition in the Flow Over anAirfoil Using the Smoke-Wire Technique,” AIAAJournal, vol. 19, no. 3, 1981, pp. 340–345. (AlsoAIAA 80-0421R.)

26Guglielmo, James J. and Michael S. Selig, “LargeSpanwise Variations in Profile Drag for Airfoils at LowReynolds Numbers,” AIAA 95-1783, 1995.

27Bastedo, W. G., Jr., and T. J. Mueller, “SpanwiseVariation of Laminar Separation Bubbles on Wings atLow Reynolds Numbers,” J. Aircraft, vol. 23, no. 9,Sept. 1986, pp. 687–694.

28Chiles, Harry R., The Design and Use of aTemperature-Compensated Hot-Film AnemometerSystem for Boundary-Layer Flow Transition Detectionon Supersonic Aircraft, NASA TM-100421, May 1988.

29Mangalam, Siva M., John P. Stack, and W. G.Sewall, “Simultaneous Detection of Separation andTransition in Surface Shear Layers,” in Fluid Dynamicsof Three-Dimensional Turbulent Shear Flows andTransition, AGARD CP-438, 1988, pp. 12-1 to 12-10.

30Rogallo, Vernon L., Effects of Wing Sweep on theUpwash at the Propeller Planes of MultiengineAirplanes, NACA TN-2795, 1952.

31Barna, P. S. and Gary R. Crossman, ExperimentalStudies on the Aerodynamic Performance and DynamicResponse of Flow Direction Sensing Vanes, NASACR-2683, May 1976.

32Friehe, Carl A. and Djamal Khelif, “Fast-ResponseAircraft Temperature Sensors,” J. Atmospheric andOceanic Tech., vol. 9, no. 6, Dec. 1992, pp. 784–795.

33Liebeck, Robert H., “Low Reynolds Number AirfoilDesign for Subsonic Compressible Flow,” in LowReynolds Number Aerodynamics Proceedings, 1989,pp. 314–330.

34McGhee, Robert J., Betty S. Walker, and Betty F.Millard, Experimental Results for the Eppler 387 Airfoilat Low Reynolds Numbers in the Langley Low-Turbulence Pressure Tunnel, NASA TM-4062,Oct. 1988.

35Gaster, M., “The Structure and Behaviour ofLaminar Separation Bubbles,” in Separated Flows,AGARD CP-4, 1966, pp. 813–854.

36Gruber, K., H. Bestek, and H. Fasel, “InteractionBetween a Tollmien-Schlichting Wave and a LaminarSeparation Bubble,” AIAA 87-1256, 1987.

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Design and Predictions for a High-Altitude (Low-Reynolds-Number)Aerodynamic Flight Experiment

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H-2340

National Aeronautics and Space AdministrationWashington, DC 20546-0001 NASA/TM-1999-206579

A sailplane being developed at NASA Dryden Flight Research Center will support a high-altitude flightexperiment. The experiment will measure the performance parameters of an airfoil at high altitudes (70,000 to100,000 ft), low Reynolds numbers (200,000 to 700,000), and high subsonic Mach numbers (0.5 and 0.65).The airfoil section lift and drag are determined from pitot and static pressure measurements. The locations ofthe separation bubble, Tollmien-Schlichting boundary layer instability frequencies, and vortex shedding aremeasured from a hot-film strip. The details of the planned flight experiment are presented. Several predictionsof the airfoil performance are also presented. Mark Drela from the Massachusetts Institute of Technologydesigned the APEX-16 airfoil, using the MSES code. Two-dimensional Navier-Stokes analyses wereperformed by Mahidhar Tatineni and Xiaolin Zhong from the University of California, Los Angeles, and by theauthors at NASA Dryden.

Airfoils, High altitude, Low Reynolds numbers, Sailplane, Transition

A03

23

Unclassified Unclassified Unclassified Unlimited

July 1999 Technical Memorandum

Presented at the 17th Applied Aerodynamics Conference and 14th Computational Fluid DynamicsConference, Norfolk, Virginia, June 28–July 1, 1999, AIAA 99-3183.

Unclassified—UnlimitedSubject Category 02

design and predictions for a high-altitude (low-reynolds ... · pdf filenasa/tm-1999-206579...

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